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.

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.

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.

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.

Model Integration in Computational Biology: The Role of Reproducibility, Credibility and Utility.

During the COVID-19 pandemic, mathematical modeling of disease transmission has become a cornerstone of key state decisions. To advance the state-of-the-art host viral modeling to handle future pandemics, many scientists working on related issues assembled to discuss the topics. These discussions exposed the reproducibility crisis that leads to inability to reuse and integrate models. This document summarizes these discussions, presents difficulties, and mentions existing efforts towards future solutions that will allow future model utility and integration. We argue that without addressing these challenges, scientists will have diminished ability to build, disseminate, and implement high-impact multi-scale modeling that is needed to understand the health crises we face.

Iterative community-driven development of a SARS-CoV-2 tissue simulator.

The 2019 novel coronavirus, SARS-CoV-2, is a pathogen of critical significance to international public health. Knowledge of the interplay between molecular-scale virus-receptor interactions, single-cell viral replication, intracellular-scale viral transport, and emergent tissue-scale viral propagation is limited. Moreover, little is known about immune system-virus-tissue interactions and how these can result in low-level (asymptomatic) infections in some cases and acute respiratory distress syndrome (ARDS) in others, particularly with respect to presentation in different age groups or pre-existing inflammatory risk factors. Given the nonlinear interactions within and among each of these processes, multiscale simulation models can shed light on the emergent dynamics that lead to divergent outcomes, identify actionable "choke points" for pharmacologic interventions, screen potential therapies, and identify potential biomarkers that differentiate patient outcomes. Given the complexity of the problem and the acute need for an actionable model to guide therapy discovery and optimization, we introduce and iteratively refine a prototype of a multiscale model of SARS-CoV-2 dynamics in lung tissue. The first prototype model was built and shared internationally as open source code and an online interactive model in under 12 hours, and community domain expertise is driving regular refinements. In a sustained community effort, this consortium is integrating data and expertise across virology, immunology, mathematical biology, quantitative systems physiology, cloud and high performance computing, and other domains to accelerate our response to this critical threat to international health. More broadly, this effort is creating a reusable, modular framework for studying viral replication and immune response in tissues, which can also potentially be adapted to related problems in immunology and immunotherapy.

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.

MCell-R: A Particle-Resolution Network-Free Spatial Modeling Framework.

Spatial heterogeneity can have dramatic effects on the biochemical networks that drive cell regulation and decision-making. For this reason, a number of methods have been developed to model spatial heterogeneity and incorporated into widely used modeling platforms. Unfortunately, the standard approaches for specifying and simulating chemical reaction networks become untenable when dealing with multistate, multicomponent systems that are characterized by combinatorial complexity. To address this issue, we developed MCell-R, a framework that extends the particle-based spatial Monte Carlo simulator, MCell, with the rule-based model specification and simulation capabilities provided by BioNetGen and NFsim. The BioNetGen syntax enables the specification of biomolecules as structured objects whose components can have different internal states that represent such features as covalent modification and conformation and which can bind components of other molecules to form molecular complexes. The network-free simulation algorithm used by NFsim enables efficient simulation of rule-based models even when the size of the network implied by the biochemical rules is too large to enumerate explicitly, which frequently occurs in detailed models of biochemical signaling. The result is a framework that can efficiently simulate systems characterized by combinatorial complexity at the level of spatially resolved individual molecules over biologically relevant time and length scales.

Evaluation of Parallel Tempering to Accelerate Bayesian Parameter Estimation in Systems Biology.

Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the best-fit parameters are insufficient when models are high dimensional and under-constrained. As a result, Bayesian methods, which treat model parameters as random variables and attempt to estimate their probability distributions given data, have become popular in systems biology. Bayesian parameter estimation often relies on Markov Chain Monte Carlo (MCMC) methods to sample model parameter distributions, but the slow convergence of MCMC sampling can be a major bottleneck. One approach to improving performance is parallel tempering (PT), a physics-based method that uses swapping between multiple Markov chains run in parallel at different temperatures to accelerate sampling. The temperature of a Markov chain determines the probability of accepting an unfavorable move, so swapping with higher temperatures chains enables the sampling chain to escape from local minima. In this work we compared the MCMC performance of PT and the commonly-used Metropolis-Hastings (MH) algorithm on six biological models of varying complexity. We found that for simpler models PT accelerated convergence and sampling, and that for more complex models, PT often converged in cases MH became trapped in non-optimal local minima. We also developed a freely-available MATLAB package for Bayesian parameter estimation called PTEMPEST (http://github.com/RuleWorld/ptempest), which is closely integrated with the popular BioNetGen software for rule-based modeling of biological systems.

Shift from stochastic to spatially-ordered expression of serine-glycine synthesis enzymes in 3D microtumors.

Cell-to-cell differences in protein expression in normal tissues and tumors are a common phenomenon, but the underlying principles that govern this heterogeneity are largely unknown. Here, we show that in monolayer cancer cell-line cultures, the expression of the five metabolic enzymes of serine-glycine synthesis (SGS), including its rate-limiting enzyme, phosphoglycerate dehydrogenase (PHGDH), displays stochastic cell-to-cell variation. By contrast, in cancer cell line-derived three-dimensional (3D) microtumors PHGDH expression is restricted to the outermost part of the microtumors' outer proliferative cell layer, while the four other SGS enzymes display near uniform expression throughout the microtumor. A mathematical model suggests that metabolic stress in the microtumor core activates factors that restrict PHGDH expression. Thus, intracellular enzyme expression in growing cell ecosystems can shift to spatially ordered patterns in 3D structured environments due to emergent cell-cell communication, with potential implications for the design of effective anti-metabolic cancer therapies.

Heterogeneities in Axonal Structure and Transporter Distribution Lower Dopamine Reuptake Efficiency.

Efficient clearance of dopamine (DA) from the synapse is key to regulating dopaminergic signaling. This role is fulfilled by DA transporters (DATs). Recent advances in the structural characterization of DAT from Drosophila (dDAT) and in high-resolution imaging of DA neurons and the distribution of DATs in living cells now permit us to gain a mechanistic understanding of DA reuptake events in silico. Using electron microscopy images and immunofluorescence of transgenic knock-in mouse brains that express hemagglutinin-tagged DAT in DA neurons, we reconstructed a realistic environment for MCell simulations of DA reuptake, wherein the identity, population and kinetics of homology-modeled human DAT (hDAT) substates were derived from molecular simulations. The complex morphology of axon terminals near active zones was observed to give rise to large variations in DA reuptake efficiency, and thereby in extracellular DA density. Comparison of the effect of different firing patterns showed that phasic firing would increase the probability of reaching local DA levels sufficiently high to activate low-affinity DA receptors, mainly owing to high DA levels transiently attained during the burst phase. The experimentally observed nonuniform surface distribution of DATs emerged as a major modulator of DA signaling: reuptake was slower, and the peaks/width of transient DA levels were sharper/wider under nonuniform distribution of DATs, compared with uniform. Overall, the study highlights the importance of accurate descriptions of extrasynaptic morphology, DAT distribution, and conformational kinetics for quantitative evaluation of dopaminergic transmission and for providing deeper understanding of the mechanisms that regulate DA transmission.

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.

NF-κB Dynamics Discriminate between TNF Doses in Single Cells.

Although cytokine-dependent dynamics of nuclear factor κB (NF-κB) are known to encode information that regulates cell fate decisions, it is unclear whether single-cell responses are switch-like or encode more information about cytokine dose. Here, we measure the dynamic subcellular localization of NF-κB in response to a range of tumor necrosis factor (TNF) stimulation conditions to determine the prevailing mechanism of single-cell dose discrimination. Using an information theory formalism that accounts for signaling dynamics and non-responsive cell subpopulations, we find that the information transmission capacity of single cells exceeds that predicted from a switch-like response. Instead, we observe that NF-κB dynamics within single cells contain sufficient information to encode multiple, TNF-dependent cellular states, and have an activation threshold that varies across the population. By comparing single-cell responses to an internal, experimentally observed reference, we demonstrate that cells can grade responses to TNF across several orders of magnitude in concentration. This suggests that cells contain additional control points to fine-tune their cytokine responses beyond the decision to activate.

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.

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.

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.