Virtual Cell: computational tools for modeling in cell biology

Asymmetric stem cell division maintains the genetic heterogeneity of tissue cells

Within a given tissue, the stem cell niche provides the microenvironment for stem cells suitable for their self-renewal. Conceptually, the niche space constrains the size of a stem-cell pool, as the cells sharing the niche compete for its space. It has been suggested that either neutral- or non-neutral-competition of stem cells changes the clone dynamics of stem cells. Theoretically, if the rate of asymmetric division is high, the stem cell competition is limited, thus suppressing clonal expansion. However, the effects of asymmetric division on clone dynamics have never been experimentally tested. Here, using the Drosophila germline stem cell (GSC) system, as a simple model of the in-vivo niche, we examine the effect of division modes (asymmetric or symmetric) on clonal dynamics by combining experimental approaches with mathematical modeling. Our experimental data and computational model both suggest that the rate of asymmetric division is proportional to the time a stem cell clone takes to expand. Taken together, our data suggests that asymmetric division is essential for maintaining the genetic variation of stem cells and thus serves as a critical mechanism for safeguarding fertility over the animal age or preventing multiple disorders caused by the clonal expansion of stem cells.

Cell4D: a general purpose spatial stochastic simulator for cellular pathways

BACKGROUND

With the generation of vast compendia of biological datasets, the challenge is how best to interpret 'omics data alongside biochemical and other small-scale experiments to gain meaningful biological insights. Key to this challenge are computational methods that enable domain-users to generate novel hypotheses that can be used to guide future experiments. Of particular interest are flexible modeling platforms, capable of simulating a diverse range of biological systems with low barriers of adoption to those with limited computational expertise.

RESULTS

We introduce Cell4D, a spatial-temporal modeling platform combining a robust simulation engine with integrated graphics visualization, a model design editor, and an underlying XML data model capable of capturing a variety of cellular functions. Cell4D provides an interactive visualization mode, allowing intuitive feedback on model behavior and exploration of novel hypotheses, together with a non-graphics mode, compatible with high performance cloud compute solutions, to facilitate generation of statistical data. To demonstrate the flexibility and effectiveness of Cell4D, we investigate the dynamics of CEACAM1 localization in T-cell activation. We confirm the importance of Ca2+ microdomains in activating calmodulin and highlight a key role of activated calmodulin on the surface expression of CEACAM1. We further show how lymphocyte-specific protein tyrosine kinase can help regulate this cell surface expression and exploit spatial modeling features of Cell4D to test the hypothesis that lipid rafts regulate clustering of CEACAM1 to promote trans-binding to neighbouring cells.

CONCLUSIONS

Through demonstrating its ability to test and generate hypotheses, Cell4D represents an effective tool to help integrate knowledge across diverse, large and small-scale datasets.

Spine apparatus modulates Ca 2+ in spines through spatial localization of sources and sinks

Dendritic spines are small protrusions on dendrites in neurons and serve as sites of postsynaptic activity. Some of these spines contain smooth endoplasmic reticulum (SER), and sometimes an even further specialized SER known as the spine apparatus (SA). In this work, we developed a stochastic spatial model to investigate the role of the SER and the SA in modulating Ca 2+ dynamics. Using this model, we investigated how ryanodine receptor (RyR) localization, spine membrane geometry, and SER geometry can impact Ca 2+ transients in the spine and in the dendrite. Our simulations found that RyR opening is dependent on where it is localized in the SER and on the SER geometry. In order to maximize Ca 2+ in the dendrites (for activating clusters of spines and spine-spine communication), a laminar SA was favorable with RyRs localized in the neck region, closer to the dendrite. We also found that the presence of the SER without the laminar structure, coupled with RyR localization at the head, leads to higher Ca 2+ presence in the spine. These predictions serve as design principles for understanding how spines with an ER can regulate Ca 2+ dynamics differently from spines without ER through a combination of geometry and receptor localization.

Highlights

1RyR opening in dendritic spine ER is location dependent and spine geometry dependent. Ca 2+ buffers and SERCA can buffer against runaway potentiation of spines even when CICR is activated. RyRs located towards the ER neck allow for more Ca 2+ to reach the dendrites. RyRs located towards the spine head are favorable for increased Ca 2+ in spines.

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.

Nuclear lamina strain states revealed by intermolecular force biosensor

Nuclear lamins have been considered an important structural element of the nucleus. The nuclear lamina is thought both to shield DNA from excessive mechanical forces and to transmit mechanical forces onto the DNA. However, to date there is not yet a technical approach to directly measure mechanical forces on nuclear lamins at the protein level. To overcome this limitation, we developed a nanobody-based intermolecular tension FRET biosensor capable of measuring the mechanical strain of lamin filaments. Using this sensor, we were able to show that the nuclear lamina is subjected to significant force. These forces are dependent on nuclear volume, actomyosin contractility, functional LINC complex, chromatin condensation state, cell cycle, and EMT. Interestingly, large forces were also present on nucleoplasmic lamins, indicating that these lamins may also have an important mechanical role in the nucleus. Overall, we demonstrate that the nanobody-based approach allows construction of biosensors for complex protein structures for mechanobiology studies.

Animal-derived products in science and current alternatives

More than fifty years after the 3Rs definition and despite the continuous implementation of regulatory measures, animals continue to be widely used in basic research. Their use comprises not only in vivo experiments with animal models, but also the production of a variety of supplements and products of animal origin for cell and tissue culture, cell-based assays, and therapeutics. The animal-derived products most used in basic research are fetal bovine serum (FBS), extracellular matrix proteins such as Matrigel™, and antibodies. However, their production raises several ethical issues regarding animal welfare. Additionally, their biological origin is associated with a high risk of contamination, resulting, frequently, in poor scientific data for clinical translation. These issues support the search for new animal-free products able to replace FBS, Matrigel™, and antibodies in basic research. In addition, in silico methodologies play an important role in the reduction of animal use in research by refining the data previously to in vitro and in vivo experiments. In this review, we depicted the current available animal-free alternatives in in vitro research.

Machine Learning and Hybrid Methods for Metabolic Pathway Modeling

Computational cell metabolism models seek to provide metabolic explanations of cell behavior under different conditions or following genetic alterations, help in the optimization of in vitro cell growth environments, or predict cellular behavior in vivo and in vitro. In the extremes, mechanistic models can include highly detailed descriptions of a small number of metabolic reactions or an approximate representation of an entire metabolic network. To date, all mechanistic models have required details of individual metabolic reactions, either kinetic parameters or metabolic flux, as well as information about extracellular and intracellular metabolite concentrations. Despite the extensive efforts and the increasing availability of high-quality data, required in vivo data are not available for the majority of known metabolic reactions; thus, mechanistic models are based primarily on ex vivo kinetic measurements and limited flux information. Machine learning approaches provide an alternative for derivation of functional dependencies from existing data. The increasing availability of metabolomic and lipidomic data, with growing feature coverage as well as sample set size, is expected to provide new data options needed for derivation of machine learning models of cell metabolic processes. Moreover, machine learning analysis of longitudinal data can lead to predictive models of cell behaviors over time. Conversely, machine learning models trained on steady-state data can provide descriptive models for the comparison of metabolic states in different environments or disease conditions. Additionally, inclusion of metabolic network knowledge in these analyses can further help in the development of models with limited data.This chapter will explore the application of machine learning to the modeling of cell metabolism. We first provide a theoretical explanation of several machine learning and hybrid mechanistic machine learning methods currently being explored to model metabolism. Next, we introduce several avenues for improving these models with machine learning. Finally, we provide protocols for specific examples of the utilization of machine learning in the development of predictive cell metabolism models using metabolomic data. We describe data preprocessing, approaches for training of machine learning models for both descriptive and predictive models, and the utilization of these models in synthetic and systems biology. Detailed protocols provide a list of software tools and libraries used for these applications, step-by-step modeling protocols, troubleshooting, as well as an overview of existing limitations to these approaches.

Influence of T-Bar on Calcium Concentration Impacting Release Probability

The relation of form and function, namely the impact of the synaptic anatomy on calcium dynamics in the presynaptic bouton, is a major challenge of present (computational) neuroscience at a cellular level. The Drosophila larval neuromuscular junction (NMJ) is a simple model system, which allows studying basic effects in a rather simple way. This synapse harbors several special structures. In particular, in opposite to standard vertebrate synapses, the presynaptic boutons are rather large, and they have several presynaptic zones. In these zones, different types of anatomical structures are present. Some of the zones bear a so-called T-bar, a particular anatomical structure. The geometric form of the T-bar resembles the shape of the letter “T” or a table with one leg. When an action potential arises, calcium influx is triggered. The probability of vesicle docking and neurotransmitter release is superlinearly proportional to the concentration of calcium close to the vesicular release site. It is tempting to assume that the T-bar causes some sort of calcium accumulation and hence triggers a higher release probability and thus enhances neurotransmitter exocytosis. In order to study this influence in a quantitative manner, we constructed a typical T-bar geometry and compared the calcium concentration close to the active zones (AZs). We compared the case of synapses with and without T-bars. Indeed, we found a substantial influence of the T-bar structure on the presynaptic calcium concentrations close to the AZs, indicating that this anatomical structure increases vesicle release probability. Therefore, our study reveals how the T-bar zone implies a strong relation between form and function. Our study answers the question of experimental studies (namely “Wichmann and Sigrist, Journal of neurogenetics 2010”) concerning the sense of the anatomical structure of the T-bar.

Hybrid modelling of biological systems: current progress and future prospects

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

A Modular Workflow for Model Building, Analysis, and Parameter Estimation in Systems Biology and Neuroscience

Neuroscience incorporates knowledge from a range of scales, from single molecules to brain wide neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interactions between two adjacent scales and researchers use a variety of different software tools in the model building and analysis process. Here we focus on the scale of biochemical pathways, which is one of the main objects of study in systems biology. While systems biology is among the more standardized fields, conversion between different model formats and interoperability between various tools is still somewhat problematic. To offer our take on tackling these shortcomings and by keeping in mind the FAIR (findability, accessibility, interoperability, reusability) data principles, we have developed a workflow for building and analyzing biochemical pathway models, using pre-existing tools that could be utilized for the storage and refinement of models in all phases of development. We have chosen the SBtab format which allows the storage of biochemical models and associated data in a single file and provides a human readable set of syntax rules. Next, we implemented custom-made MATLAB® scripts to perform parameter estimation and global sensitivity analysis used in model refinement. Additionally, we have developed a web-based application for biochemical models that allows simulations with either a network free solver or stochastic solvers and incorporating geometry. Finally, we illustrate convertibility and use of a biochemical model in a biophysically detailed single neuron model by running multiscale simulations in NEURON. Using this workflow, we can simulate the same model in three different simulators, with a smooth conversion between the different model formats, enhancing the characterization of different aspects of the model.

Rules of Engagement: A Guide to Developing Agent-Based Models

Agent-based models (ABM), also called individual-based models, first appeared several decades ago with the promise of nearly real-time simulations of active, autonomous individuals such as animals or objects. The goal of ABMs is to represent a population of individuals (agents) interacting with one another and their environment. Because of their flexible framework, ABMs have been widely applied to study systems in engineering, economics, ecology, and biology. This chapter is intended to guide the users in the development of an agent-based model by discussing conceptual issues, implementation, and pitfalls of ABMs from first principles. As a case study, we consider an ABM of the multi-scale dynamics of cellular interactions in a microbial community. We develop a lattice-free agent-based model of individual cells whose actions of growth, movement, and division are influenced by both their individual processes (cell cycle) and their contact with other cells (adhesion and contact inhibition).

Modeling cholesterol metabolism and atherosclerosis

Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.

Nuclear-capture of endosomes depletes nuclear G-actin to promote SRF/MRTF activation and cancer cell invasion

Signals are relayed from receptor tyrosine kinases (RTKs) at the cell surface to effector systems in the cytoplasm and nucleus, and coordination of this process is important for the execution of migratory phenotypes, such as cell scattering and invasion. The endosomal system influences how RTK signalling is coded, but the ways in which it transmits these signals to the nucleus to influence gene expression are not yet clear. Here we show that hepatocyte growth factor, an activator of MET (an RTK), promotes Rab17- and clathrin-dependent endocytosis of EphA2, another RTK, followed by centripetal transport of EphA2-positive endosomes. EphA2 then mediates physical capture of endosomes on the outer surface of the nucleus; a process involving interaction between the nuclear import machinery and a nuclear localisation sequence in EphA2's cytodomain. Nuclear capture of EphA2 promotes RhoG-dependent phosphorylation of the actin-binding protein, cofilin to oppose nuclear import of G-actin. The resulting depletion of nuclear G-actin drives transcription of Myocardin-related transcription factor (MRTF)/serum-response factor (SRF)-target genes to implement cell scattering and the invasive behaviour of cancer cells.

Mad dephosphorylation at the nuclear pore is essential for asymmetric stem cell division

Stem cells divide asymmetrically to generate a stem cell and a differentiating daughter cell. Yet, it remains poorly understood how a stem cell and a differentiating daughter cell can receive distinct levels of niche signal and thus acquire different cell fates (self-renewal versus differentiation), despite being adjacent to each other and thus seemingly exposed to similar levels of niche signaling. In the Drosophila ovary, germline stem cells (GSCs) are maintained by short range bone morphogenetic protein (BMP) signaling; the BMP ligands activate a receptor that phosphorylates the downstream molecule mothers against decapentaplegic (Mad). Phosphorylated Mad (pMad) accumulates in the GSC nucleus and activates the stem cell transcription program. Here, we demonstrate that pMad is highly concentrated in the nucleus of the GSC, while it quickly decreases in the nucleus of the differentiating daughter cell, the precystoblast (preCB), before the completion of cytokinesis. We show that a known Mad phosphatase, Dullard (Dd), is required for the asymmetric partitioning of pMad. Our mathematical modeling recapitulates the high sensitivity of the ratio of pMad levels to the Mad phosphatase activity and explains how the asymmetry arises in a shared cytoplasm. Together, these studies reveal a mechanism for breaking the symmetry of daughter cells during asymmetric stem cell division.

Mathematical modelling in cell migration: tackling biochemistry in changing geometries

Directed cell migration poses a rich set of theoretical challenges. Broadly, these are concerned with (1) how cells sense external signal gradients and adapt; (2) how actin polymerisation is localised to drive the leading cell edge and Myosin-II molecular motors retract the cell rear; and (3) how the combined action of cellular forces and cell adhesion results in cell shape changes and net migration. Reaction-diffusion models for biological pattern formation going back to Turing have long been used to explain generic principles of gradient sensing and cell polarisation in simple, static geometries like a circle. In this minireview, we focus on recent research which aims at coupling the biochemistry with cellular mechanics and modelling cell shape changes. In particular, we want to contrast two principal modelling approaches: (1) interface tracking where the cell membrane, interfacing cell interior and exterior, is explicitly represented by a set of moving points in 2D or 3D space and (2) interface capturing. In interface capturing, the membrane is implicitly modelled analogously to a level line in a hilly landscape whose topology changes according to forces acting on the membrane. With the increased availability of high-quality 3D microscopy data of complex cell shapes, such methods will become increasingly important in data-driven, image-based modelling to better understand the mechanochemistry underpinning cell motion.

Stochastic models for single-cell data: Current challenges and the way forward

Although the quantity and quality of single-cell data have progressed rapidly, making quantitative predictions with single-cell stochastic models remains challenging. The stochastic nature of cellular processes leads to at least three challenges in building models with single-cell data: (a) because variability in single-cell data can be attributed to multiple different sources, it is difficult to rule out conflicting mechanistic models that explain the same data equally well; (b) the distinction between interesting biological variability and experimental variability is sometimes ambiguous; (c) the nonstandard distributions of single-cell data can lead to violations of the assumption of symmetric errors in least-squares fitting. In this review, we first discuss recent studies that overcome some of the challenges or set up a promising direction and then introduce some powerful statistical approaches utilized in these studies. We conclude that applying and developing statistical approaches could lead to further progress in building stochastic models for single-cell data.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

BioModels-15 years of sharing computational models in life science

Computational modelling has become increasingly common in life science research. To provide a platform to support universal sharing, easy accessibility and model reproducibility, BioModels (https://www.ebi.ac.uk/biomodels/), a repository for mathematical models, was established in 2005. The current BioModels platform allows submission of models encoded in diverse modelling formats, including SBML, CellML, PharmML, COMBINE archive, MATLAB, Mathematica, R, Python or C++. The models submitted to BioModels are curated to verify the computational representation of the biological process and the reproducibility of the simulation results in the reference publication. The curation also involves encoding models in standard formats and annotation with controlled vocabularies following MIRIAM (minimal information required in the annotation of biochemical models) guidelines. BioModels now accepts large-scale submission of auto-generated computational models. With gradual growth in content over 15 years, BioModels currently hosts about 2000 models from the published literature. With about 800 curated models, BioModels has become the world’s largest repository of curated models and emerged as the third most used data resource after PubMed and Google Scholar among the scientists who use modelling in their research. Thus, BioModels benefits modellers by providing access to reliable and semantically enriched curated models in standard formats that are easy to share, reproduce and reuse.

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the finite element method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.

Harnessing the Potential of Stem Cells for Disease Modeling: Progress and Promises

Ex vivo cell/tissue-based models are an essential step in the workflow of pathophysiology studies, assay development, disease modeling, drug discovery, and development of personalized therapeutic strategies. For these purposes, both scientific and pharmaceutical research have adopted ex vivo stem cell models because of their better predictive power. As matter of a fact, the advancing in isolation and in vitro expansion protocols for culturing autologous human stem cells, and the standardization of methods for generating patient-derived induced pluripotent stem cells has made feasible to generate and investigate human cellular disease models with even greater speed and efficiency. Furthermore, the potential of stem cells on generating more complex systems, such as scaffold-cell models, organoids, or organ-on-a-chip, allowed to overcome the limitations of the two-dimensional culture systems as well as to better mimic tissues structures and functions. Finally, the advent of genome-editing/gene therapy technologies had a great impact on the generation of more proficient stem cell-disease models and on establishing an effective therapeutic treatment. In this review, we discuss important breakthroughs of stem cell-based models highlighting current directions, advantages, and limitations and point out the need to combine experimental biology with computational tools able to describe complex biological systems and deliver results or predictions in the context of personalized medicine.

Applications and Challenges of Machine Learning to Enable Realistic Cellular Simulations

In this perspective, we examine three key aspects of an end-to-end pipeline for realistic cellular simulations: reconstruction and segmentation of cellular structures; generation of cellular structures; and mesh generation, simulation, and data analysis. We highlight some of the relevant prior work in these distinct but overlapping areas, with a particular emphasis on current use of machine learning technologies, as well as on future opportunities.

LASSI: A lattice model for simulating phase transitions of multivalent proteins

Many biomolecular condensates form via spontaneous phase transitions that are driven by multivalent proteins. These molecules are biological instantiations of associative polymers that conform to a so-called stickers-and-spacers architecture. The stickers are protein-protein or protein-RNA interaction motifs and / or domains that can form reversible, non-covalent crosslinks with one another. Spacers are interspersed between stickers and their preferential interactions with solvent molecules determine the cooperativity of phase transitions. Here, we report the development of an open source computational engine known as LASSI (LAttice simulation engine for Sticker and Spacer Interactions) that enables the calculation of full phase diagrams for multicomponent systems comprising of coarse-grained representations of multivalent proteins. LASSI is designed to enable computationally efficient phenomenological modeling of spontaneous phase transitions of multicomponent mixtures comprising of multivalent proteins and RNA molecules. We demonstrate the application of LASSI using simulations of linear and branched multivalent proteins. We show that dense phases are best described as droplet-spanning networks that are characterized by reversible physical crosslinks among multivalent proteins. We connect recent observations regarding correlations between apparent stoichiometry and dwell times of condensates to being proxies for the internal structural organization, specifically the convolution of internal density and extent of networking, within condensates. Finally, we demonstrate that the concept of saturation concentration thresholds does not apply to multicomponent systems where obligate heterotypic interactions drive phase transitions. This emerges from the ellipsoidal structures of phase diagrams for multicomponent systems and it has direct implications for the regulation of biomolecular condensates in vivo.

Modeling heterogeneous tumor growth dynamics and cell-cell interactions at single-cell and cell-population resolution

Cancer is a complex, dynamic disease that despite recent advances remains mostly incurable. Inter- and intratumoral heterogeneity are generally considered major drivers of therapy resistance, metastasis, and treatment failure. Recent advances in high-throughput experimentation have produced a wealth of data on tumor heterogeneity and researchers are increasingly turning to mathematical modeling to aid in the interpretation of these complex datasets. In this mini-review, we discuss three important classes of approaches for modeling cellular dynamics within heterogeneous tumors: agent-based models, population dynamics, and multiscale models. An important new focus, for which we provide an example, is the role of intratumoral cell-cell interactions.

Design and evaluation of engineered protein biosensors for live-cell imaging of EGFR phosphorylation

Live-cell fluorescence microscopy is broadly applied to study the dynamics of receptor-mediated cell signaling, but the availability of intracellular biosensors is limited. A biosensor based on the tandem SH2 domains from phospholipase C-γ1 (PLCγ1), tSH2-WT, has been used to measure phosphorylation of the epidermal growth factor receptor (EGFR). Here, we found that tSH2-WT lacked specificity for phosphorylated EGFR, consistent with the known promiscuity of SH2 domains. Further, EGF-stimulated membrane recruitment of tSH2-WT differed qualitatively from the expected kinetics of EGFR phosphorylation. Analysis of a mathematical model suggested, and experiments confirmed, that the high avidity of tSH2-WT resulted in saturation of its target and interference with EGFR endocytosis. To overcome the apparent target specificity and saturation issues, we implemented two protein engineering strategies. In the first approach, we screened a combinatorial library generated by random mutagenesis of the C-terminal SH2 domain (cSH2) of PLCγ1 and isolated a mutant form (mSH2) with enhanced specificity for phosphorylated Tyr992 (pTyr992) of EGFR. A biosensor based on mSH2 closely reported the kinetics of EGFR phosphorylation but retained cross-reactivity similar to tSH2-WT. In the second approach, we isolated a pTyr992-binding protein (SPY992) from a combinatorial library generated by mutagenesis of the Sso7d protein scaffold. Compared to tSH2-WT and mSH2, SPY992 exhibited superior performance as a specific, moderate-affinity biosensor. We extended this approach to isolate a biosensor for EGFR pTyr1148 (SPY1148). This approach of integrating theoretical considerations with protein engineering strategies can be generalized to design and evaluate suitable biosensors for various phospho-specific targets.

Computational Structural Biology: Successes, Future Directions, and Challenges

Computational biology has made powerful advances. Among these, trends in human health have been uncovered through heterogeneous 'big data' integration, and disease-associated genes were identified and classified. Along a different front, the dynamic organization of chromatin is being elucidated to gain insight into the fundamental question of genome regulation. Powerful conformational sampling methods have also been developed to yield a detailed molecular view of cellular processes. when combining these methods with the advancements in the modeling of supramolecular assemblies, including those at the membrane, we are finally able to get a glimpse into how cells' actions are regulated. Perhaps most intriguingly, a major thrust is on to decipher the mystery of how the brain is coded. Here, we aim to provide a broad, yet concise, sketch of modern aspects of computational biology, with a special focus on computational structural biology. We attempt to forecast the areas that computational structural biology will embrace in the future and the challenges that it may face. We skirt details, highlight successes, note failures, and map directions.

Emerging whole-cell modeling principles and methods

Whole-cell computational models aim to predict cellular phenotypes from genotype by representing the entire genome, the structure and concentration of each molecular species, each molecular interaction, and the extracellular environment. Whole-cell models have great potential to transform bioscience, bioengineering, and medicine. However, numerous challenges remain to achieve whole-cell models. Nevertheless, researchers are beginning to leverage recent progress in measurement technology, bioinformatics, data sharing, rule-based modeling, and multi-algorithmic simulation to build the first whole-cell models. We anticipate that ongoing efforts to develop scalable whole-cell modeling tools will enable dramatically more comprehensive and more accurate models, including models of human cells.

Compartmental and Spatial Rule-Based Modeling with Virtual Cell

In rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations deterministic solvers or the Smoldyn stochastic simulator.

Integrative biological simulation praxis: Considerations from physics, philosophy, and data/model curation practices

Integrative biological simulations have a varied and controversial history in the biological sciences. From computational models of organelles, cells, and simple organisms, to physiological models of tissues, organ systems, and ecosystems, a diverse array of biological systems have been the target of large-scale computational modeling efforts. Nonetheless, these research agendas have yet to prove decisively their value among the broader community of theoretical and experimental biologists. In this commentary, we examine a range of philosophical and practical issues relevant to understanding the potential of integrative simulations. We discuss the role of theory and modeling in different areas of physics and suggest that certain sub-disciplines of physics provide useful cultural analogies for imagining the future role of simulations in biological research. We examine philosophical issues related to modeling which consistently arise in discussions about integrative simulations and suggest a pragmatic viewpoint that balances a belief in philosophy with the recognition of the relative infancy of our state of philosophical understanding. Finally, we discuss community workflow and publication practices to allow research to be readily discoverable and amenable to incorporation into simulations. We argue that there are aligned incentives in widespread adoption of practices which will both advance the needs of integrative simulation efforts as well as other contemporary trends in the biological sciences, ranging from open science and data sharing to improving reproducibility.

Snoopy's hybrid simulator: a tool to construct and simulate hybrid biological models

BACKGROUND

Hybrid simulation of (computational) biochemical reaction networks, which combines stochastic and deterministic dynamics, is an important direction to tackle future challenges due to complex and multi-scale models. Inherently hybrid computational models of biochemical networks entail two time scales: fast and slow. Therefore, it is intricate to efficiently and accurately analyse them using only either deterministic or stochastic simulation. However, there are only a few software tools that support such an approach. These tools are often limited with respect to the number as well as the functionalities of the provided hybrid simulation algorithms.

RESULTS

We present Snoopy's hybrid simulator, an efficient hybrid simulation software which builds on Snoopy, a tool to construct and simulate Petri nets. Snoopy's hybrid simulator provides a wide range of state-of-the-art hybrid simulation algorithms. Using this tool, a computational model of biochemical networks can be constructed using a (coloured) hybrid Petri net's graphical notations, or imported from other compatible formats (e.g. SBML), and afterwards executed via dynamic or static hybrid simulation.

CONCLUSION

Snoopy's hybrid simulator is a platform-independent tool providing an accurate and efficient simulation of hybrid (biological) models. It can be downloaded free of charge as part of Snoopy from http://www-dssz.informatik.tu-cottbus.de/DSSZ/Software/Snoopy .

Quantitative computational models of molecular self-assembly in systems biology

Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.

Graphical Modeling Meets Systems Pharmacology

A main source of failures in systems projects (including systems pharmacology) is poor communication level and different expectations among the stakeholders. A common and not ambiguous language that is naturally comprehensible by all the involved players is a boost to success. We present bStyle, a modeling tool that adopts a graphical language close enough to cartoons to be a common media to exchange ideas and data and that it is at the same time formal enough to enable modeling, analysis, and dynamic simulations of a system. Data analysis and simulation integrated in the same application are fundamental to understand the mechanisms of actions of drugs: a core aspect of systems pharmacology.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Modelling with ANIMO: between fuzzy logic and differential equations

BACKGROUND

Computational support is essential in order to reason on the dynamics of biological systems. We have developed the software tool ANIMO (Analysis of Networks with Interactive MOdeling) to provide such computational support and allow insight into the complex networks of signaling events occurring in living cells. ANIMO makes use of timed automata as an underlying model, thereby enabling analysis techniques from computer science like model checking. Biology experts are able to use ANIMO via a user interface specifically tailored for biological applications. In this paper we compare the use of ANIMO with some established formalisms on two case studies.

RESULTS

ANIMO is a powerful and user-friendly tool that can compete with existing continuous and discrete paradigms. We show this by presenting ANIMO models for two case studies: Drosophila melanogaster circadian clock, and signal transduction events downstream of TNF α and EGF in HT-29 human colon carcinoma cells. The models were originally developed with ODEs and fuzzy logic, respectively.

CONCLUSIONS

Two biological case studies that have been modeled with respectively ODE and fuzzy logic models can be conveniently modeled using ANIMO. The ANIMO models require less parameters than ODEs and are more precise than fuzzy logic. For this reason we position the modelling paradigm of ANIMO between ODEs and fuzzy logic.

The dynamic mechanical properties of cellularised aggregates

Cellularised materials are composed of cells interfaced through specialised intercellular junctions that link the cytoskeleton of one cell to that of its neighbours allowing for transmission of forces. Cellularised materials are common in early development and adult tissues where they can be found in the form of cell sheets, cysts, or amorphous aggregates and in pathophysiological conditions such as cancerous tumours. Given the growing realisation that forces can regulate cell physiology and developmental processes, understanding how cellularised materials deform under mechanical stress or dissipate stress appear as key biological questions. In this review, we will discuss the dynamic mechanical properties of cellularised materials devoid of extracellular matrix.

A cell-centered, agent-based framework that enables flexible environment granularities

BACKGROUND

Mechanistic explanations of cell-level phenomena typically adopt an observer perspective. Explanations developed from a cell's perspective may offer new insights. Agent-based models lend themselves to model from an individual perspective, and existing agent-based models generally utilize a regular lattice-based environment. A framework which utilizes a cell's perspective in an off-lattice environment could improve the overall understanding of biological phenomena.

RESULTS

We present an agent-based, discrete event framework, with a demonstrative focus on biomimetic agents. The framework was first developed in 2-dimensions and then extended, with a subset of behaviors, to 3-dimensions. The framework is expected to facilitate studies of more complex biological phenomena through exploitation of a dynamic Delaunay and Voronoi off-lattice environment. We used the framework to model biological cells and to specifically demonstrate basic biological cell behaviors in two- and three-dimensional space. Potential use cases are highlighted, suggesting the utility of the framework in various scenarios.

CONCLUSIONS

The framework presented in this manuscript expands on existing cell- and agent-centered methods by offering a new perspective in an off-lattice environment. As the demand for biomimetic models grows, the demand for new methods, such as the presented Delaunay and Voronoi framework, is expected to increase.

Modeling Excitable Dynamics of Chemotactic Networks

The study of chemotaxis has benefited greatly from computational models that describe the response of cells to chemoattractant stimuli. These models must keep track of spatially and temporally varying distributions of numerous intracellular species. Moreover, recent evidence suggests that these are not deterministic interactions, but also include the effect of stochastic variations that trigger an excitable network. In this chapter we illustrate how to create simulations of excitable networks using the Virtual Cell modeling environment.

Emerging proteomic technologies for elucidating context-dependent cellular signaling events: A big challenge of tiny proportions

Aberrant cell signaling events either drive or compensate for nearly all pathologies. A thorough description and quantification of maladaptive signaling flux in disease is a critical step in drug development, and complex proteomic approaches can provide valuable mechanistic insights. Traditional proteomics-based signaling analyses rely heavily on in vitro cellular monoculture. The characterization of these simplified systems generates a rich understanding of the basic components and complex interactions of many signaling networks, but they cannot capture the full complexity of the microenvironments in which pathologies are ultimately made manifest. Unfortunately, techniques that can directly interrogate signaling in situ often yield mass-limited starting materials that are incompatible with traditional proteomics workflows. This review provides an overview of established and emerging techniques that are applicable to context-dependent proteomics. Analytical approaches are illustrated through recent proteomics-based studies in which selective sample acquisition strategies preserve context-dependent information, and where the challenge of minimal starting material is met by optimized sensitivity and coverage. This review is organized into three major technological themes: (i) LC methods in line with MS; (ii) antibody-based approaches; (iii) MS imaging with a discussion of data integration and systems modeling. Finally, we conclude with future perspectives and implications of context-dependent proteomics.

Improving collaboration by standardization efforts in systems biology

Collaborative genome-scale reconstruction endeavors of metabolic networks would not be possible without a common, standardized formal representation of these systems. The ability to precisely define biological building blocks together with their dynamic behavior has even been considered a prerequisite for upcoming synthetic biology approaches. Driven by the requirements of such ambitious research goals, standardization itself has become an active field of research on nearly all levels of granularity in biology. In addition to the originally envisaged exchange of computational models and tool interoperability, new standards have been suggested for an unambiguous graphical display of biological phenomena, to annotate, archive, as well as to rank models, and to describe execution and the outcomes of simulation experiments. The spectrum now even covers the interaction of entire neurons in the brain, three-dimensional motions, and the description of pharmacometric studies. Thereby, the mathematical description of systems and approaches for their (repeated) simulation are clearly separated from each other and also from their graphical representation. Minimum information definitions constitute guidelines and common operation protocols in order to ensure reproducibility of findings and a unified knowledge representation. Central database infrastructures have been established that provide the scientific community with persistent links from model annotations to online resources. A rich variety of open-source software tools thrives for all data formats, often supporting a multitude of programing languages. Regular meetings and workshops of developers and users lead to continuous improvement and ongoing development of these standardization efforts. This article gives a brief overview about the current state of the growing number of operation protocols, mark-up languages, graphical descriptions, and fundamental software support with relevance to systems biology.

A conservative algorithm for parabolic problems in domains with moving boundaries

We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior. Consequently, our algorithm is free of the CFL stability issue due to moving interfaces and does not involve cell-merging or mass redistribution. Local mass conservation is ensured by finite-volume discretization and natural-neighbor interpolation. Numerical experiments with two-dimensional geometries demonstrate exact mass conservation and indicate an order of convergence in space between one and two. The use of standard meshing techniques makes extension of the method to three dimensions conceptually straightforward.

1D-3D hybrid modeling-from multi-compartment models to full resolution models in space and time

Investigation of cellular and network dynamics in the brain by means of modeling and simulation has evolved into a highly interdisciplinary field, that uses sophisticated modeling and simulation approaches to understand distinct areas of brain function. Depending on the underlying complexity, these models vary in their level of detail, in order to cope with the attached computational cost. Hence for large network simulations, single neurons are typically reduced to time-dependent signal processors, dismissing the spatial aspect of each cell. For single cell or networks with relatively small numbers of neurons, general purpose simulators allow for space and time-dependent simulations of electrical signal processing, based on the cable equation theory. An emerging field in Computational Neuroscience encompasses a new level of detail by incorporating the full three-dimensional morphology of cells and organelles into three-dimensional, space and time-dependent, simulations. While every approach has its advantages and limitations, such as computational cost, integrated and methods-spanning simulation approaches, depending on the network size could establish new ways to investigate the brain. In this paper we present a hybrid simulation approach, that makes use of reduced 1D-models using e.g., the NEURON simulator—which couples to fully resolved models for simulating cellular and sub-cellular dynamics, including the detailed three-dimensional morphology of neurons and organelles. In order to couple 1D- and 3D-simulations, we present a geometry-, membrane potential- and intracellular concentration mapping framework, with which graph- based morphologies, e.g., in the swc- or hoc-format, are mapped to full surface and volume representations of the neuron and computational data from 1D-simulations can be used as boundary conditions for full 3D simulations and vice versa. Thus, established models and data, based on general purpose 1D-simulators, can be directly coupled to the emerging field of fully resolved, highly detailed 3D-modeling approaches. We present the developed general framework for 1D/3D hybrid modeling and apply it to investigate electrically active neurons and their intracellular spatio-temporal calcium dynamics.

A quantitative framework for the 3D characterization of the osteocyte lacunar system

Assessing the role of osteocyte lacunae and the ways in which they communicate with one another is important for determining the function and viability of bone tissue. Osteocytes are able to play a significant role in bone development and remodeling because they can receive nourishment from, interact with, and communicate with other cells. In this sense the immediate environment of an osteocyte is crucial for understanding its function. Modern imaging techniques, ranging from synchrotron radiation-based computed tomography (SR CT) to confocal laser scanning microscopy, produce large volumes of high-quality imaging data of bone tissue on the micrometer scale in rapidly shortening times. These images often contain tens of thousands of osteocytes and their lacunae, void spaces which enclose the osteocytes. While theoretically possible, quantitative analysis of the osteocyte lacunar system is too time consuming to be practical without highly automated tools. Moreover, quantitative morphometry of the osteocyte lacunar system necessitates clearly defined, robust, and three-dimensional (3D) measures. Here, we introduce a framework for the quantitative characterization of millions of osteocyte lacunae and their spatial relationships in 3D. The metrics complement and expand previous works looking at shape and number density while providing novel measures for quantifying spatial distribution and alignment. We developed model, in silico systems to visualize and validate the metrics and provide a concrete example of the attribute being classified with each metric. We then illustrate the applicability to biological samples in a first study comparing two strains of mice and the effect of growth hormone. We found significant differences in shape and distribution between strains for alignment. The proposed quantitative framework can be used in future studies examining differences and treatment effects in bone microstructure at the cell scale. Furthermore, the proposed strategy for quantitative bone cell morphometry will allow investigating structure-function relationships in bone tissue, for example by linking cellular morphometry to bone remodeling.

The systems biology simulation core algorithm

BACKGROUND

With the increasing availability of high dimensional time course data for metabolites, genes, and fluxes, the mathematical description of dynamical systems has become an essential aspect of research in systems biology. Models are often encoded in formats such as SBML, whose structure is very complex and difficult to evaluate due to many special cases.

RESULTS

This article describes an efficient algorithm to solve SBML models that are interpreted in terms of ordinary differential equations. We begin our consideration with a formal representation of the mathematical form of the models and explain all parts of the algorithm in detail, including several preprocessing steps. We provide a flexible reference implementation as part of the Systems Biology Simulation Core Library, a community-driven project providing a large collection of numerical solvers and a sophisticated interface hierarchy for the definition of custom differential equation systems. To demonstrate the capabilities of the new algorithm, it has been tested with the entire SBML Test Suite and all models of BioModels Database.

CONCLUSIONS

The formal description of the mathematics behind the SBML format facilitates the implementation of the algorithm within specifically tailored programs. The reference implementation can be used as a simulation backend for Java™-based programs. Source code, binaries, and documentation can be freely obtained under the terms of the LGPL version 3 from http://simulation-core.sourceforge.net. Feature requests, bug reports, contributions, or any further discussion can be directed to the mailing list simulation-core-development@lists.sourceforge.net.

Finding novel pharmaceuticals in the systems biology era using multiple effective drug targets, phenotypic screening and knowledge of transporters: where drug discovery went wrong and how to fix it

Despite the sequencing of the human genome, the rate of innovative and successful drug discovery in the pharmaceutical industry has continued to decrease. Leaving aside regulatory matters, the fundamental and interlinked intellectual issues proposed to be largely responsible for this are: (a) the move from 'function-first' to 'target-first' methods of screening and drug discovery; (b) the belief that successful drugs should and do interact solely with single, individual targets, despite natural evolution's selection for biochemical networks that are robust to individual parameter changes; (c) an over-reliance on the rule-of-5 to constrain biophysical and chemical properties of drug libraries; (d) the general abandoning of natural products that do not obey the rule-of-5; (e) an incorrect belief that drugs diffuse passively into (and presumably out of) cells across the bilayers portions of membranes, according to their lipophilicity; (f) a widespread failure to recognize the overwhelmingly important role of proteinaceous transporters, as well as their expression profiles, in determining drug distribution in and between different tissues and individual patients; and (g) the general failure to use engineering principles to model biology in parallel with performing 'wet' experiments, such that 'what if?' experiments can be performed in silico to assess the likely success of any strategy. These facts/ideas are illustrated with a reasonably extensive literature review. Success in turning round drug discovery consequently requires: (a) decent systems biology models of human biochemical networks; (b) the use of these (iteratively with experiments) to model how drugs need to interact with multiple targets to have substantive effects on the phenotype; (c) the adoption of polypharmacology and/or cocktails of drugs as a desirable goal in itself; (d) the incorporation of drug transporters into systems biology models, en route to full and multiscale systems biology models that incorporate drug absorption, distribution, metabolism and excretion; (e) a return to 'function-first' or phenotypic screening; and (f) novel methods for inferring modes of action by measuring the properties on system variables at all levels of the 'omes. Such a strategy offers the opportunity of achieving a state where we can hope to predict biological processes and the effect of pharmaceutical agents upon them. Consequently, this should both lower attrition rates and raise the rates of discovery of effective drugs substantially.

Spatial modeling of cell signaling networks

The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling.