MCell4 with BioNetGen: A Monte Carlo simulator of rule-based reaction-diffusion systems with Python interface.

Biochemical signaling pathways in living cells are often highly organized into spatially segregated volumes, membranes, scaffolds, subcellular compartments, and organelles comprising small numbers of interacting molecules. At this level of granularity stochastic behavior dominates, well-mixed continuum approximations based on concentrations break down and a particle-based approach is more accurate and more efficient. We describe and validate a new version of the open-source MCell simulation program (MCell4), which supports generalized 3D Monte Carlo modeling of diffusion and chemical reaction of discrete molecules and macromolecular complexes in solution, on surfaces representing membranes, and combinations thereof. The main improvements in MCell4 compared to the previous versions, MCell3 and MCell3-R, include a Python interface and native BioNetGen reaction language (BNGL) support. MCell4's Python interface opens up completely new possibilities for interfacing with external simulators to allow creation of sophisticated event-driven multiscale/multiphysics simulations. The native BNGL support, implemented through a new open-source library libBNG (also introduced in this paper), provides the capability to run a given BNGL model spatially resolved in MCell4 and, with appropriate simplifying assumptions, also in the BioNetGen simulation environment, greatly accelerating and simplifying model validation and comparison.

BioSimulators: a central registry of simulation engines and services for recommending specific tools.

Computational models have great potential to accelerate bioscience, bioengineering, and medicine. However, it remains challenging to reproduce and reuse simulations, in part, because the numerous formats and methods for simulating various subsystems and scales remain siloed by different software tools. For example, each tool must be executed through a distinct interface. To help investigators find and use simulation tools, we developed BioSimulators (https://biosimulators.org), a central registry of the capabilities of simulation tools and consistent Python, command-line and containerized interfaces to each version of each tool. The foundation of BioSimulators is standards, such as CellML, SBML, SED-ML and the COMBINE archive format, and validation tools for simulation projects and simulation tools that ensure these standards are used consistently. To help modelers find tools for particular projects, we have also used the registry to develop recommendation services. We anticipate that BioSimulators will help modelers exchange, reproduce, and combine simulations.

SBML Level 3: an extensible format for the exchange and reuse of biological models.

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

Parallel Tempering with Lasso for model reduction in systems biology.

Systems Biology models reveal relationships between signaling inputs and observable molecular or cellular behaviors. The complexity of these models, however, often obscures key elements that regulate emergent properties. We use a Bayesian model reduction approach that combines Parallel Tempering with Lasso regularization to identify minimal subsets of reactions in a signaling network that are sufficient to reproduce experimentally observed data. The Bayesian approach finds distinct reduced models that fit data equivalently. A variant of this approach that uses Lasso to perform selection at the level of reaction modules is applied to the NF-κB signaling network to test the necessity of feedback loops for responses to pulsatile and continuous pathway stimulation. Taken together, our results demonstrate that Bayesian parameter estimation combined with regularization can isolate and reveal core motifs sufficient to explain data from complex signaling systems.

Harnessing Human Microphysiology Systems as Key Experimental Models for Quantitative Systems Pharmacology.

Two technologies that have emerged in the last decade offer a new paradigm for modern pharmacology, as well as drug discovery and development. Quantitative systems pharmacology (QSP) is a complementary approach to traditional, target-centric pharmacology and drug discovery and is based on an iterative application of computational and systems biology methods with multiscale experimental methods, both of which include models of ADME-Tox and disease. QSP has emerged as a new approach due to the low efficiency of success in developing therapeutics based on the existing target-centric paradigm. Likewise, human microphysiology systems (MPS) are experimental models complementary to existing animal models and are based on the use of human primary cells, adult stem cells, and/or induced pluripotent stem cells (iPSCs) to mimic human tissues and organ functions/structures involved in disease and ADME-Tox. Human MPS experimental models have been developed to address the relatively low concordance of human disease and ADME-Tox with engineered, experimental animal models of disease. The integration of the QSP paradigm with the use of human MPS has the potential to enhance the process of drug discovery and development.

Automated visualization of rule-based models.

Frameworks such as BioNetGen, Kappa and Simmune use "reaction rules" to specify biochemical interactions compactly, where each rule specifies a mechanism such as binding or phosphorylation and its structural requirements. Current rule-based models of signaling pathways have tens to hundreds of rules, and these numbers are expected to increase as more molecule types and pathways are added. Visual representations are critical for conveying rule-based models, but current approaches to show rules and interactions between rules scale poorly with model size. Also, inferring design motifs that emerge from biochemical interactions is an open problem, so current approaches to visualize model architecture rely on manual interpretation of the model. Here, we present three new visualization tools that constitute an automated visualization framework for rule-based models: (i) a compact rule visualization that efficiently displays each rule, (ii) the atom-rule graph that conveys regulatory interactions in the model as a bipartite network, and (iii) a tunable compression pipeline that incorporates expert knowledge and produces compact diagrams of model architecture when applied to the atom-rule graph. The compressed graphs convey network motifs and architectural features useful for understanding both small and large rule-based models, as we show by application to specific examples. Our tools also produce more readable diagrams than current approaches, as we show by comparing visualizations of 27 published models using standard graph metrics. We provide an implementation in the open source and freely available BioNetGen framework, but the underlying methods are general and can be applied to rule-based models from the Kappa and Simmune frameworks also. We expect that these tools will promote communication and analysis of rule-based models and their eventual integration into comprehensive whole-cell models.

BioNetGen 2.2: advances in rule-based modeling.

: BioNetGen is an open-source software package for rule-based modeling of complex biochemical systems. Version 2.2 of the software introduces numerous new features for both model specification and simulation. Here, we report on these additions, discussing how they facilitate the construction, simulation and analysis of larger and more complex models than previously possible. AVAILABILITY AND IMPLEMENTATION: Stable BioNetGen releases (Linux, Mac OS/X and Windows), with documentation, are available at http://bionetgen.org Source code is available at http://github.com/RuleWorld/bionetgen CONTACT: bionetgen.help@gmail.comSupplementary information: Supplementary data are available at Bioinformatics online.

Demystifying the cytokine network: Mathematical models point the way.

Cytokines provide the means by which immune cells communicate with each other and with parenchymal cells. There are over one hundred cytokines and many exist in families that share receptor components and signal transduction pathways, creating complex networks. Reductionist approaches to understanding the role of specific cytokines, through the use of gene-targeted mice, have revealed further complexity in the form of redundancy and pleiotropy in cytokine function. Creating an understanding of the complex interactions between cytokines and their target cells is challenging experimentally. Mathematical and computational modeling provides a robust set of tools by which complex interactions between cytokines can be studied and analyzed, in the process creating novel insights that can be further tested experimentally. This review will discuss and provide examples of the different modeling approaches that have been used to increase our understanding of cytokine networks. This includes discussion of knowledge-based and data-driven modeling approaches and the recent advance in single-cell analysis. The use of modeling to optimize cytokine-based therapies will also be discussed.

Unbiased Rare Event Sampling in Spatial Stochastic Systems Biology Models Using a Weighted Ensemble of Trajectories.

The long-term goal of connecting scales in biological simulation can be facilitated by scale-agnostic methods. We demonstrate that the weighted ensemble (WE) strategy, initially developed for molecular simulations, applies effectively to spatially resolved cell-scale simulations. The WE approach runs an ensemble of parallel trajectories with assigned weights and uses a statistical resampling strategy of replicating and pruning trajectories to focus computational effort on difficult-to-sample regions. The method can also generate unbiased estimates of non-equilibrium and equilibrium observables, sometimes with significantly less aggregate computing time than would be possible using standard parallelization. Here, we use WE to orchestrate particle-based kinetic Monte Carlo simulations, which include spatial geometry (e.g., of organelles, plasma membrane) and biochemical interactions among mobile molecular species. We study a series of models exhibiting spatial, temporal and biochemical complexity and show that although WE has important limitations, it can achieve performance significantly exceeding standard parallel simulation--by orders of magnitude for some observables.

Cutting Edge: Differential Regulation of PTEN by TCR, Akt, and FoxO1 Controls CD4+ T Cell Fate Decisions.

Signaling via the Akt/mammalian target of rapamycin pathway influences CD4(+) T cell differentiation; low levels favor regulatory T cell induction and high levels favor Th induction. Although the lipid phosphatase phosphatase and tensin homolog (PTEN) suppresses Akt activity, the control of PTEN activity is poorly studied in T cells. In this study, we identify multiple mechanisms that regulate PTEN expression. During Th induction, PTEN function is suppressed via lower mRNA levels, lower protein levels, and an increase in C-terminal phosphorylation. Conversely, during regulatory T cell induction, PTEN function is maintained through the stabilization of PTEN mRNA transcription and sustained protein levels. We demonstrate that differential Akt/mammalian target of rapamycin signaling regulates PTEN transcription via the FoxO1 transcription factor. A mathematical model that includes multiple modes of PTEN regulation recapitulates our experimental findings and demonstrates how several feedback loops determine differentiation outcomes. Collectively, this work provides novel mechanistic insights into how differential regulation of PTEN controls alternate CD4(+) T cell fate outcomes.

Modeling for (physical) biologists: an introduction to the rule-based approach.

Models that capture the chemical kinetics of cellular regulatory networks can be specified in terms of rules for biomolecular interactions. A rule defines a generalized reaction, meaning a reaction that permits multiple reactants, each capable of participating in a characteristic transformation and each possessing certain, specified properties, which may be local, such as the state of a particular site or domain of a protein. In other words, a rule defines a transformation and the properties that reactants must possess to participate in the transformation. A rule also provides a rate law. A rule-based approach to modeling enables consideration of mechanistic details at the level of functional sites of biomolecules and provides a facile and visual means for constructing computational models, which can be analyzed to study how system-level behaviors emerge from component interactions.

Exact hybrid particle/population simulation of rule-based models of biochemical systems.

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This "network-free" approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of "partial network expansion" into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

MOSBIE: a tool for comparison and analysis of rule-based biochemical models.

BACKGROUND: Mechanistic models that describe the dynamical behaviors of biochemical systems are common in computational systems biology, especially in the realm of cellular signaling. The development of families of such models, either by a single research group or by different groups working within the same area, presents significant challenges that range from identifying structural similarities and differences between models to understanding how these differences affect system dynamics. RESULTS: We present the development and features of an interactive model exploration system, MOSBIE, which provides utilities for identifying similarities and differences between models within a family. Models are clustered using a custom similarity metric, and a visual interface is provided that allows a researcher to interactively compare the structures of pairs of models as well as view simulation results. CONCLUSIONS: We illustrate the usefulness of MOSBIE via two case studies in the cell signaling domain. We also present feedback provided by domain experts and discuss the benefits, as well as the limitations, of the approach.

Efficient modeling, simulation and coarse-graining of biological complexity with NFsim.

Managing the overwhelming numbers of molecular states and interactions is a fundamental obstacle to building predictive models of biological systems. Here we introduce the Network-Free Stochastic Simulator (NFsim), a general-purpose modeling platform that overcomes the combinatorial nature of molecular interactions. Unlike standard simulators that represent molecular species as variables in equations, NFsim uses a biologically intuitive representation: objects with binding and modification sites acted on by reaction rules. During simulations, rules operate directly on molecular objects to produce exact stochastic results with performance that scales independently of the reaction network size. Reaction rates can be defined as arbitrary functions of molecular states to provide powerful coarse-graining capabilities, for example to merge Boolean and kinetic representations of biological networks. NFsim enables researchers to simulate many biological systems that were previously inaccessible to general-purpose software, as we illustrate with models of immune system signaling, microbial signaling, cytoskeletal assembly and oscillating gene expression.

Modeling the T cell immune response: a fascinating challenge.

The immune system is designed to protect the organism from infection and to repair damaged tissue. An effective response requires recognition of the threat, the appropriate effector mechanism to clear the pathogen and a return to homeostasis with minimal damage to self-tissues. T cells play a central role in orchestrating the immune response at all stages of the response and have been the subject of intense study by both experimental immunologists and modelers. This review examines some of the more critical questions in T cell biology and describes the latest attempts to address those questions using approaches that combine mathematical modeling and experiments.

Predicting gene-level sensitivity to JAK-STAT signaling perturbation using a mechanistic-to-machine learning framework.

The Janus kinase (JAK)-signal transducer and activator of transcription (STAT) pathway integrates complex cytokine signals via a limited number of molecular components, inspiring numerous efforts to clarify the diversity and specificity of STAT transcription factor function. We developed a computational framework to make global cytokine-induced gene predictions from STAT phosphorylation dynamics, modeling macrophage responses to interleukin (IL)-6 and IL-10, which signal through common STATs, but with distinct temporal dynamics and contrasting functions. Our mechanistic-to-machine learning model identified cytokine-specific genes associated with late pSTAT3 time frames and a preferential pSTAT1 reduction upon JAK2 inhibition. We predicted and validated the impact of JAK2 inhibition on gene expression, identifying genes that were sensitive or insensitive to JAK2 variation. Thus, we successfully linked STAT signaling dynamics to gene expression to support future efforts targeting pathology-associated STAT-driven gene sets. This serves as a first step in developing multi-level prediction models to understand and perturb gene expression outputs from signaling systems. A record of this paper's transparent peer review process is included in the supplemental information.

In vivo, in vitro, and in silico studies suggest a conserved immune module that regulates malaria parasite transmission from mammals to mosquitoes.

Human malaria can be caused by the parasite Plasmodium falciparum that is transmitted by female Anopheles mosquitoes. "Immunological crosstalk" between the mammalian and anopheline hosts for Plasmodium functions to control parasite numbers. Key to this process is the mammalian cytokine transforming growth factor-ß1 (TGF-ß1). In mammals, TGF-ß1 regulates inducible nitric oxide (NO) synthase (iNOS) both positively and negatively. In some settings, high levels of NO activate latent TGF-ß1, which in turn suppresses iNOS expression. In the mosquito, ingested TGF-ß1 induces A. stephensi NOS (AsNOS), which limits parasite development and which in turn is suppressed by activation of the mosquito homolog of the mitogen-activated protein kinases MEK and ERK. Computational models linking TGF-ß1, AsNOS, and MEK/ERK were developed to provide insights into this complex biology. An initial Boolean model suggested that, as occurs in mammalian cells, MEK/ERK and AsNOS would oscillate upon ingestion of TGF-ß1. An ordinary differential equation (ODE) model further supported the hypothesis of TGF-ß1-induced multiphasic behavior of MEK/ERK and AsNOS. To achieve this multiphasic behavior, the ODE model was predicated on the presence of constant levels of TGF-ß1 in the mosquito midgut. Ingested TGF-ß1, however, did not exhibit this behavior. Accordingly, we hypothesized and experimentally verified that ingested TGF-ß1 induces the expression of the endogenous mosquito TGF-ß superfamily ligand As60A. Computational simulation of these complex, cross-species interactions suggested that TGF-ß1 and NO-mediated induction of As60A expression together may act to maintain multiphasic AsNOS expression via MEK/ERK-dependent signaling. We hypothesize that multiphasic behavior as represented in this model allows the mosquito to balance the conflicting demands of parasite killing and metabolic homeostasis in the face of damaging inflammation.

Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories.

We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study, WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent "brute-force" calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over "brute-force" in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ~10(12) to ~10(18) for characterizing rare states in a distribution, and ~10(2) to ~10(4) for finding mean first passage times.

Predicting gene level sensitivity to JAK-STAT signaling perturbation using a mechanistic-to-machine learning framework.

The JAK-STAT pathway integrates complex cytokine signals via a limited number of molecular components, inspiring numerous efforts to clarify the diversity and specificity of STAT transcription factor function. We developed a computational workflow to make global cytokine-induced gene predictions from STAT phosphorylation dynamics, modeling macrophage responses to IL-6 and IL-10, which signal through common STATs, but with distinct temporal dynamics and contrasting functions. Our mechanistic-to-machine learning model identified select cytokine-induced gene sets associated with late pSTAT3 timeframes and a preferential pSTAT1 reduction upon JAK2 inhibition. We predicted and validated the impact of JAK2 inhibition on gene expression, identifying dynamically regulated genes that were sensitive or insensitive to JAK2 variation. Thus, we successfully linked STAT signaling dynamics to gene expression to support future efforts targeting pathology-associated STAT-driven gene sets. This serves as a first step in developing multi-level prediction models to understand and perturb gene expression outputs from signaling systems.

A Suite of Tutorials for the WESTPA 2.0 Rare-Events Sampling Software [Article v2.0].

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present two sets of tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. The first set of more basic tutorials describes a range of simulation types, from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding. The second set ecompasses six advanced tutorials instructing users in the best practices of using key new features and plugins/extensions of the WESTPA 2.0 software package, which consists of major upgrades for larger systems and/or slower processes. The advanced tutorials demonstrate the use of the following key features: (i) a generalized resampler module for the creation of "binless" schemes, (ii) a minimal adaptive binning scheme for more efficient surmounting of free energy barriers, (iii) streamlined handling of large simulation datasets using an HDF5 framework, (iv) two different schemes for more efficient rate-constant estimation, (v) a Python API for simplified analysis of WE simulations, and (vi) plugins/extensions for Markovian Weighted Ensemble Milestoning and WE rule-based modeling for systems biology models. Applications of the advanced tutorials include atomistic and non-spatial models, and consist of complex processes such as protein folding and the membrane permeability of a drug-like molecule. Users are expected to already have significant experience with running conventional molecular dynamics or systems biology simulations.