Programming biological models in Python using PySB

Generating synthetic signaling networks for in silico modeling studies

Predictive models of signaling pathways have proven to be difficult to develop. Traditional approaches to developing mechanistic models rely on collecting experimental data and fitting a single model to that data. This approach works for simple systems but has proven unreliable for complex systems such as biological signaling networks. Thus, there is a need to develop new approaches to create predictive mechanistic models of complex systems. To meet this need, we developed a method for generating artificial signaling networks that were reasonably realistic and thus could be treated as ground truth models. These synthetic models could then be used to generate synthetic data for developing and testing algorithms designed to recover the underlying network topology and associated parameters. We defined the reaction degree and reaction distance to measure the topology of reaction networks, especially to consider enzymes. To determine whether our generated signaling networks displayed meaningful behavior, we compared them with signaling networks from the BioModels Database. This comparison indicated that our generated signaling networks had high topological similarities with BioModels signaling networks with respect to the reaction degree and distance distributions. In addition, our synthetic signaling networks had similar behavioral dynamics with respect to both steady states and oscillations, suggesting that our method generated synthetic signaling networks comparable with BioModels and thus could be useful for building network evaluation tools.

Cell-specific models reveal conformation-specific RAF inhibitor combinations that synergistically inhibit ERK signaling in pancreatic cancer cells

Pancreatic ductal adenocarcinoma (PDAC) presents significant challenges for targeted clinical interventions due to prevalent KRAS mutations, rendering PDAC resistant to RAF and MEK inhibitors (RAFi and MEKi). In addition, responses to targeted therapies vary between patients. Here, we explored the differential sensitivities of PDAC cell lines to RAFi and MEKi and developed an isogenic pair comprising the most sensitive and resistant PDAC cells. To simulate patient- or tumor-specific variations, we constructed cell-line-specific mechanistic models based on protein expression profiling and differential properties of KRAS mutants. These models predicted synergy between two RAFi with different conformation specificity (type I½ and type II RAFi) in inhibiting phospho-ERK (ppERK) and reducing PDAC cell viability. This synergy was experimentally validated across all four studied PDAC cell lines. Our findings underscore the need for combination approaches to inhibit the ERK pathway in PDAC.

Poincaré and SimBio: a versatile and extensible Python ecosystem for modeling systems

MOTIVATION

Chemical reaction networks (CRNs) play a pivotal role in diverse fields such as systems biology, biochemistry, chemical engineering, and epidemiology. High-level definitions of CRNs enables to use various simulation approaches, including deterministic and stochastic methods, from the same model. However, existing Python tools for simulation of CRN typically wrap external C/C++ libraries for model definition, translation into equations and/or numerically solving them, limiting their extensibility and integration with the broader Python ecosystem.

RESULTS

In response, we developed Poincaré and SimBio, two novel Python packages for simulation of dynamical systems and CRNs. Poincaré serves as a foundation for dynamical systems modeling, while SimBio extends this functionality to CRNs, including support for the Systems Biology Markup Language (SBML). Poincaré and SimBio are developed as pure Python packages enabling users to easily extend their simulation capabilities by writing new or leveraging other Python packages. Moreover, this does not compromise the performance, as code can be just-in-time compiled with Numba. Our benchmark tests using curated models from the BioModels repository demonstrate that these tools may provide a potentially superior performance advantage compared to other existing tools. In addition, to ensure a user-friendly experience, our packages use standard typed modern Python syntax that provides a seamless integration with integrated development environments. Our Python-centric approach significantly enhances code analysis, error detection, and refactoring capabilities, positioning Poincaré and SimBio as valuable tools for the modeling community.

AVAILABILITY AND IMPLEMENTATION

Poincaré and SimBio are released under the MIT license. Their source code is available on GitHub (https://github.com/maurosilber/poincare and https://github.com/hgrecco/simbio) and can be installed from PyPI or conda-forge.

Cell State Transition Models Stratify Breast Cancer Cell Phenotypes and Reveal New Therapeutic Targets

Understanding signaling patterns of transformation and controlling cell phenotypes is a challenge of current biology. Here we applied a cell State Transition Assessment and Regulation (cSTAR) approach to a perturbation dataset of single cell phosphoproteomic patterns of multiple breast cancer (BC) and normal breast tissue-derived cell lines. Following a separation of luminal, basal, and normal cell states, we identified signaling nodes within core control networks, delineated causal connections, and determined the primary drivers underlying oncogenic transformation and transitions across distinct BC subtypes. Whereas cell lines within the same BC subtype have different mutational and expression profiles, the architecture of the core network was similar for all luminal BC cells, and mTOR was a main oncogenic driver. In contrast, core networks of basal BC were heterogeneous and segregated into roughly four major subclasses with distinct oncogenic and BC subtype drivers. Likewise, normal breast tissue cells were separated into two different subclasses. Based on the data and quantified network topologies, we derived mechanistic cSTAR models that serve as digital cell twins and allow the deliberate control of cell movements within a Waddington landscape across different cell states. These cSTAR models suggested strategies of normalizing phosphorylation networks of BC cell lines using small molecule inhibitors.

Signal execution modes emerge in biochemical reaction networks calibrated to experimental data

Mathematical models of biomolecular networks are commonly used to study cellular processes; however, their usefulness to explain and predict dynamic behaviors is often questioned due to the unclear relationship between parameter uncertainty and network dynamics. In this work, we introduce PyDyNo (Python dynamic analysis of biochemical networks), a non-equilibrium reaction-flux based analysis to identify dominant reaction paths within a biochemical reaction network calibrated to experimental data. We first show, in a simplified apoptosis execution model, that despite the thousands of parameter vectors with equally good fits to experimental data, our framework identifies the dynamic differences between these parameter sets and outputs three dominant execution modes, which exhibit varying sensitivity to perturbations. We then apply our methodology to JAK2/STAT5 network in colony-forming unit-erythroid (CFU-E) cells and provide previously unrecognized mechanistic explanation for the survival responses of CFU-E cell population that would have been impossible to deduce with traditional protein-concentration based analyses.

bnglViz: online visualization of rule-based models

MOTIVATION

Rule-based modeling is a powerful method to describe and simulate interactions among multi-site molecules and multi-molecular species, accounting for the internal connectivity of molecules in chemical species. This modeling technique is implemented in BioNetGen software that is used by various tools and software frameworks, such as BioNetGen stand-alone software, NFSim simulation engine, Virtual Cell simulation and modeling framework, SmolDyn and PySB software tools. These tools exchange models using BioNetGen scripting language (BNGL). Until now, there was no online visualization of such rule-based models. Modelers and researchers reading the manuscripts describing rule-based models had to learn BNGL scripting or master one of these tools to understand the models.

RESULTS

Here, we introduce bnglViz, an online platform for visualizing BNGL files as graphical cartoons, empowering researchers to grasp the nuances of rule-based models swiftly and efficiently, and making the exploration of complex biological systems more accessible than ever before. The produced visualizations can be used as supplemental figures in publications or as a way to annotate BNGL models on web repositories.

AVAILABILITY AND IMPLEMENTATION

Available at https://bnglviz.github.io/.

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.

DyCeModel: a tool for 1D simulation for distribution of plant hormones controlling tissue patterning

To study the mechanisms of growth and development, it is necessary to analyze the dynamics of the tissue patterning regulators in time and space and to take into account their effect on the cellular dynamics within a tissue. Plant hormones are the main regulators of the cell dynamics in plant tissues; they form gradients and maxima and control molecular processes in a concentration-dependent manner. Here, we present DyCeModel, a software tool implemented in MATLAB for one-dimensional simulation of tissue with a dynamic cellular ensemble, where changes in hormone (or other active substance) concentration in the cells are described by ordinary differential equations (ODEs). We applied DyCeModel to simulate cell dynamics in plant meristems with different cellular structures and demonstrated that DyCeModel helps to identify the relationships between hormone concentration and cellular behaviors. The tool visualizes the simulation progress and presents a video obtained during the calculation. Importantly, the tool is capable of automatically adjusting the parameters by fitting the distribution of the substance concentrations predicted in the model to experimental data taken from the microscopic images. Noteworthy, DyCeModel makes it possible to build models for distinct types of plant meristems with the same ODEs, recruiting specific input characteristics for each meristem. We demonstrate the tool's efficiency by simulation of the effect of auxin and cytokinin distributions on tissue patterning in two types of Arabidopsis thaliana stem cell niches: the root and shoot apical meristems. The resulting models represent a promising framework for further study of the role of hormone-controlled gene regulatory networks in cell dynamics.

Catalyst: Fast and flexible modeling of reaction networks

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst's broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

SBcoyote: An extensible Python-based reaction editor and viewer

SBcoyote is an open-source cross-platform biochemical reaction viewer and editor released under the liberal MIT license. It is written in Python and uses wxPython to implement the GUI and the drawing canvas. It supports the visualization and editing of compartments, species, and reactions. It includes many options to stylize each of these components. For instance, species can be in different colors and shapes. Other core features include the ability to create alias nodes, alignment of groups of nodes, network zooming, as well as an interactive bird-eye view of the network to allow easy navigation on large networks. A unique feature of the tool is the extensive Python plugin API, where third-party developers can include new functionality. To assist third-party plugin developers, we provide a variety of sample plugins, including, random network generation, a simple auto layout tool, export to Antimony, export SBML, import SBML, etc. Of particular interest are the export and import SBML plugins since these support the SBML level 3 layout and render standard, which is exchangeable with other software packages. Plugins are stored in a GitHub repository, and an included plugin manager can retrieve and install new plugins from the repository on demand. Plugins have version metadata associated with them to make it install plugin updates. Availability: https://github.com/sys-bio/SBcoyote.

BioNetGMMFit: estimating parameters of a BioNetGen model from time-stamped snapshots of single cells

Mechanistic models are commonly employed to describe signaling and gene regulatory kinetics in single cells and cell populations. Recent advances in single-cell technologies have produced multidimensional datasets where snapshots of copy numbers (or abundances) of a large number of proteins and mRNA are measured across time in single cells. The availability of such datasets presents an attractive scenario where mechanistic models are validated against experiments, and estimated model parameters enable quantitative predictions of signaling or gene regulatory kinetics. To empower the systems biology community to easily estimate parameters accurately from multidimensional single-cell data, we have merged a widely used rule-based modeling software package BioNetGen, which provides a user-friendly way to code for mechanistic models describing biochemical reactions, and the recently introduced CyGMM, that uses cell-to-cell differences to improve parameter estimation for such networks, into a single software package: BioNetGMMFit. BioNetGMMFit provides parameter estimates of the model, supplied by the user in the BioNetGen markup language (BNGL), which yield the best fit for the observed single-cell, time-stamped data of cellular components. Furthermore, for more precise estimates, our software generates confidence intervals around each model parameter. BioNetGMMFit is capable of fitting datasets of increasing cell population sizes for any mechanistic model specified in the BioNetGen markup language. By streamlining the process of developing mechanistic models for large single-cell datasets, BioNetGMMFit provides an easily-accessible modeling framework designed for scale and the broader biochemical signaling community.

SBcoyote: An Extensible Python-Based Reaction Editor and Viewer

SBcoyote is an open-source cross-platform biochemical reaction viewer and editor released under the liberal MIT license. It is written in Python and uses wxPython to implement the GUI and the drawing canvas. It supports the visualization and editing of compartments, species, and reactions. It includes many options to stylize each of these components. For instance, species can be in different colors and shapes. Other core features include the ability to create alias nodes, alignment of groups of nodes, network zooming, as well as an interactive bird-eye view of the network to allow easy navigation on large networks. A unique feature of the tool is the extensive Python plugin API, where third-party developers can include new functionality. To assist third-party plugin developers, we provide a variety of sample plugins, including, random network generation, a simple auto layout tool, export to Antimony, export SBML, import SBML, etc. Of particular interest are the export and import SBML plugins since these support the SBML level 3 layout and render standard, which is exchangeable with other software packages. Plugins are stored in a GitHub repository, and an included plugin manager can retrieve and install new plugins from the repository on demand. Plugins have version metadata associated with them to make it install plugin updates. Availability: https://github.com/sys-bio/SBcoyote.

Targeting alternative splicing in cancer immunotherapy

Tumor immunotherapy has made great progress in cancer treatment but still faces several challenges, such as a limited number of targetable antigens and varying responses among patients. Alternative splicing (AS) is an essential process for the maturation of nearly all mammalian mRNAs. Recent studies show that AS contributes to expanding cancer-specific antigens and modulating immunogenicity, making it a promising solution to the above challenges. The organoid technology preserves the individual immune microenvironment and reduces the time/economic costs of the experiment model, facilitating the development of splicing-based immunotherapy. Here, we summarize three critical roles of AS in immunotherapy: resources for generating neoantigens, targets for immune-therapeutic modulation, and biomarkers to guide immunotherapy options. Subsequently, we highlight the benefits of adopting organoids to develop AS-based immunotherapies. Finally, we discuss the current challenges in studying AS-based immunotherapy in terms of existing bioinformatics algorithms and biological technologies.

A Combination of Conformation-Specific RAF Inhibitors Overcome Drug Resistance Brought about by RAF Overexpression

Cancer cells often adapt to targeted therapies, yet the molecular mechanisms underlying adaptive resistance remain only partially understood. Here, we explore a mechanism of RAS/RAF/MEK/ERK (MAPK) pathway reactivation through the upregulation of RAF isoform (RAFs) abundance. Using computational modeling and in vitro experiments, we show that the upregulation of RAFs changes the concentration range of paradoxical pathway activation upon treatment with conformation-specific RAF inhibitors. Additionally, our data indicate that the signaling output upon loss or downregulation of one RAF isoform can be compensated by overexpression of other RAF isoforms. We furthermore demonstrate that, while single RAF inhibitors cannot efficiently inhibit ERK reactivation caused by RAF overexpression, a combination of two structurally distinct RAF inhibitors synergizes to robustly suppress pathway reactivation.

Unified tumor growth mechanisms from multimodel inference and dataset integration

Mechanistic models of biological processes can explain observed phenomena and predict responses to a perturbation. A mathematical model is typically constructed using expert knowledge and informal reasoning to generate a mechanistic explanation for a given observation. Although this approach works well for simple systems with abundant data and well-established principles, quantitative biology is often faced with a dearth of both data and knowledge about a process, thus making it challenging to identify and validate all possible mechanistic hypothesis underlying a system behavior. To overcome these limitations, we introduce a Bayesian multimodel inference (Bayes-MMI) methodology, which quantifies how mechanistic hypotheses can explain a given experimental datasets, and concurrently, how each dataset informs a given model hypothesis, thus enabling hypothesis space exploration in the context of available data. We demonstrate this approach to probe standing questions about heterogeneity, lineage plasticity, and cell-cell interactions in tumor growth mechanisms of small cell lung cancer (SCLC). We integrate three datasets that each formulated different explanations for tumor growth mechanisms in SCLC, apply Bayes-MMI and find that the data supports model predictions for tumor evolution promoted by high lineage plasticity, rather than through expanding rare stem-like populations. In addition, the models predict that in the presence of cells associated with the SCLC-N or SCLC-A2 subtypes, the transition from the SCLC-A subtype to the SCLC-Y subtype through an intermediate is decelerated. Together, these predictions provide a testable hypothesis for observed juxtaposed results in SCLC growth and a mechanistic interpretation for tumor treatment resistance.

Automated assembly of molecular mechanisms at scale from text mining and curated databases

The analysis of omic data depends on machine-readable information about protein interactions, modifications, and activities as found in protein interaction networks, databases of post-translational modifications, and curated models of gene and protein function. These resources typically depend heavily on human curation. Natural language processing systems that read the primary literature have the potential to substantially extend knowledge resources while reducing the burden on human curators. However, machine-reading systems are limited by high error rates and commonly generate fragmentary and redundant information. Here, we describe an approach to precisely assemble molecular mechanisms at scale using multiple natural language processing systems and the Integrated Network and Dynamical Reasoning Assembler (INDRA). INDRA identifies full and partial overlaps in information extracted from published papers and pathway databases, uses predictive models to improve the reliability of machine reading, and thereby assembles individual pieces of information into non-redundant and broadly usable mechanistic knowledge. Using INDRA to create high-quality corpora of causal knowledge we show it is possible to extend protein-protein interaction databases and explain co-dependencies in the Cancer Dependency Map.

Computational modeling of TGF-β2:TβRI:TβRII receptor complex assembly as mediated by the TGF-β coreceptor betaglycan

Transforming growth factor-β1, -β2, and -β3 (TGF-β1, -β2, and -β3) are secreted signaling ligands that play essential roles in tissue development, tissue maintenance, immune response, and wound healing. TGF-β ligands form homodimers and signal by assembling a heterotetrameric receptor complex comprised of two type I receptor (TβRI):type II receptor (TβRII) pairs. TGF-β1 and TGF-β3 ligands signal with high potency due to their high affinity for TβRII, which engenders high-affinity binding of TβRI through a composite TGF-β:TβRII binding interface. However, TGF-β2 binds TβRII 200-500 more weakly than TGF-β1 and TGF-β3 and signals with lower potency compared with these ligands. Remarkably, the presence of an additional membrane-bound coreceptor, known as betaglycan, increases TGF-β2 signaling potency to levels similar to TGF-β1 and -β3. The mediating effect of betaglycan occurs even though it is displaced from and not present in the heterotetrameric receptor complex through which TGF-β2 signals. Published biophysics studies have experimentally established the kinetic rates of the individual ligand-receptor and receptor-receptor interactions that initiate heterotetrameric receptor complex assembly and signaling in the TGF-β system; however, current experimental approaches are not able to directly measure kinetic rates for the intermediate and latter steps of assembly. To characterize these steps in the TGF-β system and determine the mechanism of betaglycan in the potentiation of TGF-β2 signaling, we developed deterministic computational models with different modes of betaglycan binding and varying cooperativity between receptor subtypes. The models identified conditions for selective enhancement of TGF-β2 signaling. The models provide support for additional receptor binding cooperativity that has been hypothesized but not evaluated in the literature. The models further showed that betaglycan binding to the TGF-β2 ligand through two domains provides an effective mechanism for transfer to the signaling receptors that has been tuned to efficiently promote assembly of the TGF-β2(TβRII)2(TβRI)2 signaling complex.

Computational speed-up of large-scale, single-cell model simulations via a fully integrated SBML-based format

Summary

Large-scale and whole-cell modeling has multiple challenges, including scalable model building and module communication bottlenecks (e.g. between metabolism, gene expression, signaling, etc.). We previously developed an open-source, scalable format for a large-scale mechanistic model of proliferation and death signaling dynamics, but communication bottlenecks between gene expression and protein biochemistry modules remained. Here, we developed two solutions to communication bottlenecks that speed-up simulation by ∼4-fold for hybrid stochastic-deterministic simulations and by over 100-fold for fully deterministic simulations. Fully deterministic speed-up facilitates model initialization, parameter estimation and sensitivity analysis tasks.

Availability and implementation

Source code is freely available at https://github.com/birtwistlelab/SPARCED/releases/tag/v1.3.0 implemented in python, and supported on Linux, Windows and MacOS (via Docker).

MEMMAL: A tool for expanding large-scale mechanistic models with machine learned associations and big datasets

Computational models that can explain and predict complex sub-cellular, cellular, and tissue-level drug response mechanisms could speed drug discovery and prioritize patient-specific treatments (i.e., precision medicine). Some models are mechanistic with detailed equations describing known (or supposed) physicochemical processes, while some are statistical or machine learning-based approaches, that explain datasets but have no mechanistic or causal guarantees. These two types of modeling are rarely combined, missing the opportunity to explore possibly causal but data-driven new knowledge while explaining what is already known. Here, we explore combining machine learned associations with mechanistic models to develop computational models that could more fully represent cellular behavior. In this proposed MEMMAL (MEchanistic Modeling with MAchine Learning) framework, machine learning/statistical models built using omics datasets provide predictions for new interactions between genes and proteins where there is physicochemical uncertainty. These interactions are used as a basis for new reactions in mechanistic models. As a test case, we focused on incorporating novel IFNγ/PD-L1 related associations into a large-scale mechanistic model for cell proliferation and death to better recapitulate the recently released NIH LINCS Consortium MCF10A dataset and enable description of the cellular response to checkpoint inhibitor immunotherapies. This work is a template for combining big-data-inferred interactions with mechanistic models, which could be more broadly applicable for building multi-scale precision medicine and whole cell models.

A biochemical necroptosis model explains cell-type-specific responses to cell death cues

Necroptosis is a form of regulated cell death associated with degenerative disorders, autoimmune and inflammatory diseases, and cancer. To better understand the biochemical mechanisms regulating necroptosis, we constructed a detailed computational model of tumor necrosis factor-induced necroptosis based on known molecular interactions from the literature. Intracellular protein levels, used as model inputs, were quantified using label-free mass spectrometry, and the model was calibrated using Bayesian parameter inference to experimental protein time course data from a well-established necroptosis-executing cell line. The calibrated model reproduced the dynamics of phosphorylated mixed lineage kinase domain-like protein, an established necroptosis reporter. A subsequent dynamical systems analysis identified four distinct modes of necroptosis signal execution, distinguished by rate constant values and the roles of the RIP1 deubiquitinating enzymes A20 and CYLD. In one case, A20 and CYLD both contribute to RIP1 deubiquitination, in another RIP1 deubiquitination is driven exclusively by CYLD, and in two modes either A20 or CYLD acts as the driver with the other enzyme, counterintuitively, inhibiting necroptosis. We also performed sensitivity analyses of initial protein concentrations and rate constants to identify potential targets for modulating necroptosis sensitivity within each mode. We conclude by associating numerous contrasting and, in some cases, counterintuitive experimental results reported in the literature with one or more of the model-predicted modes of necroptosis execution. In all, we demonstrate that a consensus pathway model of tumor necrosis factor-induced necroptosis can provide insights into unresolved controversies regarding the molecular mechanisms driving necroptosis execution in numerous cell types under different experimental conditions.

Rule-based modelling of biological systems using regulated rewriting

In systems biology, models play a crucial role in understanding studied systems. There are many modelling approaches, among which rewriting systems provide a framework for describing systems on a mechanistic level. Describing biochemical processes often requires incorporating knowledge on an abstract level to simplify the system description or substitute the missing details. For this purpose, we present regulation mechanisms, an extension of this formalism with additional controls on the rewriting process. We introduce several regulation mechanisms and apply them to a rule-based language, a notation suitable for modelling biological phenomena. Finally, we demonstrate the usage of such regulations on several case studies from the biochemical domain.

Mechanistic model of MAPK signaling reveals how allostery and rewiring contribute to drug resistance

BRAF is prototypical of oncogenes that can be targeted therapeutically and the treatment of BRAF^V600E melanomas with RAF and MEK inhibitors results in rapid tumor regression. However, drug-induced rewiring generates a drug adapted state thought to be involved in acquired resistance and disease recurrence. In this article, we study mechanisms of adaptive rewiring in BRAF^V600E melanoma cells using an energy-based implementation of ordinary differential equation (ODE) modeling in combination with proteomic, transcriptomic and imaging data. We develop a method for causal tracing of ODE models and identify two parallel MAPK reaction channels that are differentially sensitive to RAF and MEK inhibitors due to differences in protein oligomerization and drug binding. We describe how these channels, and timescale separation between immediate-early signaling and transcriptional feedback, create a state in which the RAS-regulated MAPK channel can be activated by growth factors under conditions in which the BRAF^V600E -driven channel is fully inhibited. Further development of the approaches in this article is expected to yield a unified model of adaptive drug resistance in melanoma.

Targeted Quantification of Protein Phosphorylation and Its Contributions towards Mathematical Modeling of Signaling Pathways

Post-translational modifications (PTMs) are key regulatory mechanisms that can control protein function. Of these, phosphorylation is the most common and widely studied. Because of its importance in regulating cell signaling, precise and accurate measurements of protein phosphorylation across wide dynamic ranges are crucial to understanding how signaling pathways function. Although immunological assays are commonly used to detect phosphoproteins, their lack of sensitivity, specificity, and selectivity often make them unreliable for quantitative measurements of complex biological samples. Recent advances in Mass Spectrometry (MS)-based targeted proteomics have made it a more useful approach than immunoassays for studying the dynamics of protein phosphorylation. Selected reaction monitoring (SRM)-also known as multiple reaction monitoring (MRM)-and parallel reaction monitoring (PRM) can quantify relative and absolute abundances of protein phosphorylation in multiplexed fashions targeting specific pathways. In addition, the refinement of these tools by enrichment and fractionation strategies has improved measurement of phosphorylation of low-abundance proteins. The quantitative data generated are particularly useful for building and parameterizing mathematical models of complex phospho-signaling pathways. Potentially, these models can provide a framework for linking analytical measurements of clinical samples to better diagnosis and treatment of disease.

libRoadRunner 2.0: a high performance SBML simulation and analysis library

MOTIVATION

This article presents libRoadRunner 2.0, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models expressed using the systems biology markup language (SBML).

RESULTS

libRoadRunner is a self-contained library, able to run either as a component inside other tools via its C++, C and Python APIs, or interactively through its Python or Julia interface. libRoadRunner uses a custom just-in-time (JIT) compiler built on the widely used LLVM JIT compiler framework. It compiles SBML-specified models directly into native machine code for a large variety of processors, making it fast enough to simulate extremely large models or repeated runs in reasonable timeframes. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and non-linear algebraic equations) as well as several SBML extensions such as hierarchical composition and probability distributions. It offers multiple deterministic and stochastic integrators, as well as tools for steady-state, sensitivity, stability and structural analyses.

AVAILABILITY AND IMPLEMENTATION

libRoadRunner binary distributions for Windows, Mac OS and Linux, Julia and Python bindings, source code and documentation are all available at https://github.com/sys-bio/roadrunner, and Python bindings are also available via pip. The source code can be compiled for the supported systems as well as in principle any system supported by LLVM-13, such as ARM-based computers like the Raspberry Pi. The library is licensed under the Apache License Version 2.0.

A Practical Guide for the Efficient Formulation and Calibration of Large, Energy- and Rule-Based Models of Cellular Signal Transduction

Aberrant signal transduction leads to complex diseases such as cancer. To rationally design treatment strategies with small molecule inhibitors, computational models have to be employed. Energy- and rule-based models allow the construction of mechanistic ordinary differential equation models based on structural insights. The detailed, energy-based description often generates large models, which are difficult to calibrate on experimental data. In this chapter, we provide a detailed, interactive protocol for the programmatic formulation and calibration of such large, energy- and rule-based models of cellular signal transduction based on an example model describing the action of RAF inhibitors on MAPK signaling. An interactive version of this chapter is available as Jupyter Notebook at github.com/FFroehlich/energy_modeling_chapter .

A Practical Guide to Reproducible Modeling for Biochemical Networks

While scientific disciplines revere reproducibility, many studies - experimental and computational alike - fall short of this ideal and cannot be reproduced or even repeated when the model is shared. For computational modeling of biochemical networks, there is a dearth of formal training and resources available describing how to practically implement reproducible methods, despite a wealth of existing tools and formats which could be used to support reproducibility. This chapter points the reader to useful software tools and standardized formats that support reproducible modeling of biochemical networks and provides suggestions on how to implement reproducible methods in practice. Many of the suggestions encourage readers to use best practices from the software development community in order to automate, test, and version control their model components. A Jupyter Notebook demonstrating several of the key steps in building a reproducible biochemical network model is included to supplement the recommendations in the text.

Microbench: automated metadata management for systems biology benchmarking and reproducibility in Python

MOTIVATION

Computational systems biology analyses typically make use of multiple software and their dependencies, which are often run across heterogeneous compute environments. This can introduce differences in performance and reproducibility. Capturing metadata (e.g. package versions, GPU model) currently requires repetitious code and is difficult to store centrally for analysis. Even where virtual environments and containers are used, updates over time mean that versioning metadata should still be captured within analysis pipelines to guarantee reproducibility.

RESULTS

Microbench is a simple and extensible Python package to automate metadata capture to a file or Redis database. Captured metadata can include execution time, software package versions, environment variables, hardware information, Python version and more, with plugins. We present three case studies demonstrating Microbench usage to benchmark code execution and examine environment metadata for reproducibility purposes.

AVAILABILITY AND IMPLEMENTATION

Install from the Python Package Index using pip install microbench. Source code is available from https://github.com/alubbock/microbench.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A physical wiring diagram for the human immune system

The human immune system is composed of a distributed network of cells circulating throughout the body, which must dynamically form physical associations and communicate using interactions between their cell-surface proteomes1. Despite their therapeutic potential2, our map of these surface interactions remains incomplete3,4. Here, using a high-throughput surface receptor screening method, we systematically mapped the direct protein interactions across a recombinant library that encompasses most of the surface proteins that are detectable on human leukocytes. We independently validated and determined the biophysical parameters of each novel interaction, resulting in a high-confidence and quantitative view of the receptor wiring that connects human immune cells. By integrating our interactome with expression data, we identified trends in the dynamics of immune interactions and constructed a reductionist mathematical model that predicts cellular connectivity from basic principles. We also developed an interactive multi-tissue single-cell atlas that infers immune interactions throughout the body, revealing potential functional contexts for new interactions and hubs in multicellular networks. Finally, we combined targeted protein stimulation of human leukocytes with multiplex high-content microscopy to link our receptor interactions to functional roles, in terms of both modulating immune responses and maintaining normal patterns of intercellular associations. Together, our work provides a systematic perspective on the intercellular wiring of the human immune system that extends from systems-level principles of immune cell connectivity down to mechanistic characterization of individual receptors, which could offer opportunities for therapeutic intervention.

A scalable, open-source implementation of a large-scale mechanistic model for single cell proliferation and death signaling

Mechanistic models of how single cells respond to different perturbations can help integrate disparate big data sets or predict response to varied drug combinations. However, the construction and simulation of such models have proved challenging. Here, we developed a python-based model creation and simulation pipeline that converts a few structured text files into an SBML standard and is high-performance- and cloud-computing ready. We applied this pipeline to our large-scale, mechanistic pan-cancer signaling model (named SPARCED) and demonstrate it by adding an IFNγ pathway submodel. We then investigated whether a putative crosstalk mechanism could be consistent with experimental observations from the LINCS MCF10A Data Cube that IFNγ acts as an anti-proliferative factor. The analyses suggested this observation can be explained by IFNγ-induced SOCS1 sequestering activated EGF receptors. This work forms a foundational recipe for increased mechanistic model-based data integration on a single-cell level, an important building block for clinically-predictive mechanistic models.

A semantics, energy-based approach to automate biomodel composition

Hierarchical modelling is essential to achieving complex, large-scale models. However, not all modelling schemes support hierarchical composition, and correctly mapping points of connection between models requires comprehensive knowledge of each model's components and assumptions. To address these challenges in integrating biosimulation models, we propose an approach to automatically and confidently compose biosimulation models. The approach uses bond graphs to combine aspects of physical and thermodynamics-based modelling with biological semantics. We improved on existing approaches by using semantic annotations to automate the recognition of common components. The approach is illustrated by coupling a model of the Ras-MAPK cascade to a model of the upstream activation of EGFR. Through this methodology, we aim to assist researchers and modellers in readily having access to more comprehensive biological systems models.

BioSANS: A software package for symbolic and numeric biological simulation

Modeling biochemical systems can provide insights into behaviors that are difficult to observe or understand. It requires software, programming, and understanding of the system to build a model and study it. Softwares exist for systems biology modeling, but most support only certain types of modeling tasks. Desirable features including ease in preparing input, symbolic or analytical computation, parameter estimation, graphical user interface, and systems biology markup language (SBML) support are not seen concurrently in one software package. In this study, we developed a python-based software that supports these features, with both deterministic and stochastic propagations. The software can be used by graphical user interface, command line, or as a python import. We also developed a semi-programmable and intuitively easy topology input method for the biochemical reactions. We tested the software with semantic and stochastic SBML test cases. Tests on symbolic solution and parameter estimation were also included. The software we developed is reliable, well performing, convenient to use, and compliant with most of the SBML tests. So far it is the only systems biology software that supports symbolic, deterministic, and stochastic modeling in one package that also features parameter estimation and SBML support. This work offers a comprehensive set of tools and allows for better availability and accessibility for studying kinetics and dynamics in biochemical systems.

BioCRNpyler: Compiling chemical reaction networks from biomolecular parts in diverse contexts

Biochemical interactions in systems and synthetic biology are often modeled with chemical reaction networks (CRNs). CRNs provide a principled modeling environment capable of expressing a huge range of biochemical processes. In this paper, we present a software toolbox, written in Python, that compiles high-level design specifications represented using a modular library of biochemical parts, mechanisms, and contexts to CRN implementations. This compilation process offers four advantages. First, the building of the actual CRN representation is automatic and outputs Systems Biology Markup Language (SBML) models compatible with numerous simulators. Second, a library of modular biochemical components allows for different architectures and implementations of biochemical circuits to be represented succinctly with design choices propagated throughout the underlying CRN automatically. This prevents the often occurring mismatch between high-level designs and model dynamics. Third, high-level design specification can be embedded into diverse biomolecular environments, such as cell-free extracts and in vivo milieus. Finally, our software toolbox has a parameter database, which allows users to rapidly prototype large models using very few parameters which can be customized later. By using BioCRNpyler, users ranging from expert modelers to novice script-writers can easily build, manage, and explore sophisticated biochemical models using diverse biochemical implementations, environments, and modeling assumptions.

This paper describes a new software package BioCRNpyler (pronounced “Biocompiler”) designed to support rapid development and exploration of mathematical models of biochemical networks and circuits by computational biologists, systems biologists, and synthetic biologists. BioCRNpyler allows its users to generate large complex models using very few lines of code in a way that is modular. To do this, BioCRNpyler uses a powerful new representation of biochemical circuits which defines their parts, underlying biochemical mechanisms, and chemical context independently. BioCRNpyler was developed as a Python scripting language designed to be accessible to beginning users as well as easily extendable and customizable for advanced users. Ultimately, we see Biocrnpyler being used to accelerate computer automated design of biochemical circuits and model driven hypothesis generation in biology.

Implementation of a practical Markov chain Monte Carlo sampling algorithm in PyBioNetFit

SUMMARY

Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable. Here, we present the implementation of a practical MCMC method in the open-source software package PyBioNetFit (PyBNF), which is designed to support parameterization of mathematical models for biological systems. The new MCMC method, am, incorporates an adaptive move proposal distribution. For warm starts, sampling can be initiated at a specified location in parameter space and with a multivariate Gaussian proposal distribution defined initially by a specified covariance matrix. Multiple chains can be generated in parallel using a computer cluster. We demonstrate that am can be used to successfully solve real-world Bayesian inference problems, including forecasting of new Coronavirus Disease 2019 case detection with Bayesian quantification of forecast uncertainty.

AVAILABILITY AND IMPLEMENTATION

PyBNF version 1.1.9, the first stable release with am, is available at PyPI and can be installed using the pip package-management system on platforms that have a working installation of Python 3. PyBNF relies on libRoadRunner and BioNetGen for simulations (e.g. numerical integration of ordinary differential equations defined in SBML or BNGL files) and Dask.Distributed for task scheduling on Linux computer clusters. The Python source code can be freely downloaded/cloned from GitHub and used and modified under terms of the BSD-3 license (https://github.com/lanl/pybnf). Online documentation covering installation/usage is available (https://pybnf.readthedocs.io/en/latest/). A tutorial video is available on YouTube (https://www.youtube.com/watch?v=2aRqpqFOiS4&t=63s).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Structure-function relationships of the disease-linked A218T oxytocin receptor variant

Various single nucleotide polymorphisms (SNPs) in the oxytocin receptor (OXTR) gene have been associated with behavioral traits, autism spectrum disorder (ASD) and other diseases. The non-synonymous SNP rs4686302 results in the OXTR variant A218T and has been linked to core characteristics of ASD, trait empathy and preterm birth. However, the molecular and intracellular mechanisms underlying those associations are still elusive. Here, we uncovered the molecular and intracellular consequences of this mutation that may affect the psychological or behavioral outcome of oxytocin (OXT)-treatment regimens in clinical studies, and provide a mechanistic explanation for an altered receptor function. We created two monoclonal HEK293 cell lines, stably expressing either the wild-type or A218T OXTR. We detected an increased OXTR protein stability, accompanied by a shift in Ca²⁺ dynamics and reduced MAPK pathway activation in the A218T cells. Combined whole-genome and RNA sequencing analyses in OXT-treated cells revealed 7823 differentially regulated genes in A218T compared to wild-type cells, including 429 genes being associated with ASD. Furthermore, computational modeling provided a molecular basis for the observed change in OXTR stability suggesting that the OXTR mutation affects downstream events by altering receptor activation and signaling, in agreement with our in vitro results. In summary, our study provides the cellular mechanism that links the OXTR rs4686302 SNP with genetic dysregulations associated with aspects of ASD.

Analysing and simulating energy-based models in biology using BondGraphTools

Like all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

Determinants of Ligand Specificity and Functional Plasticity in Type I Interferon Signaling

The Type I Interferon family of cytokines all act through the same cell surface receptor and induce phosphorylation of the same subset of response regulators of the STAT family. Despite their shared receptor, different Type I Interferons have different functions during immune response to infection. In particular, they differ in the potency of their induced anti-viral and anti-proliferative responses in target cells. It remains not fully understood how these functional differences can arise in a ligand-specific manner both at the level of STAT phosphorylation and the downstream function. We use a minimal computational model of Type I Interferon signaling, focusing on Interferon-α and Interferon-β. We validate the model with quantitative experimental data to identify the key determinants of specificity and functional plasticity in Type I Interferon signaling. We investigate different mechanisms of signal discrimination, and how multiple system components such as binding affinity, receptor expression levels and their variability, receptor internalization, short-term negative feedback by SOCS1 protein, and differential receptor expression play together to ensure ligand specificity on the level of STAT phosphorylation. Based on these results, we propose phenomenological functional mappings from STAT activation to downstream anti-viral and anti-proliferative activity to investigate differential signal processing steps downstream of STAT phosphorylation. We find that the negative feedback by the protein USP18, which enhances differences in signaling between Interferons via ligand-dependent refractoriness, can give rise to functional plasticity in Interferon-α and Interferon-β signaling, and explore other factors that control functional plasticity. Beyond Type I Interferon signaling, our results have a broad applicability to questions of signaling specificity and functional plasticity in signaling systems with multiple ligands acting through a bottleneck of a small number of shared receptors.

Heterodimer-heterotetramer formation mediates enhanced sensor activity in a biophysical model for BMP signaling

Numerous stages of organismal development rely on the cellular interpretation of gradients of secreted morphogens including members of the Bone Morphogenetic Protein (BMP) family through transmembrane receptors. Early gradients of BMPs drive dorsal/ventral patterning throughout the animal kingdom in both vertebrates and invertebrates. Growing evidence in Drosophila, zebrafish, murine and other systems suggests that BMP ligand heterodimers are the primary BMP signaling ligand, even in systems in which mixtures of BMP homodimers and heterodimers are present. Signaling by heterodimers occurs through a hetero-tetrameric receptor complex comprising of two distinct type one BMP receptors and two type II receptors. To understand the system dynamics and determine whether kinetic assembly of heterodimer-heterotetramer BMP complexes is favored, as compared to other plausible BMP ligand-receptor configurations, we developed a kinetic model for BMP tetramer formation based on current measurements for binding rates and affinities. We find that contrary to a common hypothesis, heterodimer-heterotetramer formation is not kinetically favored over the formation of homodimer-tetramer complexes under physiological conditions of receptor and ligand concentrations and therefore other mechanisms, potentially including differential kinase activities of the formed heterotetramer complexes, must be the cause of heterodimer-heterotetramer signaling primacy. Further, although BMP complex assembly favors homodimer and homomeric complex formation over a wide range of parameters, ignoring these signals and instead relying on the heterodimer improves the range of morphogen interpretation in a broad set of conditions, suggesting a performance advantage for heterodimer signaling in patterning multiple cell types in a gradient.

TGF-β signaling is an important cell signaling system through which cells respond to external information. In the TGF-β system, signaling is initiated when a ligand dimer pair binds to a receptor tetramer. Interestingly, in numerous developmental contexts, TGF-β signaling has a greater response to heterodimeric ligands (dimers of multiple ligands), as compared to homomeric ligands (dimers made of two molecules of a single ligand). However, neither the cause of heterodimer signaling primacy, nor the systemic effects of heterodimeric vs homomeric signaling are understood. We use a biophysically-informed computational modeling approach to investigate the system dynamics of heterodimer-heterotetramer BMP signaling, to understand the cause and consequence of the requirement for Bmp2/7-mediated signaling in dorsoventral patterning in zebrafish development. Using our model, we demonstrate that BMP heterodimer signaling complex formation is not kinetically favored over homodimer signaling complexes, suggesting subfunctionalization of BMP receptors may be required to explain heterodimer signaling. Additionally, we show that heterodimer signaling provides a performance advantage via increased range of morphogen interpretation. Our findings provide insight into the systems principles involved in developmental signaling.

Modular assembly of dynamic models in systems biology

It is widely acknowledged that the construction of large-scale dynamic models in systems biology requires complex modelling problems to be broken up into more manageable pieces. To this end, both modelling and software frameworks are required to enable modular modelling. While there has been consistent progress in the development of software tools to enhance model reusability, there has been a relative lack of consideration for how underlying biophysical principles can be applied to this space. Bond graphs combine the aspects of both modularity and physics-based modelling. In this paper, we argue that bond graphs are compatible with recent developments in modularity and abstraction in systems biology, and are thus a desirable framework for constructing large-scale models. We use two examples to illustrate the utility of bond graphs in this context: a model of a mitogen-activated protein kinase (MAPK) cascade to illustrate the reusability of modules and a model of glycolysis to illustrate the ability to modify the model granularity.

Programmatic modeling for biological systems

Computational modeling has become an established technique to encode mathematical representations of cellular processes and gain mechanistic insights that drive testable predictions. These models are often constructed using graphical user interfaces or domain-specific languages, with community standards used for interchange. Models undergo steady state or dynamic analysis, which can include simulation and calibration within a single application, or transfer across various tools. Here, we describe a novel programmatic modeling paradigm, whereby modeling is augmented with software engineering best practices. We focus on Python - a popular programming language with a large scientific package ecosystem. Models can be encoded as programs, adding benefits such as modularity, testing, and automated documentation generators, while still being extensible and exportable to standardized formats for use with external tools if desired. Programmatic modeling is a key technology to enable collaborative model development and enhance dissemination, transparency, and reproducibility.

FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks

Mathematical models of biochemical networks can largely facilitate the comprehension of the mechanisms at the basis of cellular processes, as well as the formulation of hypotheses that can be tested by means of targeted laboratory experiments. However, two issues might hamper the achievement of fruitful outcomes. On the one hand, detailed mechanistic models can involve hundreds or thousands of molecular species and their intermediate complexes, as well as hundreds or thousands of chemical reactions, a situation generally occurring in rule-based modeling. On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration, or to test the effect of perturbations. As a consequence, the computational capabilities of modern Central Processing Units can be easily overtaken, possibly making the modeling of biochemical networks a worthless or ineffective effort. To the aim of overcoming the limitations of the current state-of-the-art simulation approaches, we present in this paper FiCoS, a novel "black-box" deterministic simulator that effectively realizes both a fine-grained and a coarse-grained parallelization on Graphics Processing Units. In particular, FiCoS exploits two different integration methods, namely, the Dormand-Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations. We tested the performance of FiCoS against different deterministic simulators, by considering models of increasing size and by running analyses with increasing computational demands. FiCoS was able to dramatically speedup the computations up to 855×, showing to be a promising solution for the simulation and analysis of large-scale models of complex biological processes.

BiPSim: a flexible and generic stochastic simulator for polymerization processes

Detailed whole-cell modeling requires an integration of heterogeneous cell processes having different modeling formalisms, for which whole-cell simulation could remain tractable. Here, we introduce BiPSim, an open-source stochastic simulator of template-based polymerization processes, such as replication, transcription and translation. BiPSim combines an efficient abstract representation of reactions and a constant-time implementation of the Gillespie’s Stochastic Simulation Algorithm (SSA) with respect to reactions, which makes it highly efficient to simulate large-scale polymerization processes stochastically. Moreover, multi-level descriptions of polymerization processes can be handled simultaneously, allowing the user to tune a trade-off between simulation speed and model granularity. We evaluated the performance of BiPSim by simulating genome-wide gene expression in bacteria for multiple levels of granularity. Finally, since no cell-type specific information is hard-coded in the simulator, models can easily be adapted to other organismal species. We expect that BiPSim should open new perspectives for the genome-wide simulation of stochastic phenomena in biology.

Characteristics of mathematical modeling languages that facilitate model reuse in systems biology: a software engineering perspective

Reuse of mathematical models becomes increasingly important in systems biology as research moves toward large, multi-scale models composed of heterogeneous subcomponents. Currently, many models are not easily reusable due to inflexible or confusing code, inappropriate languages, or insufficient documentation. Best practice suggestions rarely cover such low-level design aspects. This gap could be filled by software engineering, which addresses those same issues for software reuse. We show that languages can facilitate reusability by being modular, human-readable, hybrid (i.e., supporting multiple formalisms), open, declarative, and by supporting the graphical representation of models. Modelers should not only use such a language, but be aware of the features that make it desirable and know how to apply them effectively. For this reason, we compare existing suitable languages in detail and demonstrate their benefits for a modular model of the human cardiac conduction system written in Modelica.

Inhibition of RPS6K reveals context-dependent Akt activity in luminal breast cancer cells

Aberrant signaling through insulin (Ins) and insulin-like growth factor I (IGF1) receptors contribute to the risk and advancement of many cancer types by activating cell survival cascades. Similarities between these pathways have thus far prevented the development of pharmacological interventions that specifically target either Ins or IGF1 signaling. To identify differences in early Ins and IGF1 signaling mechanisms, we developed a dual receptor (IGF1R & InsR) computational response model. The model suggested that ribosomal protein S6 kinase (RPS6K) plays a critical role in regulating MAPK and Akt activation levels in response to Ins and IGF1 stimulation. As predicted, perturbing RPS6K kinase activity led to an increased Akt activation with Ins stimulation compared to IGF1 stimulation. Being able to discern differential downstream signaling, we can explore improved anti-IGF1R cancer therapies by eliminating the emergence of compensation mechanisms without disrupting InsR signaling.

An in vitro model of tumor heterogeneity resolves genetic, epigenetic, and stochastic sources of cell state variability

Tumor heterogeneity is a primary cause of treatment failure and acquired resistance in cancer patients. Even in cancers driven by a single mutated oncogene, variability in response to targeted therapies is well known. The existence of additional genomic alterations among tumor cells can only partially explain this variability. As such, nongenetic factors are increasingly seen as critical contributors to tumor relapse and acquired resistance in cancer. Here, we show that both genetic and nongenetic factors contribute to targeted drug response variability in an experimental model of tumor heterogeneity. We observe significant variability to epidermal growth factor receptor (EGFR) inhibition among and within multiple versions and clonal sublines of PC9, a commonly used EGFR mutant nonsmall cell lung cancer (NSCLC) cell line. We resolve genetic, epigenetic, and stochastic components of this variability using a theoretical framework in which distinct genetic states give rise to multiple epigenetic "basins of attraction," across which cells can transition driven by stochastic noise. Using mutational impact analysis, single-cell differential gene expression, and correlations among Gene Ontology (GO) terms to connect genomics to transcriptomics, we establish a baseline for genetic differences driving drug response variability among PC9 cell line versions. Applying the same approach to clonal sublines, we conclude that drug response variability in all but one of the sublines is due to epigenetic differences; in the other, it is due to genetic alterations. Finally, using a clonal drug response assay together with stochastic simulations, we attribute subclonal drug response variability within sublines to stochastic cell fate decisions and confirm that one subline likely contains genetic resistance mutations that emerged in the absence of drug treatment.

Computational methods for characterizing and learning from heterogeneous cell signaling data

Heterogeneity in cell signaling pathways is increasingly appreciated as a fundamental feature of cell biology and a driver of clinically relevant disease phenotypes. Understanding the causes of heterogeneity, the cellular mechanisms used to control heterogeneity, and the downstream effects of heterogeneity in single cells are all key obstacles for manipulating cellular populations and treating disease. Recent advances in genetic engineering, including multiplexed fluorescent reporters, have provided unprecedented measurements of signaling heterogeneity, but these vast data sets are often difficult to interpret, necessitating the use of computational techniques to extract meaning from the data. Here, we review recent advances in computational methods for extracting meaning from these novel data streams. In particular, we evaluate how machine learning methods related to dimensionality reduction and classification can identify structure in complex, dynamic datasets, simplifying interpretation. We also discuss how mechanistic models can be merged with heterogeneous data to understand the underlying differences between cells in a population. These methods are still being developed, but the work reviewed here offers useful applications of specific analysis techniques that could enable the translation of single-cell signaling data to actionable biological understanding.

Constructing and analysing dynamic models with modelbase v1.2.3: a software update

BACKGROUND

Computational mathematical models of biological and biomedical systems have been successfully applied to advance our understanding of various regulatory processes, metabolic fluxes, effects of drug therapies, and disease evolution and transmission. Unfortunately, despite community efforts leading to the development of SBML and the BioModels database, many published models have not been fully exploited, largely due to a lack of proper documentation or the dependence on proprietary software. To facilitate the reuse and further development of systems biology and systems medicine models, an open-source toolbox that makes the overall process of model construction more consistent, understandable, transparent, and reproducible is desired.

RESULTS AND DISCUSSION

We provide an update on the development of modelbase, a free, expandable Python package for constructing and analysing ordinary differential equation-based mathematical models of dynamic systems. It provides intuitive and unified methods to construct and solve these systems. Significantly expanded visualisation methods allow for convenient analysis of the structural and dynamic properties of models. After specifying reaction stoichiometries and rate equations modelbase can automatically assemble the associated system of differential equations. A newly provided library of common kinetic rate laws reduces the repetitiveness of the computer programming code. modelbase is also fully compatible with SBML. Previous versions provided functions for the automatic construction of networks for isotope labelling studies. Now, using user-provided label maps, modelbase v1.2.3 streamlines the expansion of classic models to their isotope-specific versions. Finally, the library of previously published models implemented in modelbase is growing continuously. Ranging from photosynthesis to tumour cell growth to viral infection evolution, all these models are now available in a transparent, reusable and unified format through modelbase.

CONCLUSION

With this new Python software package, which is written in currently one of the most popular programming languages, the user can develop new models and actively profit from the work of others. modelbase enables reproducing and replicating models in a consistent, tractable and expandable manner. Moreover, the expansion of models to their isotopic label-specific versions enables simulating label propagation, thus providing quantitative information regarding network topology and metabolic fluxes.

AMICI: High-Performance Sensitivity Analysis for Large Ordinary Differential Equation Models

Summary

Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be limiting. AMICI is a modular toolbox implemented in C++/Python/MATLAB that provides efficient simulation and sensitivity analysis routines tailored for scalable, gradient-based parameter estimation and uncertainty quantification.

Availabilityand implementation

AMICI is published under the permissive BSD-3-Clause license with source code publicly available on https://github.com/AMICI-dev/AMICI. Citeable releases are archived on Zenodo.

Supplementary information

Supplementary data are available at Bioinformatics online.

Atlas: automatic modeling of regulation of bacterial gene expression and metabolism using rule-based languages

MOTIVATION

Cells are complex systems composed of hundreds of genes whose products interact to produce elaborated behaviors. To control such behaviors, cells rely on transcription factors to regulate gene expression, and gene regulatory networks (GRNs) are employed to describe and understand such behavior. However, GRNs are static models, and dynamic models are difficult to obtain due to their size, complexity, stochastic dynamics and interactions with other cell processes.

RESULTS

We developed Atlas, a Python software that converts genome graphs and gene regulatory, interaction and metabolic networks into dynamic models. The software employs these biological networks to write rule-based models for the PySB framework. The underlying method is a divide-and-conquer strategy to obtain sub-models and combine them later into an ensemble model. To exemplify the utility of Atlas, we used networks of varying size and complexity of Escherichia coli and evaluated in silico modifications, such as gene knockouts and the insertion of promoters and terminators. Moreover, the methodology could be applied to the dynamic modeling of natural and synthetic networks of any bacteria.

AVAILABILITY AND IMPLEMENTATION

Code, models and tutorials are available online (https://github.com/networkbiolab/atlas).

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.