NIAID/SMB Workshop on Multiscale Modeling of Infectious and Immune-Mediated Diseases

On July 19th, 2023, the National Institute of Allergy and Infectious Diseases co-organized a workshop with the Society of Mathematical Biology, with the authors of this paper as the organizing committee. The workshop, "Bridging multiscale modeling and practical clinical applications in infectious diseases" sought to create an environment for mathematical modelers, statisticians, and infectious disease researchers and clinicians to exchange ideas and perspectives.

Toward mechanistic medical digital twins: some use cases in immunology

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.

Digital twins in medicine

Medical digital twins, which are potentially vital for personalized medicine, have become a recent focus in medical research. Here we present an overview of the state of the art in medical digital twin development, especially in oncology and cardiology, where it is most advanced. We discuss major challenges, such as data integration and privacy, and provide an outlook on future advancements. Emphasizing the importance of this technology in healthcare, we highlight the potential for substantial improvements in patient-specific treatments and diagnostics.

Forum on immune digital twins: a meeting report

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.

Modular Control of Biological Networks

The concept of control is central to understanding and applications of biological network models. Some of their key structural features relate to control functions, through gene regulation, signaling, or metabolic mechanisms, and computational models need to encode these. Applications of models often focus on model-based control, such as in biomedicine or metabolic engineering. This paper presents an approach to model-based control that exploits two common features of biological networks, namely their modular structure and canalizing features of their regulatory mechanisms. The paper focuses on intracellular regulatory networks, represented by Boolean network models. A main result of this paper is that control strategies can be identified by focusing on one module at a time. This paper also presents a criterion based on canalizing features of the regulatory rules to identify modules that do not contribute to network control and can be excluded. For even moderately sized networks, finding global control inputs is computationally very challenging. The modular approach presented here leads to a highly efficient approach to solving this problem. This approach is applied to a published Boolean network model of blood cancer large granular lymphocyte (T-LGL) leukemia to identify a minimal control set that achieves a desired control objective.

Modularity of biological systems: a link between structure and function

This paper addresses two topics in systems biology, the hypothesis that biological systems are modular and the problem of relating structure and function of biological systems. The focus here is on gene regulatory networks, represented by Boolean network models, a commonly used tool. Most of the research on gene regulatory network modularity has focused on network structure, typically represented through either directed or undirected graphs. But since gene regulation is a highly dynamic process as it determines the function of cells over time, it is natural to consider functional modularity as well. One of the main results is that the structural decomposition of a network into modules induces an analogous decomposition of the dynamic structure, exhibiting a strong relationship between network structure and function. An extensive simulation study provides evidence for the hypothesis that modularity might have evolved to increase phenotypic complexity while maintaining maximal dynamic robustness to external perturbations.

Modularity of biological systems: a link between structure and function

This paper addresses two topics in systems biology, the hypothesis that biological systems are modular and the problem of relating structure and function of biological systems. The focus here is on gene regulatory networks, represented by Boolean network models, a commonly used tool. Most of the research on gene regulatory network modularity has focused on network structure, typically represented through either directed or undirected graphs. But since gene regulation is a highly dynamic process as it determines the function of cells over time, it is natural to consider functional modularity as well. One of the main results is that the structural decomposition of a network into modules induces an analogous decomposition of the dynamic structure, exhibiting a strong relationship between network structure and function. An extensive simulation study provides evidence for the hypothesis that modularity might have evolved to increase phenotypic complexity while maintaining maximal dynamic robustness to external perturbations.

COVID-19-associated pulmonary aspergillosis in immunocompetent patients: a virtual patient cohort study

The opportunistic fungus Aspergillus fumigatus infects the lungs of immunocompromised hosts, including patients undergoing chemotherapy or organ transplantation. More recently however, immunocompetent patients with severe SARS-CoV2 have been reported to be affected by COVID-19 Associated Pulmonary Aspergillosis (CAPA), in the absence of the conventional risk factors for invasive aspergillosis. This paper explores the hypothesis that contributing causes are the destruction of the lung epithelium permitting colonization by opportunistic pathogens. At the same time, the exhaustion of the immune system, characterized by cytokine storms, apoptosis, and depletion of leukocytes may hinder the response to A. fumigatus infection. The combination of these factors may explain the onset of invasive aspergillosis in immunocompetent patients. We used a previously published computational model of the innate immune response to infection with Aspergillus fumigatus. Variation of model parameters was used to create a virtual patient population. A simulation study of this virtual patient population to test potential causes for co-infection in immunocompetent patients. The two most important factors determining the likelihood of CAPA were the inherent virulence of the fungus and the effectiveness of the neutrophil population, as measured by granule half-life and ability to kill fungal cells. Varying these parameters across the virtual patient population generated a realistic distribution of CAPA phenotypes observed in the literature. Computational models are an effective tool for hypothesis generation. Varying model parameters can be used to create a virtual patient population for identifying candidate mechanisms for phenomena observed in actual patient populations.

Corrected and Republished from: "Understanding Lactobacillus paracasei and Streptococcus oralis Biofilm Interactions through Agent-Based Modeling"

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.

COVID-19-associated pulmonary aspergillosis in immunocompetent patients: A virtual patient cohort study

Purpose

The opportunistic fungus Aspergillus fumigatus infects the lungs of immunocompromised hosts, including patients undergoing chemotherapy or organ transplantation. More recently however, immunocompetent patients with severe SARS-CoV2 have been reported to be affected by COVID-19 Associated Pulmonary Aspergillosis (CAPA), in the absence of the conventional risk factors for invasive aspergillosis. This paper explores the hypothesis that contributing causes are the destruction of the lung epithelium permitting colonization by opportunistic pathogens. At the same time, the exhaustion of the immune system, characterized by cytokine storms, apoptosis, and depletion of leukocytes may hinder the response to A. fumigatus infection. The combination of these factors may explain the onset of invasive aspergillosis in immunocompetent patients.

Methods

We used a previously published computational model of the innate immune response to infection with Aspergillus fumigatus . Variation of model parameters was used to create a virtual patient population. A simulation study of this virtual patient population to test potential causes for co-infection in immunocompetent patients.

Results

The two most important factors determining the likelihood of CAPA were the inherent virulence of the fungus and the effectiveness of the neutrophil population, as measured by granule half-life and ability to kill fungal cells. Varying these parameters across the virtual patient population generated a realistic distribution of CAPA phenotypes observed in the literature.

Conclusions

Computational models are an effective tool for hypothesis generation. Varying model parameters can be used to create a virtual patient population for identifying candidate mechanisms for phenomena observed in actual patient populations.

Topological data analysis in biomedicine: A review

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.

Building digital twins of the human immune system: toward a roadmap

Digital twins, customized simulation models pioneered in industry, are beginning to be deployed in medicine and healthcare, with some major successes, for instance in cardiovascular diagnostics and in insulin pump control. Personalized computational models are also assisting in applications ranging from drug development to treatment optimization. More advanced medical digital twins will be essential to making precision medicine a reality. Because the immune system plays an important role in such a wide range of diseases and health conditions, from fighting pathogens to autoimmune disorders, digital twins of the immune system will have an especially high impact. However, their development presents major challenges, stemming from the inherent complexity of the immune system and the difficulty of measuring many aspects of a patient’s immune state in vivo. This perspective outlines a roadmap for meeting these challenges and building a prototype of an immune digital twin. It is structured as a four-stage process that proceeds from a specification of a concrete use case to model constructions, personalization, and continued improvement.

Aspergillus Utilizes Extracellular Heme as an Iron Source During Invasive Pneumonia, Driving Infection Severity

BACKGROUND

Depriving microbes of iron is critical to host defense. Hemeproteins, the largest source of iron within vertebrates, are abundant in infected tissues in aspergillosis due to hemorrhage, but Aspergillus species have been thought to lack heme import mechanisms. We hypothesized that heme provides iron to Aspergillus during invasive pneumonia, thereby worsening the outcomes of the infection.

METHODS

We assessed the effect of heme on fungal phenotype in various in vitro conditions and in a neutropenic mouse model of invasive pulmonary aspergillosis.

RESULTS

In mice with neutropenic invasive aspergillosis, we found a progressive and compartmentalized increase in lung heme iron. Fungal cells cultured under low iron conditions took up heme, resulting in increased fungal iron content, resolution of iron starvation, increased conidiation, and enhanced resistance to oxidative stress. Intrapulmonary administration of heme to mice with neutropenic invasive aspergillosis resulted in markedly increased lung fungal burden, lung injury, and mortality, whereas administration of heme analogs or heme with killed Aspergillus did not. Finally, infection caused by fungal germlings cultured in the presence of heme resulted in a more severe infection.

CONCLUSIONS

Invasive aspergillosis induces local hemolysis in infected tissues, thereby supplying heme iron to the fungus, leading to lethal infection.

Multi-scale mechanistic modelling of the host defence in invasive aspergillosis reveals leucocyte activation and iron acquisition as drivers of infection outcome

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.

SteadyCellPhenotype: a web-based tool for the modeling of biological networks with ternary logic

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.

Mathematical modeling of the Candida albicans yeast to hyphal transition reveals novel control strategies

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.

Agent Based Models of Polymicrobial Biofilms and the Microbiome-A Review

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.

Optimization of Agent-Based Models Through Coarse-Graining: A Case Study in Microbial Ecology

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.

A Near-Optimal Control Method for Stochastic Boolean Networks

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.

The contribution of microRNA-mediated regulation to short- and long-term gene expression predictability

MicroRNAs are a class of short, noncoding RNAs which are essential for the coordination and timing of cell differentiation and embryonic development. However, despite their guiding role in development, microRNAs are dysregulated in many pathologies, including nearly all cases of cancer. While both development and oncogenesis can be thought of as extremes of phenotypic plasticity, they characteristically manifest on much different time scales: one taking place over a matter of weeks, the other typically requiring decades. Because microRNAs are believed to support this plasticity, a critically important question is how microRNAs affect phenotypic stability on different time scales, and what dynamical characteristics shift the balance between these two roles. To address this question, we extend a well-established mathematical model of transcriptional gene regulation to include translational regulation by microRNAs, and examine their effects on both short- and long-term gene expression predictability. Our findings show that microRNAs greatly improve short-term predictability for earlier, developmental phenotypes while causing a small decrease in long-term predictability, and that these effects are difficult to separate. In addition to providing a theoretical explanation for this seemingly duplicitous behavior, we describe some of the properties which determine the cost-benefit balance between short-term stabilization and long-term destabilization.

The Dynamics of Canalizing Boolean Networks

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.

PlantSimLab - a modeling and simulation web tool for plant biologists

BACKGROUND

At the molecular level, nonlinear networks of heterogeneous molecules control many biological processes, so that systems biology provides a valuable approach in this field, building on the integration of experimental biology with mathematical modeling. One of the biggest challenges to making this integration a reality is that many life scientists do not possess the mathematical expertise needed to build and manipulate mathematical models well enough to use them as tools for hypothesis generation. Available modeling software packages often assume some modeling expertise. There is a need for software tools that are easy to use and intuitive for experimentalists.

RESULTS

This paper introduces PlantSimLab, a web-based application developed to allow plant biologists to construct dynamic mathematical models of molecular networks, interrogate them in a manner similar to what is done in the laboratory, and use them as a tool for biological hypothesis generation. It is designed to be used by experimentalists, without direct assistance from mathematical modelers.

CONCLUSIONS

Mathematical modeling techniques are a useful tool for analyzing complex biological systems, and there is a need for accessible, efficient analysis tools within the biological community. PlantSimLab enables users to build, validate, and use intuitive qualitative dynamic computer models, with a graphical user interface that does not require mathematical modeling expertise. It makes analysis of complex models accessible to a larger community, as it is platform-independent and does not require extensive mathematical expertise.

Connecting the molecular function of microRNAs to cell differentiation dynamics

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.

Fostering bioinformatics education through skill development of professors: Big Genomic Data Skills Training for Professors

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.

An important role for periplasmic storage in Pseudomonas aeruginosa copper homeostasis revealed by a combined experimental and computational modeling study

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.

The innate immune response to ischemic injury: a multiscale modeling perspective

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.

Activated Oncogenic Pathway Modifies Iron Network in Breast Epithelial Cells: A Dynamic Modeling Perspective

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.

Iron is required for cellular metabolism and growth, but can be toxic due to its ability to cause high oxidative stress and consequently DNA damage. To prevent damage, all organisms that require iron have developed mechanisms to tightly control iron levels. Dysregulation of iron metabolism is detrimental and can contribute to a wide range of diseases, including cancer. This paper presents a predictive mathematical model of iron regulation linked to iron utilization, oxidative stress, and the oncogenic response specific to normal breast epithelial cells. The model uses a discrete modeling framework to generate novel biological hypotheses for an investigation of how normal breast cells become malignant cells, capturing a breast cancer phenotype of iron homeostasis through overexpression and knockout simulations. The new biology discovered is (1) IRP2 overexpression alters the iron homeostasis pathway in breast cells, without affecting the oxidative stress response or oncogenic pathways, (2) an activated oncogenic pathway disrupts iron regulation in breast cancer cells.

Optimization and Control of Agent-Based Models in Biology: A Perspective

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.

Identification of control targets in Boolean molecular network models via computational algebra

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.

The phagosome: Meeting point of the Myddosome, NLRs, and degraded Borrelia burgdorferi

Phagocytosis of the extracellular bacterium Borrelia burgdorferi (Bb) enhances toll-like receptor, NF-κB mediated cytokine responses in human and murine phagocytic cells. TLR adaptor molecule MyD88 is recruited to Bb containing phagosomes, and the spirochetal cargo does not appear to leak from the phagosome into the cytosol. Transcriptome and Network reconstruction analysis identified several master regulators of diverse cellular and molecular processes, including regulation of the TLR-MyD88 pathway, IRFs, cytoskeletal rearrangement, and resolution of inflammation. Surprisingly, genes that code for inflammasome proteins (NLRP3, NOD2 and caspase-1) were also differentially-expressed. We thereby examined the cellular localization of these molecules in Bb-infected WT BMDMs and observed that NLRP3 and NOD2 were observed to colocalize to phagosomes containing degraded spirochetes. NLRP3 also colocalized with MyD88, but only in phagosomes containing degraded spirochetal cargo. Although caspase-1 also colocalized to the phagosome, infection with Bb did not result in an increase in speck formation or secretion of IL-1β.

Our results show that the phagosome is a crucial cellular location not only for degradation of the spirochete, but where components of the Myddosome and inflammasome are recruited. Our findings are in line with recent studies showing that cytosolic receptors can localize to endosomal membranes, and can potentially have an alternate role in regulating an adequate functionality of the phagosome. Our study evidences the complexity of phagosomal signaling in which MyD88 plays a critical role not only in the generation of inflammatory but inducing regulatory signals in murine macrophages upon Bb infection.

A computational model of invasive aspergillosis in the lung and the role of iron

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.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-016-0275-2) contains supplementary material, which is available to authorized users.

AlgoRun: a Docker-based packaging system for platform-agnostic implemented algorithms

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.

Costimulation Endows Immunotherapeutic CD8 T Cells with IL-36 Responsiveness during Aerobic Glycolysis

CD134- and CD137-primed CD8 T cells mount powerful effector responses upon recall, but even without recall these dual-costimulated T cells respond to signal 3 cytokines such as IL-12. We searched for alternative signal 3 receptor pathways and found the IL-1 family member IL-36R. Although IL-36 alone did not stimulate effector CD8 T cells, in combination with IL-12, or more surprisingly IL-2, it induced striking and rapid TCR-independent IFN-γ synthesis. To understand how signal 3 responses functioned in dual-costimulated T cells we showed that IL-2 induced IL-36R gene expression in a JAK/STAT-dependent manner. These data help delineate a sequential stimulation process where IL-2 conditioning must precede IL-36 for IFN-γ synthesis. Importantly, this responsive state was transient and functioned only in effector T cells capable of aerobic glycolysis. Specifically, as the effector T cells metabolized glucose and consumed O2, they also retained potential to respond through IL-36R. This suggests that T cells use innate receptor pathways such as the IL-36R/axis when programmed for aerobic glycolysis. To explore a function for IL-36R in vivo, we showed that dual costimulation therapy reduced B16 melanoma tumor growth while increasing IL-36R gene expression. In summary, cytokine therapy to eliminate tumors may target effector T cells, even outside of TCR specificity, as long as the effectors are in the correct metabolic state.

Iron acquisition and oxidative stress response in aspergillus fumigatus

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.

Optimal harvesting for a predator-prey agent-based model using difference equations

In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory—we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted κ is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.

Steady state analysis of Boolean molecular network models via model reduction and computational algebra

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.

The genome-wide early temporal response of Saccharomyces cerevisiae to oxidative stress induced by cumene hydroperoxide

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.

Stabilizing gene regulatory networks through feedforward loops

The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this robustness has been identified as the action of so-called microRNAs that operate via feedforward loops. We present results of a computational study, using the modeling framework of stochastic Boolean networks, which explores the role that such network motifs play in stabilizing global dynamics. The paper introduces a new measure for the stability of stochastic networks. The results show that certain types of feedforward loops do indeed buffer the network against stochastic effects.

Modeling stochasticity and variability in gene regulatory networks

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.

Bioinformatics tools for cancer metabolomics

It is well known that significant metabolic change take place as cells are transformed from normal to malignant. This review focuses on the use of different bioinformatics tools in cancer metabolomics studies. The article begins by describing different metabolomics technologies and data generation techniques. Overview of the data pre-processing techniques is provided and multivariate data analysis techniques are discussed and illustrated with case studies, including principal component analysis, clustering techniques, self-organizing maps, partial least squares, and discriminant function analysis. Also included is a discussion of available software packages.

Regulatory patterns in molecular interaction networks

Understanding design principles of molecular interaction networks is an important goal of molecular systems biology. Some insights have been gained into features of their network topology through the discovery of graph theoretic patterns that constrain network dynamics. This paper contributes to the identification of patterns in the mechanisms that govern network dynamics. The control of nodes in gene regulatory, signaling, and metabolic networks is governed by a variety of biochemical mechanisms, with inputs from other network nodes that act additively or synergistically. This paper focuses on a certain type of logical rule that appears frequently as a regulatory pattern. Within the context of the multistate discrete model paradigm, a rule type is introduced that reduces to the concept of nested canalyzing function in the Boolean network case. It is shown that networks that employ this type of multivalued logic exhibit more robust dynamics than random networks, with few attractors and short limit cycles. It is also shown that the majority of regulatory functions in many published models of gene regulatory and signaling networks are nested canalyzing.

ADAM: analysis of discrete models of biological systems using computer algebra

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.