Mathematical modelling of cell-fate decision in response to death receptor engagement

Building multiscale models with PhysiBoSS, an agent-based modeling tool

Multiscale models provide a unique tool for studying complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. They aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms - coupled with a graphical interface - is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to easily construct such models, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as a Supplementary Material and all models are provided at: https://physiboss.github.io/tutorial/.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

Modulating the dynamics of NFκB and PI3K enhances the ensemble-level TNFR1 signaling mediated apoptotic response

Cell-to-cell variability during TNFα stimulated Tumor Necrosis Factor Receptor 1 (TNFR1) signaling can lead to single-cell level pro-survival and apoptotic responses. This variability stems from the heterogeneity in signal flow through intracellular signaling entities that regulate the balance between these two phenotypes. Using systematic Boolean dynamic modeling of a TNFR1 signaling network, we demonstrate that the signal flow path variability can be modulated to enable cells favour apoptosis. We developed a computationally efficient approach "Boolean Modeling based Prediction of Steady-state probability of Phenotype Reachability (BM-ProSPR)" to accurately predict the network's ability to settle into different phenotypes. Model analysis juxtaposed with the experimental observations revealed that NFκB and PI3K transient responses guide the XIAP behaviour to coordinate the crucial dynamic cross-talk between the pro-survival and apoptotic arms at the single-cell level. Model predicted the experimental observations that ~31% apoptosis increase can be achieved by arresting Comp1 - IKK* activity which regulates the NFκB and PI3K dynamics. Arresting Comp1 - IKK* activity causes signal flow path re-wiring towards apoptosis without significantly compromising NFκB levels, which govern adequate cell survival. Priming an ensemble of cancerous cells with inhibitors targeting the specific interaction involving Comp1 and IKK* prior to TNFα exposure could enable driving them towards apoptosis.

PhysiBoSS 2.0: a sustainable integration of stochastic Boolean and agent-based modelling frameworks

In systems biology, mathematical models and simulations play a crucial role in understanding complex biological systems. Different modelling frameworks are employed depending on the nature and scales of the system under study. For instance, signalling and regulatory networks can be simulated using Boolean modelling, whereas multicellular systems can be studied using agent-based modelling. Herein, we present PhysiBoSS 2.0, a hybrid agent-based modelling framework that allows simulating signalling and regulatory networks within individual cell agents. PhysiBoSS 2.0 is a redesign and reimplementation of PhysiBoSS 1.0 and was conceived as an add-on that expands the PhysiCell functionalities by enabling the simulation of intracellular cell signalling using MaBoSS while keeping a decoupled, maintainable and model-agnostic design. PhysiBoSS 2.0 also expands the set of functionalities offered to the users, including custom models and cell specifications, mechanistic submodels of substrate internalisation and detailed control over simulation parameters. Together with PhysiBoSS 2.0, we introduce PCTK, a Python package developed for handling and processing simulation outputs, and generating summary plots and 3D renders. PhysiBoSS 2.0 allows studying the interplay between the microenvironment, the signalling pathways that control cellular processes and population dynamics, suitable for modelling cancer. We show different approaches for integrating Boolean networks into multi-scale simulations using strategies to study the drug effects and synergies in models of cancer cell lines and validate them using experimental data. PhysiBoSS 2.0 is open-source and publicly available on GitHub with several repositories of accompanying interoperable tools.

Normalizing Input-Output Relationships of Cancer Networks for Reversion Therapy

Accumulated genetic alterations in cancer cells distort cellular stimulus-response (or input-output) relationships, resulting in uncontrolled proliferation. However, the complex molecular interaction network within a cell implicates a possibility of restoring such distorted input-output relationships by rewiring the signal flow through controlling hidden molecular switches. Here, a system framework of analyzing cellular input-output relationships in consideration of various genetic alterations and identifying possible molecular switches that can normalize the distorted relationships based on Boolean network modeling and dynamics analysis is presented. Such reversion is demonstrated by the analysis of a number of cancer molecular networks together with a focused case study on bladder cancer with in vitro experiments and patient survival data analysis. The origin of reversibility from an evolutionary point of view based on the redundancy and robustness intrinsically embedded in complex molecular regulatory networks is further discussed.

Reducing Boolean networks with backward equivalence

BACKGROUND

Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis.

RESULTS

We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance.

CONCLUSIONS

BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

Effective Reversal of Macrophage Polarization by Inhibitory Combinations Predicted by a Boolean Protein–Protein Interaction Model

Background: The function and polarization of macrophages has a significant impact on the outcome of many diseases. Targeting tumor-associated macrophages (TAMs) is among the greatest challenges to solve because of the low in vitro reproducibility of the heterogeneous tumor microenvironment (TME). To create a more comprehensive model and to understand the inner workings of the macrophage and its dependence on extracellular signals driving polarization, we propose an in silico approach. Methods: A Boolean control network was built based on systematic manual curation of the scientific literature to model the early response events of macrophages by connecting extracellular signals (input) with gene transcription (output). The network consists of 106 nodes, classified as 9 input, 75 inner and 22 output nodes, that are connected by 217 edges. The direction and polarity of edges were manually verified and only included in the model if the literature plainly supported these parameters. Single or combinatory inhibitions were simulated mimicking therapeutic interventions, and output patterns were analyzed to interpret changes in polarization and cell function. Results: We show that inhibiting a single target is inadequate to modify an established polarization, and that in combination therapy, inhibiting numerous targets with individually small effects is frequently required. Our findings show the importance of JAK1, JAK3 and STAT6, and to a lesser extent STK4, Sp1 and Tyk2, in establishing an M1-like pro-inflammatory polarization, and NFAT5 in creating an anti-inflammatory M2-like phenotype. Conclusions: Here, we demonstrate a protein–protein interaction (PPI) network modeling the intracellular signalization driving macrophage polarization, offering the possibility of therapeutic repolarization and demonstrating evidence for multi-target methods.

Modeling Cellular Signaling Variability Based on Single-Cell Data: The TGFβ-SMAD Signaling Pathway

Nongenetic heterogeneity is key to cellular decisions, as even genetically identical cells respond in very different ways to the same external stimulus, e.g., during cell differentiation or therapeutic treatment of disease. Strong heterogeneity is typically already observed at the level of signaling pathways that are the first sensors of external inputs and transmit information to the nucleus where decisions are made. Since heterogeneity arises from random fluctuations of cellular components, mathematical models are required to fully describe the phenomenon and to understand the dynamics of heterogeneous cell populations. Here, we review the experimental and theoretical literature on cellular signaling heterogeneity, with special focus on the TGFβ/SMAD signaling pathway.

Modulation of signaling cross-talk between pJNK and pAKT generates optimal apoptotic response

Tumor necrosis factor alpha (TNFα) is a well-known modulator of apoptosis by maintaining a balance between proliferation and cell-death in normal cells. Cancer cells often evade apoptotic response following TNFα stimulation by altering signaling cross-talks. Thus, varying the extent of signaling cross-talk could enable optimal TNFα mediated apoptotic dynamics. Herein, we use an experimental data-driven mathematical modeling to quantitate the extent of synergistic signaling cross-talk between the intracellular entities phosphorylated JNK (pJNK) and phosphorylated AKT (pAKT) that orchestrate the phenotypic apoptosis level by modulating the activated Caspase3 dynamics. Our study reveals that this modulation is orchestrated by the distinct dynamic nature of the synergism at early and late phases. We show that this synergism in signal flow is governed by branches originating from either TNFα receptor and NFκB, which facilitates signaling through survival pathways. We demonstrate that the experimentally quantified apoptosis levels semi-quantitatively correlates with the model simulated Caspase3 transients. Interestingly, perturbing pJNK and pAKT transient dynamics fine-tunes this accumulated Caspase3 guided apoptotic response. Thus, our study offers useful insights for identifying potential targeted therapies for optimal apoptotic response.

Modeling signaling pathways in biology with MaBoSS: From one single cell to a dynamic population of heterogeneous interacting cells

As a result of the development of experimental technologies and the accumulation of data, biological and molecular processes can be described as complex networks of signaling pathways. These networks are often directed and signed, where nodes represent entities (genes/proteins) and arrows interactions. They are translated into mathematical models by adding a dynamic layer onto them. Such mathematical models help to understand and interpret non-intuitive experimental observations and to anticipate the response to external interventions such as drug effects on phenotypes. Several frameworks for modeling signaling pathways exist. The choice of the appropriate framework is often driven by the experimental context. In this review, we present MaBoSS, a tool based on Boolean modeling using a continuous time approach, which predicts time-dependent probabilities of entities in different biological contexts. MaBoSS was initially built to model the intracellular signaling in non-interacting homogeneous cell populations. MaBoSS was then adapted to model heterogeneous cell populations (EnsembleMaBoSS) by considering families of models rather than a unique model. To account for more complex questions, MaBoSS was extended to simulate dynamical interacting populations (UPMaBoSS), with a precise spatial distribution (PhysiBoSS). To illustrate all these levels of description, we show how each of these tools can be used with a running example of a simple model of cell fate decisions. Finally, we present practical applications to cancer biology and studies of the immune response.

Mathematical Models of Death Signaling Networks

This review provides an overview of the progress made by computational and systems biologists in characterizing different cell death regulatory mechanisms that constitute the cell death network. We define the cell death network as a comprehensive decision-making mechanism that controls multiple death execution molecular circuits. This network involves multiple feedback and feed-forward loops and crosstalk among different cell death-regulating pathways. While substantial progress has been made in characterizing individual cell death execution pathways, the cell death decision network is poorly defined and understood. Certainly, understanding the dynamic behavior of such complex regulatory mechanisms can be only achieved by applying mathematical modeling and system-oriented approaches. Here, we provide an overview of mathematical models that have been developed to characterize different cell death mechanisms and intend to identify future research directions in this field.

Mathematical modeling of the molecular switch of TNFR1-mediated signaling pathways applying Petri net formalism and in silico knockout analysis

The paper describes a mathematical model of the molecular switches of cell survival, apoptosis, and necroptosis in cellular signaling pathways initiated by tumor necrosis factor 1. Based on experimental findings in the literature, we constructed a Petri net model based on detailed molecular reactions of the molecular players, protein complexes, post-translational modifications, and cross talk. The model comprises 118 biochemical entities, 130 reactions, and 299 edges. We verified the model by evaluating invariant properties of the system at steady state and by in silico knockout analysis. Applying Petri net analysis techniques, we found 279 pathways, which describe signal flows from receptor activation to cellular response, representing the combinatorial diversity of functional pathways.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic and led to multiple possible outcomes. We investigated the in silico knockout behavior and identified important checkpoints of the TNFR1 signaling pathway in terms of ubiquitination within complex I and the gene expression dependent on NF-κB, which controls the caspase activity in complex II and apoptosis induction. Despite not knowing enough kinetic data of sufficient quality, we estimated system’s dynamics using a discrete, semi-quantitative Petri net model.

It is still a challenge to develop mechanistic models for big molecular systems without the knowledge of enough kinetic parameters of sufficient quality. At the same time, more qualitative and semi-quantitative data have been produced in increasing numbers, e.g., by new high-throughput technologies. This has generated demands for new concepts at appropriate abstraction levels. The Petri net formalism enables the integration of qualitative as well as quantitative data and provides algorithms and methods for model verification and model simulation. Moreover, Petri nets exhibit a clear and coherent visualization. Here, we modeled the molecular switches between cell survival, apoptosis, and necroptosis induced by tumor necrosis factor 1. We were interested not only in an exhaustive exploration of all possible signaling pathways, but also in finding the system’s checkpoints. Our Petri net model comprises 118 biochemical entities, 130 reactions, and 299 edges. We found 279 pathways that describe signal flows from receptor activation to cellular response.120 pathways steered the cell to survival, whereas 58 and 35 pathways led to apoptosis and necroptosis, respectively. For 65 pathways, the triggered response was not deterministic, leading to multiple possible outcomes. We applied in silico knockout analyses to the Petri net model and could identify important checkpoints of the tumor necrosis factor 1 signaling pathway.

Predictive Modelling in Clinical Bioinformatics: Key Concepts for Startups

Clinical bioinformatics is a newly emerging field that applies bioinformatics techniques for facilitating the identification of diseases, discovery of biomarkers, and therapy decision. Mathematical modelling is part of bioinformatics analysis pipelines and a fundamental step to extract clinical insights from genomes, transcriptomes and proteomes of patients. Often, the chosen modelling techniques relies on either statistical, machine learning or deterministic approaches. Research that combines bioinformatics with modelling techniques have been generating innovative biomedical technology, algorithms and models with biotech applications, attracting private investment to develop new business; however, startups that emerge from these technologies have been facing difficulties to implement clinical bioinformatics pipelines, protect their technology and generate profit. In this commentary, we discuss the main concepts that startups should know for enabling a successful application of predictive modelling in clinical bioinformatics. Here we will focus on key modelling concepts, provide some successful examples and briefly discuss the modelling framework choice. We also highlight some aspects to be taken into account for a successful implementation of cost-effective bioinformatics from a business perspective.

Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows

Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.

A probabilistic Boolean model on hair follicle cell fate regulation by TGF-β

Hair follicles (HFs) are mini skin organs that undergo cyclic growth. Various signals regulate HF cell fate decisions jointly. Recent experimental results suggest that transforming growth factor beta (TGF-β) exhibits a dual role in HF cell fate regulation that can be either anti- or pro-apoptosis. To understand the underlying mechanisms of HF cell fate control, we develop a novel probabilistic Boolean network (pBN) model on the HF epithelial cell gene regulation dynamics. First, the model is derived from literature, then refined using single-cell RNA sequencing data. Using the model, we both explore the mechanisms underlying HF cell fate decisions and make predictions that could potentially guide future experiments: 1) we propose that a threshold-like switch in the TGF-β strength may necessitate the dual roles of TGF-β in either activating apoptosis or cell proliferation, in cooperation with Bmp and tumor necrosis factor (TNF) and at different stages of a follicle growth cycle; 2) our model shows concordance with the high-activator-low-inhibitor theory of anagen initiation; 3) we predict that TNF may be more effective in catagen initiation than TGF-β, and they may cooperate in a two-step fashion; 4) finally, predictions of gene knockout and overexpression reveal the roles in HF cell fate regulations of each gene. Attractor and motif analysis from the associated Boolean networks reveal the relations between the topological structure of the gene regulation network and the cell fate regulation mechanism. A discrete spatial model equipped with the pBN illustrates how TGF-β and TNF cooperate in initiating and driving the apoptosis wave during catagen.

Optimizing Dosage-Specific Treatments in a Multi-Scale Model of a Tumor Growth

The emergence of cell resistance in cancer treatment is a complex phenomenon that emerges from the interplay of processes that occur at different scales. For instance, molecular mechanisms and population-level dynamics such as competition and cell–cell variability have been described as playing a key role in the emergence and evolution of cell resistances. Multi-scale models are a useful tool for studying biology at very different times and spatial scales, as they can integrate different processes occurring at the molecular, cellular, and intercellular levels. In the present work, we use an extended hybrid multi-scale model of 3T3 fibroblast spheroid to perform a deep exploration of the parameter space of effective treatment strategies based on TNF pulses. To explore the parameter space of effective treatments in different scenarios and conditions, we have developed an HPC-optimized model exploration workflow based on EMEWS. We first studied the effect of the cells’ spatial distribution in the values of the treatment parameters by optimizing the supply strategies in 2D monolayers and 3D spheroids of different sizes. We later study the robustness of the effective treatments when heterogeneous populations of cells are considered. We found that our model exploration workflow can find effective treatments in all the studied conditions. Our results show that cells’ spatial geometry and population variability should be considered when optimizing treatment strategies in order to find robust parameter sets.

Identification of dynamic driver sets controlling phenotypical landscapes

Controlling phenotypical landscapes is of vital interest to modern biology. This task becomes highly demanding because cellular decisions involve complex networks engaging in crosstalk interactions. Previous work on control theory indicates that small sets of compounds can control single phenotypes. However, a dynamic approach is missing to determine the drivers of the whole network dynamics. By analyzing 35 biologically motivated Boolean networks, we developed a method to identify small sets of compounds sufficient to decide on the entire phenotypical landscape. These compounds do not strictly prefer highly related compounds and show a smaller impact on the stability of the attractor landscape. The dynamic driver sets include many intervention targets and cellular reprogramming drivers in human networks. Finally, by using a new comprehensive model of colorectal cancer, we provide a complete workflow on how to implement our approach to shift from in silico to in vitro guided experiments.

UPMaBoSS: A Novel Framework for Dynamic Cell Population Modeling

Mathematical modeling aims at understanding the effects of biological perturbations, suggesting ways to intervene and to reestablish proper cell functioning in diseases such as cancer or in autoimmune disorders. This is a difficult task for obvious reasons: the level of details needed to describe the intra-cellular processes involved, the numerous interactions between cells and cell types, and the complex dynamical properties of such populations where cells die, divide and interact constantly, to cite a few. Another important difficulty comes from the spatial distribution of these cells, their diffusion and motility. All of these aspects cannot be easily resolved in a unique mathematical model or with a unique formalism. To cope with some of these issues, we introduce here a novel framework, UPMaBoSS (for Update Population MaBoSS), dedicated to modeling dynamic populations of interacting cells. We rely on the preexisting tool MaBoSS, which enables probabilistic simulations of cellular networks. A novel software layer is added to account for cell interactions and population dynamics, but without considering the spatial dimension. This modeling approach can be seen as an intermediate step towards more complex spatial descriptions. We illustrate our methodology by means of a case study dealing with TNF-induced cell death. Interestingly, the simulation of cell population dynamics with UPMaBoSS reveals a mechanism of resistance triggered by TNF treatment. Relatively easy to encode, UPMaBoSS simulations require only moderate computational power and execution time. To ease the reproduction of simulations, we provide several Jupyter notebooks that can be accessed within the CoLoMoTo Docker image, which contains all software and models used for this study.

Patient-specific Boolean models of signalling networks guide personalised treatments

Prostate cancer is the second most occurring cancer in men worldwide. To better understand the mechanisms of tumorigenesis and possible treatment responses, we developed a mathematical model of prostate cancer which considers the major signalling pathways known to be deregulated. We personalised this Boolean model to molecular data to reflect the heterogeneity and specific response to perturbations of cancer patients. A total of 488 prostate samples were used to build patient-specific models and compared to available clinical data. Additionally, eight prostate cell line-specific models were built to validate our approach with dose-response data of several drugs. The effects of single and combined drugs were tested in these models under different growth conditions. We identified 15 actionable points of interventions in one cell line-specific model whose inactivation hinders tumorigenesis. To validate these results, we tested nine small molecule inhibitors of five of those putative targets and found a dose-dependent effect on four of them, notably those targeting HSP90 and PI3K. These results highlight the predictive power of our personalised Boolean models and illustrate how they can be used for precision oncology.

A model for the regulation of apoptosis intrinsic pathway: The potential role of the transcriptional regulator E2F in the point of no return

Apoptosis has been extensively characterized by both experimental approaches and model simulations. However, it is still not fully understood how the regulation occurs, especially in the intrinsic pathway, which can be activated by a great variety of signals. In addition, the conditions in which a point of no return could be reached remain elusive. In this work, we use differential equations models to approach these issues. Our starting point was the model for caspase activation of Legewie et al. (Legewie S, et al., PLoS Computational Biology 2006, 2(9): e120), which exhibits irreversible bistability. We added an activation module to this model, with the main events related to mitochondrial outer membrane permeabilization, which includes cytochrome C release by the mitochondria and its effects on caspase activation and respiratory chain disruption. This "Extended Legewie Model" (ELM) uses BAK as the apoptotic stimulus and active caspase 3 as a measure of apoptosis activation. Unexpectedly, in the extended model, BAK cannot trigger apoptosis activation using physiologically sound initial values of the variables, due to limitations in apoptosome concentration increase. Therefore, the next step was to find a regulatory mechanism, allowing apoptosis activation in the ELM, starting from physiological initial concentrations. For this aim, we performed a sensitivity analysis on the 61 parameters of the system, finding that those producing the most relevant changes in the qualitative behaviour were the rates of synthesis of caspase 3, caspase 9 and XIAP. Based on these results, the transcription factor E2F was included in the ELM because it directly regulates the rate of synthesis of caspase 3 and 9. Depending on the concentration of E2F, the ELM shows different qualitative behaviours. On one hand, for low E2F apoptosis is impossible and for high E2F apoptosis is inevitable. Therefore, if E2F is sufficiently increased, the point of no return is crossed. On the other hand, for intermediate values of E2F there is a bistable region where the fate of the system also depends on the concentration of BAK and other signalling species.

Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits

Qualitative modeling approaches are promising and still underexploited tools for the analysis and design of synthetic circuits. They can make predictions of circuit behavior in the absence of precise, quantitative information. Moreover, they provide direct insight into the relation between the feedback structure and the dynamical properties of a network. We review qualitative modeling approaches by focusing on two specific formalisms, Boolean networks and piecewise-linear differential equations, and illustrate their application by means of three well-known synthetic circuits. We describe various methods for the analysis of state transition graphs, discrete representations of the network dynamics that are generated in both modeling frameworks. We also briefly present the problem of controlling synthetic circuits, an emerging topic that could profit from the capacity of qualitative modeling approaches to rapidly scan a space of design alternatives.

Systems biology of ferroptosis: A modeling approach

Ferroptosis is a recently discovered form of iron-dependent regulated cell death (RCD) that occurs via peroxidation of phospholipids containing polyunsaturated fatty acid (PUFA) moieties. Activating this form of cell death is an emerging strategy in cancer treatment. Because multiple pathways and molecular species contribute to the ferroptotic process, predicting which tumors will be sensitive to ferroptosis is a challenge. We thus develop a mathematical model of several critical pathways to ferroptosis in order to perform a systems-level analysis of the process. We show that sensitivity to ferroptosis depends on the activity of multiple upstream cascades, including PUFA incorporation into the phospholipid membrane, and the balance between levels of pro-oxidant factors (reactive oxygen species, lipoxogynases) and antioxidant factors (GPX4). We perform a systems-level analysis of ferroptosis sensitivity as an outcome of five input variables (ACSL4, SCD1, ferroportin, transferrin receptor, and p53) and organize the resulting simulations into 'high' and 'low' ferroptosis sensitivity groups. We make a novel prediction corresponding to the combinatorial requirements of ferroptosis sensitivity to SCD1 and ACSL4 activity. To validate our prediction, we model the ferroptotic response of an ovarian cancer stem cell line following single- and double-knockdown of SCD1 and ACSL4. We find that the experimental outcomes are consistent with our simulated predictions. This work suggests that a systems-level approach is beneficial for understanding the complex combined effects of ferroptotic input, and in predicting cancer susceptibility to ferroptosis.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

Conceptual and computational framework for logical modelling of biological networks deregulated in diseases

Mathematical models can serve as a tool to formalize biological knowledge from diverse sources, to investigate biological questions in a formal way, to test experimental hypotheses, to predict the effect of perturbations and to identify underlying mechanisms. We present a pipeline of computational tools that performs a series of analyses to explore a logical model's properties. A logical model of initiation of the metastatic process in cancer is used as a transversal example. We start by analysing the structure of the interaction network constructed from the literature or existing databases. Next, we show how to translate this network into a mathematical object, specifically a logical model, and how robustness analyses can be applied to it. We explore the visualization of the stable states, defined as specific attractors of the model, and match them to cellular fates or biological read-outs. With the different tools we present here, we explain how to assign to each solution of the model a probability and how to identify genetic interactions using mutant phenotype probabilities. Finally, we connect the model to relevant experimental data: we present how some data analyses can direct the construction of the network, and how the solutions of a mathematical model can also be compared with experimental data, with a particular focus on high-throughput data in cancer biology. A step-by-step tutorial is provided as a Supplementary Material and all models, tools and scripts are provided on an accompanying website: https://github.com/sysbio-curie/Logical_modelling_pipeline.

PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling

MOTIVATION

Due to the complexity and heterogeneity of multicellular biological systems, mathematical models that take into account cell signalling, cell population behaviour and the extracellular environment are particularly helpful. We present PhysiBoSS, an open source software which combines intracellular signalling using Boolean modelling (MaBoSS) and multicellular behaviour using agent-based modelling (PhysiCell).

RESULTS

PhysiBoSS provides a flexible and computationally efficient framework to explore the effect of environmental and genetic alterations of individual cells at the population level, bridging the critical gap from single-cell genotype to single-cell phenotype and emergent multicellular behaviour. PhysiBoSS thus becomes very useful when studying heterogeneous population response to treatment, mutation effects, different modes of invasion or isomorphic morphogenesis events. To concretely illustrate a potential use of PhysiBoSS, we studied heterogeneous cell fate decisions in response to TNF treatment. We explored the effect of different treatments and the behaviour of several resistant mutants. We highlighted the importance of spatial information on the population dynamics by considering the effect of competition for resources like oxygen.

AVAILABILITY AND IMPLEMENTATION

PhysiBoSS is freely available on GitHub (https://github.com/sysbio-curie/PhysiBoSS), with a Docker image (https://hub.docker.com/r/gletort/physiboss/). It is distributed as open source under the BSD 3-clause license.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A feedback loop of conditionally stable circuits drives the cell cycle from checkpoint to checkpoint

We perform logic-based network analysis on a model of the mammalian cell cycle. This model is composed of a Restriction Switch driving cell cycle commitment and a Phase Switch driving mitotic entry and exit. By generalizing the concept of stable motif, i.e., a self-sustaining positive feedback loop that maintains an associated state, we introduce the concept of a conditionally stable motif, the stability of which is contingent on external conditions. We show that the stable motifs of the Phase Switch are contingent on the state of three nodes through which it receives input from the rest of the network. Biologically, these conditions correspond to cell cycle checkpoints. Holding these nodes locked (akin to a checkpoint-free cell) transforms the Phase Switch into an autonomous oscillator that robustly toggles through the cell cycle phases G1, G2 and mitosis. The conditionally stable motifs of the Phase Switch Oscillator are organized into an ordered sequence, such that they serially stabilize each other but also cause their own destabilization. Along the way they channel the dynamics of the module onto a narrow path in state space, lending robustness to the oscillation. Self-destabilizing conditionally stable motifs suggest a general negative feedback mechanism leading to sustained oscillations.

From Discrete to Continuous Modeling of Lymphocyte Development and Plasticity in Chronic Diseases

The molecular events leading to differentiation, development, and plasticity of lymphoid cells have been subject of intense research due to their key roles in multiple pathologies, such as lymphoproliferative disorders, tumor growth maintenance and chronic diseases. The emergent roles of lymphoid cells and the use of high-throughput technologies have led to an extensive accumulation of experimental data allowing the reconstruction of gene regulatory networks (GRN) by integrating biochemical signals provided by the microenvironment with transcriptional modules of lineage-specific genes. Computational modeling of GRN has been useful for the identification of molecular switches involved in lymphoid specification, prediction of microenvironment-dependent cell plasticity, and analyses of signaling events occurring downstream the activation of antigen recognition receptors. Among most common modeling strategies to analyze the dynamical behavior of GRN, discrete dynamic models are widely used for their capacity to capture molecular interactions when a limited knowledge of kinetic parameters is present. However, they are less powerful when modeling complex systems sensitive to biochemical gradients. To compensate it, discrete models may be transformed into regulatory networks that includes state variables and parameters varying within a continuous range. This approach is based on a system of differential equations dynamics with regulatory interactions described by fuzzy logic propositions. Here, we discuss the applicability of this method on modeling of development and plasticity processes of adaptive lymphocytes, and its potential implications in the study of pathological landscapes associated to chronic diseases.

Boolean model of growth signaling, cell cycle and apoptosis predicts the molecular mechanism of aberrant cell cycle progression driven by hyperactive PI3K

The PI3K/AKT signaling pathway plays a role in most cellular functions linked to cancer progression, including cell growth, proliferation, cell survival, tissue invasion and angiogenesis. It is generally recognized that hyperactive PI3K/AKT1 are oncogenic due to their boost to cell survival, cell cycle entry and growth-promoting metabolism. That said, the dynamics of PI3K and AKT1 during cell cycle progression are highly nonlinear. In addition to negative feedback that curtails their activity, protein expression of PI3K subunits has been shown to oscillate in dividing cells. The low-PI3K/low-AKT1 phase of these oscillations is required for cytokinesis, indicating that oncogenic PI3K may directly contribute to genome duplication. To explore this, we construct a Boolean model of growth factor signaling that can reproduce PI3K oscillations and link them to cell cycle progression and apoptosis. The resulting modular model reproduces hyperactive PI3K-driven cytokinesis failure and genome duplication and predicts the molecular drivers responsible for these failures by linking hyperactive PI3K to mis-regulation of Polo-like kinase 1 (Plk1) expression late in G2. To do this, our model captures the role of Plk1 in cell cycle progression and accurately reproduces multiple effects of its loss: G2 arrest, mitotic catastrophe, chromosome mis-segregation / aneuploidy due to premature anaphase, and cytokinesis failure leading to genome duplication, depending on the timing of Plk1 inhibition along the cell cycle. Finally, we offer testable predictions on the molecular drivers of PI3K oscillations, the timing of these oscillations with respect to division, and the role of altered Plk1 and FoxO activity in genome-level defects caused by hyperactive PI3K. Our model is an important starting point for the predictive modeling of cell fate decisions that include AKT1-driven senescence, as well as the non-intuitive effects of drugs that interfere with mitosis.

Personalization of Logical Models With Multi-Omics Data Allows Clinical Stratification of Patients

Logical models of cancer pathways are typically built by mining the literature for relevant experimental observations. They are usually generic as they apply for large cohorts of individuals. As a consequence, they generally do not capture the heterogeneity of patient tumors and their therapeutic responses. We present here a novel framework, referred to as PROFILE, to tailor logical models to a particular biological sample such as a patient tumor. This methodology permits to compare the model simulations to individual clinical data, i.e., survival time. Our approach focuses on integrating mutation data, copy number alterations (CNA), and expression data (transcriptomics or proteomics) to logical models. These data need first to be either binarized or set between 0 and 1, and can then be incorporated in the logical model by modifying the activity of the node, the initial conditions or the state transition rates. The use of MaBoSS, a tool based on Monte-Carlo kinetic algorithm to perform stochastic simulations on logical models results in model state probabilities, and allows for a semi-quantitative study of the model phenotypes and perturbations. As a proof of concept, we use a published generic model of cancer signaling pathways and molecular data from METABRIC breast cancer patients. For this example, we test several combinations of data incorporation and discuss that, with these data, the most comprehensive patient-specific cancer models are obtained by modifying the nodes' activity of the model with mutations, in combination or not with CNA data, and altering the transition rates with RNA expression. We conclude that these model simulations show good correlation with clinical data such as patients' Nottingham prognostic index (NPI) subgrouping and survival time. We observe that two highly relevant cancer phenotypes derived from personalized models, Proliferation and Apoptosis, are biologically consistent prognostic factors: patients with both high proliferation and low apoptosis have the worst survival rate, and conversely. Our approach aims to combine the mechanistic insights of logical modeling with multi-omics data integration to provide patient-relevant models. This work leads to the use of logical modeling for precision medicine and will eventually facilitate the choice of patient-specific drug treatments by physicians.

Structural and In Vitro Functional Comparability Analysis of Altebrel™, a Proposed Etanercept Biosimilar: Focus on Primary Sequence and Glycosylation

The demand for reliable comparability studies of biosimilars grows with their increased market share. These studies focus on physicochemical, structural, functional and clinical properties to ensure that a biosimilar has no significant differences to the originator product and can be released into the market without extensive clinical trials. In the current study, Enbrel^® (etanercept, the originator) and Altebrel™ (the proposed biosimilar) underwent direct comparison. “Bottom-up” mass spectrometric analysis was used for primary sequence analysis, evaluation of N/O-glycosylation sites and quantification of methionine oxidation. N/O-glycans were analyzed after permethylation derivatization and the effect of N-glycans on in-vitro functionality of etanercept was assayed. Three enzyme peptide mapping resulted in complete identification of the primary structure. It was confirmed that total ion chromatograms are valuable datasets for the analysis of the primary structure of biodrugs. New N/O-glycan structures were identified and all the N-glycans were quantified. Finally, investigation of the functional properties of N-deglycosylated and non-modified etanercept samples using surface plasmon resonance analysis and in-vitro bioassay showed that N-glycosylation has no significant effect on its in-vitro functionality. Analysis of etanercept and its biosimilar, revealed a high similarity in terms of glycosylation, primary structure and in-vitro functionality.

Betulinic acid as apoptosis activator: Molecular mechanisms, mathematical modeling and chemical modifications

A natural product betulinic acid (BA) has gained a huge significance in the recent years for its strong cytotoxicity. Surprisingly, in spite of being an interesting cancer protecting agent on a variety of tumor cells, the normal cells and tissues are rarely affected by BA. Betulinic acid and analogues (BAs) generally exert through the mechanisms that provokes an event of direct cell death and bypass the resistance to normal chemotherapeutics. Although the major mechanism associated with its ability to induce direct cell death is mitochondrial apoptosis, there are several other mechanisms explored recently. Importantly, mathematical modeling of apoptosis has been an important tool to explore the precise mechanism involved in mitochondrial apoptosis. Thus, this review is an endeavor to sum up the molecular mechanisms underlying the action of BA and future directions to apply mathematical modeling technique to better understand the precise mechanism of BA-induced apoptosis. The last section of the review encompasses the plausible structural modifications and formulations to enhance the therapeutic efficacy of BA.

Estimating Attractor Reachability in Asynchronous Logical Models

Logical models are well-suited to capture salient dynamical properties of regulatory networks. For networks controlling cell fate decisions, cell fates are associated with model attractors (stable states or cyclic attractors) whose identification and reachability properties are particularly relevant. While synchronous updates assume unlikely instantaneous or identical rates associated with component changes, the consideration of asynchronous updates is more realistic but, for large models, may hinder the analysis of the resulting non-deterministic concurrent dynamics. This complexity hampers the study of asymptotical behaviors, and most existing approaches suffer from efficiency bottlenecks, being generally unable to handle cyclical attractors and quantify attractor reachability. Here, we propose two algorithms providing probability estimates of attractor reachability in asynchronous dynamics. The first algorithm, named Firefront, exhaustively explores the state space from an initial state, and provides quasi-exact evaluations of the reachability probabilities of model attractors. The algorithm progresses in breadth, propagating the probabilities of each encountered state to its successors. Second, Avatar is an adapted Monte Carlo approach, better suited for models with large and intertwined transient and terminal cycles. Avatar iteratively explores the state space by randomly selecting trajectories and by using these random walks to estimate the likelihood of reaching an attractor. Unlike Monte Carlo simulations, Avatar is equipped to avoid getting trapped in transient cycles and to identify cyclic attractors. Firefront and Avatar are validated and compared to related methods, using as test cases logical models of synthetic and biological networks. Both algorithms are implemented as new functionalities of GINsim 3.0, a well-established software tool for logical modeling, providing executable GUI, Java API, and scripting facilities.

Logical Modeling and Analysis of Cellular Regulatory Networks With GINsim 3.0

The logical formalism is well adapted to model large cellular networks, in particular when detailed kinetic data are scarce. This tutorial focuses on this well-established qualitative framework. Relying on GINsim (release 3.0), a software implementing this formalism, we guide the reader step by step toward the definition, the analysis and the simulation of a four-node model of the mammalian p53-Mdm2 network.

Analysis Tools for Interconnected Boolean Networks With Biological Applications

Boolean networks with asynchronous updates are a class of logical models particularly well adapted to describe the dynamics of biological networks with uncertain measures. The state space of these models can be described by an asynchronous state transition graph, which represents all the possible exits from every single state, and gives a global image of all the possible trajectories of the system. In addition, the asynchronous state transition graph can be associated with an absorbing Markov chain, further providing a semi-quantitative framework where it becomes possible to compute probabilities for the different trajectories. For large networks, however, such direct analyses become computationally untractable, given the exponential dimension of the graph. Exploiting the general modularity of biological systems, we have introduced the novel concept of asymptotic graph, computed as an interconnection of several asynchronous transition graphs and recovering all asymptotic behaviors of a large interconnected system from the behavior of its smaller modules. From a modeling point of view, the interconnection of networks is very useful to address for instance the interplay between known biological modules and to test different hypotheses on the nature of their mutual regulatory links. This paper develops two new features of this general methodology: a quantitative dimension is added to the asymptotic graph, through the computation of relative probabilities for each final attractor and a companion cross-graph is introduced to complement the method on a theoretical point of view.

Toward A variable RBE for proton beam therapy

In the clinic, proton beam therapy (PBT) is based on the use of a generic relative biological effectiveness (RBE) of 1.1 compared to photons in human cancers and normal tissues. However, the experimental basis for this RBE lacks any significant number of representative tumor models and clinically relevant endpoints for dose-limiting organs at risk. It is now increasingly appreciated that much of the variations of treatment responses in cancers are due to inter-tumoral genomic heterogeneity. Indeed, recently it has been shown that defects in certain DNA repair pathways, which are found in subsets of many cancers, are associated with a RBE increase in vitro. However, there currently exist little in vivo or clinical data that confirm the existence of similarly increased RBE values in human cancers. Furthermore, evidence for variable RBE values for normal tissue toxicity has been sparse and conflicting to date. If we could predict variable RBE values in patients, we would be able to optimally use and personalize PBT. For example, predictive tumor biomarkers may facilitate selection of patients with proton-sensitive cancers previously ineligible for PBT. Dose de-escalation may be possible to reduce normal tissue toxicity, especially in pediatric patients. Knowledge of increased tumor RBE may allow us to develop biologically optimized therapies to enhance local control while RBE biomarkers for normal tissues could lead to a better understanding and prevention of unusual PBT-associated toxicity. Here, we will review experimental data on the repair of proton damage to DNA that impact both RBE values and biophysical modeling to predict RBE variations. Experimental approaches for studying proton sensitivity in vitro and in vivo will be reviewed as well and recent clinical findings discussed. Ultimately, therapeutically exploiting the understudied biological advantages of protons and developing approaches to limit treatment toxicity should fundamentally impact the clinical use of PBT.

State observation and sensor selection for nonlinear networks

A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the trade-off between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that, owing to the crucial role played by the dynamics, purely graph-theoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.

Boolean network modeling in systems pharmacology

Quantitative systems pharmacology (QSP) is an emerging discipline that aims to discover how drugs modulate the dynamics of biological components in molecular and cellular networks and the impact of those perturbations on human pathophysiology. The integration of systems-based experimental and computational approaches is required to facilitate the advancement of this field. QSP models typically consist of a series of ordinary differential equations (ODE). However, this mathematical framework requires extensive knowledge of parameters pertaining to biological processes, which is often unavailable. An alternative framework that does not require knowledge of system-specific parameters, such as Boolean network modeling, could serve as an initial foundation prior to the development of an ODE-based model. Boolean network models have been shown to efficiently describe, in a qualitative manner, the complex behavior of signal transduction and gene/protein regulatory processes. In addition to providing a starting point prior to quantitative modeling, Boolean network models can also be utilized to discover novel therapeutic targets and combinatorial treatment strategies. Identifying drug targets using a network-based approach could supplement current drug discovery methodologies and help to fill the innovation gap across the pharmaceutical industry. In this review, we discuss the process of developing Boolean network models and the various analyses that can be performed to identify novel drug targets and combinatorial approaches. An example for each of these analyses is provided using a previously developed Boolean network of signaling pathways in multiple myeloma. Selected examples of Boolean network models of human (patho-)physiological systems are also reviewed in brief.

Inferring hidden causal relations between pathway members using reduced Google matrix of directed biological networks

Signaling pathways represent parts of the global biological molecular network which connects them into a seamless whole through complex direct and indirect (hidden) crosstalk whose structure can change during development or in pathological conditions. We suggest a novel methodology, called Googlomics, for the structural analysis of directed biological networks using spectral analysis of their Google matrices, using parallels with quantum scattering theory, developed for nuclear and mesoscopic physics and quantum chaos. We introduce analytical "reduced Google matrix" method for the analysis of biological network structure. The method allows inferring hidden causal relations between the members of a signaling pathway or a functionally related group of genes. We investigate how the structure of hidden causal relations can be reprogrammed as a result of changes in the transcriptional network layer during cancerogenesis. The suggested Googlomics approach rigorously characterizes complex systemic changes in the wiring of large causal biological networks in a computationally efficient way.

A polynomial based model for cell fate prediction in human diseases

BACKGROUND

Cell fate regulation directly affects tissue homeostasis and human health. Research on cell fate decision sheds light on key regulators, facilitates understanding the mechanisms, and suggests novel strategies to treat human diseases that are related to abnormal cell development.

RESULTS

In this study, we proposed a polynomial based model to predict cell fate. This model was derived from Taylor series. As a case study, gene expression data of pancreatic cells were adopted to test and verify the model. As numerous features (genes) are available, we employed two kinds of feature selection methods, i.e. correlation based and apoptosis pathway based. Then polynomials of different degrees were used to refine the cell fate prediction function. 10-fold cross-validation was carried out to evaluate the performance of our model. In addition, we analyzed the stability of the resultant cell fate prediction model by evaluating the ranges of the parameters, as well as assessing the variances of the predicted values at randomly selected points. Results show that, within both the two considered gene selection methods, the prediction accuracies of polynomials of different degrees show little differences. Interestingly, the linear polynomial (degree 1 polynomial) is more stable than others. When comparing the linear polynomials based on the two gene selection methods, it shows that although the accuracy of the linear polynomial that uses correlation analysis outcomes is a little higher (achieves 86.62%), the one within genes of the apoptosis pathway is much more stable.

CONCLUSIONS

Considering both the prediction accuracy and the stability of polynomial models of different degrees, the linear model is a preferred choice for cell fate prediction with gene expression data of pancreatic cells. The presented cell fate prediction model can be extended to other cells, which may be important for basic research as well as clinical study of cell development related diseases.

Logic Modeling in Quantitative Systems Pharmacology

Here we present logic modeling as an approach to understand deregulation of signal transduction in disease and to characterize a drug's mode of action. We discuss how to build a logic model from the literature and experimental data and how to analyze the resulting model to obtain insights of relevance for systems pharmacology. Our workflow uses the free tools OmniPath (network reconstruction from the literature), CellNOpt (model fit to experimental data), MaBoSS (model analysis), and Cytoscape (visualization).

Sig2GRN: a software tool linking signaling pathway with gene regulatory network for dynamic simulation

Background

Linking computational models of signaling pathways to predicted cellular responses such as gene expression regulation is a major challenge in computational systems biology. In this work, we present Sig2GRN, a Cytoscape plugin that is able to simulate time-course gene expression data given the user-defined external stimuli to the signaling pathways.

Methods

A generalized logical model is used in modeling the upstream signaling pathways. Then a Boolean model and a thermodynamics-based model are employed to predict the downstream changes in gene expression based on the simulated dynamics of transcription factors in signaling pathways.

Results

Our empirical case studies show that the simulation of Sig2GRN can predict changes in gene expression patterns induced by DNA damage signals and drug treatments.

Conclusions

As a software tool for modeling cellular dynamics, Sig2GRN can facilitate studies in systems biology by hypotheses generation and wet-lab experimental design.

Availability: http://histone.scse.ntu.edu.sg/Sig2GRN/

Knowledge-guided fuzzy logic modeling to infer cellular signaling networks from proteomic data

Modeling of signaling pathways is crucial for understanding and predicting cellular responses to drug treatments. However, canonical signaling pathways curated from literature are seldom context-specific and thus can hardly predict cell type-specific response to external perturbations; purely data-driven methods also have drawbacks such as limited biological interpretability. Therefore, hybrid methods that can integrate prior knowledge and real data for network inference are highly desirable. In this paper, we propose a knowledge-guided fuzzy logic network model to infer signaling pathways by exploiting both prior knowledge and time-series data. In particular, the dynamic time warping algorithm is employed to measure the goodness of fit between experimental and predicted data, so that our method can model temporally-ordered experimental observations. We evaluated the proposed method on a synthetic dataset and two real phosphoproteomic datasets. The experimental results demonstrate that our model can uncover drug-induced alterations in signaling pathways in cancer cells. Compared with existing hybrid models, our method can model feedback loops so that the dynamical mechanisms of signaling networks can be uncovered from time-series data. By calibrating generic models of signaling pathways against real data, our method supports precise predictions of context-specific anticancer drug effects, which is an important step towards precision medicine.

Neuroimmunological interactions in stroke

INTRODUCTION

Stroke is one of the leading causes of death in the world; its incidence is increasing due to increased life expectancy. However, treatment options for these patients are limited since no clinically effective drugs have been developed to date.

DEVELOPMENT

According to clinical evidence, a number of neurochemical changes take place after stroke, including energy depletion, increased free radical synthesis, calcium accumulation, neurotransmitter imbalance, excitotoxicity, and, at a later stage, immune system activation leading to inflammation. Immune response has been shown to be a major factor in disease progression. The release of proinflammatory cytokines such as TNF increase brain damage secondary to excitotoxicity and calcium accumulation, and promote free radical synthesis and cell death through various mechanisms. On the other hand, certain anti-inflammatory cytokines, such as IL-10 and IL-4, have been shown to have a neuroprotective effect and even promote neurogenesis and synapse remodeling, which makes immune modulation a promising treatment approach.

CONCLUSIONS

Understanding the relationship between the immune system and the nervous system not only deepens our knowledge of stroke but also provides new diagnostic, prognostic, and therapeutic strategies that may increase the quality of life of stroke patients.

Power-Law Modeling of Cancer Cell Fates Driven by Signaling Data to Reveal Drug Effects

Extracellular signals are captured and transmitted by signaling proteins inside a cell. An important type of cellular responses to the signals is the cell fate decision, e.g., apoptosis. However, the underlying mechanisms of cell fate regulation are still unclear, thus comprehensive and detailed kinetic models are not yet available. Alternatively, data-driven models are promising to bridge signaling data with the phenotypic measurements of cell fates. The traditional linear model for data-driven modeling of signaling pathways has its limitations because it assumes that the a cell fate is proportional to the activities of signaling proteins, which is unlikely in the complex biological systems. Therefore, we propose a power-law model to relate the activities of all the measured signaling proteins to the probabilities of cell fates. In our experiments, we compared our nonlinear power-law model with the linear model on three cancer datasets with phosphoproteomics and cell fate measurements, which demonstrated that the nonlinear model has superior performance on cell fates prediction. By in silico simulation of virtual protein knock-down, the proposed model is able to reveal drug effects which can complement traditional approaches such as binding affinity analysis. Moreover, our model is able to capture cell line specific information to distinguish one cell line from another in cell fate prediction. Our results show that the power-law data-driven model is able to perform better in cell fate prediction and provide more insights into the signaling pathways for cancer cell fates than the linear model.

Boolean regulatory network reconstruction using literature based knowledge with a genetic algorithm optimization method

Background

Prior knowledge networks (PKNs) provide a framework for the development of computational biological models, including Boolean models of regulatory networks which are the focus of this work. PKNs are created by a painstaking process of literature curation, and generally describe all relevant regulatory interactions identified using a variety of experimental conditions and systems, such as specific cell types or tissues. Certain of these regulatory interactions may not occur in all biological contexts of interest, and their presence may dramatically change the dynamical behaviour of the resulting computational model, hindering the elucidation of the underlying mechanisms and reducing the usefulness of model predictions. Methods are therefore required to generate optimized contextual network models from generic PKNs.

Results

We developed a new approach to generate and optimize Boolean networks, based on a given PKN. Using a genetic algorithm, a model network is built as a sub-network of the PKN and trained against experimental data to reproduce the experimentally observed behaviour in terms of attractors and the transitions that occur between them under specific perturbations. The resulting model network is therefore contextualized to the experimental conditions and constitutes a dynamical Boolean model closer to the observed biological process used to train the model than the original PKN. Such a model can then be interrogated to simulate response under perturbation, to detect stable states and their properties, to get insights into the underlying mechanisms and to generate new testable hypotheses.

Conclusions

Generic PKNs attempt to synthesize knowledge of all interactions occurring in a biological process of interest, irrespective of the specific biological context. This limits their usefulness as a basis for the development of context-specific, predictive dynamical Boolean models. The optimization method presented in this article produces specific, contextualized models from generic PKNs. These contextualized models have improved utility for hypothesis generation and experimental design. The general applicability of this methodological approach makes it suitable for a variety of biological systems and of general interest for biological and medical research. Our method was implemented in the software optimusqual, available online at http://www.vital-it.ch/software/optimusqual/.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1287-z) contains supplementary material, which is available to authorized users.