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Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

A fundamental challenge for personalized medicine is to capture enough of the complexity of an individual patient to determine an optimal way to keep them healthy or restore their health. This will require personalized computational models of sufficient resolution and with enough mechanistic information to provide actionable information to the clinician. Such personalized models are increasingly referred to as medical digital twins. Digital twin technology for health applications is still in its infancy, and extensive research and development is required. This article focuses on several projects in different stages of development that can lead to specific-and practical-medical digital twins or digital twin modeling platforms. It emerged from a two-day forum on problems related to medical digital twins, particularly those involving an immune system component. Open access video recordings of the forum discussions are available., Competing Interests: TH: majority stakeholder in ImmuNovus, Inc and Discovery Collective, Inc. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. FA, FC, LF, TH, DK, PM, BM, VP, AS, and TZ declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision., (© 2024 Laubenbacher, Adler, An, Castiglione, Eubank, Fonseca, Glazier, Helikar, Jett-Tilton, Kirschner, Macklin, Mehrad, Moore, Pasour, Shmulevich, Smith, Voigt, Yankeelov and Ziemssen.)

Medical digital twins are computational models of human biology relevant to a given medical condition, which are tailored to an individual patient, thereby predicting the course of disease and individualized treatments, an important goal of personalized medicine. The immune system, which has a central role in many diseases, is highly heterogeneous between individuals, and thus poses a major challenge for this technology. In February 2023, an international group of experts convened for two days to discuss these challenges related to immune digital twins. The group consisted of clinicians, immunologists, biologists, and mathematical modelers, representative of the interdisciplinary nature of medical digital twin development. A video recording of the entire event is available. This paper presents a synopsis of the discussions, brief descriptions of ongoing digital twin projects at different stages of progress. It also proposes a 5-year action plan for further developing this technology. The main recommendations are to identify and pursue a small number of promising use cases, to develop stimulation-specific assays of immune function in a clinical setting, and to develop a database of existing computational immune models, as well as advanced modeling technology and infrastructure., (© 2024. The Author(s).)

As common commensals residing on mucosal tissues, Lactobacillus species are known to promote health, while some Streptococcus species act to enhance the pathogenicity of other organisms in those environments. In this study we used a combination of in vitro imaging of live biofilms and computational modeling to explore biofilm interactions between Streptococcus oralis, an accessory pathogen in oral candidiasis, and Lactobacillus paracasei, an organism with known probiotic properties. A computational agent-based model was created where the two species interact only by competing for space, oxygen, and glucose. Quantification of bacterial growth in live biofilms indicated that S. oralis biomass and cell numbers were much lower than predicted by the model. Two subsequent models were then created to examine more complex interactions between these species, one where L. paracasei secretes a surfactant and another where L. paracasei secretes an inhibitor of S. oralis growth. We observed that the growth of S. oralis could be affected by both mechanisms. Further biofilm experiments support the hypothesis that L. paracasei may secrete an inhibitor of S. oralis growth, although they do not exclude that a surfactant could also be involved. This contribution shows how agent-based modeling and experiments can be used in synergy to address multiple-species biofilm interactions, with important roles in mucosal health and disease. IMPORTANCE We previously discovered a role of the oral commensal Streptococcus oralis as an accessory pathogen. S. oralis increases the virulence of Candida albicans infections in murine oral candidiasis and epithelial cell models through mechanisms which promote the formation of tissue-damaging biofilms. Lactobacillus species have known inhibitory effects on biofilm formation of many microbes, including Streptococcus species. Agent-based modeling has great advantages as a means of exploring multifaceted relationships between organisms in complex environments such as biofilms. Here, we used an iterative collaborative process between experimentation and modeling to reveal aspects of the mostly unexplored relationship between S. oralis and L. paracasei in biofilm growth. The inhibitory nature of L. paracasei on S. oralis in biofilms may be exploited as a means of preventing or alleviating mucosal fungal infections.

Melanoma is considered to be the most serious and aggressive type of skin cancer, and metastasis appears to be the most important factor in its prognosis. Herein, we developed a transfer learning-based biomarker discovery model that could aid in the diagnosis and prognosis of this disease. After applying it to the ensemble machine learning model, results revealed that the genes found were consistent with those found using other methodologies previously applied to the same TCGA (The Cancer Genome Atlas) data set. Further novel biomarkers were also found. Our ensemble model achieved an AUC of 0.9861, an accuracy of 91.05, and an F1 score of 90.60 using an independent validation data set. This study was able to identify potential genes for diagnostic classification (C7 and GRIK5) and diagnostic and prognostic biomarkers (S100A7, S100A7, KRT14, KRT17, KRT6B, KRTDAP, SERPINB4, TSHR, PVRL4, WFDC5, IL20RB) in melanoma. The results show the utility of a transfer learning approach for biomarker discovery in melanoma.

Iron is essential to the virulence of Aspergillus species, and restricting iron availability is a critical mechanism of antimicrobial host defense. Macrophages recruited to the site of infection are at the crux of this process, employing multiple intersecting mechanisms to orchestrate iron sequestration from pathogens. To gain an integrated understanding of how this is achieved in aspergillosis, we generated a transcriptomic time series of the response of human monocyte-derived macrophages to Aspergillus and used this and the available literature to construct a mechanistic computational model of iron handling of macrophages during this infection. We found an overwhelming macrophage response beginning 2 to 4 h after exposure to the fungus, which included upregulated transcription of iron import proteins transferrin receptor-1, divalent metal transporter-1, and ZIP family transporters, and downregulated transcription of the iron exporter ferroportin. The computational model, based on a discrete dynamical systems framework, consisted of 21 3-state nodes, and was validated with additional experimental data that were not used in model generation. The model accurately captures the steady state and the trajectories of most of the quantitatively measured nodes. In the experimental data, we surprisingly found that transferrin receptor-1 upregulation preceded the induction of inflammatory cytokines, a feature that deviated from model predictions. Model simulations suggested that direct induction of transferrin receptor-1 (TfR1) after fungal recognition, independent of the iron regulatory protein-labile iron pool (IRP-LIP) system, explains this finding. We anticipate that this model will contribute to a quantitative understanding of iron regulation as a fundamental host defense mechanism during aspergillosis. IMPORTANCE Invasive pulmonary aspergillosis is a major cause of death among immunosuppressed individuals despite the best available therapy. Depriving the pathogen of iron is an essential component of host defense in this infection, but the mechanisms by which the host achieves this are complex. To understand how recruited macrophages mediate iron deprivation during the infection, we developed and validated a mechanistic computational model that integrates the available information in the field. The insights provided by this approach can help in designing iron modulation therapies as anti-fungal treatments.

Introduction: Yoga has been shown to reduce pain and improve function in populations with chronic low back pain (cLBP), yet the underlying molecular mechanisms remain elusive. This study examined the feasibility and acceptability of a yoga research protocol, including recruitment, retention, and data collection, and investigated the preliminary effects of yoga on psychological and neurophysiological functions, including gene expression and DNA methylation profiles, in participants with cLBP., Methods: A one-arm trial was conducted with 11 participants with cLBP who enrolled in a 12-week yoga intervention. Data on subjective pain characteristics, quantitative sensory testing, and blood for analysis of differentially expressed genes and CpG methylation was collected prior to the start of the intervention and at study completion., Results: Based on pre-determined feasibility and acceptability criteria, the yoga intervention was found to be feasible and highly acceptable to participants. There was a reduction in pain severity, interference, and mechanical pain sensitivity post-yoga and an increase in emotion regulation and self-efficacy. No adverse reactions were reported. Differential expression analysis demonstrated that the yoga intervention induced increased expression of antisense genes, some of which serve as antisense to known pain genes. In addition, there were 33 differentially hypomethylated positions after yoga (log2 fold change ≥ 1), with enrichment of genes involved in NIK/NF-kB signaling, a major pathway that modulates immune function and inflammation., Discussion/conclusions: The study supports the feasibility and acceptability of the proposed protocol to test a specific mechanism of action for yoga in individuals with cLBP. These results also support the notion that yoga may operate through our identified psychological and neurophysiologic pathways to influence reduced pain severity and interference., (© 2022. The Author(s).)

Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics., (Copyright © 2022 The Authors. Published by Elsevier Inc. All rights reserved.)

Summary: We introduce SteadyCellPhenotype, a browser-based interface for the analysis of ternary biological networks. It includes tools for deterministically finding all steady states of a network, as well as the simulation and visualization of trajectories with publication quality graphics. Simulations allow us to approximate the size of the basin for attractors and deterministic simulations of trajectories nearby specified points allow us to explore the behavior of the system in that neighborhood., Availability and Implementation: https://github.com/knappa/steadycellphenotype MIT License., (© The Author(s) 2022. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Aspergillus species are ubiquitous environmental moulds, with spores inhaled daily by most humans. Immunocompromised hosts can develop an invasive infection resulting in high mortality. There is, therefore, a pressing need for host-centric therapeutics for this infection. To address it, we created a multi-scale computational model of the infection, focused on its interaction with the innate immune system and iron, a critical nutrient for the pathogen. The model, parameterized using published data, was found to recapitulate a wide range of biological features and was experimentally validated in vivo . Conidial swelling was identified as critical in fungal strains with high growth, whereas the siderophore secretion rate seems to be an essential prerequisite for the establishment of the infection in low-growth strains. In immunocompetent hosts, high growth, high swelling probability and impaired leucocyte activation lead to a high conidial germination rate. Similarly, in neutropenic hosts, high fungal growth was achieved through synergy between high growth rate, high swelling probability, slow leucocyte activation and high siderophore secretion. In summary, the model reveals a small set of parameters related to fungal growth, iron acquisition and leucocyte activation as critical determinants of the fate of the infection.

As common commensals residing on mucosal tissues, Lactobacillus species are known to promote health, while some Streptococcus species act to enhance the pathogenicity of other organisms in those environments. In this study, we used a combination of in vitro imaging of live biofilms and computational modeling to explore biofilm interactions between Streptococcus oralis, an accessory pathogen in oral candidiasis, and Lactobacillus paracasei, an organism with known probiotic properties. A computational agent-based model was created where the two species interact only by competing for space, oxygen and glucose. Quantification of bacterial growth in live biofilms indicated that S. oralis biomass and cell numbers were much lower than predicted by the model. Two subsequent models were then created to examine more complex interactions between these species, one where L. paracasei secretes a surfactant, and another where L. paracasei secretes an inhibitor of S. oralis growth. We observed that the growth of S. oralis could be affected by both mechanisms. Further biofilm experiments support the hypothesis that L. paracasei may secrete an inhibitor of S. oralis growth, although they do not exclude that a surfactant could also be involved. This contribution shows how agent-based modeling and experiments can be used in synergy to address multiple species biofilm interactions, with important roles in mucosal health and disease. IMPORTANCE We previously discovered a role of the oral commensal Streptococcus oralis as an accessory pathogen. S. oralis increases the virulence of Candida albicans infections in murine oral candidiasis and epithelial cell models through mechanisms which promote the formation of tissue-damaging biofilms. Lactobacillus species have known inhibitory effects on biofilm formation of many microbes, including Streptococcus species. Agent-based modeling has great advantages as a means of exploring multifaceted relationships between organisms in complex environments such as biofilms. Here, we used an iterative collaborative process between experimentation and modeling to reveal aspects of the mostly unexplored relationship between S. oralis and L. paracasei in biofilm growth. The inhibitory nature of L. paracasei on S. oralis in biofilms may be exploited as a means of preventing or alleviating mucosal fungal infections.

Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating multiple environmental factors and regulatory mechanisms. We validate the model by a systematic comparison to prior experiments, which led to agreement in 17 out of 22 cases. The discrepancies motivate alternative hypotheses that are testable by follow-up experiments. Analysis of this model revealed two time-constrained windows of opportunity that must be met for the complete transition from the yeast to hyphal phenotype, as well as control strategies that can robustly prevent this transition. We experimentally validate two of these control predictions in C. albicans strains lacking the transcription factor UME6 and the histone deacetylase HDA1, respectively. This model will serve as a strong base from which to develop a systems biology understanding of C. albicans morphogenesis., Competing Interests: The authors have declared that no competing interests exist.

Optimization and control are important objectives across biology and biomedicine, and mathematical models are a key enabling technology. This paper reports a computational study of model-based multi-objective optimization in the setting of microbial ecology, using agent-based models. This modeling framework is well-suited to the field, but is not amenable to standard control-theoretic approaches. Furthermore, due to computational complexity, simulation-based optimization approaches are often challenging to implement. This paper presents the results of an approach that combines control-dependent coarse-graining with Pareto optimization, applied to two models of multi-species bacterial biofilms. It shows that this approach can be successful for models whose computational complexity prevents effective simulation-based optimization.

The human microbiome has been a focus of intense study in recent years. Most of the living organisms comprising the microbiome exist in the form of biofilms on mucosal surfaces lining our digestive, respiratory, and genito-urinary tracts. While health-associated microbiota contribute to digestion, provide essential nutrients, and protect us from pathogens, disturbances due to illness or medical interventions contribute to infections, some that can be fatal. Myriad biological processes influence the make-up of the microbiota, for example: growth, division, death, and production of extracellular polymers (EPS), and metabolites. Inter-species interactions include competition, inhibition, and symbiosis. Computational models are becoming widely used to better understand these interactions. Agent-based modeling is a particularly useful computational approach to implement the various complex interactions in microbial communities when appropriately combined with an experimental approach. In these models, each cell is represented as an autonomous agent with its own set of rules, with different rules for each species. In this review, we will discuss innovations in agent-based modeling of biofilms and the microbiota in the past five years from the biological and mathematical perspectives and discuss how agent-based models can be further utilized to enhance our comprehension of the complex world of polymicrobial biofilms and the microbiome.

One of the ultimate goals in systems biology is to develop control strategies to find efficient medical treatments. One step towards this goal is to develop methods for changing the state of a cell into a desirable state. We propose an efficient method that determines combinations of network perturbations to direct the system towards a predefined state. The method requires a set of control actions such as the silencing of a gene or the disruption of the interaction between two genes. An optimal control policy defined as the best intervention at each state of the system can be obtained using existing methods. However, these algorithms are computationally prohibitive for models with tens of nodes. Our method generates control actions that approximates the optimal control policy with high probability with a computational efficiency that does not depend on the size of the state space. Our C++ code is available at https://github.com/boaguilar/SDDScontrol.

Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by regulatory rules driving the dynamics that have certain so-called canalizing properties. In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models. These properties are relevant to many biological applications. Moreover, our results show that, from the standpoint of the attractor structure, high canalizing depth, compared to relatively small positive canalizing depth, has a very modest impact on dynamics. Motivated by these observations, we conduct mathematical study of the attractor structure of a random Boolean network of canalizing depth one (i.e., the smallest positive depth). For every positive integer ℓ , we give an explicit formula for the limit of the expected number of attractors of length ℓ in an n -state random Boolean network as n goes to infinity., Competing Interests: Conflicts of Interest The authors declare that they have no conflicts of interest.

MicroRNAs form a class of short, non-coding RNA molecules which are essential for proper development in tissue-based plants and animals. To help explain their role in gene regulation, a number of mathematical and computational studies have demonstrated the potential canalizing effects of microRNAs. However, such studies have typically focused on the effects of microRNAs on only one or a few target genes. Consequently, it remains unclear how these small-scale effects add up to the experimentally observed developmental outcomes resulting from microRNA perturbation at the whole-genome level. To answer this question, we built a general computational model of cell differentiation to study the effect of microRNAs in genome-scale gene regulatory networks. Our experiments show that in large gene regulatory networks, microRNAs can control differentiation time without significantly changing steady-state gene expression profiles. This temporal regulatory role cannot be naturally replicated using protein-based transcription factors alone. While several microRNAs have been shown to regulate differentiation time in vivo , our findings provide a new explanation of how the cumulative molecular actions of individual microRNAs influence genome-scale cellular dynamics. Taken together, these results may help explain why tissue-based organisms exclusively depend on miRNA-mediated regulation, while their more primitive counterparts do not.

Bioinformatics has become an indispensable part of life science over the past 2 decades. However, bioinformatics education is not well integrated at the undergraduate level, especially in liberal arts colleges and regional universities in the United States. One significant obstacle pointed out by the Network for Integrating Bioinformatics into Life Sciences Education is the lack of faculty in the bioinformatics area. Most current life science professors did not acquire bioinformatics analysis skills during their own training. Consequently, a great number of undergraduate and graduate students do not get the chance to learn bioinformatics or computational biology skills within a structured curriculum during their education. To address this gap, we developed a module-based, week-long short course to train small college and regional university professors with essential bioinformatics skills. The bioinformatics modules were built to be adapted by the professor-trainees afterward and used in their own classes. All the course materials can be accessed at https://github.com/TheJacksonLaboratory/JAXBD2K-ShortCourse., Competing Interests: The authors have declared that no competing interests exist.

Biological systems require precise copper homeostasis enabling metallation of cuproproteins while preventing metal toxicity. In bacteria, sensing, transport, and storage molecules act in coordination to fulfill these roles. However, there is not yet a kinetic schema explaining the system integration. Here, we report a model emerging from experimental and computational approaches that describes the dynamics of copper distribution in Pseudomonas aeruginosa. Based on copper uptake experiments, a minimal kinetic model describes well the copper distribution in the wild-type bacteria but is unable to explain the behavior of the mutant strain lacking CopA1, a key Cu + efflux ATPase. The model was expanded through an iterative hypothesis-driven approach, arriving to a mechanism that considers the induction of compartmental pools and the parallel function of CopA and Cus efflux systems. Model simulations support the presence of a periplasmic copper storage with a crucial role under dyshomeostasis conditions in P. aeruginosa. Importantly, the model predicts not only the interplay of periplasmic and cytoplasmic pools but also the existence of a threshold in the concentration of external copper beyond which cells lose their ability to control copper levels., (© 2018 John Wiley & Sons Ltd.)

Background: Cell death as a result of ischemic injury triggers powerful mechanisms regulated by germline-encoded Pattern Recognition Receptors (PRRs) with shared specificity that recognize invading pathogens and endogenous ligands released from dying cells, and as such are essential to human health. Alternatively, dysregulation of these mechanisms contributes to extreme inflammation, deleterious tissue damage and impaired healing in various diseases. The Toll-like receptors (TLRs) are a prototypical family of PRRs that may be powerful anti-inflammatory targets if agents can be designed that antagonize their harmful effects while preserving host defense functions. This requires an understanding of the complex interactions and consequences of targeting the TLR-mediated pathways as well as technologies to analyze and interpret these, which will then allow the simulation of perturbations targeting specific pathway components, predict potential outcomes and identify safe and effective therapeutic targets., Results: We constructed a multiscale mathematical model that spans the tissue and intracellular scales, and captures the consequences of targeting various regulatory components of injury-induced TLR4 signal transduction on potential pro-inflammatory or pro-healing outcomes. We applied known interactions to simulate how inactivation of specific regulatory nodes affects dynamics in the context of injury and to predict phenotypes of potential therapeutic interventions. We propose rules to link model behavior to qualitative estimates of pro-inflammatory signal activation, macrophage infiltration, production of reactive oxygen species and resolution. We tested the validity of the model by assessing its ability to reproduce published data not used in its construction., Conclusions: These studies will enable us to form a conceptual framework focusing on TLR4-mediated ischemic repair to assess potential molecular targets that can be utilized therapeutically to improve efficacy and safety in treating ischemic/inflammatory injury.

Dysregulation of iron metabolism in cancer is well documented and it has been suggested that there is interdependence between excess iron and increased cancer incidence and progression. In an effort to better understand the linkages between iron metabolism and breast cancer, a predictive mathematical model of an expanded iron homeostasis pathway was constructed that includes species involved in iron utilization, oxidative stress response and oncogenic pathways. The model leads to three predictions. The first is that overexpression of iron regulatory protein 2 (IRP2) recapitulates many aspects of the alterations in free iron and iron-related proteins in cancer cells without affecting the oxidative stress response or the oncogenic pathways included in the model. This prediction was validated by experimentation. The second prediction is that iron-related proteins are dramatically affected by mitochondrial ferritin overexpression. This prediction was validated by results in the pertinent literature not used for model construction. The third prediction is that oncogenic Ras pathways contribute to altered iron homeostasis in cancer cells. This prediction was validated by a combination of simulation experiments of Ras overexpression and catalase knockout in conjunction with the literature. The model successfully captures key aspects of iron metabolism in breast cancer cells and provides a framework upon which more detailed models can be built., Competing Interests: The authors have declared that no competing interests exist.

Background: Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system., Results: This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg ., Conclusions: This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.

Motivation: There is a growing need in bioinformatics for easy-to-use software implementations of algorithms that are usable across platforms. At the same time, reproducibility of computational results is critical and often a challenge due to source code changes over time and dependencies., Results: The approach introduced in this paper addresses both of these needs with AlgoRun, a dedicated packaging system for implemented algorithms, using Docker technology. Implemented algorithms, packaged with AlgoRun, can be executed through a user-friendly interface directly from a web browser or via a standardized RESTful web API to allow easy integration into more complex workflows. The packaged algorithm includes the entire software execution environment, thereby eliminating the common problem of software dependencies and the irreproducibility of computations over time. AlgoRun-packaged algorithms can be published on http://algorun.org, a centralized searchable directory to find existing AlgoRun-packaged algorithms., Availability and Implementation: AlgoRun is available at http://algorun.org and the source code under GPL license is available at https://github.com/algorun, Contact: laubenbacher@uchc.edu, Supplementary Information: Supplementary data are available at Bioinformatics online., (© The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.)

Background: Invasive aspergillosis is a severe infection of immunocompromised hosts, caused by the inhalation of the spores of the ubiquitous environmental molds of the Aspergillus genus. The innate immune response in this infection entails a series of complex and inter-related interactions between multiple recruited and resident cell populations with each other and with the fungal cell; in particular, iron is critical for fungal growth., Results: A computational model of invasive aspergillosis is presented here; the model can be used as a rational hypothesis-generating tool to investigate host responses to this infection. Using a combination of laboratory data and published literature, an in silico model of a section of lung tissue was generated that includes an alveolar duct, adjacent capillaries, and surrounding lung parenchyma. The three-dimensional agent-based model integrates temporal events in fungal cells, epithelial cells, monocytes, and neutrophils after inhalation of spores with cellular dynamics at the tissue level, comprising part of the innate immune response. Iron levels in the blood and tissue play a key role in the fungus' ability to grow, and the model includes iron recruitment and consumption by the different types of cells included. Parameter sensitivity analysis suggests the model is robust with respect to unvalidated parameters, and thus is a viable tool for an in silico investigation of invasive aspergillosis., Conclusions: Using laboratory data from a mouse model of invasive aspergillosis in the context of transient neutropenia as validation, the model predicted qualitatively similar time course changes in fungal burden, monocyte and neutrophil populations, and tissue iron levels. This model lays the groundwork for a multi-scale dynamic mathematical model of the immune response to Aspergillus species.

Background: Aspergillus fumigatus is a ubiquitous airborne fungal pathogen that presents a life-threatening health risk to individuals with weakened immune systems. A. fumigatus pathogenicity depends on its ability to acquire iron from the host and to resist host-generated oxidative stress. Gaining a deeper understanding of the molecular mechanisms governing A. fumigatus iron acquisition and oxidative stress response may ultimately help to improve the diagnosis and treatment of invasive aspergillus infections., Results: This study follows a systems biology approach to investigate how adaptive behaviors emerge from molecular interactions underlying A. fumigatus iron regulation and oxidative stress response. We construct a Boolean network model from known interactions and simulate how changes in environmental iron and superoxide levels affect network dynamics. We propose rules for linking long term model behavior to qualitative estimates of cell growth and cell death. These rules are used to predict phenotypes of gene deletion strains. The model is validated on the basis of its ability to reproduce literature data not used in model generation., Conclusions: The model reproduces gene expression patterns in experimental time course data when A. fumigatus is switched from a low iron to a high iron environment. In addition, the model is able to accurately represent the phenotypes of many knockout strains under varying iron and superoxide conditions. Model simulations support the hypothesis that intracellular iron regulates A. fumigatus transcription factors, SreA and HapX, by a post-translational, rather than transcriptional, mechanism. Finally, the model predicts that blocking siderophore-mediated iron uptake reduces resistance to oxidative stress. This indicates that combined targeting of siderophore-mediated iron uptake and the oxidative stress response network may act synergistically to increase fungal cell killing.

Pseudomonas aeruginosa is a metabolically flexible member of the Gammaproteobacteria. Under anaerobic conditions and the presence of nitrate, P. aeruginosa can perform (complete) denitrification, a respiratory process of dissimilatory nitrate reduction to nitrogen gas via nitrite (NO2), nitric oxide (NO) and nitrous oxide (N2O). This study focuses on understanding the influence of environmental conditions on bacterial denitrification performance, using a mathematical model of a metabolic network in P. aeruginosa. To our knowledge, this is the first mathematical model of denitrification for this bacterium. Analysis of the long-term behavior of the network under changing concentration levels of oxygen (O2), nitrate (NO3), and phosphate (PO4) suggests that PO4 concentration strongly affects denitrification performance. The model provides three predictions on denitrification activity of P. aeruginosa under various environmental conditions, and these predictions are either experimentally validated or supported by pertinent biological literature. One motivation for this study is to capture the effect of PO4 on a denitrification metabolic network of P. aeruginosa in order to shed light on mechanisms for greenhouse gas N2O accumulation during seasonal oxygen depletion in aquatic environments such as Lake Erie (Laurentian Great Lakes, USA). Simulating the microbial production of greenhouse gases in anaerobic aquatic systems such as Lake Erie allows a deeper understanding of the contributing environmental effects that will inform studies on, and remediation strategies for, other hypoxic sites worldwide.

Background: A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general., Results: This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author., Conclusions: The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem.

Background: The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used., Results: This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the dynamic patterns present in the network., Conclusions: Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html.

Duchenne muscular dystrophy (DMD) is a genetic disease that results in the death of affected boys by early adulthood. The genetic defect responsible for DMD has been known for over 25 years, yet at present there is neither cure nor effective treatment for DMD. During early disease onset, the mdx mouse has been validated as an animal model for DMD and use of this model has led to valuable but incomplete insights into the disease process. For example, immune cells are thought to be responsible for a significant portion of muscle cell death in the mdx mouse; however, the role and time course of the immune response in the dystrophic process have not been well described. In this paper we constructed a simple mathematical model to investigate the role of the immune response in muscle degeneration and subsequent regeneration in the mdx mouse model of Duchenne muscular dystrophy. Our model suggests that the immune response contributes substantially to the muscle degeneration and regeneration processes. Furthermore, the analysis of the model predicts that the immune system response oscillates throughout the life of the mice, and the damaged fibers are never completely cleared.

Oxidative stress is a well-known biological process that occurs in all respiring cells and is involved in pathophysiological processes such as aging and apoptosis. Oxidative stress agents include peroxides such as hydrogen peroxide, cumene hydroperoxide, and linoleic acid hydroperoxide, the thiol oxidant diamide, and menadione, a generator of superoxide, amongst others. The present study analyzed the early temporal genome-wide transcriptional response of Saccharomyces cerevisiae to oxidative stress induced by the aromatic peroxide cumene hydroperoxide. The accurate dataset obtained, supported by the use of temporal controls, biological replicates and well controlled growth conditions, provided a detailed picture of the early dynamics of the process. We identified a set of genes previously not implicated in the oxidative stress response, including several transcriptional regulators showing a fast transient response, suggesting a coordinated process in the transcriptional reprogramming. We discuss the role of the glutathione, thioredoxin and reactive oxygen species-removing systems, the proteasome and the pentose phosphate pathway. A data-driven clustering of the expression patterns identified one specific cluster that mostly consisted of genes known to be regulated by the Yap1p and Skn7p transcription factors, emphasizing their mediator role in the transcriptional response to oxidants. Comparison of our results with data reported for hydrogen peroxide identified 664 genes that specifically respond to cumene hydroperoxide, suggesting distinct transcriptional responses to these two peroxides. Genes up-regulated only by cumene hydroperoxide are mainly related to the cell membrane and cell wall, and proteolysis process, while those down-regulated only by this aromatic peroxide are involved in mitochondrial function.

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This article contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed., Results: We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second., Conclusions: Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

Motivation: An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation., Results: This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis., Contact: alanavc@vt.edu, Supplementary Information: Supplementary data are available at Bioinformatics online.

An increasing number of algorithms for biochemical network inference from experimental data require discrete data as input. For example, dynamic Bayesian network methods and methods that use the framework of finite dynamical systems, such as Boolean networks, all take discrete input. Experimental data, however, are typically continuous and represented by computer floating point numbers. The translation from continuous to discrete data is crucial in preserving the variable dependencies and thus has a significant impact on the performance of the network inference algorithms. We compare the performance of two such algorithms that use discrete data using several different discretization algorithms. One of the inference methods uses a dynamic Bayesian network framework, the other-a time-and state-discrete dynamical system framework. The discretization algorithms are quantile, interval discretization, and a new algorithm introduced in this article, SSD. SSD is especially designed for short time series data and is capable of determining the optimal number of discretization states. The experiments show that both inference methods perform better with SSD than with the other methods. In addition, SSD is demonstrated to preserve the dynamic features of the time series, as well as to be robust to noise in the experimental data. A C++ implementation of SSD is available from the authors at http://polymath.vbi.vt.edu/discretization .