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Cox regression is commonly used to predict the outcome by the time to an event of interest and in addition, identify relevant features for survival analysis in cancer genomics. Due to the high-dimensionality of high-throughput genomic data, existing Cox models trained on any particular dataset usually generalize poorly to other independent datasets. In this paper, we propose a network-based Cox regression model called Net-Cox and applied Net-Cox for a large-scale survival analysis across multiple ovarian cancer datasets. Net-Cox integrates gene network information into the Cox's proportional hazard model to explore the co-expression or functional relation among high-dimensional gene expression features in the gene network. Net-Cox was applied to analyze three independent gene expression datasets including the TCGA ovarian cancer dataset and two other public ovarian cancer datasets. Net-Cox with the network information from gene co-expression or functional relations identified highly consistent signature genes across the three datasets, and because of the better generalization across the datasets, Net-Cox also consistently improved the accuracy of survival prediction over the Cox models regularized by or . This study focused on analyzing the death and recurrence outcomes in the treatment of ovarian carcinoma to identify signature genes that can more reliably predict the events. The signature genes comprise dense protein-protein interaction subnetworks, enriched by extracellular matrix receptors and modulators or by nuclear signaling components downstream of extracellular signal-regulated kinases. In the laboratory validation of the signature genes, a tumor array experiment by protein staining on an independent patient cohort from Mayo Clinic showed that the protein expression of the signature gene FBN1 is a biomarker significantly associated with the early recurrence after 12 months of the treatment in the ovarian cancer patients who are initially sensitive to chemotherapy. Net-Cox toolbox is available at http://compbio.cs.umn.edu/Net-Cox/., Author Summary Network-based computational models are attracting increasing attention in studying cancer genomics because molecular networks provide valuable information on the functional organizations of molecules in cells. Survival analysis mostly with the Cox proportional hazard model is widely used to predict or correlate gene expressions with time to an event of interest (outcome) in cancer genomics. Surprisingly, network-based survival analysis has not received enough attention. In this paper, we studied resistance to chemotherapy in ovarian cancer with a network-based Cox model, called Net-Cox. The experiments confirm that networks representing gene co-expression or functional relations can be used to improve the accuracy and the robustness of survival prediction of outcome in ovarian cancer treatment. The study also revealed subnetwork signatures that are enriched by extracellular matrix receptors and modulators and the downstream nuclear signaling components of extracellular signal-regulators, respectively. In particular, FBN1, which was detected as a signature gene of high confidence by Net-Cox with network information, was validated as a biomarker for predicting early recurrence in platinum-sensitive ovarian cancer patients in laboratory.

Single-cell RNA sequencing (scRNA-seq) has been widely applied to discover new cell types by detecting sub-populations in a heterogeneous group of cells. Since scRNA-seq experiments have lower read coverage/tag counts and introduce more technical biases compared to bulk RNA-seq experiments, the limited number of sampled cells combined with the experimental biases and other dataset specific variations presents a challenge to cross-dataset analysis and discovery of relevant biological variations across multiple cell populations. In this paper, we introduce a method of variance-driven multitask clustering of single-cell RNA-seq data (scVDMC) that utilizes multiple single-cell populations from biological replicates or different samples. scVDMC clusters single cells in multiple scRNA-seq experiments of similar cell types and markers but varying expression patterns such that the scRNA-seq data are better integrated than typical pooled analyses which only increase the sample size. By controlling the variance among the cell clusters within each dataset and across all the datasets, scVDMC detects cell sub-populations in each individual experiment with shared cell-type markers but varying cluster centers among all the experiments. Applied to two real scRNA-seq datasets with several replicates and one large-scale droplet-based dataset on three patient samples, scVDMC more accurately detected cell populations and known cell markers than pooled clustering and other recently proposed scRNA-seq clustering methods. In the case study applied to in-house Recessive Dystrophic Epidermolysis Bullosa (RDEB) scRNA-seq data, scVDMC revealed several new cell types and unknown markers validated by flow cytometry. MATLAB/Octave code available at https://github.com/kuanglab/scVDMC., Author summary scRNA-seq enables detailed profiling of heterogeneous cell populations and can be used to reveal lineage relationships or discover new cell types. In the literature, there has been little effort directed towards developing computational methods for cross-population transcriptome analysis of multiple single-cell populations. The cross-cell-population clustering problem is different from the traditional clustering problem because single-cell populations can be collected from different patients, different samples of a tissue, or different experimental replicates. The accompanying biological and technical variation tends to dominate the signals for clustering the pooled single cells from the multiple populations. In this work, we have developed a multitask clustering method to address the cross-population clustering problem. The method simultaneously clusters each individual cell population and controls variance among the cell-type cluster centers within each cell population and across the cell populations. We demonstrate that our multitask clustering method significantly improves clustering accuracy and marker discovery in three public scRNA-seq datasets and also apply the method to an in-house Recessive Dystrophic Epidermolysis Bullosa (RDEB) dataset. Our results make it evident that multitask clustering is a promising new approach for cross-population analysis of scRNA-seq data.

Neural circuit development requires that synapses be formed between appropriate neurons. In addition, for a hierarchical network, successful development involves a sequencing of developmental events. It has been suggested that one mechanism that helps speed up development of proper connections is an early overproduction of synapses. Using a computational model of synapse development, such as adaptive synaptogenesis, it is possible to study such overproduction and its role in speeding up development; it is also possible to study other outcomes of synapse overproduction that are seemingly new to the literature. With a fixed number of neurons, adaptive synaptogenesis can control the speed of synaptic development in two ways: by altering the rate constants of the adaptive processes or by altering the initial number of rapidly but non-selectively accrued synapses. Using either mechanism, the simulations reveal that synapse overproduction appears as an unavoidable concomitant of rapid adaptive synaptogenesis. However, the shortest development times, which always produces the greatest amount of synapse overproduction, reduce adult performance by three measures: energy use, discrimination error rates, and proportional neuron allocation. Thus, the results here lead to the hypothesis that the observed speed of neural network development represents a particular inter-generational compromise: quick development benefits parental fecundity while slow development benefits offspring fecundity., Author summary The brain processes information by building and adjusting neural connections, and as an organism learns about the environment, it incorporates associations between features of the environment into these adjustable connections. Organisms, however, are not born with these connections; synapses must develop from a connectionless set of neurons. An important aspect of normal brain development is the timely development of the brain and of hierarchically arranged brain regions. In this paper, we show that an unsupervised algorithm, called adaptive synaptogenesis, builds neurons with stable connections and allows these neurons to appropriately discriminate patterns. Here, we show that larger rates of synaptogenesis and synaptic modification speed up development of stable connections. However, such a speed-up produces larger, steady-state energy-costs. We conjecture that these synaptic modification rates have evolved as a compromise via natural selection. In this regard, the evolution-theoretic idea of parent-offspring conflict arises as a developmental consideration; that is, time to stable connectivity must balance with subsequent neural performance. Importantly, we illustrate that the widely-observed phenomenon of synapse overproduction during development can be understood as a compromise between speedy and efficient development.

Across the nervous system, certain population spiking patterns are observed far more frequently than others. A hypothesis about this structure is that these collective activity patterns function as population codewords–collective modes–carrying information distinct from that of any single cell. We investigate this phenomenon in recordings of ∼150 retinal ganglion cells, the retina’s output. We develop a novel statistical model that decomposes the population response into modes; it predicts the distribution of spiking activity in the ganglion cell population with high accuracy. We found that the modes represent localized features of the visual stimulus that are distinct from the features represented by single neurons. Modes form clusters of activity states that are readily discriminated from one another. When we repeated the same visual stimulus, we found that the same mode was robustly elicited. These results suggest that retinal ganglion cells’ collective signaling is endowed with a form of error-correcting code–a principle that may hold in brain areas beyond retina., Author Summary Neurons in most parts of the nervous system represent and process information in a collective fashion, yet the nature of this collective code is poorly understood. An important constraint placed on any such collective processing comes from the fact that individual neurons’ signaling is prone to corruption by noise. The information theory and engineering literatures have studied error-correcting codes that allow individual noise-prone coding units to “check” each other, forming an overall representation that is robust to errors. In this paper, we have analyzed the population code of one of the best-studied neural systems, the retina, and found that it is structured in a manner analogous to error-correcting schemes. Indeed, we found that the complex activity patterns over ~150 retinal ganglion cells, the output neurons of the retina, could be mapped onto collective code words, and that these code words represented precise visual information while suppressing noise. In order to analyze this coding scheme, we introduced a novel quantitative model of the retinal output that predicted neural activity patterns more accurately than existing state-of-the-art approaches.

The liver is the central organ for detoxification of xenobiotics in the body. In pharmacokinetic modeling, hepatic metabolization capacity is typically quantified as hepatic clearance computed as degradation in well-stirred compartments. This is an accurate mechanistic description once a quasi-equilibrium between blood and surrounding tissue is established. However, this model structure cannot be used to simulate spatio-temporal distribution during the first instants after drug injection. In this paper, we introduce a new spatially resolved model to simulate first pass perfusion of compounds within the naive liver. The model is based on vascular structures obtained from computed tomography as well as physiologically based mass transfer descriptions obtained from pharmacokinetic modeling. The physiological architecture of hepatic tissue in our model is governed by both vascular geometry and the composition of the connecting hepatic tissue. In particular, we here consider locally distributed mass flow in liver tissue instead of considering well-stirred compartments. Experimentally, the model structure corresponds to an isolated perfused liver and provides an ideal platform to address first pass effects and questions of hepatic heterogeneity. The model was evaluated for three exemplary compounds covering key aspects of perfusion, distribution and metabolization within the liver. As pathophysiological states we considered the influence of steatosis and carbon tetrachloride-induced liver necrosis on total hepatic distribution and metabolic capacity. Notably, we found that our computational predictions are in qualitative agreement with previously published experimental data. The simulation results provide an unprecedented level of detail in compound concentration profiles during first pass perfusion, both spatio-temporally in liver tissue itself and temporally in the outflowing blood. We expect our model to be the foundation of further spatially resolved models of the liver in the future., Author Summary The liver continuously removes xenobiotic compounds from the blood in the mammalian body. Most computational models represent the liver as composed of few well-stirred subcompartments so that a spatially resolved simulation of hepatic perfusion and compound distribution right after drug administration is currently not available. To mechanistically describe the local distribution of compounds in liver tissue during first pass perfusion, we here present a computational model which combines micro-CT based vascular structures with mass transfer descriptions used in physiologically based pharmacokinetic modeling. In the resulting spatio-temporal model, hepatic mass transfer is governed by the physiological architecture and the composition of the connecting hepatic tissue, such that hepatic heterogeneity and spatial distribution can be described mechanistically. The performance of our model is shown for exemplary compounds addressing key aspects of distribution and metabolization of drugs within a mouse liver. We furthermore investigate the impact of steatosis and carbon tetrachloride-induced liver necrosis. Notably, we find that our computational predictions are in qualitative agreement with previous experimental results in animal models. In the future, our spatially resolved model will be extended by including additional physiological information and by taking into account recirculation through the body.

It is a long-established fact that neuronal plasticity occupies the central role in generating neural function and computation. Nevertheless, no unifying account exists of how neurons in a recurrent cortical network learn to compute on temporally and spatially extended stimuli. However, these stimuli constitute the norm, rather than the exception, of the brain's input. Here, we introduce a geometric theory of learning spatiotemporal computations through neuronal plasticity. To that end, we rigorously formulate the problem of neural representations as a relation in space between stimulus-induced neural activity and the asymptotic dynamics of excitable cortical networks. Backed up by computer simulations and numerical analysis, we show that two canonical and widely spread forms of neuronal plasticity, that is, spike-timing-dependent synaptic plasticity and intrinsic plasticity, are both necessary for creating neural representations, such that these computations become realizable. Interestingly, the effects of these forms of plasticity on the emerging neural code relate to properties necessary for both combating and utilizing noise. The neural dynamics also exhibits features of the most likely stimulus in the network's spontaneous activity. These properties of the spatiotemporal neural code resulting from plasticity, having their grounding in nature, further consolidate the biological relevance of our findings., Author Summary The world is not perceived as a chain of segmented sensory still lifes. Instead, it appears that the brain is capable of integrating the temporal dependencies of the incoming sensory stream with the spatial aspects of that input. It then transfers the resulting whole in a useful manner, in order to reach a coherent and causally sound image of our physical surroundings, and to act within it. These spatiotemporal computations are made possible through a cluster of local and coexisting adaptation mechanisms known collectively as neuronal plasticity. While this role is widely known and supported by experimental evidence, no unifying theory of how the brain, through the interaction of plasticity mechanisms, gets to represent spatiotemporal computations in its spatiotemporal activity. In this paper, we aim at such a theory. We develop a rigorous mathematical formalism of spatiotemporal representations within the input-driven dynamics of cortical networks. We demonstrate that the interaction of two of the most common plasticity mechanisms, intrinsic and synaptic plasticity, leads to representations that allow for spatiotemporal computations. We also show that these representations are structured to tolerate noise and to even benefit from it.

Since the discovery of tumour initiating cells (TICs) in solid tumours, studies focussing on their role in cancer initiation and progression have abounded. The biological interrogation of these cells continues to yield volumes of information on their pro-tumourigenic behaviour, but actionable generalised conclusions have been scarce. Further, new information suggesting a dependence of tumour composition and growth on the microenvironment has yet to be studied theoretically. To address this point, we created a hybrid, discrete/continuous computational cellular automaton model of a generalised stem-cell driven tissue with a simple microenvironment. Using the model we explored the phenotypic traits inherent to the tumour initiating cells and the effect of the microenvironment on tissue growth. We identify the regions in phenotype parameter space where TICs are able to cause a disruption in homeostasis, leading to tissue overgrowth and tumour maintenance. As our parameters and model are non-specific, they could apply to any tissue TIC and do not assume specific genetic mutations. Targeting these phenotypic traits could represent a generalizable therapeutic strategy across cancer types. Further, we find that the microenvironmental variable does not strongly affect the outcomes, suggesting a need for direct feedback from the microenvironment onto stem-cell behaviour in future modelling endeavours., Author Summary In this paper, we present a mathematical/computational model of a tumour growing according to the canonical cancer stem-cell hypothesis with a simplified microenvironment. We explore the parameters of this model and find good agreement between our model and other theoretical models in terms of the intrinsic cellular parameters, which are difficult to study biologically. We find, however, disagreement between novel biological data and our model in terms of the microenvironmental changes. We conclude that future theoretical models of stem-cell driven tumours must include specific feedback from the microenvironment onto the individual cellular behavior. Further, we identify several cell intrinsic parameters which govern loss of homeostasis into a state of uncontrolled growth.

Most chronic viral infections are managed with small molecule therapies that inhibit replication but are not curative because non-replicating viral forms can persist despite decades of suppressive treatment. There are therefore numerous strategies in development to eradicate all non-replicating viruses from the body. We are currently engineering DNA cleavage enzymes that specifically target hepatitis B virus covalently closed circular DNA (HBV cccDNA), the episomal form of the virus that persists despite potent antiviral therapies. DNA cleavage enzymes, including homing endonucleases or meganucleases, zinc-finger nucleases (ZFNs), TAL effector nucleases (TALENs), and CRISPR-associated system 9 (Cas9) proteins, can disrupt specific regions of viral DNA. Because DNA repair is error prone, the virus can be neutralized after repeated cleavage events when a target sequence becomes mutated. DNA cleavage enzymes will be delivered as genes within viral vectors that enter hepatocytes. Here we develop mathematical models that describe the delivery and intracellular activity of DNA cleavage enzymes. Model simulations predict that high vector to target cell ratio, limited removal of delivery vectors by humoral immunity, and avid binding between enzyme and its DNA target will promote the highest level of cccDNA disruption. Development of de novo resistance to cleavage enzymes may occur if DNA cleavage and error prone repair does not render the viral episome replication incompetent: our model predicts that concurrent delivery of multiple enzymes which target different vital cccDNA regions, or sequential delivery of different enzymes, are both potentially useful strategies for avoiding multi-enzyme resistance. The underlying dynamics of cccDNA persistence are unlikely to impact the probability of cure provided that antiviral therapy is given concurrently during eradication trials. We conclude by describing experiments that can be used to validate the model, which will in turn provide vital information for dose selection for potential curative trials in animals and ultimately humans., Author Summary Innovative new approaches are being developed to eradicate viral infections that until recently were considered incurable. We are interested in engineering DNA cleavage enzymes that can cut and incapacitate persistent viruses. One hurdle is that these enzymes must be delivered to infected cells as genes within viral vectors that are not harmful to humans. In this paper, we developed a series of equations that describe the delivery of these enzymes to their intended targets, as well the activity of DNA cutting within the cell. While our mathematical model is catered towards hepatitis B virus infection, it is widely applicable to other infections such as HIV, as well as oncologic and metabolic diseases characterized by aberrant gene expression. Certain enzymes may bind DNA more avidly than others, while different enzymes may also bind cooperatively if targeted to different regions of viral DNA. We predict that such enzymes, if delivered efficiently to a high proportion of infected cells, will be critical to increase the probability of cure. We also demonstrate that our equations will serve as a useful tool for identifying the most important features of a curative regimen, and ultimately for guiding clinical trial dosing schedules to ensure hepatitis B eradication with the smallest number of possible doses.

Influenza virus infection remains a public health problem worldwide. The mechanisms underlying viral control during an uncomplicated influenza virus infection are not fully understood. Here, we developed a mathematical model including both innate and adaptive immune responses to study the within-host dynamics of equine influenza virus infection in horses. By comparing modeling predictions with both interferon and viral kinetic data, we examined the relative roles of target cell availability, and innate and adaptive immune responses in controlling the virus. Our results show that the rapid and substantial viral decline (about 2 to 4 logs within 1 day) after the peak can be explained by the killing of infected cells mediated by interferon activated cells, such as natural killer cells, during the innate immune response. After the viral load declines to a lower level, the loss of interferon-induced antiviral effect and an increased availability of target cells due to loss of the antiviral state can explain the observed short phase of viral plateau in which the viral level remains unchanged or even experiences a minor second peak in some animals. An adaptive immune response is needed in our model to explain the eventual viral clearance. This study provides a quantitative understanding of the biological factors that can explain the viral and interferon kinetics during a typical influenza virus infection., Author Summary Influenza, commonly referred to as the flu, is a contagious respiratory illness caused by influenza virus infections. Although most infected subjects with intact immune systems are able to clear the virus without developing serious flu complications, the mechanisms underlying viral control are not fully understood. In this paper, we address this question by developing mathematical models that include both innate and adaptive immune responses, and fitting them to experimental data from horses infected with equine influenza virus. We find that the innate immune response, such as natural killer cell-mediated infected cell killing and interferon's antiviral effect, can explain the first rapid viral decline and subsequent second peak viremia, and that the adaptive immune response is needed to eventually clear the virus. This study improves our understanding of influenza virus dynamics and may provide more information for future research in influenza pathogenesis, treatment, and vaccination.

Heterogeneity in host populations is an important factor affecting the ability of a pathogen to invade, yet the quantitative investigation of its effects on epidemic spread is still an open problem. In this paper, we test recent theoretical results, which extend the established “percolation paradigm” to the spread of a pathogen in discrete heterogeneous host populations. In particular, we test the hypothesis that the probability of epidemic invasion decreases when host heterogeneity is increased. We use replicated experimental microcosms, in which the ubiquitous pathogenic fungus Rhizoctonia solani grows through a population of discrete nutrient sites on a lattice, with nutrient sites representing hosts. The degree of host heterogeneity within different populations is adjusted by changing the proportion and the nutrient concentration of nutrient sites. The experimental data are analysed via Bayesian inference methods, estimating pathogen transmission parameters for each individual population. We find a significant, negative correlation between heterogeneity and the probability of pathogen invasion, thereby validating the theory. The value of the correlation is also in remarkably good agreement with the theoretical predictions. We briefly discuss how our results can be exploited in the design and implementation of disease control strategies., Author Summary Pathogen spread and epidemic invasion in plant, animal and human populations depend on host properties (infectivity, susceptibility) that can vary amongst hosts within the same population. However, such host variability (or heterogeneity) is typically difficult to control experimentally, and little explicit research has been done on its effects on pathogen invasion. We present the first systematic investigation on the spread of a pathogen (the fungal plant pathogen Rhizoctonia solani) in repeatable microcosm populations (nutrient sites, representing hosts, on a lattice) with varying heterogeneity. Recent theoretical models for heterogeneity make the following prediction, that we set as our hypothesis: increasing heterogeneity (keeping all other properties fixed) results in a decrease of the probability of pathogen invasion. We validate the hypothesis using a combination of statistical methods. Moreover, we find that the decrease in probability of invasion is also in good quantitative agreement with the theoretical predictions. We discuss how our results can be exploited for disease control strategies that increase the heterogeneity of a system in order to limit pathogen spread.

The discovery of small molecules targeted to specific oncogenic pathways has revolutionized anti-cancer therapy. However, such therapy often fails due to the evolution of acquired resistance. One long-standing question in clinical cancer research is the identification of optimum therapeutic administration strategies so that the risk of resistance is minimized. In this paper, we investigate optimal drug dosing schedules to prevent, or at least delay, the emergence of resistance. We design and analyze a stochastic mathematical model describing the evolutionary dynamics of a tumor cell population during therapy. We consider drug resistance emerging due to a single (epi)genetic alteration and calculate the probability of resistance arising during specific dosing strategies. We then optimize treatment protocols such that the risk of resistance is minimal while considering drug toxicity and side effects as constraints. Our methodology can be used to identify optimum drug administration schedules to avoid resistance conferred by one (epi)genetic alteration for any cancer and treatment type., Author Summary Recently, the field of anti-cancer therapy has witnessed a revolution by the discovery of targeted therapy, which refers to compounds targeting specific pathways causing abnormal growth of cancer cells. The clinical success of such drugs has been limited by the evolution of acquired resistance to these compounds, which leads to a relapse after initial response to therapy. Current dosing procedures are not designed to optimally delay the emergence of resistance; the identification of such optimal dosing schedules represents an important challenge in clinical cancer research. Here, we design a novel methodology to identify the optimum drug administration strategies that reach this clinical goal. Our model describes the evolutionary dynamics of a tumor cell population during therapy. We consider drug resistance emerging due to a single (epi)genetic alteration and calculate the probability of resistance arising during specific dosing strategies. We then optimize treatment protocols such that the risk of resistance is minimal while considering drug toxicity and side effects as constraints. Since this methodology can be extended to describe situations arising during administration of cytotoxic chemotherapy as well, it can be used to identify optimum drug administration schedules to avoid resistance for any cancer and treatment type.