Virtual Cell modelling and simulation software environment

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.

SGABU computational platform for multiscale modeling: Bridging the gap between education and research

BACKGROUND AND OBJECTIVE

In accordance with the latest aspirations in the field of bioengineering, there is a need to create a web accessible, but powerful cloud computational platform that combines datasets and multiscale models related to bone modeling, cancer, cardiovascular diseases and tissue engineering. The SGABU platform may become a powerful information system for research and education that can integrate data, extract information, and facilitate knowledge exchange with the goal of creating and developing appropriate computing pipelines to provide accurate and comprehensive biological information from the molecular to organ level.

METHODS

The datasets integrated into the platform are obtained from experimental and/or clinical studies and are mainly in tabular or image file format, including metadata. The implementation of multiscale models, is an ambitious effort of the platform to capture phenomena at different length scales, described using partial and ordinary differential equations, which are solved numerically on complex geometries with the use of the finite element method. The majority of the SGABU platform's simulation pipelines are provided as Common Workflow Language (CWL) workflows. Each of them requires creating a CWL implementation on the backend and a user-friendly interface using standard web technologies. Platform is available at https://sgabu-test.unic.kg.ac.rs/login.

RESULTS

The main dashboard of the SGABU platform is divided into sections for each field of research, each one of which includes a subsection of datasets and multiscale models. The datasets can be presented in a simple form as tabular data, or using technologies such as Plotly.js for 2D plot interactivity, Kitware Paraview Glance for 3D view. Regarding the models, the usage of Docker containerization for packing the individual tools and CWL orchestration for describing inputs with validation forms and outputs with tabular views for output visualization, interactive diagrams, 3D views and animations.

CONCLUSIONS

In practice, the structure of SGABU platform means that any of the integrated workflows can work equally well on any other bioengineering platform. The key advantage of the SGABU platform over similar efforts is its versatility offered with the use of modern, modular, and extensible technology for various levels of architecture.

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.

MakeSBML: A tool for converting between Antimony and SBML

We describe a web-based tool, MakeSBML (https://sys-bio.github.io/makesbml/), that provides an installation-free application for creating, editing, and searching the Biomodels repository for SBML-based models. MakeSBML is a client-based web application that translates models expressed in human-readable Antimony to the System Biology Markup Language (SBML) and vice-versa. Since MakeSBML is a web-based application it requires no installation on the user's part. Currently, MakeSBML is hosted on a GitHub page where the client-based design makes it trivial to move to other hosts. This model for software deployment also reduces maintenance costs since an active server is not required. The SBML modeling language is often used in systems biology research to describe complex biochemical networks and makes reproducing models much easier. However, SBML is designed to be computer-readable, not human-readable. We therefore employ the human-readable Antimony language to make it easy to create and edit SBML models.

Reproducibility and FAIR principles: the case of a segment polarity network model

The issue of reproducibility of computational models and the related FAIR principles (findable, accessible, interoperable, and reusable) are examined in a specific test case. I analyze a computational model of the segment polarity network in Drosophila embryos published in 2000. Despite the high number of citations to this publication, 23 years later the model is barely accessible, and consequently not interoperable. Following the text of the original publication allowed successfully encoding the model for the open source software COPASI. Subsequently saving the model in the SBML format allowed it to be reused in other open source software packages. Submission of this SBML encoding of the model to the BioModels database enables its findability and accessibility. This demonstrates how the FAIR principles can be successfully enabled by using open source software, widely adopted standards, and public repositories, facilitating reproducibility and reuse of computational cell biology models that will outlive the specific software used.

Dynamic model assuming mutually inhibitory biomarkers of frailty suggests bistability with contrasting mobility phenotypes

Bistability is a fundamental biological phenomenon associated with "switch-like" behavior reflecting the capacity of a system to exist in either of two stable states. It plays a role in gene regulation, cell fate switch, signal transduction and cell oscillation, with relevance for cognition, hearing, vision, sleep, gait and voiding. Here we consider a potential role for bistability in the existence of specific frailty states or phenotypes as part of disablement pathways. We use mathematical modeling with two frailty biomarkers (insulin growth factor-1, IGF-1 and interleukin-6, IL-6), which mutually inhibit each other. In our model, we demonstrate that small variations around critical IGF-1 or IL-6 blood levels lead to strikingly different mobility outcomes. We employ deterministic modeling of mobility outcomes, calculating the average trends in population health. Our model predicts the bistability of clinical outcomes: the deterministically-computed likelihood of an individual remaining mobile, becoming less mobile, or dying over time either increases to almost 100% or decreases to almost zero. Contrary to statistical models that attempt to estimate the likelihood of final outcomes based on probabilities and correlations, our model predicts functional outcomes over time based on specific hypothesized molecular mechanisms. Instead of estimating probabilities based on stochastic distributions and arbitrary priors, we deterministically simulate model outcomes over a wide range of physiological parameter values within experimentally derived boundaries. Our study is "a proof of principle" as it is based on a major assumption about mutual inhibition of pathways that is oversimplified. However, by making such an assumption, interesting effects can be described qualitatively. As our understanding of molecular mechanisms involved in aging deepens, we believe that such modeling will not only lead to more accurate predictions, but also help move the field from using mostly studies of associations to mechanistically guided approaches.

Mechanisms underlying divergent relationships between Ca2+ and YAP/TAZ signalling

Yes-associated protein (YAP) and its homologue TAZ are transducers of several biochemical and biomechanical signals, integrating multiplexed inputs from the microenvironment into higher level cellular functions such as proliferation, differentiation and migration. Emerging evidence suggests that Ca2+ is a key second messenger that connects microenvironmental input signals and YAP/TAZ regulation. However, studies that directly modulate Ca2+ have reported contradictory YAP/TAZ responses: in some studies, a reduction in Ca2+ influx increases the activity of YAP/TAZ, while in others, an increase in Ca2+ influx activates YAP/TAZ. Importantly, Ca2+ and YAP/TAZ exhibit distinct spatiotemporal dynamics, making it difficult to unravel their connections from a purely experimental approach. In this study, we developed a network model of Ca2+ -mediated YAP/TAZ signalling to investigate how temporal dynamics and crosstalk of signalling pathways interacting with Ca2+ can alter the YAP/TAZ response, as observed in experiments. By including six signalling modules (e.g. GPCR, IP3-Ca2+ , kinases, RhoA, F-actin and Hippo-YAP/TAZ) that interact with Ca2+ , we investigated both transient and steady-state cell response to angiotensin II and thapsigargin stimuli. The model predicts that stimuli, Ca2+ transients and frequency-dependent relationships between Ca2+ and YAP/TAZ are primarily mediated by cPKC, DAG, CaMKII and F-actin. Simulation results illustrate the role of Ca2+ dynamics and CaMKII bistable response in switching the direction of changes in Ca2+ -induced YAP/TAZ activity. A frequency-dependent YAP/TAZ response revealed the competition between upstream regulators of LATS1/2, leading to the YAP/TAZ non-monotonic response to periodic GPCR stimulation. This study provides new insights into underlying mechanisms responsible for the controversial Ca2+ -YAP/TAZ relationship observed in experiments. KEY POINTS: YAP/TAZ integrates biochemical and biomechanical inputs to regulate cellular functions, and Ca2+ acts as a key second messenger linking cellular inputs to YAP/TAZ. Studies have reported contradictory Ca2+ -YAP/TAZ relationships for different cell types and stimuli. A network model of Ca2+ -mediated YAP/TAZ signalling was developed to investigate the underlying mechanisms of divergent Ca2+ -YAP/TAZ relationships. The model predicts context-dependent Ca2+ transient, CaMKII bistable response and frequency-dependent activation of LATS1/2 upstream regulators as mechanisms governing the Ca2+ -YAP/TAZ relationship. This study provides new insights into the underlying mechanisms of the controversial Ca2+ -YAP/TAZ relationship to better understand the dynamics of cellular functions controlled by YAP/TAZ activity.

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.

Integrative modeling of the cell

A whole-cell model represents certain aspects of the cell structure and/or function. Due to the high complexity of the cell, an integrative modeling approach is often taken to utilize all available information including experimental data, prior knowledge and prior models. In this review, we summarize an emerging workflow of whole-cell modeling into five steps: (i) gather information; (ii) represent the modeled system into modules; (iii) translate input information into scoring function; (iv) sample the whole-cell model; (v) validate and interpret the model. In particular, we propose the integrative modeling of the cell by combining available (whole-cell) models to maximize the accuracy, precision, and completeness. In addition, we list quantitative predictions of various aspects of cell biology from existing whole-cell models. Moreover, we discuss the remaining challenges and future directions, and highlight the opportunity to establish an integrative spatiotemporal multi-scale whole-cell model based on a community approach.

Computational framework for single-cell spatiotemporal dynamics of optogenetic membrane recruitment

We describe a modular computational framework for analyzing cell-wide spatiotemporal signaling dynamics in single-cell microscopy experiments that accounts for the experiment-specific geometric and diffractive complexities that arise from heterogeneous cell morphologies and optical instrumentation. Inputs are unique cell geometries and protein concentrations derived from confocal stacks and spatiotemporally varying environmental stimuli. After simulating the system with a model of choice, the output is convolved with the microscope point-spread function for direct comparison with the observable image. We experimentally validate this approach in single cells with BcLOV4, an optogenetic membrane recruitment system for versatile control over cell signaling, using a three-dimensional non-linear finite element model with all parameters experimentally derived. The simulations recapitulate observed subcellular and cell-to-cell variability in BcLOV4 signaling, allowing for inter-experimental differences of cellular and instrumentation origins to be elucidated and resolved for improved interpretive robustness. This single-cell approach will enhance optogenetics and spatiotemporally resolved signaling studies.

Engineering cell-based microstructures to study the effect of structural complexity on in vitro bioaccessibility of a lipophilic bioactive compound

A fundamental understanding of the influence of food microstructures on the bioaccessibility of micronutrients is vital for the design of functionally efficient foods. This study investigated the effect of microstructural features of model foods on the bioaccessibility of a bioactive compound - curcumin, using a unique bottom-up approach. In this approach, individual yeast cells with infused curcumin were coated with oppositely charged polyelectrolytes: first in poly(diallyl-dimethylammonium chloride), then in dextran sulfate or alginate, and assembled electrostatically to generate two types of cell clusters. These cell clusters were embedded in an alginate film to form a tissue-like structure. The influence of cell clustering and extracellular matrix on the release of encapsulated curcumin from cell-based microcarriers during simulated digestion was evaluated. Cell clusters that maintained their integrity during in vitro simulated digestion retained up to twice as much curcumin upon addition of the simulated intestinal fluid (SIF) compared to single cells during the first hour of intestinal digestion. Despite significant differences in the release profile, no spatial heterogeneity of curcumin release across a cell cluster was observed with the imaging measurements. Embedding single cells or cell clusters in calcium-crosslinked alginate films resulted in another 20-30% increase in curcumin retention and a prolonged barrier effect for more than 2 hours compared to microstructures without the films. This bottom-up approach of engineering cell-based tissue-like structures proves to be an effective method for investigating the contributions of microstructural properties of food matrices to influencing bioaccessibility of bioactives and guides future development of functional food materials.

The Role of in silico Research in Developing Nanoparticle-Based Therapeutics

Nanoparticles (NPs) hold great potential as therapeutics, particularly in the realm of drug delivery. They are effective at functional cargo delivery and offer a great degree of amenability that can be used to offset toxic side effects or to target drugs to specific regions in the body. However, there are many challenges associated with the development of NP-based drug formulations that hamper their successful clinical translation. Arguably, the most significant barrier in the way of efficacious NP-based drug delivery systems is the tedious and time-consuming nature of NP formulation—a process that needs to account for downstream effects, such as the onset of potential toxicity or immunogenicity, in vivo biodistribution and overall pharmacokinetic profiles, all while maintaining desirable therapeutic outcomes. Computational and AI-based approaches have shown promise in alleviating some of these restrictions. Via predictive modeling and deep learning, in silico approaches have shown the ability to accurately model NP-membrane interactions and cellular uptake based on minimal data, such as the physicochemical characteristics of a given NP. More importantly, machine learning allows computational models to predict how specific changes could be made to the physicochemical characteristics of a NP to improve functional aspects, such as drug retention or endocytosis. On a larger scale, they are also able to predict the in vivo pharmacokinetics of NP-encapsulated drugs, predicting aspects such as circulatory half-life, toxicity, and biodistribution. However, the convergence of nanomedicine and computational approaches is still in its infancy and limited in its applicability. The interactions between NPs, the encapsulated drug and the body form an intricate network of interactions that cannot be modeled with absolute certainty. Despite this, rapid advancements in the area promise to deliver increasingly powerful tools capable of accelerating the development of advanced nanoscale therapeutics. Here, we describe computational approaches that have been utilized in the field of nanomedicine, focusing on approaches for NP design and engineering.

Capturing Biomarkers and Molecular Targets in Cellular Landscapes From Dynamic Reaction Network Models and Machine Learning

Computational dynamic ODE models of cell function describing biochemical reactions have been created for decades, but on a small scale. Still, they have been highly effective in describing and predicting behaviors. For example, oscillatory phospho-ERK levels were predicted and confirmed in MAPK signaling encompassing both positive and negative feedback loops. These models typically were limited and not adapted to large datasets so commonly found today. But importantly, ODE models describe reaction networks in well-mixed systems representing the cell and can be simulated with ordinary differential equations that are solved deterministically. Stochastic solutions, which can account for noisy reaction networks, in some cases, also improve predictions. Today, dynamic ODE models rarely encompass an entire cell even though it might be expected that an upload of the large genomic, transcriptomic, and proteomic datasets may allow whole cell models. It is proposed here to combine output from simulated dynamic ODE models, completed with omics data, to discover both biomarkers in cancer a priori and molecular targets in the Machine Learning setting.

SMGen: A Generator of Synthetic Models of Biochemical Reaction Networks

Several software tools for the simulation and analysis of biochemical reaction networks have been developed in the last decades; however, assessing and comparing their computational performance in executing the typical tasks of computational systems biology can be limited by the lack of a standardized benchmarking approach. To overcome these limitations, we propose here a novel tool, named SMGen, designed to automatically generate synthetic models of reaction networks that, by construction, are characterized by relevant features (e.g., system connectivity and reaction discreteness) and non-trivial emergent dynamics of real biochemical networks. The generation of synthetic models in SMGen is based on the definition of an undirected graph consisting of a single connected component that, generally, results in a computationally demanding task; to speed up the overall process, SMGen exploits a main–worker paradigm. SMGen is also provided with a user-friendly graphical user interface, which allows the user to easily set up all the parameters required to generate a set of synthetic models with any number of reactions and species. We analysed the computational performance of SMGen by generating batches of symmetric and asymmetric reaction-based models (RBMs) of increasing size, showing how a different number of reactions and/or species affects the generation time. Our results show that when the number of reactions is higher than the number of species, SMGen has to identify and correct a large number of errors during the creation process of the RBMs, a circumstance that increases the running time. Still, SMGen can generate synthetic models with hundreds of species and reactions in less than 7 s.

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.

Systems Biology is an interdisciplinary research area focusing on the integration of biological data with mathematical and computational methods in order to unravel and predict the emergent behavior of complex biological systems. The ultimate goal is the understanding of the complex mechanisms at the basis of biological processes, together with the formulation of novel hypotheses that can be then tested by means of laboratory experiments. In such a context, mechanistic models can be used to describe and investigate biochemical reaction networks by taking into account all the details related to their stoichiometry and kinetics. Unfortunately, these models can be characterized by hundreds or thousands of molecular species and biochemical reactions, making their simulation unfeasible with classic simulators running on Central Processing Units (CPUs). In addition, a large number of simulations might be required to calibrate the models and/or to test the effect of perturbations. In order to overcome the limitations imposed by CPUs, Graphics Processing Units (GPUs) can be effectively used to accelerate the simulations of these models. We thus designed and developed a novel GPU-based tool, called FiCoS, to speed-up the computational analyses typically required in Systems Biology.

Bayesian metamodeling of complex biological systems across varying representations

Comprehensive modeling of a whole cell requires an integration of vast amounts of information on various aspects of the cell and its parts. To divide and conquer this task, we introduce Bayesian metamodeling, a general approach to modeling complex systems by integrating a collection of heterogeneous input models. Each input model can in principle be based on any type of data and can describe a different aspect of the modeled system using any mathematical representation, scale, and level of granularity. These input models are 1) converted to a standardized statistical representation relying on probabilistic graphical models, 2) coupled by modeling their mutual relations with the physical world, and 3) finally harmonized with respect to each other. To illustrate Bayesian metamodeling, we provide a proof-of-principle metamodel of glucose-stimulated insulin secretion by human pancreatic β-cells. The input models include a coarse-grained spatiotemporal simulation of insulin vesicle trafficking, docking, and exocytosis; a molecular network model of glucose-stimulated insulin secretion signaling; a network model of insulin metabolism; a structural model of glucagon-like peptide-1 receptor activation; a linear model of a pancreatic cell population; and ordinary differential equations for systemic postprandial insulin response. Metamodeling benefits from decentralized computing, while often producing a more accurate, precise, and complete model that contextualizes input models as well as resolves conflicting information. We anticipate Bayesian metamodeling will facilitate collaborative science by providing a framework for sharing expertise, resources, data, and models, as exemplified by the Pancreatic β-Cell Consortium.

Toward Full-Stack In Silico Synthetic Biology: Integrating Model Specification, Simulation, Verification, and Biological Compilation

We present the Infobiotics Workbench (IBW), a user-friendly, scalable, and integrated computational environment for the computer-aided design of synthetic biological systems. It supports an iterative workflow that begins with specification of the desired synthetic system, followed by simulation and verification of the system in high-performance environments and ending with the eventual compilation of the system specification into suitable genetic constructs. IBW integrates modeling, simulation, verification, and biocompilation features into a single software suite. This integration is achieved through a new domain-specific biological programming language, the Infobiotics Language (IBL), which tightly combines these different aspects of in silico synthetic biology into a full-stack integrated development environment. Unlike existing synthetic biology modeling or specification languages, IBL uniquely blends modeling, verification, and biocompilation statements into a single file. This allows biologists to incorporate design constraints within the specification file rather than using decoupled and independent formalisms for different in silico analyses. This novel approach offers seamless interoperability across different tools as well as compatibility with SBOL and SBML frameworks and removes the burden of doing manual translations for standalone applications. We demonstrate the features, usability, and effectiveness of IBW and IBL using well-established synthetic biological circuits.

Occurrence of Calcium Oscillations in Human Spermatozoa Is Based on Spatial Signaling Enzymes Distribution

In human spermatozoa, calcium dynamics control most of fertilization events. Progesterone, present in the female reproductive system, can trigger several types of calcium responses, such as low-frequency oscillations. Here we aimed to identify the mechanisms of progesterone-induced calcium signaling in human spermatozoa. Progesterone-induced activation of fluorophore-loaded spermatozoa was studied by fluorescent microscopy. Two computational models were developed to describe the spermatozoa calcium responses: a homogeneous one based on a system of ordinary differential equations and a three-dimensional one with added space dimensions and diffusion for the cytosolic species. In response to progesterone, three types of calcium responses were observed in human spermatozoa: a single transient rise of calcium concentration in cytosol, a steady elevation, or low-frequency oscillations. The homogenous model provided qualitative description of the oscillatory and the single spike responses, while the three-dimensional model captured the calcium peak shape and the frequency of calcium oscillations. The model analysis demonstrated that an increase in the calcium diffusion coefficient resulted in the disappearance of the calcium oscillations. Additionally, in silico analysis suggested that the spatial distribution of calcium signaling enzymes governs the appearance of calcium oscillations in progesterone-activated human spermatozoa.

RunBioSimulations: an extensible web application that simulates a wide range of computational modeling frameworks, algorithms, and formats

Comprehensive, predictive computational models have significant potential for science, bioengineering, and medicine. One promising way to achieve more predictive models is to combine submodels of multiple subsystems. To capture the multiple scales of biology, these submodels will likely require multiple modeling frameworks and simulation algorithms. Several community resources are already available for working with many of these frameworks and algorithms. However, the variety and sheer number of these resources make it challenging to find and use appropriate tools for each model, especially for novice modelers and experimentalists. To make these resources easier to use, we developed RunBioSimulations (https://run.biosimulations.org), a single web application for executing a broad range of models. RunBioSimulations leverages community resources, including BioSimulators, a new open registry of simulation tools. These resources currently enable RunBioSimulations to execute nine frameworks and 44 algorithms, and they make RunBioSimulations extensible to additional frameworks and algorithms. RunBioSimulations also provides features for sharing simulations and interactively visualizing their results. We anticipate that RunBioSimulations will foster reproducibility, stimulate collaboration, and ultimately facilitate the creation of more predictive models.

Nanoscape, a data-driven 3D real-time interactive virtual cell environment

Our understanding of cellular and structural biology has reached unprecedented levels of detail, and computer visualisation techniques can be used to create three-dimensional (3D) representations of cells and their environment that are useful in both teaching and research. However, extracting and integrating the relevant scientific data, and then presenting them in an effective way, can pose substantial computational and aesthetic challenges. Here we report how computer artists, experts in computer graphics and cell biologists have collaborated to produce a tool called Nanoscape that allows users to explore and interact with 3D representations of cells and their environment that are both scientifically accurate and visually appealing. We believe that using Nanoscape as an immersive learning application will lead to an improved understanding of the complexities of cellular scales, densities and interactions compared with traditional learning modalities.

Parameter estimation in fluorescence recovery after photobleaching: quantitative analysis of protein binding reactions and diffusion

Fluorescence recovery after photobleaching (FRAP) is a common experimental method for investigating rates of molecular redistribution in biological systems. Many mathematical models of FRAP have been developed, the purpose of which is usually the estimation of certain biological parameters such as the diffusivity and chemical reaction rates of a protein, this being accomplished by fitting the model to experimental data. In this article, we consider a two species reaction–diffusion FRAP model. Using asymptotic analysis, we derive new FRAP recovery curve approximation formulae, and formally re-derive existing ones. On the basis of these formulae, invoking the concept of Fisher information, we predict, in terms of biological and experimental parameters, sufficient conditions to ensure that the values all model parameters can be estimated from data. We verify our predictions with extensive computational simulations. We also use computational methods to investigate cases in which some or all biological parameters are theoretically inestimable. In these cases, we propose methods which can be used to extract the maximum possible amount of information from the FRAP data.

A Sight on Single-Cell Transcriptomics in Plants Through the Prism of Cell-Based Computational Modeling Approaches: Benefits and Challenges for Data Analysis

Single-cell technology is a relatively new and promising way to obtain high-resolution transcriptomic data mostly used for animals during the last decade. However, several scientific groups developed and applied the protocols for some plant tissues. Together with deeply-developed cell-resolution imaging techniques, this achievement opens up new horizons for studying the complex mechanisms of plant tissue architecture formation. While the opportunities for integrating data from transcriptomic to morphogenetic levels in a unified system still present several difficulties, plant tissues have some additional peculiarities. One of the plants' features is that cell-to-cell communication topology through plasmodesmata forms during tissue growth and morphogenesis and results in mutual regulation of expression between neighboring cells affecting internal processes and cell domain development. Undoubtedly, we must take this fact into account when analyzing single-cell transcriptomic data. Cell-based computational modeling approaches successfully used in plant morphogenesis studies promise to be an efficient way to summarize such novel multiscale data. The inverse problem's solutions for these models computed on the real tissue templates can shed light on the restoration of individual cells' spatial localization in the initial plant organ-one of the most ambiguous and challenging stages in single-cell transcriptomic data analysis. This review summarizes new opportunities for advanced plant morphogenesis models, which become possible thanks to single-cell transcriptome data. Besides, we show the prospects of microscopy and cell-resolution imaging techniques to solve several spatial problems in single-cell transcriptomic data analysis and enhance the hybrid modeling framework opportunities.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Tools for time-course simulation in systems biology: a brief overview

Dynamic modeling of biological systems is essential for understanding all properties of a given organism as it allows us to look not only at the static picture of an organism but also at its behavior under various conditions. With the increasing amount of experimental data, the number of tools that enable dynamic analysis also grows. However, various tools are based on different approaches, use different types of data and offer different functions for analyses; so it can be difficult to choose the most suitable tool for a selected type of model. Here, we bring a brief overview containing descriptions of 50 tools for the reconstruction of biological models, their time-course simulation and dynamic analysis. We examined each tool using test data and divided them based on the qualitative and quantitative nature of the mathematical apparatus they use.

Modeling protein-protein interactions in axon initial segment to understand their potential impact on action potential initiation

The axon initial segment (AIS) region is crucial for action potential initiation due to the presence of high-density AIS protein voltage-gated sodium channels (Na_v). Na_v channels comprise several serine residues responsible for the recruitment of Na_v channels into the structure of AIS through interactions with ankyrin-G (AnkG). In this study, a series of computational experiments are performed to understand the role of AIS proteins casein kinase 2 and AnkG on Na_v channel recruitment into the AIS. The computational simulation results using Virtual cell software indicate that Na_v channels with all serine sites available for phosphorylation bind to AnkG with strong affinity. At the low initial concentration of AnkG and casein kinase 2, the concentration of Na_v channels reduces significantly, suggesting the importance of casein kinase 2 and AnkG in the recruitment of Na_v channels.

The tissue proteome in the multi-omic landscape of kidney disease

Kidney research is entering an era of 'big data' and molecular omics data can provide comprehensive insights into the molecular footprints of cells. In contrast to transcriptomics, proteomics and metabolomics generate data that relate more directly to the pathological symptoms and clinical parameters observed in patients. Owing to its complexity, the proteome still holds many secrets, but has great potential for the identification of drug targets. Proteomics can provide information about protein synthesis, modification and degradation, as well as insight into the physical interactions between proteins, and between proteins and other biomolecules. Thus far, proteomics in nephrology has largely focused on the discovery and validation of biomarkers, but the systematic analysis of the nephroproteome can offer substantial additional insights, including the discovery of mechanisms that trigger and propagate kidney disease. Moreover, proteome acquisition might provide a diagnostic tool that complements the assessment of a kidney biopsy sample by a pathologist. Such applications are becoming increasingly feasible with the development of high-throughput and high-coverage technologies, such as versatile mass spectrometry-based techniques and protein arrays, and encourage further proteomics research in nephrology.

Best Practices for Making Reproducible Biochemical Models

Like many scientific disciplines, dynamical biochemical modeling is hindered by irreproducible results. This limits the utility of biochemical models by making them difficult to understand, trust, or reuse. We comprehensively list the best practices that biochemical modelers should follow to build reproducible biochemical model artifacts-all data, model descriptions, and custom software used by the model-that can be understood and reused. The best practices provide advice for all steps of a typical biochemical modeling workflow in which a modeler collects data; constructs, trains, simulates, and validates the model; uses the predictions of a model to advance knowledge; and publicly shares the model artifacts. The best practices emphasize the benefits obtained by using standard tools and formats and provides guidance to modelers who do not or cannot use standards in some stages of their modeling workflow. Adoption of these best practices will enhance the ability of researchers to reproduce, understand, and reuse biochemical models.

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.

The first 10 years of the international coordination network for standards in systems and synthetic biology (COMBINE)

This paper presents a report on outcomes of the 10th Computational Modeling in Biology Network (COMBINE) meeting that was held in Heidelberg, Germany, in July of 2019. The annual event brings together researchers, biocurators and software engineers to present recent results and discuss future work in the area of standards for systems and synthetic biology. The COMBINE initiative coordinates the development of various community standards and formats for computational models in the life sciences. Over the past 10 years, COMBINE has brought together standard communities that have further developed and harmonized their standards for better interoperability of models and data. COMBINE 2019 was co-located with a stakeholder workshop of the European EU-STANDS4PM initiative that aims at harmonized data and model standardization for in silico models in the field of personalized medicine, as well as with the FAIRDOM PALs meeting to discuss findable, accessible, interoperable and reusable (FAIR) data sharing. This report briefly describes the work discussed in invited and contributed talks as well as during breakout sessions. It also highlights recent advancements in data, model, and annotation standardization efforts. Finally, this report concludes with some challenges and opportunities that this community will face during the next 10 years.

Validation of Modeling and Simulation Methods in Computational Biology

In recent years, a highly sophisticated array of modeling and simulation tools in all areas of biological and biomedical research has been developed. These tools have the potential to provide new insights into biological mechanisms integrating subcellular, cellular, tissue, organ, and potentially whole organism levels. Current research is focused on how to use these methods for translational medical research, such as for disease diagnosis and understanding, as well as drug discovery. In addition, these approaches enhance the ability to use human-derived data and to contribute to the refinement of high-cost experimental-based research. Additionally, the conflicting conceptual frameworks and conceptions of modeling and simulation methods from the broad public of users could have a significant impact on the successful implementation of aforementioned applications. This in turn could result in successful collaborations across academic, clinical, and industrial sectors. To that end, this study provides an overview of the frameworks and disciplines used for validation of computational methodologies in biomedical sciences.

NERDSS: A Nonequilibrium Simulator for Multibody Self-Assembly at the Cellular Scale

Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reaction-diffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.

Two MYB Proteins in a Self-Organizing Activator-Inhibitor System Produce Spotted Pigmentation Patterns

Many organisms exhibit visually striking spotted or striped pigmentation patterns. Developmental models predict that such spatial patterns can form when a local autocatalytic feedback loop and a long-range inhibitory feedback loop interact. At its simplest, this self-organizing network only requires one self-activating activator that also activates a repressor, which inhibits the activator and diffuses to neighboring cells. However, the molecular activators and inhibitors fully fitting this versatile model remain elusive in pigmentation systems. Here, we characterize an R2R3-MYB activator and an R3-MYB repressor in monkeyflowers (Mimulus). Through experimental perturbation and mathematical modeling, we demonstrate that the properties of these two proteins correspond to an activator-inhibitor pair in a two-component, reaction-diffusion system, explaining the formation of dispersed anthocyanin spots in monkeyflower petals. Notably, disrupting this pattern impacts pollinator visitation. Thus, subtle changes in simple activator-inhibitor systems are likely essential contributors to the evolution of the remarkable diversity of pigmentation patterns in flowers.

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics

Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.

NetLogo agent-based models as tools for understanding the self-organization of cell fate, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium

Interactions between primordium cells and their environment determines the self-organization of the zebrafish posterior Lateral Line primordium as it migrates under the skin from the ear to the tip of the tail forming and depositing neuromasts to spearhead formation of the posterior Lateral Line sensory system. In this review we describe how the NetLogo agent-based programming environment has been used in our lab to visualize and explore how self-generated chemokine gradients determine collective migration, how the dynamics of Wnt signaling can be used to predict patterns of neuromast deposition, and how previously defined interactions between Wnt and Fgf signaling systems have the potential to determine the periodic formation of center-biased Fgf signaling centers in the wake of a shrinking Wnt system. We also describe how NetLogo was used as a database for storing and visualizing the results of in toto lineage analysis of all cells in the migrating primordium. Together, the models illustrate how this programming environment can be used in diverse ways to integrate what has been learnt from biological experiments about the nature of interactions between cells and their environment, and explore how these interactions could potentially determine emergent patterns of cell fate specification, morphogenesis and collective migration of the zebrafish posterior Lateral Line primordium.

Mathematical modelling of cell migration

The complexity of biological systems creates challenges for fully understanding their behaviour. This is particularly true for cell migration which requires the co-ordinated activity of hundreds of individual components within cells. Mathematical modelling can help understand these complex systems by breaking the system into discrete steps which can then be interrogated in silico. In this review, we highlight scenarios in cell migration where mathematical modelling can be applied and discuss what types of modelling are most suited. Almost any aspect of cell migration is amenable to mathematical modelling from the modelling of intracellular processes such as chemokine receptor signalling and actin filament branching to larger scale processes such as the movement of individual cells or populations of cells through their environment. Two common ways of approaching this modelling are the use of models based on differential equations or agent-based modelling. The application of both these approaches to cell migration are discussed with specific examples along with common software tools to facilitate the process for non-mathematicians. We also highlight the challenges of modelling cell migration and the need for rigorous experimental work to effectively parameterise a model.

ModelBricks-modules for reproducible modeling improving model annotation and provenance

Most computational models in biology are built and intended for "single-use"; the lack of appropriate annotation creates models where the assumptions are unknown, and model elements are not uniquely identified. Simply recreating a simulation result from a publication can be daunting; expanding models to new and more complex situations is a herculean task. As a result, new models are almost always created anew, repeating literature searches for kinetic parameters, initial conditions and modeling specifics. It is akin to building a brick house starting with a pile of clay. Here we discuss a concept for building annotated, reusable models, by starting with small well-annotated modules we call ModelBricks. Curated ModelBricks, accessible through an open database, could be used to construct new models that will inherit ModelBricks annotations and thus be easier to understand and reuse. Key features of ModelBricks include reliance on a commonly used standard language (SBML), rule-based specification describing species as a collection of uniquely identifiable molecules, association with model specific numerical parameters, and more common annotations. Physical bricks can vary substantively; likewise, to be useful the structure of ModelBricks must be highly flexible-it should encapsulate mechanisms from single reactions to multiple reactions in a complex process. Ultimately, a modeler would be able to construct large models by using multiple ModelBricks, preserving annotations and provenance of model elements, resulting in a highly annotated model. We envision the library of ModelBricks to rapidly grow from community contributions. Persistent citable references will incentivize model creators to contribute new ModelBricks.

An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology

Localization of proteins to a membrane is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion methods offer a powerful tool for capturing lipid-specific binding to membrane surfaces by treating lipids explicitly as individual diffusible binding sites. However, modeling lipid particle populations is expensive. Here, we present an algorithm for reversible binding of proteins to continuum surfaces with implicit lipids, providing dramatic speed-ups to many body simulations. Our algorithm can be readily integrated into most reaction-diffusion software packages. We characterize changes to kinetics that emerge from explicit vs implicit lipids as well as surface adsorption models, showing excellent agreement between our method and the full explicit lipid model. Compared to models of surface adsorption, which couple together binding affinity and lipid concentration, our implicit lipid model decouples them to provide more flexibility for controlling surface binding properties and lipid inhomogeneity, thus reproducing binding kinetics and equilibria. Crucially, we demonstrate our method's application to membranes of arbitrary curvature and topology, modeled via a subdivision limit surface, again showing excellent agreement with explicit lipid simulations. Unlike adsorption models, our method retains the ability to bind lipids after proteins are localized to the surface (through, e.g., a protein-protein interaction), which can greatly increase the stability of multiprotein complexes on the surface. Our method will enable efficient cell-scale simulations involving proteins localizing to realistic membrane models, which is a critical step for predictive modeling and quantification of in vitro and in vivo dynamics.

SABIO-RK: an updated resource for manually curated biochemical reaction kinetics

SABIO-RK (http://sabiork.h-its.org/) is a manually curated database containing data about biochemical reactions and their reaction kinetics. The data are primarily extracted from scientific literature and stored in a relational database. The content comprises both naturally occurring and alternatively measured biochemical reactions and is not restricted to any organism class. The data are made available to the public by a web-based search interface and by web services for programmatic access. In this update we describe major improvements and extensions of SABIO-RK since our last publication in the database issue of Nucleic Acid Research (2012). (i) The website has been completely revised and (ii) allows now also free text search for kinetics data. (iii) Additional interlinkages with other databases in our field have been established; this enables users to gain directly comprehensive knowledge about the properties of enzymes and kinetics beyond SABIO-RK. (iv) Vice versa, direct access to SABIO-RK data has been implemented in several systems biology tools and workflows. (v) On request of our experimental users, the data can be exported now additionally in spreadsheet formats. (vi) The newly established SABIO-RK Curation Service allows to respond to specific data requirements.

Efficiently Encoding Complex Biochemical Models with the Multistate Model Builder (MSMB)

Biologists seek to create increasingly complex molecular regulatory network models. Writing such a model is a creative effort that requires flexible analysis tools and better modeling languages than offered by many of today's biochemical model editors. Our Multistate Model Builder (MSMB) supports multistate models created using different modeling styles that suit the modeler rather than the software. MSMB defines a simple but powerful syntax to describe multistate species. Our syntax reduces the number of reactions needed to encode the model, thereby reducing the cognitive load involved with model creation. MSMB gives extensive feedback during all stages of model creation. Users can activate error notifications, and use these notifications as a guide toward a consistent, syntactically correct model. Any consistent model can be exported to SBML or COPASI formats. We show the effectiveness of MSMB's multistate syntax through realistic models of cell cycle regulation and mRNA transcription. MSMB is an open-source project implemented in Java and it uses the COPASI API. Complete information and the installation package can be found at http://copasi.org/Projects/ .

eGFRD in all dimensions

Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present "eGFRD2," a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions.

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.

Modeling the Self-Assembly of Protein Complexes through a Rigid-Body Rotational Reaction-Diffusion Algorithm

The reaction-diffusion equations provide a powerful framework for modeling nonequilibrium, cell-scale dynamics over the long time scales that are inaccessible by traditional molecular modeling approaches. Single-particle reaction-diffusion offers the highest resolution technique for tracking such dynamics, but it has not been applied to the study of protein self-assembly due to its treatment of reactive species as single-point particles. Here, we develop a relatively simple but accurate approach for building rigid structure and rotation into single-particle reaction-diffusion methods, providing a rate-based method for studying protein self-assembly. Our simplifying assumption is that reactive collisions can be evaluated purely on the basis of the separations between the sites, and not their orientations. The challenge of evaluating reaction probabilities can then be performed using well-known equations based on translational diffusion in both 3D and 2D, by employing an effective diffusion constant we derive here. We show how our approach reproduces both the kinetics of association, which is altered by rotational diffusion, and the equilibrium of reversible association, which is not. Importantly, the macroscopic kinetics of association can be predicted on the basis of the microscopic parameters of our structurally resolved model, allowing for critical comparisons with theory and other rate-based simulations. We demonstrate this method for efficient, rate-based simulations of self-assembly of clathrin trimers, highlighting how formation of regular lattices impacts the kinetics of association.

Reproducible Research Using Biomodels

Like other types of computational research, modeling and simulation of biological processes (biomodels) is still largely communicated without sufficient detail to allow independent reproduction of results. But reproducibility in this area of research could easily be achieved by making use of existing resources, such as supplying models in standard formats and depositing code, models, and results in public repositories.

Tellurium notebooks-An environment for reproducible dynamical modeling in systems biology

The considerable difficulty encountered in reproducing the results of published dynamical models limits validation, exploration and reuse of this increasingly large biomedical research resource. To address this problem, we have developed Tellurium Notebook, a software system for model authoring, simulation, and teaching that facilitates building reproducible dynamical models and reusing models by 1) providing a notebook environment which allows models, Python code, and narrative to be intermixed, 2) supporting the COMBINE archive format during model development for capturing model information in an exchangeable format and 3) enabling users to easily simulate and edit public COMBINE-compliant models from public repositories to facilitate studying model dynamics, variants and test cases. Tellurium Notebook, a Python–based Jupyter–like environment, is designed to seamlessly inter-operate with these community standards by automating conversion between COMBINE standards formulations and corresponding in–line, human–readable representations. Thus, Tellurium brings to systems biology the strategy used by other literate notebook systems such as Mathematica. These capabilities allow users to edit every aspect of the standards–compliant models and simulations, run the simulations in–line, and re–export to standard formats. We provide several use cases illustrating the advantages of our approach and how it allows development and reuse of models without requiring technical knowledge of standards. Adoption of Tellurium should accelerate model development, reproducibility and reuse.

There is considerable value to systems and synthetic biology in creating reproducible models. An essential element of reproducibility is the use of community standards, an often challenging undertaking for modelers. This article describes Tellurium Notebook, a tool for developing dynamical models that provides an intuitive approach to building and reusing models built with community standards. Tellurium automates embedding human–readable representations of COMBINE archives in literate coding notebooks, bringing to systems biology this strategy central to other literate notebook systems such as Mathematica. We show that the ability to easily edit this human–readable representation enables users to test models under a variety of conditions, thereby providing a way to create, reuse, and modify standard–encoded models and simulations, regardless of the user’s level of technical knowledge of said standards.

Cell studio: A platform for interactive, 3D graphical simulation of immunological processes

The field of computer modeling and simulation of biological systems is rapidly advancing, backed by significant progress in the fields of experimentation techniques, computer hardware, and programming software. The result of a simulation may be delivered in several ways, from numerical results, through graphs of the simulated run, to a visualization of the simulation. The vision of an in-silico experiment mimicking an in-vitro or in-vivo experiment as it is viewed under a microscope is appealing but technically demanding and computationally intensive. Here, we report “Cell Studio,” a generic, hybrid platform to simulate an immune microenvironment with biological and biophysical rules. We use game engines—generic programs for game creation which offer ready-made assets and tools—to create a visualized, interactive 3D simulation. We also utilize a scalable architecture that delegates the computational load to a server. The user may view the simulation, move the “camera” around, stop, fast-forward, and rewind it and inject soluble molecules into the extracellular medium at any point in time. During simulation, graphs are created in real time for a broad view of system-wide processes. The model is parametrized using a user-friendly Graphical User Interface (GUI). We show a simple validation simulation and compare its results with those from a “classical” simulation, validated against a “wet” experiment. We believe that interactive, real-time 3D visualization may aid in generating insights from the model and encourage intuition about the immunological scenario.

Multiscale smeared finite element model for mass transport in biological tissue: From blood vessels to cells and cellular organelles

One of the basic and vital processes in living organisms is mass exchange, which occurs on several levels: it goes from blood vessels to cells and organelles within cells. On that path, molecules, as oxygen, metabolic products, drugs, etc. Traverse different macro and micro environments - blood, extracellular/intracellular space, and interior of organelles; and also biological barriers such as walls of blood vessels and membranes of cells and organelles. Many aspects of this mass transport remain unknown, particularly the biophysical mechanisms governing drug delivery. The main research approach relies on laboratory and clinical investigations. In parallel, considerable efforts have been directed to develop computational tools for additional insight into the intricate process of mass exchange and transport. Along these lines, we have recently formulated a composite smeared finite element (CSFE) which is composed of the smeared continuum pressure and concentration fields of the capillary and lymphatic system, and of these fields within tissue. The element offers an elegant and simple procedure which opens up new lines of inquiry and can be applied to large systems such as organs and tumors models. Here, we extend this concept to a multiscale scheme which concurrently couples domains that span from large blood vessels, capillaries and lymph, to cell cytosol and further to organelles of nanometer size. These spatial physical domains are coupled by the appropriate connectivity elements representing biological barriers. The composite finite element has "degrees of freedom" which include pressures and concentrations of all compartments of the vessels-tissue assemblage. The overall model uses the standard, measurable material properties of the continuum biological environments and biological barriers. It can be considered as a framework into which we can incorporate various additional effects (such as electrical or biochemical) for transport through membranes or within cells. This concept and the developed FE software within our package PAK offers a computational tool that can be applied to whole-organ systems, while also including specific domains such as tumors. The solved examples demonstrate the accuracy of this model and its applicability to large biological systems.

Efficient Modeling and Simulation of Space-Dependent Biological Systems

We recently demonstrated the possibility to model and to simulate biological functions using hardware description languages (HDLs) and associated simulators traditionally used for microelectronics. Nevertheless, those languages are not suitable to model and simulate space-dependent systems described by partial differential equations. However, in more and more applications space- and time-dependent models are unavoidable. For this purpose, we investigated a new modeling approach to simulate molecular diffusion on a mesoscopic scale still based on HDL. Our work relies on previous investigations on an electrothermal simulation tool for integrated circuits, and analogies that can be drawn between electronics, thermodynamics, and biology. The tool is composed of four main parts: a simple but efficient mesher that divides space into parallelepipeds (or rectangles in 2D) of adaptable size, a set of interconnected biological models, a SPICE simulator that handles the model and Python scripts that interface the different tools. Simulation results obtained with our tool have been validated on simple cases for which an analytical solution exists and compared with experimental data gathered from literature. Compared with existing approaches, our simulator has three main advantages: a very simple algorithm providing a direct interface between the diffusion model and biological model of each cell, the use of a powerful and widely proven simulation core (SPICE) and the ability to interface biological models with other domains of physics, enabling the study of transdisciplinary systems.

Credibility, Replicability, and Reproducibility in Simulation for Biomedicine and Clinical Applications in Neuroscience

Modeling and simulation in computational neuroscience is currently a research enterprise to better understand neural systems. It is not yet directly applicable to the problems of patients with brain disease. To be used for clinical applications, there must not only be considerable progress in the field but also a concerted effort to use best practices in order to demonstrate model credibility to regulatory bodies, to clinics and hospitals, to doctors, and to patients. In doing this for neuroscience, we can learn lessons from long-standing practices in other areas of simulation (aircraft, computer chips), from software engineering, and from other biomedical disciplines. In this manuscript, we introduce some basic concepts that will be important in the development of credible clinical neuroscience models: reproducibility and replicability; verification and validation; model configuration; and procedures and processes for credible mechanistic multiscale modeling. We also discuss how garnering strong community involvement can promote model credibility. Finally, in addition to direct usage with patients, we note the potential for simulation usage in the area of Simulation-Based Medical Education, an area which to date has been primarily reliant on physical models (mannequins) and scenario-based simulations rather than on numerical simulations.

Opportunities and Challenges in Building a Spatiotemporal Multi-scale Model of the Human Pancreatic β Cell

The construction of a predictive model of an entire eukaryotic cell that describes its dynamic structure from atomic to cellular scales is a grand challenge at the intersection of biology, chemistry, physics, and computer science. Having such a model will open new dimensions in biological research and accelerate healthcare advancements. Developing the necessary experimental and modeling methods presents abundant opportunities for a community effort to realize this goal. Here, we present a vision for creation of a spatiotemporal multi-scale model of the pancreatic β-cell, a relevant target for understanding and modulating the pathogenesis of diabetes.

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.