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In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

Recurrent neural networks with memory and attention mechanisms are widely used in natural language processing because they can capture short and long term sequential information for diverse tasks. We propose an integrated deep learning model for microbial DNA sequence data, which exploits convolutional neural networks, recurrent neural networks, and attention mechanisms to predict taxonomic classifications and sample-associated attributes, such as the relationship between the microbiome and host phenotype, on the read/sequence level. In this paper, we develop this novel deep learning approach and evaluate its application to amplicon sequences. We apply our approach to short DNA reads and full sequences of 16S ribosomal RNA (rRNA) marker genes, which identify the heterogeneity of a microbial community sample. We demonstrate that our implementation of a novel attention-based deep network architecture, Read2Pheno, achieves read-level phenotypic prediction. Training Read2Pheno models will encode sequences (reads) into dense, meaningful representations: learned embedded vectors output from the intermediate layer of the network model, which can provide biological insight when visualized. The attention layer of Read2Pheno models can also automatically identify nucleotide regions in reads/sequences which are particularly informative for classification. As such, this novel approach can avoid pre/post-processing and manual interpretation required with conventional approaches to microbiome sequence classification. We further show, as proof-of-concept, that aggregating read-level information can robustly predict microbial community properties, host phenotype, and taxonomic classification, with performance at least comparable to conventional approaches. An implementation of the attention-based deep learning network is available at https://github.com/EESI/sequence_attention (a python package) and https://github.com/EESI/seq2att (a command line tool)., Author summary Microbiomes are communities of microscopic organisms found everywhere, including on and in the human body. For example, the gut microbiome plays an important role in digestion, and changes in composition are associated with changes in health or disease, e.g., inflammatory bowel disease (IBD). Today, microbiome composition is often obtained from high-throughput sequencing, which generates many short DNA reads from multiple organisms in a sample. In this paper, we present a novel deep learning framework, Read2Pheno, to predict phenotype from all the reads in a set of biological samples. An attention mechanism allows visualization of specific subregions (sets of bases) which are important in classifying the reads according to phenotype or taxon labels. We evaluate the framework on sequencing data for 16S rRNA genes, genetic markers used to identify microbial taxonomy. We show that Read2Pheno performs comparably as conventional methods on three distinct data sets from the American Gut Project, IBD patients and controls, and a comprehensive taxonomic database. Moreover, Read2Pheno results can be readily interpreted—e.g., to identify regions of the 16S rRNA gene to target for PCR diagnostics—without additional pre/post-processing steps that can introduce complexity and error.

Striatal oscillatory activity is associated with movement, reward, and decision-making, and observed in several interacting frequency bands. Local field potential recordings in rodent striatum show dopamine- and reward-dependent transitions between two states: a “spontaneous” state involving β (∼15-30 Hz) and low γ (∼40-60 Hz), and a state involving θ (∼4-8 Hz) and high γ (∼60-100 Hz) in response to dopaminergic agonism and reward. The mechanisms underlying these rhythmic dynamics, their interactions, and their functional consequences are not well understood. In this paper, we propose a biophysical model of striatal microcircuits that comprehensively describes the generation and interaction of these rhythms, as well as their modulation by dopamine. Building on previous modeling and experimental work suggesting that striatal projection neurons (SPNs) are capable of generating β oscillations, we show that networks of striatal fast-spiking interneurons (FSIs) are capable of generating δ/θ (ie, 2 to 6 Hz) and γ rhythms. Under simulated low dopaminergic tone our model FSI network produces low γ band oscillations, while under high dopaminergic tone the FSI network produces high γ band activity nested within a δ/θ oscillation. SPN networks produce β rhythms in both conditions, but under high dopaminergic tone, this β oscillation is interrupted by δ/θ-periodic bursts of γ-frequency FSI inhibition. Thus, in the high dopamine state, packets of FSI γ and SPN β alternate at a δ/θ timescale. In addition to a mechanistic explanation for previously observed rhythmic interactions and transitions, our model suggests a hypothesis as to how the relationship between dopamine and rhythmicity impacts motor function. We hypothesize that high dopamine-induced periodic FSI γ-rhythmic inhibition enables switching between β-rhythmic SPN cell assemblies representing the currently active motor program, and thus that dopamine facilitates movement in part by allowing for rapid, periodic shifts in motor program execution., Author summary Striatal oscillatory activity is associated with movement, reward, and decision-making, and observed in several interacting frequency bands. The mechanisms underlying these rhythmic dynamics, their interactions, and their functional consequences are not well understood. In this paper, we propose a biophysical model of striatal microcircuits that comprehensively describes the generation and interaction of striatal rhythms, as well as their modulation by dopamine. Our model suggests a hypothesis as to how the relationship between dopamine and rhythmicity impacts the function of the motor system, enabling rapid, periodic shifts in motor program execution.

As antimicrobial resistance increases, it is crucial to develop new treatment strategies to counter the emerging threat. In this paper, we consider combination therapies involving conventional antibiotics and debridement, coupled with a novel anti-adhesion therapy, and their use in the treatment of antimicrobial resistant burn wound infections. Our models predict that anti-adhesion–antibiotic–debridement combination therapies can eliminate a bacterial infection in cases where each treatment in isolation would fail. Antibiotics are assumed to have a bactericidal mode of action, killing bacteria, while debridement involves physically cleaning a wound (e.g. with a cloth); removing free bacteria. Anti-adhesion therapy can take a number of forms. Here we consider adhesion inhibitors consisting of polystyrene microbeads chemically coupled to a protein known as multivalent adhesion molecule 7, an adhesin which mediates the initial stages of attachment of many bacterial species to host cells. Adhesion inhibitors competitively inhibit bacteria from binding to host cells, thus rendering them susceptible to removal through debridement. An ordinary differential equation model is developed and the antibiotic-related parameters are fitted against new in vitro data gathered for the present study. The model is used to predict treatment outcomes and to suggest optimal treatment strategies. Our model predicts that anti-adhesion and antibiotic therapies will combine synergistically, producing a combined effect which is often greater than the sum of their individual effects, and that anti-adhesion–antibiotic–debridement combination therapy will be more effective than any of the treatment strategies used in isolation. Further, the use of inhibitors significantly reduces the minimum dose of antibiotics required to eliminate an infection, reducing the chances that bacteria will develop increased resistance. Lastly, we use our model to suggest treatment regimens capable of eliminating bacterial infections within clinically relevant timescales., Author summary Since the development of the first antibiotics, bacteria have utilised and developed resistance mechanisms, helping them to avoid being eliminated and to survive within a host. Traditionally, the solution to this problem has been to treat with multiple antibiotics, switching to a new type when the one currently in use proves ineffective. However, the development of antibiotics has slowed significantly in the past two decades, while multi-drug resistant strains, otherwise known as ‘super bugs’, are on the rise. In answer to this challenge, alternative approaches, such as anti-adhesion therapy, are being developed as a complement or alternative to traditional antimicrobials. In this paper we formulate and analyse a mathematical model of a combination therapy, applied in the context of an infected burn wound, bringing together antibiotics, anti-adhesion therapy and debridement (the physical cleaning of a wound). We use our models to make sense of how these treatments interact to combat a bacterial infection, to predict treatment outcomes for a range of strategies and to suggest optimal treatment regimens. It is hoped that this study will guide future experimental and clinical research, helping biomedical researchers to identify the most promising approaches to treatment.

The presence of treatment-resistant cells is an important factor that limits the efficacy of cancer therapy, and the prospect of resistance is considered the major cause of the treatment strategy. Several recent studies have employed mathematical models to elucidate the dynamics of generating resistant cancer cells and attempted to predict the probability of emerging resistant cells. The purpose of this paper is to present numerical approach to compute the number of resistant cells and the emerging probability of resistance. Stochastic model was designed and developed a method to approximately but efficiently compute the number of resistant cells and the probability of resistance. To model the progression of cancer, a discrete-state, two-dimensional Markov process whose states are the total number of cells and the number of resistant cells was employed. Then exact analysis and approximate aggregation approaches were proposed to calculate the number of resistant cells and the probability of resistance when the cell population reaches detection size. To confirm the accuracy of computed results of approximation, relative errors between exact analysis and approximation were computed. The numerical values of our approximation method were very close to those of exact analysis calculated in the range of small detection size M = 500, 100, and 1500. Then computer simulation was performed to confirm the accuracy of computed results of approximation when the detection size was M = 10000,30000,50000,100000 and 1000000. All the numerical results of approximation fell between the upper level and the lower level of 95% confidential intervals and our method took less time to compute over a broad range of cell size. The effects of parameter change on emerging probabilities of resistance were also investigated by computed values using approximation method. The results showed that the number of divisions until the cell population reached the detection size is important for emerging the probability of resistance. The next step of numerical approach is to compute the emerging probabilities of resistance under drug administration and with multiple mutation. Another effective approximation would be necessary for the analysis of the latter case., Author summary Drug therapies for cancer have dramatically succeeded since molecular-targeted drugs have been introduced in medical practice; however, drug treatment often fails owing to the emergence of drug-resistant cells. A variety of approaches, including mathematical modeling, has been undertaken to clarify the mechanism of resistance and subsequently avoid resistance to therapy. This paper proposes one of the mathematical approaches that uses a stochastic model and provides the emerging probabilities of resistance at detection size.

Complex eukaryotic promoters normally contain multiple cis-regulatory sequences for different transcription factors (TFs). The binding patterns of the TFs to these sites, as well as the way the TFs interact with each other and with the RNA polymerase (RNAp), lead to combinatorial problems rarely understood in detail, especially under varying epigenetic conditions. The aim of this paper is to build a model describing how the main regulatory cluster of the olfactory receptor Or59b drives transcription of this gene in Drosophila. The cluster-driven expression of this gene is represented as the equilibrium probability of RNAp being bound to the promoter region, using a statistical thermodynamic approach. The RNAp equilibrium probability is computed in terms of the occupancy probabilities of the single TFs of the cluster to the corresponding binding sites, and of the interaction rules among TFs and RNAp, using experimental data of Or59b expression to tune the model parameters. The model reproduces correctly the changes in RNAp binding probability induced by various mutation of specific sites and epigenetic modifications. Some of its predictions have also been validated in novel experiments., Author summary The paper proposes and validates experimentally a model for the fine-graded regulation of a gene, called Or59b, coding for an olfactory receptor in Drosophila. The model is based on statistical thermodynamical theory, theory that so far has been mostly used for prokaryotes. In order to apply it to our more complex eukaryotic system, we have performed a large number of “perturbative” in vivo experiments (mutations, knockdown, knockout, epigenetic conditions) meant to unravel the regulatory rules by which the Or59b main regulatory cluster drives gene expression in as much detail as possible. We make use of the knowledge of the Or59b cis-regulatory module acquired in this way to set up the model and to identify its parameters. The model predictions are then tested experimentally in new epigenetic conditions. These new experiments validate the model behavior and confirm its predictive power.

This paper uses mathematical modeling to study the mechanisms of surround suppression in the primate visual cortex. We present a large-scale neural circuit model consisting of three interconnected components: LGN and two input layers (Layer 4Ca and Layer 6) of the primary visual cortex V1, covering several hundred hypercolumns. Anatomical structures are incorporated and physiological parameters from realistic modeling work are used. The remaining parameters are chosen to produce model outputs that emulate experimentally observed size-tuning curves. Our two main results are: (i) we discovered the character of the long-range connections in Layer 6 responsible for surround effects in the input layers; and (ii) we showed that a net-inhibitory feedback, i.e., feedback that excites I-cells more than E-cells, from Layer 6 to Layer 4 is conducive to producing surround properties consistent with experimental data. These results are obtained through parameter selection and model analysis. The effects of nonlinear recurrent excitation and inhibition are also discussed. A feature that distinguishes our model from previous modeling work on surround suppression is that we have tried to reproduce realistic lengthscales that are crucial for quantitative comparison with data. Due to its size and the large number of unknown parameters, the model is computationally challenging. We demonstrate a strategy that involves first locating baseline values for relevant parameters using a linear model, followed by the introduction of nonlinearities where needed. We find such a methodology effective, and propose it as a possibility in the modeling of complex biological systems., Author summary The visual cortex is a part of the cortex that processes visual signal. The visual signal from the retina is relayed through the lateral geniculate nucleus (LGN), and enters the primary visual cortex directly. The primary visual cortex consists of many layers. A phenomenon called surround suppression, which means a reduction of neuronal activities in response to stimuli of increasing size, is well-observed in all layers of the primate primary visual cortex. In this paper, we built a large scale mathematical model consisting of the LGN input and tens of thousands of neuron groups in Layer 4 and Layer 6 of the primary visual cortex to study the mechanism of surround suppression. This model is constrained by both anatomical structures and realistic physiological parameters. Remaining unknown parameters are reverse-engineered from experimental data. We showed how the character of the surround suppression depends on the long-range connections in the feedback layer, as well as the feedback current from Layer 6 to Layer 4.

During early human immunodeficiency virus (HIV) infection multiple CD8+ T cell responses are elicited almost simultaneously. These responses exert strong selective pressures on different parts of HIV’s genome, and select for mutations that escape recognition and are thus beneficial to the virus. Some studies reveal that the later these escape mutations emerge, the more slowly they go to fixation. This pattern of escape rate decrease(ERD) can arise by distinct mechanisms. In particular, in large populations with high beneficial mutation rates interference among different escape strains –an effect that can emerge in evolution with asexual reproduction and results in delayed fixation times of beneficial mutations compared to sexual reproduction– could significantly impact the escape rates of mutations. In this paper, we investigated how interference between these concurrent escape mutations affects their escape rates in systems with multiple epitopes, and whether it could be a source of the ERD pattern. To address these issues, we developed a multilocus Wright-Fisher model of HIV dynamics with selection, mutation and recombination, serving as a null-model for interference. We also derived an interference-free null model assuming initial neutral evolution before immune response elicitation. We found that interference between several equally selectively advantageous mutations can generate the observed ERD pattern. We also found that the number of loci, as well as recombination rates substantially affect ERD. These effects can be explained by the underexponential decline of escape rates over time. Lastly, we found that the observed ERD pattern in HIV infected individuals is consistent with both independent, interference-free mutations as well as interference effects. Our results confirm that interference effects should be considered when analyzing HIV escape mutations. The challenge in estimating escape rates and mutation-associated selective coefficients posed by interference effects cannot simply be overcome by improved sampling frequencies or sizes. This problem is a consequence of the fundamental shortcomings of current estimation techniques under interference regimes. Hence, accounting for the stochastic nature of competition between mutations demands novel estimation methodologies based on the analysis of HIV strains, rather than mutation frequencies., Author Summary Within-host evolution of human immunodeficiency virus (HIV) is shaped by strong immune responses mounted against the virus. Multiple CD8+ T cell populations, each recognizing a specific part of an HIV protein, simultaneously suppress HIV growth. Escape mutations that arise in HIV genome regions coding for these virion protein parts, impair CD8+ T cell recognition and are consequently strongly selected. The emergence and rise of these escape mutations exhibits an intriguing temporal pattern: the earlier an escape mutation arises, the faster it goes to fixation. This pattern is termed escape rate decrease (ERD). In this paper, we tested computationally whether interference, i.e. the coexistence of multiple genetically distinct HIV strains engaged in competitive interaction within the host, could be a possible source of ERD. As an alternative, we also mathematically derived the temporal pattern of escapes under interference-free conditions, and compared this with data. We found that interference between multiple beneficial mutations could generate ERD. However, ERD does not imply the presence of interference. Thus, more detailed data is required to unambiguously determine whether interference effects influence ERD generation. Nevertheless, interference should be considered when studying the within-host evolution of HIV. Ignoring its effects on population dynamics can severely underestimate the protective capacity of CD8+ T cells.

We describe Orbit Image Analysis, an open-source whole slide image analysis tool. The tool consists of a generic tile-processing engine which allows the execution of various image analysis algorithms provided by either Orbit itself or from other open-source platforms using a tile-based map-reduce execution framework. Orbit Image Analysis is capable of sophisticated whole slide imaging analyses due to several key features. First, Orbit has machine-learning capabilities. This deep learning segmentation can be integrated with complex object detection for analysis of intricate tissues. In addition, Orbit can run locally as standalone or connect to the open-source image server OMERO. Another important characteristic is its scale-out functionality, using the Apache Spark framework for distributed computing. In this paper, we describe the use of Orbit in three different real-world applications: quantification of idiopathic lung fibrosis, nerve fibre density quantification, and glomeruli detection in the kidney., Author summary Whole slide images (WSI) are digital scans of samples, e.g. tissue sections. It is very convenient to view samples in this digital form, and with the increasing computation power it can also be used for quantification. These images are often too large to be analysed with standard tools. To overcome this issue, we created on open-source tool called Orbit Image Analysis which divides the images into smaller parts and allows the analysis of it with either embedded algorithms or the integration of existing tools. It also provides mechanisms to process huge amounts of images in distributed computing environments, such as clusters or cloud infrastructures. In this paper we describe the Orbit system and demonstrate its application based on three real-word use-cases.

A biophysical model that captures molecular homeostatic control of ions at the perisynaptic cradle (PsC) is of fundamental importance for understanding the interplay between astroglial and neuronal compartments. In this paper, we develop a multi-compartmental mathematical model which proposes a novel mechanism whereby the flow of cations in thin processes is restricted due to negatively charged membrane lipids which result in the formation of deep potential wells near the dipole heads. These wells restrict the flow of cations to “hopping” between adjacent wells as they transverse the process, and this surface retention of cations will be shown to give rise to the formation of potassium (K+) and sodium (Na+) microdomains at the PsC. We further propose that a K+ microdomain formed at the PsC, provides the driving force for the return of K+ to the extracellular space for uptake by the neurone, thereby preventing K+ undershoot. A slow decay of Na+ was also observed in our simulation after a period of glutamate stimulation which is in strong agreement with experimental observations. The pathological implications of microdomain formation during neuronal excitation are also discussed., Author summary During periods of neuronal activity, ionic homeostasis in the surrounding extracellular space (ECS) is disturbed. To provide a healthy environment for continued neuronal function, excess ions such as potassium must be buffered away from the ECS; a vital supportive role provided by astrocyte cells. It has long been thought that astrocytes not only removed ions from the ECS but also transport them to other areas of the brain where their concentrations are lower. However, while our computational model simulations agree that astrocytes do remove these ions from the ECS they also show that these ions are mainly stored locally at the PsC to be returned to the ECS, thus restoring ionic homeostasis. Furthermore, we detail in this paper that this happens because of a previously overlooked biophysical phenomenon that is only dominant in thin astrocyte processes. The flow of these cations within thin processes is primarily by surface conduction where they experience the attraction of fixed negative charge at the membrane inner surface. This negative charge constrains cation movement along the surface and so their flow rate is restricted. Consequently, ions such as potassium that are released during neuronal excitation enter the PsC and are stored locally due to the low conductance pathway between the PsC and the astrocyte soma. Our simulations also show that this local build-up of K+ is returned to the ECS after the neuronal activity dies off which could potentially explain why K+ undershoot has not been observed; this result agrees with experimental observations. Moreover, the same mechanism can also explain the transient behaviour of Na+ ions whereby in thin processes a slow decay time constant is experimentally observed. These findings have important implications for the role of astrocytes in regulating neuronal excitability under physiological and pathological conditions, and therefore highlight the significance of the work presented in this paper.

Activities of transcription factors (TFs) are temporally modulated to regulate dynamic cellular processes, including development, homeostasis, and disease. Recent developments of bioinformatic tools have enabled the analysis of TF activities using transcriptome data. However, because these methods typically use exon-based target expression levels, the estimated TF activities have limited temporal accuracy. To address this, we proposed a TF activity measure based on intron-level information in time-series RNA-seq data, and implemented it to decode the temporal control of TF activities during dynamic processes. We showed that TF activities inferred from intronic reads can better recapitulate instantaneous TF activities compared to the exon-based measure. By analyzing public and our own time-series transcriptome data, we found that intron-based TF activities improve the characterization of temporal phasing of cycling TFs during circadian rhythm, and facilitate the discovery of two temporally opposing TF modules during T cell activation. Collectively, we anticipate that the proposed approach would be broadly applicable for decoding global transcriptional architecture during dynamic processes., Author summary Many health-related cellular processes, such as immune response and disease progression, involve dynamic changes of gene expression state, which are orchestrated by transcription factors. Dissecting the activities of transcription factors is thus important for understanding cellular processes and for interfering with dysregulated processes. Our ability to analyze transcription factor activities has been facilitated by genome-wide gene expression data from high-throughput assays such as RNA sequencing. Existing methods typically estimate transcription factor activities based on the expression levels of matured mRNAs of target genes. However, because the levels of matured mRNAs are affected by transcriptional and post-transcriptional regulatory activities, the estimated transcription factor activities may not faithfully recapitulate the regulatory activities of transcription factors. In this paper, we proposed and validated an alternative approach for analyzing transcription factor activities using the expression levels of unmatured mRNAs of target genes, allowing us to decode how transcription factor activities are temporally controlled during key biological processes. Our results provide insights into the temporal phasing of key circadian regulator activities in mouse liver, and uncover two temporally opposing modules of transcription factors that dictate the immune responses in T cells. Therefore, this approach can help understand the regulatory principles of dynamic cellular processes.

Experiments on tumor spheroids have shown that compressive stress from their environment can reversibly decrease tumor expansion rates and final sizes. Stress release experiments show that nonuniform anisotropic elastic stresses can be distributed throughout. The elastic stresses are maintained by structural proteins and adhesive molecules, and can be actively relaxed by a variety of biophysical processes. In this paper, we present a new continuum model to investigate how the growth-induced elastic stresses and active stress relaxation, in conjunction with cell size control feedback machinery, regulate the cell density and stress distributions within growing tumors as well as the tumor sizes in the presence of external physical confinement and gradients of growth-promoting chemical fields. We introduce an adaptive reference map that relates the current position with the reference position but adapts to the current position in the Eulerian frame (lab coordinates) via relaxation. This type of stress relaxation is similar to but simpler than the classical Maxwell model of viscoelasticity in its formulation. By fitting the model to experimental data from two independent studies of tumor spheroid growth and their cell density distributions, treating the tumors as incompressible, neo-Hookean elastic materials, we find that the rates of stress relaxation of tumor tissues can be comparable to volumetric growth rates. Our study provides insight on how the biophysical properties of the tumor and host microenvironment, mechanical feedback control and diffusion-limited differential growth act in concert to regulate spatial patterns of stress and growth. When the tumor is stiffer than the host, our model predicts tumors are more able to change their size and mechanical state autonomously, which may help to explain why increased tumor stiffness is an established hallmark of malignant tumors., Author summary The mechanical state of cells can modulate their growth and division dynamics via mechanotransduction, which affects both the cell size distribution and the tissue size as a whole. Experiments on tumor spheroids have shown that compressive stress from their environment can reversibly decrease tumor expansion rates and final sizes. Besides external confinement and compression on the tumor border, a heterogeneous stress field can be generated inside the tumor by nutrient-driven differential growth. Such growth-induced mechanical stresses can be relaxed by tissue rearrangement, which happens during cell neighbor exchanges, cell divisions, and extracellular matrix renewal. In this study, we have developed a continuum model that describes the above mechanical interactions and the dynamics of tissue rearrangement explicitly. Motivated by published experimental data, we consider mechanotransduction where the local compressive stress slows down cell growth and cell size reduction limits cell division. We have analyzed how external mechanical stimuli and internal processes influence the outcome of cell-and-tissue sizes and spatial patterns of cell density and mechanical stress in growing tumors.

System identification techniques -- projection pursuit regression models (PPRs) and convolutional neural networks (CNNs) -- provide state-of-the-art performance in predicting visual cortical neurons' responses to arbitrary input stimuli. However, the constituent kernels recovered by these methods are often noisy and lack coherent structure, making it difficult to understand the underlying component features of a neuron's receptive field. In this paper, we show that using a dictionary of diverse kernels with complex shapes learned from natural scenes based on efficient coding theory, as the front-end for PPRs and CNNs can improve their performance in neuronal response prediction as well as algorithmic data efficiency and convergence speed. Extensive experimental results also indicate that these sparse-code kernels provide important information on the component features of a neuron's receptive field. In addition, we find that models with the complex-shaped sparse code front-end are significantly better than models with a standard orientation-selective Gabor filter front-end for modeling V1 neurons that have been found to exhibit complex pattern selectivity. We show that the relative performance difference due to these two front-ends can be used to produce a sensitive metric for detecting complex selectivity in V1 neurons., 22 pages

Working memory is a cognitive function involving the storage and manipulation of latent information over brief intervals of time, thus making it crucial for context-dependent computation. Here, we use a top-down modeling approach to examine network-level mechanisms of working memory, an enigmatic issue and central topic of study in neuroscience. We optimize thousands of recurrent rate-based neural networks on a working memory task and then perform dynamical systems analysis on the ensuing optimized networks, wherein we find that four distinct dynamical mechanisms can emerge. In particular, we show the prevalence of a mechanism in which memories are encoded along slow stable manifolds in the network state space, leading to a phasic neuronal activation profile during memory periods. In contrast to mechanisms in which memories are directly encoded at stable attractors, these networks naturally forget stimuli over time. Despite this seeming functional disadvantage, they are more efficient in terms of how they leverage their attractor landscape and paradoxically, are considerably more robust to noise. Our results provide new hypotheses regarding how working memory function may be encoded within the dynamics of neural circuits., Author summary The ability to remember information for brief periods of time before using it is a key human ability. For example, retaining a phone number for a few moments prior to entering it into a keypad. Such ability, known as working memory, enables many more complex functions such as planning and reasoning. In this paper, we use theory and computational modeling approaches to try and better understand how circuits and networks in the brain might be achieving working memory. Specifically, we construct hypothetical network models to perform a task that embodies essential aspects of working memory. We then dissect our model to reveal how its components—simulated neural units—interact with each other to represent and maintain information. It turns out that some models can achieve memory by maintaining a fixed representation over time, i.e., the units remain ‘still’ during memory. However, other models fluctuate their activity during memory in a particular way that is seemingly quite efficient and less susceptible to distraction. In total, our computational study provides new theory for how this form of memory might be implemented in brain networks.

Animals rely on sensory feedback to generate accurate, reliable movements. In many flying insects, strain-sensitive neurons on the wings provide rapid feedback that is critical for stable flight control. While the impacts of wing structure on aerodynamic performance have been widely studied, the impacts of wing structure on sensing are largely unexplored. In this paper, we show how the structural properties of the wing and encoding by mechanosensory neurons interact to jointly determine optimal sensing strategies and performance. Specifically, we examine how neural sensors can be placed effectively on a flapping wing to detect body rotation about different axes, using a computational wing model with varying flexural stiffness. A small set of mechanosensors, conveying strain information at key locations with a single action potential per wingbeat, enable accurate detection of body rotation. Optimal sensor locations are concentrated at either the wing base or the wing tip, and they transition sharply as a function of both wing stiffness and neural threshold. Moreover, the sensing strategy and performance is robust to both external disturbances and sensor loss. Typically, only five sensors are needed to achieve near-peak accuracy, with a single sensor often providing accuracy well above chance. Our results show that small-amplitude, dynamic signals can be extracted efficiently with spatially and temporally sparse sensors in the context of flight. The demonstrated interaction of wing structure and neural encoding properties points to the importance of understanding each in the context of their joint evolution., Author summary In addition to generating forces for flight, insect wings also serve an important role as sensory structures, providing rapid feedback about wing bending that is used to stabilize flight. While much is known about how wing structure affects aerodynamic performance, the effects of wing structure on sensing remain unexplored. Using a computational model of a flapping wing, we examine how sensing strategies depend on wing stiffness and sensor properties. We show that body rotations can be accurately detected with a small number of sensors on the wing across a wide range of conditions. Optimal sensor locations are clustered at either the wing base or wing tip, depending on a combination of wing stiffness and sensor properties. Moreover, sensing performance is robust to multiple kinds of perturbations. Our work provides a basis for understanding how wing structure impacts incoming sensory information during flight.

Integrative clustering is used to identify groups of samples by jointly analysing multiple datasets describing the same set of biological samples, such as gene expression, copy number, methylation etc. Most existing algorithms for integrative clustering assume that there is a shared consistent set of clusters across all datasets, and most of the data samples follow this structure. However in practice, the structure across heterogeneous datasets can be more varied, with clusters being joined in some datasets and separated in others. In this paper, we present a probabilistic clustering method to identify groups across datasets that do not share the same cluster structure. The proposed algorithm, Clusternomics, identifies groups of samples that share their global behaviour across heterogeneous datasets. The algorithm models clusters on the level of individual datasets, while also extracting global structure that arises from the local cluster assignments. Clusters on both the local and the global level are modelled using a hierarchical Dirichlet mixture model to identify structure on both levels. We evaluated the model both on simulated and on real-world datasets. The simulated data exemplifies datasets with varying degrees of common structure. In such a setting Clusternomics outperforms existing algorithms for integrative and consensus clustering. In a real-world application, we used the algorithm for cancer subtyping, identifying subtypes of cancer from heterogeneous datasets. We applied the algorithm to TCGA breast cancer dataset, integrating gene expression, miRNA expression, DNA methylation and proteomics. The algorithm extracted clinically meaningful clusters with significantly different survival probabilities. We also evaluated the algorithm on lung and kidney cancer TCGA datasets with high dimensionality, again showing clinically significant results and scalability of the algorithm., Author summary Integrative clustering is the task of identifying groups of samples by combining information from several datasets. An example of this task is cancer subtyping, where we cluster tumour samples based on several datasets, such as gene expression, proteomics and others. Most existing algorithms assume that all such datasets share a similar cluster structure, with samples outside these clusters treated as noise. The structure can, however, be much more heterogeneous: some meaningful clusters may appear only in some datasets. In the paper, we introduce the Clusternomics algorithm that identifies groups of samples across heterogeneous datasets. It models both cluster structure of individual datasets, and the global structure that appears as a combination of local structures. The algorithm uses probabilistic modelling to identify the groups and share information across the local and global levels. We evaluated the algorithm on both simulated and real world datasets, where the algorithm found clinically significant clusters with different survival outcomes.

Voltage imaging enables monitoring neural activity at sub-millisecond and sub-cellular scale, unlocking the study of subthreshold activity, synchrony, and network dynamics with unprecedented spatio-temporal resolution. However, high data rates (>800MB/s) and low signal-to-noise ratios create bottlenecks for analyzing such datasets. Here we present VolPy, an automated and scalable pipeline to pre-process voltage imaging datasets. VolPy features motion correction, memory mapping, automated segmentation, denoising and spike extraction, all built on a highly parallelizable, modular, and extensible framework optimized for memory and speed. To aid automated segmentation, we introduce a corpus of 24 manually annotated datasets from different preparations, brain areas and voltage indicators. We benchmark VolPy against ground truth segmentation, simulations and electrophysiology recordings, and we compare its performance with existing algorithms in detecting spikes. Our results indicate that VolPy’s performance in spike extraction and scalability are state-of-the-art., Author summary Roughly 290 million electrical action potentials occur every second in the human brain, facilitating the propagation of signals among cells in the nervous system and driving most of our daily operations. New methods in brain imaging are emerging that have the speed and resolution to capture events in the brain at the pace at which neurons typically communicate. These methods measure voltage in neurons by using light, and therefore can access very detailed brain signaling patterns. However, the adoption of these methods by a larger community, and not a restricted set of experts, is limited by the lack of computational tools, thereby greatly hindering progress in this field. In this paper, we present VolPy, a software framework that greatly facilitates the preprocessing of this new type of imaging datasets. This pipeline incorporates efficient and optimized algorithms that can identify neurons and extract their activity with great accuracy. The presented software will make this new imaging modality accessible to a wide audience.

There are two distinct classes of cells in the primary visual cortex (V1): simple cells and complex cells. One defining feature of complex cells is their spatial phase invariance; they respond strongly to oriented grating stimuli with a preferred orientation but with a wide range of spatial phases. A classical model of complete spatial phase invariance in complex cells is the energy model, in which the responses are the sum of the squared outputs of two linear spatially phase-shifted filters. However, recent experimental studies have shown that complex cells have a diverse range of spatial phase invariance and only a subset can be characterized by the energy model. While several models have been proposed to explain how complex cells could learn to be selective to orientation but invariant to spatial phase, most existing models overlook many biologically important details. We propose a biologically plausible model for complex cells that learns to pool inputs from simple cells based on the presentation of natural scene stimuli. The model is a three-layer network with rate-based neurons that describes the activities of LGN cells (layer 1), V1 simple cells (layer 2), and V1 complex cells (layer 3). The first two layers implement a recently proposed simple cell model that is biologically plausible and accounts for many experimental phenomena. The neural dynamics of the complex cells is modeled as the integration of simple cells inputs along with response normalization. Connections between LGN and simple cells are learned using Hebbian and anti-Hebbian plasticity. Connections between simple and complex cells are learned using a modified version of the Bienenstock, Cooper, and Munro (BCM) rule. Our results demonstrate that the learning rule can describe a diversity of complex cells, similar to those observed experimentally., Author summary Many cortical functions originate from the learning ability of the brain. How the properties of cortical cells are learned is vital for understanding how the brain works. There are many models that explain how V1 simple cells can be learned. However, how V1 complex cells are learned still remains unclear. In this paper, we propose a model of learning in complex cells based on the Bienenstock, Cooper, and Munro (BCM) rule. We demonstrate that properties of receptive fields of complex cells can be learned using this biologically plausible learning rule. Quantitative comparisons between the model and experimental data are performed. Results show that model complex cells can account for the diversity of complex cells found in experimental studies. In summary, this study provides a plausible explanation for how complex cells can be learned using biologically plausible plasticity mechanisms. Our findings help us to better understand biological vision processing and provide us with insights into the general signal processing principles that the visual cortex employs to process visual information.

Increasingly complex in silico modeling approaches offer a way to simultaneously access cancerous processes at different spatio-temporal scales. High-level models, such as those based on partial differential equations, are computationally affordable and allow large tumor sizes and long temporal windows to be studied, but miss the discrete nature of many key underlying cellular processes. Individual-based approaches provide a much more detailed description of tumors, but have difficulties when trying to handle full-sized real cancers. Thus, there exists a trade-off between the integration of macroscopic and microscopic information, now widely available, and the ability to attain clinical tumor sizes. In this paper we put forward a stochastic mesoscopic simulation framework that incorporates key cellular processes during tumor progression while keeping computational costs to a minimum. Our framework captures a physical scale that allows both the incorporation of microscopic information, tracking the spatio-temporal emergence of tumor heterogeneity and the underlying evolutionary dynamics, and the reconstruction of clinically sized tumors from high-resolution medical imaging data, with the additional benefit of low computational cost. We illustrate the functionality of our modeling approach for the case of glioblastoma, a paradigm of tumor heterogeneity that remains extremely challenging in the clinical setting., Los enfoques de modelado in silico cada vez más complejos ofrecen una forma de acceder simultáneamente a procesos cancerosos en diferentes escalas espacio-temporales. Los modelos de alto nivel, como los que se basan en ecuaciones diferenciales parciales, son computacionalmente asequibles y permiten estudiar tumores de gran tamaño y ventanas temporales largas, pero pasan por alto la naturaleza discreta de muchos procesos celulares subyacentes clave. Los enfoques individuales brindan una descripción mucho más detallada de los tumores, pero tienen dificultades cuando se trata de tratar cánceres reales de tamaño completo. Por lo tanto, existe un compromiso entre la integración de información macroscópica y microscópica, ahora ampliamente disponible, y la capacidad de alcanzar tamaños de tumores clínicos. En este documento, presentamos un marco de simulación mesoscópica estocástica que incorpora procesos celulares clave durante la progresión del tumor y mantiene los costos computacionales al mínimo. Nuestro marco captura una escala física que permite la incorporación de información microscópica, el seguimiento de la aparición espacio-temporal de la heterogeneidad tumoral y la dinámica evolutiva subyacente, y la reconstrucción de tumores de tamaño clínico a partir de datos de imágenes médicas de alta resolución, con el beneficio adicional de bajo costo computacional. Ilustramos la funcionalidad de nuestro enfoque de modelado para el caso del glioblastoma, un paradigma de heterogeneidad tumoral que sigue siendo extremadamente desafiante en el entorno clínico. Nuestro marco captura una escala física que permite la incorporación de información microscópica, el seguimiento de la aparición espacio-temporal de la heterogeneidad tumoral y la dinámica evolutiva subyacente, y la reconstrucción de tumores de tamaño clínico a partir de datos de imágenes médicas de alta resolución, con el beneficio adicional de bajo costo computacional. Ilustramos la funcionalidad de nuestro enfoque de modelado para el caso del glioblastoma, un paradigma de heterogeneidad tumoral que sigue siendo extremadamente desafiante en el entorno clínico. Nuestro marco captura una escala física que permite la incorporación de información microscópica, el seguimiento de la aparición espacio-temporal de la heterogeneidad tumoral y la dinámica evolutiva subyacente, y la reconstrucción de tumores de tamaño clínico a partir de datos de imágenes médicas de alta resolución, con el beneficio adicional de bajo costo computacional. Ilustramos la funcionalidad de nuestro enfoque de modelado para el caso del glioblastoma, un paradigma de heterogeneidad tumoral que sigue siendo extremadamente desafiante en el entorno clínico.

We propose a developmental model inspired by the cortico-basal system (CX-BG) for vocal learning in babies and for solving the correspondence mismatch problem they face when they hear unfamiliar voices, with different tones and pitches. This model is based on the neural architecture INFERNO standing for Iterative Free-Energy Optimization of Recurrent Neural Networks. Free-energy minimization is used for rapidly exploring, selecting and learning the optimal choices of actions to perform (eg sound production) in order to reproduce and control as accurately as possible the spike trains representing desired perceptions (eg sound categories). We detail in this paper the CX-BG system responsible for linking causally the sound and motor primitives at the order of a few milliseconds. Two experiments performed with a small and a large audio database show the capabilities of exploration, generalization and robustness to noise of our neural architecture in retrieving audio primitives during vocal learning and during acoustic matching with unheared voices (different genders and tones)., Author summary We designed a developmental architecture inspired by the cortico-basal system for early vocal learning. Our neural system explores, evaluates and strengthens the motor primitives that match the best the sound repertoire created also dynamically. After a babbling process in which the network tests and aligns pronounced sound and motor vocal tracks, it is used for listening to novel voices, solving the correspondence problem.

Individual cells show variability in their signaling dynamics that often correlates with phenotypic responses, indicating that cell-to-cell variability is not merely noise but can have functional consequences. Based on this observation, we reasoned that cell-to-cell variability under the same treatment condition could be explained in part by a single signaling motif that maps different upstream signals into a corresponding set of downstream responses. If this assumption holds, then repeated measurements of upstream and downstream signaling dynamics in a population of cells could provide information about the underlying signaling motif for a given pathway, even when no prior knowledge of that motif exists. To test these two hypotheses, we developed a computer algorithm called MISC (Motif Inference from Single Cells) that infers the underlying signaling motif from paired time-series measurements from individual cells. When applied to measurements of transcription factor and reporter gene expression in the yeast stress response, MISC predicted signaling motifs that were consistent with previous mechanistic models of transcription. The ability to detect the underlying mechanism became less certain when a cell’s upstream signal was randomly paired with another cell’s downstream response, demonstrating how averaging time-series measurements across a population obscures information about the underlying signaling mechanism. In some cases, motif predictions improved as more cells were added to the analysis. These results provide evidence that mechanistic information about cellular signaling networks can be systematically extracted from the dynamical patterns of single cells., Author summary Cells use molecular signaling networks to translate dynamically changing stimuli into appropriate downstream responses. Specialized network structures, or motifs, allow cells to properly decode a variety of temporal input signals. In this paper, we present an algorithm that infers signaling motifs from multiple examples of an upstream signal paired with its downstream response in a population of single cells. We compare the predictive power of single-cell versus averaged time-series traces and the incremental benefit of adding more single-cell traces to the algorithm. We use this approach to understand how yeast respond to environmental stresses.

Learning the reliability of different sources of rewards is critical for making optimal choices. However, despite the existence of detailed theory describing how the expected reward is learned in the basal ganglia, it is not known how reward uncertainty is estimated in these circuits. This paper presents a class of models that encode both the mean reward and the spread of the rewards, the former in the difference between the synaptic weights of D1 and D2 neurons, and the latter in their sum. In the models, the tendency to seek (or avoid) options with variable reward can be controlled by increasing (or decreasing) the tonic level of dopamine. The models are consistent with the physiology of and synaptic plasticity in the basal ganglia, they explain the effects of dopaminergic manipulations on choices involving risks, and they make multiple experimental predictions., Author Summary To maximize their chances for survival, animals need to base their decisions not only on the average consequences of chosen actions, but also on the variability of the rewards resulting from these actions. For example, when an animal’s food reserves are depleted, it should prefer to forage in an area where food is guaranteed over an area where the amount of food is higher on average but variable, thus avoiding the risk of starvation. To implement such policies, animals need to be able to learn about variability of rewards resulting from taking different actions. This paper proposes how such learning may be implemented in a circuit of subcortical nuclei called the basal ganglia. It also suggests how the information about reward uncertainty can be used during decision making, so that animals can make choices that not only maximize expected rewards but also minimize risks.

Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent., Author summary Many systems in nature show bistability, which means they can evolve to one of two stable steady states under exactly the same conditions. Which state they evolve to depends on where the system comes from. Such bistability underlies the switching behavior that is essential for cells to progress in the cell division cycle. A quick switch happens when the cell jumps from one steady state to another steady state. Typical of this switching behavior is its robustness and irreversibility. In this paper, we expand this viewpoint of the dynamics of the cell cycle by considering bistable switches which themselves are changing in time. This gives the cell an extra layer of control over transitions both in time and in space, and can make those transitions more robust. Such dynamically changing bistability can appear very naturally. We show this in a model of mitotic entry, in which we include a nuclear and cytoplasmic compartment. The activity of a crucial cell cycle protein follows a bistable switch in each compartment, but the shape of its response is changing in time as proteins are imported into and exported from the nucleus.

The partial success of tumor immunotherapy induced by checkpoint blockade, which is not antigen-specific, suggests that the immune system of some patients contain antigen receptors able to specifically identify tumor cells. Here we focused on T-cell receptor (TCR) repertoires associated with spontaneous breast cancer. We studied the alpha and beta chain CDR3 domains of TCR repertoires of CD4 T cells using deep sequencing of cell populations in mice and applied the results to published TCR sequence data obtained from human patients. We screened peripheral blood T cells obtained monthly from individual mice spontaneously developing breast tumors by 5 months. We then looked at identical TCR sequences in published human studies; we used TCGA data from tumors and healthy tissues of 1,256 breast cancer resections and from 4 focused studies including sequences from tumors, lymph nodes, blood and healthy tissues, and from single cell dataset of 3 breast cancer subjects. We now report that mice spontaneously developing breast cancer manifest shared, Public CDR3 regions in both their alpha and beta and that a significant number of women with early breast cancer manifest identical CDR3 sequences. These findings suggest that the development of breast cancer is associated, across species, with biomarker, exclusive TCR repertoires., Author summary More than 1,100 cancer treatments are currently in clinical testing. Of these, 295 are immune-oncology medicines and vaccines. For Checkpoint Immunotherapy alone, 52,539 patients were enrolled in 2017. Of these treatments, 108 are for breast cancer, the leading cancer diagnosed in women. Although checkpoint immunotherapy has yet to be proven beneficial in most types of breast cancer, current observations of which specific T cell go into the tumor, and how these cells are connected to the response to treatment, have lead to a new understating of the role of the immune system. Yet, and in spite of this intense research into the role of T cells in tumors, very little is known about how clones of T cells behave during tumor formation. The paper we present here studies this clonal behavior over time. We study it during mammary tumor development in mice. We see that a set of T cell clones, which comes from a diversity of different nucleotide sequences, stands out in its behavior compared with other T cell clones. Importantly, we show that these mouse T cell clones have a strong connection to human breast cancer. The specific identification of a subset of T cell clones, together with the behavior of these clones over time, is critical to our understanding of the effect of modifications to the immune system, such as the modifications made by immunotherapy treatments, and to our understanding of how to better control the behavior of the immune system.

Millions of people worldwide develop foodborne illnesses caused by Salmonella enterica (S. enterica) every year. The pathogenesis of S. enterica depends on flagella, which are appendages that the bacteria use to move through the environment. Interestingly, populations of genetically identical bacteria exhibit heterogeneity in the number of flagella. To understand this heterogeneity and the regulation of flagella quantity, we propose a mathematical model that connects the flagellar gene regulatory network to flagellar construction. A regulatory network involving more than 60 genes controls flagellar assembly. The most important member of the network is the master operon, flhDC, which encodes the FlhD4C2 protein. FlhD4C2 controls the construction of flagella by initiating the production of hook basal bodies (HBBs), protein structures that anchor the flagella to the bacterium. By connecting a model of FlhD4C2 regulation to a model of HBB construction, we investigate the roles of various feedback mechanisms. Analysis of our model suggests that a combination of regulatory mechanisms at the protein and transcriptional levels induce bistable FlhD4C2 levels and heterogeneous numbers of flagella. Also, the balance of regulatory mechanisms that become active following HBB construction is sufficient to provide a counting mechanism for controlling the total number of flagella produced., Author summary Salmonella causes foodborne illnesses in millions of people worldwide each year. Flagella, which are appendages that the bacteria use to move through the environment, are a key factor in the infection process. Populations of genetically identical bacteria have been observed to contain both motile cells, generally with 6–10 flagella, and nonmotile cells, with no flagella. In this paper, we use mathematical models of the gene network that regulates flagellar construction to explore how the bacteria controls the number of flagella produced. We suggest that a bacterium must accumulate a threshold amount of a master regulator protein to initiate flagella production and failure to reach the threshold results in no flagella. Downstream mechanisms that impact the amount of master regulator protein are sufficient to determine how many flagella are produced.

Single-cell Hi-C (scHi-C) sequencing technologies allow us to investigate three-dimensional chromatin organization at the single-cell level. However, we still need computational tools to deal with the sparsity of the contact maps from single cells and embed single cells in a lower-dimensional Euclidean space. This embedding helps us understand relationships between the cells in different dimensions, such as cell-cycle dynamics and cell differentiation. We present an open-source computational toolbox, scHiCTools, for analyzing single-cell Hi-C data comprehensively and efficiently. The toolbox provides two methods for screening single cells, three common methods for smoothing scHi-C data, three efficient methods for calculating the pairwise similarity of cells, three methods for embedding single cells, three methods for clustering cells, and a build-in function to visualize the cells embedding in a two-dimensional or three-dimensional plot. scHiCTools, written in Python3, is compatible with different platforms, including Linux, macOS, and Windows., Author summary Single-cell Hi-C contact maps describe the numbers of interactions among genomic loci across the entire genome, and provide researchers 3D chromatin organization in each cell. There are growing demands for an easy and fast way to analyze and visualize single-cell Hi-C data, and analyzing single-cell Hi-C data exposes several inherent data analysis challenges. To move beyond existing computational tools and methods to analyze and visualize single-cell Hi-C data, we present a software package, scHiCTools, which is implemented in Python. The software package provides researchers a collection of methods to investigate the cell-to-cell similarity based on their 3D chromatin organization, cluster cells into groups accordingly, and visualize cells in two-dimensional or three-dimensional scatter plots. In this paper, we provide an overview of scHiCTools’ structure and capabilities. We then apply scHiCTools to several single-cell Hi-C datasets to benchmark the performance of the methods provided in our toolbox, and present some plots generated using the software package.

Since the seminal 1961 paper of Monod and Jacob, mathematical models of biomolecular circuits have guided our understanding of cell regulation. Model-based exploration of the functional capabilities of any given circuit requires systematic mapping of multidimensional spaces of model parameters. Despite significant advances in computational dynamical systems approaches, this analysis remains a nontrivial task. Here, we use a nonlinear system of ordinary differential equations to model oocyte selection in Drosophila, a robust symmetry-breaking event that relies on autoregulatory localization of oocyte-specification factors. By applying an algorithmic approach that implements symbolic computation and topological methods, we enumerate all phase portraits of stable steady states in the limit when nonlinear regulatory interactions become discrete switches. Leveraging this initial exact partitioning and further using numerical exploration, we locate parameter regions that are dense in purely asymmetric steady states when the nonlinearities are not infinitely sharp, enabling systematic identification of parameter regions that correspond to robust oocyte selection. This framework can be generalized to map the full parameter spaces in a broad class of models involving biological switches., Author summary Identification of qualitatively different regimes in models of biomolecular switches is essential for understanding dynamics of complex biological processes, including symmetry breaking in cells and cell networks. We demonstrate how topological methods, symbolic computation, and numerical simulations can be combined for systematic mapping of symmetry-broken states in a mathematical model of oocyte specification in Drosophila, a leading experimental system of animal oogenesis. Our algorithmic framework reveals global connectedness of parameter domains corresponding to robust oocyte specification and enables systematic navigation through multidimensional parameter spaces in a large class of biomolecular switches.

Gene expression atlases have transformed our understanding of the development, composition and function of human tissues. New technologies promise improved cellular or molecular resolution, and have led to the identification of new cell types, or better defined cell states. But as new technologies emerge, information derived on old platforms becomes obsolete. We demonstrate that it is possible to combine a large number of different profiling experiments summarised from dozens of laboratories and representing hundreds of donors, to create an integrated molecular map of human tissue. As an example, we combine 850 samples from 38 platforms to build an integrated atlas of human blood cells. We achieve robust and unbiased cell type clustering using a variance partitioning method, selecting genes with low platform bias relative to biological variation. Other than an initial rescaling, no other transformation to the primary data is applied through batch correction or renormalisation. Additional data, including single-cell datasets, can be projected for comparison, classification and annotation. The resulting atlas provides a multi-scaled approach to visualise and analyse the relationships between sets of genes and blood cell lineages, including the maturation and activation of leukocytes in vivo and in vitro. In allowing for data integration across hundreds of studies, we address a key reproduciblity challenge which is faced by any new technology. This allows us to draw on the deep phenotypes and functional annotations that accompany traditional profiling methods, and provide important context to the high cellular resolution of single cell profiling. Here, we have implemented the blood atlas in the open access Stemformatics.org platform, drawing on its extensive collection of curated transcriptome data. The method is simple, scalable and amenable for rapid deployment in other biological systems or computational workflows., Author summary Combining data from many different studies is an attractive way of capturing new aspects of the biology being studied. Biological variance attributable to cell type, cellular niche, origin, disease status or environmental stimuli is the basis of most small-n transcriptome studies. In aggregation, these promise to capture emergent dimensions of a biology that is not possible to view from any individual study. However biological signal is easily swamped by technical artifact, especially when data is generated on platforms with profoundly different data structures. This is the case when comparing microarray data to RNAseq, or RNAseq to single cell profiling. Consequently, transcriptome atlases are generally comprised from a small number of donors/conditions surveyed using one technology platform. In this paper we present a simple and scalable data integration method that is platform agnostic. We provide a proof-of-principle by constructing an atlas of blood cells that combines many data sets measured on different platforms, and that in combination, recapitulates the known blood hierarchy. The atlas provides a reference to compare external samples to, allowing users to benchmark new derivation or isolation methods. It also provides a reference point for new data types, such as the classification of single cells. The approach allows for FAIR data reuse and robust identification of molecular signatures across multiple studies and experimental conditions.

Intracellular spatial heterogeneity is frequently observed in bacteria, where the chromosome occupies part of the cell’s volume and a circuit’s DNA often localizes within the cell. How this heterogeneity affects core processes and genetic circuits is still poorly understood. In fact, commonly used ordinary differential equation (ODE) models of genetic circuits assume a well-mixed ensemble of molecules and, as such, do not capture spatial aspects. Reaction-diffusion partial differential equation (PDE) models have been only occasionally used since they are difficult to integrate and do not provide mechanistic understanding of the effects of spatial heterogeneity. In this paper, we derive a reduced ODE model that captures spatial effects, yet has the same dimension as commonly used well-mixed models. In particular, the only difference with respect to a well-mixed ODE model is that the association rate constant of binding reactions is multiplied by a coefficient, which we refer to as the binding correction factor (BCF). The BCF depends on the size of interacting molecules and on their location when fixed in space and it is equal to unity in a well-mixed ODE model. The BCF can be used to investigate how spatial heterogeneity affects the behavior of core processes and genetic circuits. Specifically, our reduced model indicates that transcription and its regulation are more effective for genes located at the cell poles than for genes located on the chromosome. The extent of these effects depends on the value of the BCF, which we found to be close to unity. For translation, the value of the BCF is always greater than unity, it increases with mRNA size, and, with biologically relevant parameters, is substantially larger than unity. Our model has broad validity, has the same dimension as a well-mixed model, yet it incorporates spatial heterogeneity. This simple-to-use model can be used to both analyze and design genetic circuits while accounting for spatial intracellular effects., Author summary A general and simple modeling framework to determine how spatial heterogeneity modulates the dynamics of gene networks is currently lacking. To this end, we provide a simple-to-use ordinary differential equation (ODE) model that can be used to both analyze and design genetic circuits while accounting for spatial intracellular effects. We apply our model to several core biological processes and determine that transcription and its regulation are more effective for genes located at the cell poles than for genes located on the chromosome and this difference increases with regulator size. For translation, we predict the effective binding between ribosomes and mRNA is higher than that predicted by a well-mixed model, and it increases with mRNA size. We provide examples where spatial effects are significant and should be considered but also where a traditional well-mixed model suffices despite severe spatial heterogeneity. Finally, we illustrate how the operation of well-known genetic circuits is impacted by spatial effects.

The brain consists of many interconnected networks with time-varying, partially autonomous activity. There are multiple sources of noise and variation yet activity has to eventually converge to a stable, reproducible state (or sequence of states) for its computations to make sense. We approached this problem from a control-theory perspective by applying contraction analysis to recurrent neural networks. This allowed us to find mechanisms for achieving stability in multiple connected networks with biologically realistic dynamics, including synaptic plasticity and time-varying inputs. These mechanisms included inhibitory Hebbian plasticity, excitatory anti-Hebbian plasticity, synaptic sparsity and excitatory-inhibitory balance. Our findings shed light on how stable computations might be achieved despite biological complexity. Crucially, our analysis is not limited to analyzing the stability of fixed geometric objects in state space (e.g points, lines, planes), but rather the stability of state trajectories which may be complex and time-varying., Author summary Stability is essential for any complex system including, and perhaps especially, the brain. The brain’s neural networks are highly dynamic and noisy. Activity fluctuates from moment to moment and can be highly variable. Yet it is critical that these networks reach a consistent state (or sequence of states) for their computations to make sense. Failures in stability have consequences ranging from mild (e.g incorrect decisions) to severe (disease states). In this paper we use tools from control theory and dynamical systems theory to find mechanisms which produce stability in recurrent neural networks (RNNs). We show that a kind of “unlearning” (inhibitory Hebbian and excitatory anti-Hebbian plasticity), balance of excitation and inhibition, and sparse anatomical connectivity all lead to stability. Crucially, we focus on the stability of neural trajectories. This is different from traditional studies of stability of fixed points or planes. We do not assess what trajectories our networks will follow but, rather, when these trajectories will all converge towards each other to achieve stability.

Epithelial sheets define organ architecture during development. Here, we employed an iterative multiscale computational modeling and quantitative experimental approach to decouple direct and indirect effects of actomyosin-generated forces, nuclear positioning, extracellular matrix, and cell-cell adhesion in shaping Drosophila wing imaginal discs. Basally generated actomyosin forces generate epithelial bending of the wing disc pouch. Surprisingly, acute pharmacological inhibition of ROCK-driven actomyosin contractility does not impact the maintenance of tissue height or curved shape. Computational simulations show that ECM tautness provides only a minor contribution to modulating tissue shape. Instead, passive ECM pre-strain serves to maintain the shape independent from actomyosin contractility. These results provide general insight into how the subcellular forces are generated and maintained within individual cells to induce tissue curvature. Thus, the results suggest an important design principle of separable contributions from ECM prestrain and actomyosin tension during epithelial organogenesis and homeostasis., Author summary The regulation and maintenance of an organ’s shape is a major outstanding problem in developmental biology. An iterative approach combining multiscale computational modelling and quantitative experimental approach was used to decouple direct and indirect roles of subcellular mechanical forces, nuclear positioning, and extracellular matrix in shaping the major axis of the wing pouch during the larval stage in fruit flies, which serves as a prototypical system for investigating epithelial morphogenesis. The research findings in this paper demonstrate that subcellular mechanical forces can effectively generate the curved tissue profile, while extracellular matrix is necessary for preserving the bent shape even in the absence of subcellular mechanical forces once the shape is generated. The developed integrated multiscale modelling environment can be readily extended to generate and test hypothesized novel mechanisms of developmental dynamics of other systems, including organoids that consist of several cellular and extracellular matrix layers.

Thoughtful use of simplifying assumptions is crucial to make systems biology models tractable while still representative of the underlying biology. A useful simplification can elucidate the core dynamics of a system. A poorly chosen assumption can, however, either render a model too complicated for making conclusions or it can prevent an otherwise accurate model from describing experimentally observed dynamics. Here, we perform a computational investigation of sequential multi-step pathway models that contain fewer pathway steps than the system they are designed to emulate. We demonstrate when such models will fail to reproduce data and how detrimental truncation of a pathway leads to detectable signatures in model dynamics and its optimised parameters. An alternative assumption is suggested for simplifying such pathways. Rather than assuming a truncated number of pathway steps, we propose to use the assumption that the rates of information propagation along the pathway is homogeneous and, instead, letting the length of the pathway be a free parameter. We first focus on linear pathways that are sequential and have first-order kinetics, and we show how this assumption results in a three-parameter model that consistently outperforms its truncated rival and a delay differential equation alternative in recapitulating observed dynamics. We then show how the proposed assumption allows for similarly terse and effective models of non-linear pathways. Our results provide a foundation for well-informed decision making during model simplifications., Author summary Mathematical modelling can be a highly effective way of condensing our understanding of biological processes and highlight the most important aspects of them. Effective models are based on simplifying assumptions that reduce complexity while still retaining the core dynamics of the original problem. Finding such assumptions is, however, not trivial. In this paper, we explore ways in which one can simplify long chains of simple reactions wherein each step is only dependent on its predecessor. After generating synthetic data from models that describe such chains in explicit detail we compare how well different simplifications retain the original dynamics. We show that the most common such simplification, which is to ignore parts of the chain, often renders models unable to account for time delays. However, we also show that when such a simplification has had a detrimental effect it leaves a detectable signature in its optimised parameter values. We also propose an alternative assumption which leads to a highly effective model with only three parameters. By comparing the effects of these simplifying assumptions in thousands of different cases and for different conditions we are able to clearly show when and why one is preferred over the other.

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However, computational models of large networks of spiking neurons are inherently hard to simulate and analyze. We evaluate a reduced mean-field model of excitatory and inhibitory adaptive exponential integrate-and-fire (AdEx) neurons which can be used to efficiently study the effects of electrical stimulation on large neural populations. The rich dynamical properties of this basic cortical model are described in detail and validated using large network simulations. Bifurcation diagrams reflecting the network’s state reveal asynchronous up- and down-states, bistable regimes, and oscillatory regions corresponding to fast excitation-inhibition and slow excitation-adaptation feedback loops. The biophysical parameters of the AdEx neuron can be coupled to an electric field with realistic field strengths which then can be propagated up to the population description. We show how on the edge of bifurcation, direct electrical inputs cause network state transitions, such as turning on and off oscillations of the population rate. Oscillatory input can frequency-entrain and phase-lock endogenous oscillations. Relatively weak electric field strengths on the order of 1 V/m are able to produce these effects, indicating that field effects are strongly amplified in the network. The effects of time-varying external stimulation are well-predicted by the mean-field model, further underpinning the utility of low-dimensional neural mass models., Author summary Weak electrical inputs to the brain in vivo using transcranial electrical stimulation or in isolated cortex in vitro can affect the dynamics of the underlying neural populations. However, it is poorly understood what the exact mechanisms are that modulate the activity of neural populations as a whole and why the responses are so diverse in stimulation experiments. Despite this, electrical stimulation techniques are being developed for the treatment of neurological diseases in humans. To better understand these interactions, it is often necessary to simulate and analyze very large networks of neurons, which can be computationally demanding. In this theoretical paper, we present a reduced model of coupled neural populations that represents a piece of cortical tissue. This efficient model retains the dynamical properties of the large network of neurons it is based on while being several orders of magnitude faster to simulate. Due to the biophysical properties of the neuron model, an electric field can be coupled to the population. We show that weak electric fields often used in stimulation experiments can lead to entrainment of neural oscillations on the population level, and argue that the responses critically depend on the dynamical state of the neural system.

The molecular mechanisms and functions in complex biological systems currently remain elusive. Recent high-throughput techniques, such as next-generation sequencing, have generated a wide variety of multiomics datasets that enable the identification of biological functions and mechanisms via multiple facets. However, integrating these large-scale multiomics data and discovering functional insights are, nevertheless, challenging tasks. To address these challenges, machine learning has been broadly applied to analyze multiomics. This review introduces multiview learning-an emerging machine learning field-and envisions its potentially powerful applications to multiomics. In particular, multiview learning is more effective than previous integrative methods for learning data's heterogeneity and revealing cross-talk patterns. Although it has been applied to various contexts, such as computer vision and speech recognition, multiview learning has not yet been widely applied to biological data-specifically, multiomics data. Therefore, this paper firstly reviews recent multiview learning methods and unifies them in a framework called multiview empirical risk minimization (MV-ERM). We further discuss the potential applications of each method to multiomics, including genomics, transcriptomics, and epigenomics, in an aim to discover the functional and mechanistic interpretations across omics. Secondly, we explore possible applications to different biological systems, including human diseases (e.g., brain disorders and cancers), plants, and single-cell analysis, and discuss both the benefits and caveats of using multiview learning to discover the molecular mechanisms and functions of these systems.

Over the past two decades, substantial amount of work has been conducted to characterize different odorant receptors, neuroanatomy and odorant response properties of the early olfactory system of Drosophila melanogaster. Yet many odorant receptors remain only partially characterized, and the odorant transduction process and the axon hillock spiking mechanism of the olfactory sensory neurons (OSNs) have yet to be fully determined. Identity and concentration, two key characteristics of the space of odorants, are encoded by the odorant transduction process. Detailed molecular models of the odorant transduction process are, however, scarce for fruit flies. To address these challenges we advance a comprehensive model of fruit fly OSNs as a cascade consisting of an odorant transduction process (OTP) and a biophysical spike generator (BSG). We model odorant identity and concentration using an odorant-receptor binding rate tensor, modulated by the odorant concentration profile, and an odorant-receptor dissociation rate tensor, and quantitatively describe the mechanics of the molecular ligand binding/dissociation of the OTP. We model the BSG as a Connor-Stevens point neuron. The resulting spatio-temporal encoding model of the Drosophila antenna provides a theoretical foundation for understanding the neural code of both odorant identity and odorant concentration and advances the state-of-the-art in a number of ways. First, it quantifies on the molecular level the spatio-temporal level of complexity of the transformation taking place in the antennae. The concentration-dependent spatio-temporal code at the output of the antenna circuits determines the level of complexity of olfactory processing in the downstream neuropils, such as odorant recognition and olfactory associative learning. Second, the model is biologically validated using multiple electrophysiological recordings. Third, the model demonstrates that the currently available data for odorant-receptor responses only enable the estimation of the affinity of the odorant-receptor pairs. The odorant-dissociation rate is only available for a few odorant-receptor pairs. Finally, our model calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies., Author summary Identity and concentration, intrinsically embedded in the odorant space, are two key characteristics of olfactory coding that define the level of complexity of neural processing throughout the olfactory system in the fruit fly. In this paper we advance a theoretical foundation for understanding these two characteristics by quantifying mathematically the odorant space and devising a biophysical model of the olfactory sensory neurons (OSNs). To validate our modeling approach, we propose and apply an algorithm to estimate the affinity value and the dissociation rate, the two characteristics that define odorant identity, of multiple odorant-receptor pairs. We then evaluate our model with a multitude of odorant waveforms and demonstrate that the model output reproduces the temporal responses of OSNs obtained from in vivo electrophysiology recordings. Furthermore, we evaluate the model at the OSN population level and quantify on the molecular level the spatio-temporal level of complexity of the transformation taking place between the odorant space and the OSNs. The resulting concentration-dependent spatio-temporal code determines the level of complexity of the input space driving olfactory processing in the downstream neuropils. Lastly, our model demonstrates that the currently available data for OSN responses only enables estimation of affinity value. This calls for new experiments for massively identifying the odorant-receptor dissociation rates of relevance to flies.

Antigen recognition by T-cells is guided by the T-cell receptor (TCR) heterodimer formed by α and β chains. A huge diversity of TCR sequences should be maintained by the immune system in order to be able to mount an effective response towards foreign pathogens, so, due to cooperative binding of α and β chains to the pathogen, any constraints on chain pairing can have a profound effect on immune repertoire structure, diversity and antigen specificity. By integrating available structural data and paired chain sequencing results we were able to show that there are almost no constraints on pairing in TCRαβ complexes, allowing naive T-cell repertoire to reach the highest possible diversity. Additional analysis reveals that the specific choice of contacting amino acids can still have a profound effect on complex conformation. Moreover, antigen-driven selection can distort the uniform landscape of chain pairing, while small, yet significant, differences in the pairing can be attributed to various specialized T-cell subsets such as MAIT and iNKT T-cells, as well as other TCR sets specific to certain antigens., Author summary In the present paper we study chain pairing preferences in the T-cell receptor (TCR) heterodimer complex. The TCR molecule is formed by α and β chains and binding of both of these chains to an antigen presented by the major histocompatibility complex (MHC) molecule is required in order to trigger an immune response against foreign pathogens and neoantigens. We show that chain pairing in the TCR complex is nearly random ensuring a highly diverse set of TCRs required for recognition of a vast set of antigens. Our results also show that chain pairing preferences can nevertheless influence TCR complex geometry and biases in TCR chain pairing can be used to identify antigen-driven selection or selection towards specialized subsets of T-cells such as mucosal-associated and natural killer invariant T-cells.

Cell-to-cell variability generates subpopulations of drug-tolerant cells that diminish the efficacy of cancer drugs. Efficacious combination therapies are thus needed to block drug-tolerant cells via minimizing the impact of heterogeneity. Probabilistic models such as Bliss independence have been developed to evaluate drug interactions and their combination efficacy based on probabilities of specific actions mediated by drugs individually and in combination. In practice, however, these models are often applied to conventional dose-response curves in which a normalized parameter with a value between zero and one, generally referred to as fraction of cells affected (fa), is used to evaluate the efficacy of drugs and their combined interactions. We use basic probability theory, computer simulations, time-lapse live cell microscopy, and single-cell analysis to show that fa metrics may bias our assessment of drug efficacy and combination effectiveness. This bias may be corrected when dynamic probabilities of drug-induced phenotypic events, i.e. induction of cell death and inhibition of division, at a single-cell level are used as metrics to assess drug efficacy. Probabilistic phenotype metrics offer the following three benefits. First, in contrast to the commonly used fa metrics, they directly represent probabilities of drug action in a cell population. Therefore, they deconvolve differential degrees of drug effect on tumor cell killing versus inhibition of cell division, which may not be correlated for many drugs. Second, they increase the sensitivity of short-term drug response assays to cell-to-cell heterogeneities and the presence of drug-tolerant subpopulations. Third, their probabilistic nature allows them to be used directly in unbiased evaluation of synergistic efficacy in drug combinations using probabilistic models such as Bliss independence. Altogether, we envision that probabilistic analysis of single-cell phenotypes complements currently available assays via improving our understanding of heterogeneity in drug response, thereby facilitating the discovery of more efficacious combination therapies to block drug-tolerant cells., Author summary Resistance to therapy due to tumor cell heterogeneity poses a major challenge to the use of cancer drugs. Cell-to-cell variability generates subpopulations of drug-tolerant cells that diminish therapeutic efficacy, even in populations of cells that are scored as highly sensitive based on drug potency. Overcoming such heterogeneity and blocking subpopulations of drug-tolerant cells motivate efforts toward identifying efficacious combination therapies. The success of these efforts depends on our ability to distinguish how heterogeneous populations of cells respond to individual drugs, and how these responses are influenced by combined drug interactions. In this paper, we propose mathematical and experimental frameworks to evaluate time-dependent drug interactions based on probabilistic metrics that quantify drug-induced tumor cell killing or inhibition of division at a single-cell level. These metrics can reveal heterogeneous drug responses and their changes with time and drug combinations. Thus, they have important implications for designing efficacious combination therapies, especially those designed to block or overcome drug-tolerant subpopulations of cancer cells.

In this paper we try to describe all possible molecular states (phenotypes) for a cell that fabricates itself at a constant rate, given its enzyme kinetics and the stoichiometry of all reactions. For this, we must understand the process of cellular growth: steady-state self-fabrication requires a cell to synthesize all of its components, including metabolites, enzymes and ribosomes, in proportions that match its own composition. Simultaneously, the concentrations of these components affect the rates of metabolism and biosynthesis, and hence the growth rate. We here derive a theory that describes all phenotypes that solve this circular problem. All phenotypes can be described as a combination of minimal building blocks, which we call Elementary Growth Modes (EGMs). EGMs can be used as the theoretical basis for all models that explicitly model self-fabrication, such as the currently popular Metabolism and Expression models. We then use our theory to make concrete biological predictions. We find that natural selection for maximal growth rate drives microorganisms to states of minimal phenotypic complexity: only one EGM will be active when growth rate is maximised. The phenotype of a cell is only extended with one more EGM whenever growth becomes limited by an additional biophysical constraint, such as a limited solvent capacity of a cellular compartment. The theory presented here extends recent results on Elementary Flux Modes: the minimal building blocks of cellular growth models that lack the self-fabrication aspect. Our theory starts from basic biochemical and evolutionary considerations, and describes unicellular life, both in growth-promoting and in stress-inducing environments, in terms of EGMs., Author summary A factory that produces identical factories with all of its machinery in the right proportions would be a wondrous thing. This is exactly what growing cells do: they self-fabricate their constituents (metabolites, enzymes, lipids, DNA) to form new cells. The production of these compounds leads to the expansion of cellular volume, and gives rise to a growth rate. To self-fabricate sustainably, also called “balanced growth”, all compounds should be produced at exactly this growth rate. How to design such a cellular factory, given a list of all machines (enzymes encoded on the genome) and their properties (enzyme kinetics)? This is a difficult circular problem, since the expressed enzymes both determine what is produced (because they catalyse the production), and what should be produced (since all expressed enzymes should be produced to fabricate an identical cell). Using a mathematical approach, we identified the minimal enzyme expression patterns needed for cellular growth: Elementary Growth Modes (EGMs). The EGMs form the basic units of all sustainable phenotypes, and we prove that usually only one of them will be selected by evolution in static conditions. Our theory of self-replication therefore forms a quantitative, biochemically-rooted, basis of cellular growth phenotypes in all unicellular life forms.

Cells contain a thiol redox regulatory network to coordinate metabolic and developmental activities with exogenous and endogenous cues. This network controls the redox state and activity of many target proteins. Electrons are fed into the network from metabolism and reach the target proteins via redox transmitters such as thioredoxin (TRX) and NADPH-dependent thioredoxin reductases (NTR). Electrons are drained from the network by reactive oxygen species (ROS) through thiol peroxidases, e.g., peroxiredoxins (PRX). Mathematical modeling promises access to quantitative understanding of the network function and was implemented by using published kinetic parameters combined with fitting to known biochemical data. Two networks were assembled, namely the ferredoxin (FDX), FDX-dependent TRX reductase (FTR), TRX, fructose-1,6-bisphosphatase (FBPase) pathway with 2-cysteine PRX/ROS as oxidant, and separately the FDX, FDX-dependent NADP reductase (FNR), NADPH, NTRC-pathway for 2-CysPRX reduction. Combining both modules allowed drawing several important conclusions of network performance. The resting H2O2 concentration was estimated to be about 30 nM in the chloroplast stroma. The electron flow to metabolism exceeds that into thiol regulation of FBPase more than 7000-fold under physiological conditions. The electron flow from NTRC to 2-CysPRX is about 5.32-times more efficient than that from TRX-f1 to 2-CysPRX. Under severe stress (30 μM H2O2) the ratio of electron flow to the thiol network relative to metabolism sinks to 1:251 whereas the ratio of e- flow from NTRC to 2-CysPRX and TRX-f1 to 2-CysPRX rises up to 1:67. Thus, the simulation provides clues on experimentally inaccessible parameters and describes the functional state of the chloroplast thiol regulatory network., Author summary The state of the thiol redox regulatory network is a fundamental feature of all cells and determines metabolic and developmental processes. However, only some parameters are quantifiable in experiments. This paper establishes simplified mathematical models which enable simulation of electron flows through the regulatory system. This in turn allows for estimating rates and states of components of the network and to tentatively address previously unknown parameters such as the resting hydrogen peroxide levels or the expenditure of reductive power for regulation relative to metabolism. The establishment of such models for simulating the performance and dynamics of the redox regulatory network is of significance not only for photosynthesis but also, e.g., in bacterial and animal cells exposed to environmental stress or pathological disorders.

Identification of induced pluripotent stem (iPS) progenitor cells, the iPS forming cells in early stage of reprogramming, could provide valuable information for studying the origin and underlying mechanism of iPS cells. However, it is very difficult to identify experimentally since there are no biomarkers known for early progenitor cells, and only about 6 days after reprogramming initiation, iPS cells can be experimentally determined via fluorescent probes. What is more, the ratio of progenitor cells during early reprograming period is below 5%, which is too low to capture experimentally in the early stage. In this paper, we propose a novel computational approach for the identification of iPS progenitor cells based on machine learning and microscopic image analysis. Firstly, we record the reprogramming process using a live cell imaging system after 48 hours of infection with retroviruses expressing Oct4, Sox2 and Klf4, later iPS progenitor cells and normal murine embryonic fibroblasts (MEFs) within 3 to 5 days after infection are labeled by retrospectively tracing the time-lapse microscopic image. We then calculate 11 types of cell morphological and motion features such as area, speed, etc., and select best time windows for modeling and perform feature selection. Finally, a prediction model using XGBoost is built based on the selected six types of features and best time windows. Our model allows several missing values/frames in the sample datasets, thus it is applicable to a wide range of scenarios. Cross-validation, holdout validation and independent test experiments show that the minimum precision is above 52%, that is, the ratio of predicted progenitor cells within 3 to 5 days after viral infection is above 52%. The results also confirm that the morphology and motion pattern of iPS progenitor cells is different from that of normal MEFs, which helps with the machine learning methods for iPS progenitor cell identification., Author summary Identification of induced pluripotent stem (iPS) progenitor cells could provide valuable information for studying the origin and underlying mechanism of iPS cells. However, it is very difficult to identify experimentally since there are no biomarkers known for early progenitor cells, and only after about 6 days of induction, iPS cells can be experimentally determined via fluorescent probes. What is more, the percentage of the progenitor cells during the early induction period is below 5%, too low to capture experimentally in early stage. In this work, we proposed an approach for the identification of iPS progenitor cells, the iPS forming cells, based on machine learning and microscopic image analysis. The aim is to help biologists to enrich iPS progenitor cells during the early stage of induction, which allows experimentalists to select iPS progenitor cells with much higher probability, and furthermore to study the biomarkers which trigger the reprogramming process.

Cortical spreading depression (SD) is a spreading disruption of ionic homeostasis in the brain during which neurons experience complete and prolonged depolarizations. SD is the basis of migraine aura and is increasingly associated with many other brain pathologies. Here, we study the role of glutamate and NMDA receptor dynamics in the context of an ionic electrodiffusion model. We perform simulations in one (1D) and two (2D) spatial dimension. Our 1D simulations reproduce the “inverted saddle” shape of the extracellular voltage signal for the first time. Our simulations suggest that SD propagation depends on two overlapping mechanisms; one dependent on extracellular glutamate diffusion and NMDA receptors and the other dependent on extracellular potassium diffusion and persistent sodium channel conductance. In 2D simulations, we study the dynamics of spiral waves. We study the properties of the spiral waves in relation to the planar 1D wave, and also compute the energy expenditure associated with the recurrent SD spirals., Author summary Cortical spreading depression is a wave of neuronal silencing and ion concentration changes that sweeps slowly through the brain. It is the basis of migraine aura, in which a migraine patient sees a defect move through ones visual field 30 minutes to an hour prior to the headache attack. In this paper, we study the mechanisms by which cortical spreading depression travels as a wave through the brain. We construct a detailed mathematical model based on the physics of ion movement as well as what is known about the molecular players of cortical spreading depression. We build a simulation program that successfully solves the resulting set of highly coupled equations. We find that cortical spreading depression can propagate as a wave by distinct but overlapping mechanisms. We also simulate spiral cortical spreading depression waves and study their properties.

Pluripotent stem cells retain the developmental timing of their species of origin in vitro, an observation that suggests the existence of a cell-intrinsic developmental clock, yet the nature and machinery of the clock remain a mystery. We hypothesize that one possible component may lie in species-specific differences in the kinetics of transcriptional responses to differentiation signals. Using a liquid-handling robot, mouse and human pluripotent stem cells were exposed to identical neural differentiation conditions and sampled for RNA-sequencing at high frequency, every 4 or 10 minutes, for the first 10 hours of differentiation to test for differences in transcriptomic response rates. The majority of initial transcriptional responses occurred within a rapid window in the first minutes of differentiation for both human and mouse stem cells. Despite similarly early onsets of gene expression changes, we observed shortened and condensed gene expression patterns in mouse pluripotent stem cells compared to protracted trends in human pluripotent stem cells. Moreover, the speed at which individual genes were upregulated, as measured by the slopes of gene expression changes over time, was significantly faster in mouse compared to human cells. These results suggest that downstream transcriptomic response kinetics to signaling cues are faster in mouse versus human cells, and may offer a partial account for the vast differences in developmental rates across species., Author summary For regenerative medicine, a slow developmental clock operating in human pluripotent stem cells imposes severe obstacles to many pluripotent stem cell therapies. Producing the desired cell types with the necessary level of physiological maturity in clinically-relevant time frames will be essential if the therapy is aimed at being patient-specific. Thus, understanding what controls species-specific rates of differentiation and identifying ways to accelerate it would have a broad impact on improving the therapeutic value of human pluripotent stem cells. In this paper, we measured the immediate-early gene expression responses to neural differentiation signals in mouse and human pluripotent stem cells. We quantitatively summarized the gene expression patterns using a flexible model that allowed us to identify shared trends and dynamic changes across species. We found that responses occurred equally early across species, but expression patterns were prolonged in human cells and the rate of upregulation in gene expression was significantly faster in mouse cells. Our results represent a significant contribution in furthering the knowledge of early developmental transcriptional programs.

Respiratory syncytial virus (RSV) infection results in millions of hospitalizations and thousands of deaths each year. Variations in the adaptive and innate immune response appear to be associated with RSV severity. To investigate the host response to RSV infection in infants, we performed a systems-level study of RSV pathophysiology, incorporating high-throughput measurements of the peripheral innate and adaptive immune systems and the airway epithelium and microbiota. We implemented a novel multi-omic data integration method based on multilayered principal component analysis, penalized regression, and feature weight back-propagation, which enabled us to identify cellular pathways associated with RSV severity. In both airway and immune cells, we found an association between RSV severity and activation of pathways controlling Th17 and acute phase response signaling, as well as inhibition of B cell receptor signaling. Dysregulation of both the humoral and mucosal response to RSV may play a critical role in determining illness severity., Author summary This paper presents a novel approach to understanding the localized molecular responses to respiratory syncytial virus (RSV) and the system-level correlates of clinical outcomes. To do this, we developed a novel statistical method able to integrate high dimensional molecular data characterizing the host airway microbota and immune and nasal gene expression. We show that this integrative approach facilitates superior performance in estimating clinical outcome as opposed to any single data type. Using this approach, we identified both cell type-specific and shared biomarkers and regulatory pathways associated with RSV severity. Specifically, we identified an association between RSV severity, activation of pathways controlling Th17, and inhibition of B cell receptor signaling, which were present in both the site of infection airway and in peripheral immune cells. These results can guide future efforts to identify biomarkers for identifying or predicting illness severity following infant RSV infection. They may also be useful as biomarkers to inform the efficacy of future interventions (e.g., therapies) or preventative measures to suppress the rate of severe disease (e.g., vaccines).

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks., Author summary The cytoskeleton is composed of semiflexible, inextensible actin filaments, dynamic cross linkers, and molecular motors, and makes the primary contribution to the structural properties of the cell. Despite its being so fundamental to cell biology, the biological complexity of the cytoskeleton hinders our ability to understand its mechanical properties through in vitro experiments. In this paper, we perform microscopic simulations of actin fibers and transient cross linkers to quantify the principle timescales involved in the network, study how these timescales influence the morphology and rheology of the system, and examine the role of hydrodynamic interactions in cytoskeletal networks. We find three principle timescales which we associate with fiber flexibility, cross linker detachment, and network remodeling, respectively. We show that the morphology of the network is more important on longer timescales, where the viscosity of links inside of fiber bundles is enhanced. We also show that hydrodynamic interactions reduce the stress inside of bundles because of entrainment flows. Finally, we propose a continuum model which can be used to coarse-grain our agent-based simulations and enable modeling of larger systems.

Regulation of cytosolic calcium (Ca2+) dynamics is fundamental to microglial function. Temporal and spatial Ca2+ fluxes are induced from a complicated signal transduction pathway linked to brain ionic homeostasis. In this paper, we develop a novel biophysical model of Ca2+ and sodium (Na+) dynamics in human microglia and evaluate the contribution of purinergic receptors (P2XRs) to both intracellular Ca2+ and Na+ levels in response to agonist/ATP binding. This is the first comprehensive model that integrates P2XRs to predict intricate Ca2+ and Na+ transient responses in microglia. Specifically, a novel compact biophysical model is proposed for the capture of whole-cell patch-clamp currents associated with P2X4 and P2X7 receptors, which is composed of only four state variables. The entire model shows that intricate intracellular ion dynamics arise from the coupled interaction between P2X4 and P2X7 receptors, the Na+/Ca2+ exchanger (NCX), Ca2+ extrusion by the plasma membrane Ca2+ ATPase (PMCA), and Ca2+ and Na+ leak channels. Both P2XRs are modelled as two separate adenosine triphosphate (ATP) gated Ca2+ and Na+ conductance channels, where the stoichiometry is the removal of one Ca2+ for the hydrolysis of one ATP molecule. Two unique sets of model parameters were determined using an evolutionary algorithm to optimise fitting to experimental data for each of the receptors. This allows the proposed model to capture both human P2X7 and P2X4 data (hP2X7 and hP2X4). The model architecture enables a high degree of simplicity, accuracy and predictability of Ca2+ and Na+ dynamics thus providing quantitative insights into different behaviours of intracellular Na+ and Ca2+ which will guide future experimental research. Understanding the interactions between these receptors and other membrane-bound transporters provides a step forward in resolving the qualitative link between purinergic receptors and microglial physiology and their contribution to brain pathology., Author summary Mathematical modelling and computer simulation are powerful tools by which we can analyse complex biological systems, particularly, neural phenomena involved in brain dysfunction. In this research, we develop a theoretical foundation for studying P2X-mediated calcium and sodium signalling in human microglial cells. Microglia, which are brain-resident macrophages, restructure their intracellular actin cytoskeleton to enable motility; this restructuring requires a complex molecular cascade involving a set of ionic channels, membrane-coupled receptors and cytosolic components. Recent studies highlight the importance for increasing our understanding of microglia physiology, since their functions play critical roles in both normal physiological and pathological dynamics of the brain. There is a need to develop reliable human cellular models to investigate the biology of microglia aimed at understanding the influence of purinergic signalling in brain dysfunction to provide novel drug discovery targets. In this work, a detailed mathematical model is built for the dynamics of human P2XRs in microglia. Subsequently, experimental whole-cell currents are used to derive P2X-mediated electrophysiology of human microglia (i.e. sodium and calcium dynamics, and membrane potential). Our predictions reveal new quantitative insights into P2XRs on how they regulate ionic concentrations in terms of physiological interactions and transient responses.

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long—potentially redundant—past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox., Author summary Even with exciting advances in recording techniques of neural spiking activity, experiments only provide a comparably short glimpse into the activity of only a tiny subset of all neurons. How can we learn from these experiments about the organization of information processing in the brain? To that end, we exploit that different properties of information processing leave distinct footprints on the firing statistics of individual spiking neurons. In our work, we focus on a particular statistical footprint: We quantify how much a single neuron’s spiking depends on its own preceding activity, which we call history dependence. By quantifying history dependence in neural spike recordings, one can, in turn, infer some of the properties of information processing. Because recording lengths are limited in practice, a direct estimation of history dependence from experiments is challenging. The embedding optimization approach that we present in this paper aims at extracting a maximum of history dependence within the limits set by a reliable estimation. The approach is highly adaptive and thereby enables a meaningful comparison of history dependence between neurons with vastly different spiking statistics, which we exemplify on a diversity of spike recordings. In conjunction with recent, highly parallel spike recording techniques, the approach could yield valuable insights on how hierarchical processing is organized in the brain.

The olfactory system faces the difficult task of identifying an enormous variety of odors independent of their intensity. Primacy coding, where the odor identity is encoded by the receptor types that respond earliest, might provide a compact and informative representation that can be interpreted efficiently by the brain. In this paper, we analyze the information transmitted by a simple model of primacy coding using numerical simulations and statistical descriptions. We show that the encoded information depends strongly on the number of receptor types included in the primacy representation, but only weakly on the size of the receptor repertoire. The representation is independent of the odor intensity and the transmitted information is useful to perform typical olfactory tasks with close to experimentally measured performance. Interestingly, we find situations in which a smaller receptor repertoire is advantageous for discriminating odors. The model also suggests that overly sensitive receptor types could dominate the entire response and make the whole array useless, which allows us to predict how receptor arrays need to adapt to stay useful during environmental changes. Taken together, we show that primacy coding is more useful than simple binary and normalized coding, essentially because the sparsity of the odor representations is independent of the odor statistics, in contrast to the alternatives. Primacy coding thus provides an efficient odor representation that is independent of the odor intensity and might thus help to identify odors in the olfactory cortex., Author summary Humans can identify odors independent of their intensity. Experimental data suggest that this is accomplished by representing the odor identity by the earliest responding receptor types. Using theoretical modeling, we here show that such a primacy code outperforms alternative encodings and allows discriminating odors with close to experimentally measured performance. This performance depends strongly on the number of receptors considered in the primacy code, but the receptor repertoire size is less important. The model also suggests a strong evolutionary pressure on the receptor sensitivities, which could explain observed receptor copy number adaptations. By predicting psycho-physical experiments, the model will thus contribute to our understanding of the olfactory system.

Neuroscience models come in a wide range of scales and specificity, from mean-field rate models to large-scale networks of spiking neurons. There are potential trade-offs between simplicity and realism, versatility and computational speed. This paper is about large-scale cortical network models, and the question we address is one of scalability: would scaling down cell density impact a network’s ability to reproduce cortical dynamics and function? We investigated this problem using a previously constructed realistic model of the monkey visual cortex that is true to size. Reducing cell density gradually up to 50-fold, we studied changes in model behavior. Size reduction without parameter adjustment was catastrophic. Surprisingly, relatively minor compensation in synaptic weights guided by a theoretical algorithm restored mean firing rates and basic function such as orientation selectivity to models 10-20 times smaller than the real cortex. Not all was normal in the reduced model cortices: intracellular dynamics acquired a character different from that of real neurons, and while the ability to relay feedforward inputs remained intact, reduced models showed signs of deficiency in functions that required dynamical interaction among cortical neurons. These findings are not confined to models of the visual cortex, and modelers should be aware of potential issues that accompany size reduction. Broader implications of this study include the importance of homeostatic maintenance of firing rates, and the functional consequences of feedforward versus recurrent dynamics, ideas that may shed light on other species and on systems suffering cell loss., Author summary With the vast numbers of neurons in the cerebral cortex, models in neuroscience are, for practical reasons, often orders of magnitude smaller than the actual network. We examine in this article the scalability of cortical networks. We find that function and dynamics in a network depend on network size. For illustration, we use a previously constructed realistic model of monkey visual cortex. Reducing the number of cells in the model, we find that small changes in synaptic weights can help maintain firing rates. However, model characteristics change fundamentally in the reduced models. Neurons have abnormal intracellular dynamics. The model becomes dominated by feedforward inputs and is less capable of functions requiring neuronal interaction. Modelers need to be aware of the potential issues with reduced cortical network models.

Circadian rhythms are generated by interlocked transcriptional-translational negative feedback loops (TTFLs), the molecular process implemented within a cell. The contributions, weighting and balancing between the multiple feedback loops remain debated. Dissociated, free-running dynamics in the expression of distinct clock genes has been described in recent experimental studies that applied various perturbations such as slice preparations, light pulses, jet-lag, and culture medium exchange. In this paper, we provide evidence that this “presumably transient” dissociation of circadian gene expression oscillations may occur at the single-cell level. Conceptual and detailed mechanistic mathematical modeling suggests that such dissociation is due to a weak interaction between multiple feedback loops present within a single cell. The dissociable loops provide insights into underlying mechanisms and general design principles of the molecular circadian clock., Author summary Circadian clocks are endogenous pacemakers that generate gene expression oscillations with a period of approximately 24h. They enable an organism to anticipate daily changes in light and temperature and allow to align physiological properties to the most beneficial time around the solar day. The suprachiasmatic nucleus (SCN) of the hypothalamus is the master circadian pacemaker in mammals that coordinates peripheral clocks throughout the body and even encodes seasons. Gene expression oscillations of circadian clock genes in this master pacemaker have been shown to dissociate after perturbations of the system such as light pulses and jet-lag. The underlying mechanism remains unknown. We show that this dissociation may occur even within a single cell of the pacemaker. Data-driven mathematical modeling suggests that the dissociation relies upon a weak interaction between interlocked gene-regulatory feedback loops. Differential responses of these feedback loops to light perturbations is consistent with the concept of morning and evening oscillators.

Basal gene expression levels have been shown to be predictive of cellular response to cytotoxic treatments. However, such analyses do not fully reveal complex genotype- phenotype relationships, which are partly encoded in highly interconnected molecular networks. Biological pathways provide a complementary way of understanding drug response variation among individuals. In this study, we integrate chemosensitivity data from a large-scale pharmacogenomics study with basal gene expression data from the CCLE project and prior knowledge of molecular networks to identify specific pathways mediating chemical response. We first develop a computational method called PACER, which ranks pathways for enrichment in a given set of genes using a novel network embedding method. It examines a molecular network that encodes known gene-gene as well as gene-pathway relationships, and determines a vector representation of each gene and pathway in the same low-dimensional vector space. The relevance of a pathway to the given gene set is then captured by the similarity between the pathway vector and gene vectors. To apply this approach to chemosensitivity data, we identify genes whose basal expression levels in a panel of cell lines are correlated with cytotoxic response to a compound, and then rank pathways for relevance to these response-correlated genes using PACER. Extensive evaluation of this approach on benchmarks constructed from databases of compound target genes and large collections of drug response signatures demonstrates its advantages in identifying compound-pathway associations compared to existing statistical methods of pathway enrichment analysis. The associations identified by PACER can serve as testable hypotheses on chemosensitivity pathways and help further study the mechanisms of action of specific cytotoxic drugs. More broadly, PACER represents a novel technique of identifying enriched properties of any gene set of interest while also taking into account networks of known gene-gene relationships and interactions., Author summary Gene expression levels have been used to study the cellular response to drug treatments. However, analysis of gene expression without considering gene interactions cannot fully reveal complex genotype-phenotype relationships. Biological pathways reveal the interactions among genes, thus providing a complementary way of understanding the drug response variation among individuals. In this paper, we aim to identify pathways that mediate the chemical response of each drug. We used the recently generated CTRP pharmacogenomics data and CCLE basal expression data to identify these pathways. We showed that using the prior knowledge encoded in molecular networks substantially improves pathway identification. In particular, we integrate genes and pathways into a large heterogeneous network in which links are protein-protein interactions and gene-pathway affiliations. We then project this heterogeneous network onto a low-dimensional space, which enables more precise similarity measurements between pathways and drug-response-correlated genes. Extensive experiments on two benchmarks show that our method substantially improved the pathway identification performance by using the molecular networks. More importantly, our method represents a novel technique of identifying enriched properties of any gene set of interest while also taking into account networks of known gene-gene relationships and interactions.