The Virtual Cell: a software environment for computational cell biology

A Multiscale Algorithm for Spatiotemporal Modeling of Multivalent Protein-Protein Interaction

This article introduces a multiscale framework for spatiotemporal modeling of protein-protein interaction. Cellular protein molecules represent multivalent species that contain modular features, such as binding domains and phosphorylation motifs. The binding and transformations of these features occur at a small time and spatial scale. On the other hand, space and time involved in protein diffusion, colocalization, and formation of complexes could be relatively large. Here, we present an agent-based framework integrated with a multiscale Brownian Dynamics (BD) simulation algorithm. The framework employs spatial graphs to describe multivalent molecules and complexes with their site-specific details. By implementing a time-adaptive feature, the BD algorithm enables efficient computation while capturing the site-specific interactions of the diffusing species at the sub-nanometer scale. We demonstrate these capabilities by modeling two multivalent molecules, one representing a ligand and the other a receptor, in a two-dimensional plane (cell membrane). Using the model, we show that the algorithm can accelerate computation by orders of magnitudes in both concentrated and dilute regimes. We also show that the algorithm enables robust model predictions against a wide range of selection of time step sizes.

Modeling and simulation of biological systems using SPICE language

The article deals with BB-SPICE (SPICE for Biochemical and Biological Systems), an extension of the famous Simulation Program with Integrated Circuit Emphasis (SPICE). BB-SPICE environment is composed of three modules: a new textual and compact description formalism for biological systems, a converter that handles this description and generates the SPICE netlist of the equivalent electronic circuit and NGSPICE which is an open-source SPICE simulator. In addition, the environment provides back and forth interfaces with SBML (System Biology Markup Language), a very common description language used in systems biology. BB-SPICE has been developed in order to bridge the gap between the simulation of biological systems on the one hand and electronics circuits on the other hand. Thus, it is suitable for applications at the interface between both domains, such as development of design tools for synthetic biology and for the virtual prototyping of biosensors and lab-on-chip. Simulation results obtained with BB-SPICE and COPASI (an open-source software used for the simulation of biochemical systems) have been compared on a benchmark of models commonly used in systems biology. Results are in accordance from a quantitative viewpoint but BB-SPICE outclasses COPASI by 1 to 3 orders of magnitude regarding the computation time. Moreover, as our software is based on NGSPICE, it could take profit of incoming updates such as the GPU implementation, of the coupling with powerful analysis and verification tools or of the integration in design automation tools (synthetic biology).

How Not To Drown in Data: A Guide for Biomaterial Engineers

High-throughput assays that produce hundreds of measurements per sample are powerful tools for quantifying cell-material interactions. With advances in automation and miniaturization in material fabrication, hundreds of biomaterial samples can be rapidly produced, which can then be characterized using these assays. However, the resulting deluge of data can be overwhelming. To the rescue are computational methods that are well suited to these problems. Machine learning techniques provide a vast array of tools to make predictions about cell-material interactions and to find patterns in cellular responses. Computational simulations allow researchers to pose and test hypotheses and perform experiments in silico. This review describes approaches from these two domains that can be brought to bear on the problem of analyzing biomaterial screening data.

The fungal UmSrt1 and maize ZmSUT1 sucrose transporters battle for plant sugar resources

The biotrophic fungus Ustilago maydis causes corn smut disease, inducing tumor formation in its host Zea mays. Upon infection, the fungal hyphae invaginate the plasma membrane of infected maize cells, establishing an interface where pathogen and host are separated only by their plasma membranes. At this interface the fungal and maize sucrose transporters, UmSrt1 and ZmSUT1, compete for extracellular sucrose in the corn smut/maize pathosystem. Here we biophysically characterized ZmSUT1 and UmSrt1 in Xenopus oocytes with respect to their voltage-, pH- and substrate-dependence and determined affinities toward protons and sucrose. In contrast to ZmSUT1, UmSrt1 has a high affinity for sucrose and is relatively pH- and voltage-independent. Using these quantitative parameters, we developed a mathematical model to simulate the competition for extracellular sucrose at the contact zone between the fungus and the host plant. This approach revealed that UmSrt1 exploits the apoplastic sucrose resource, which forces the plant transporter into a sucrose export mode providing the fungus with sugar from the phloem. Importantly, the high sucrose concentration in the phloem appeared disadvantageous for the ZmSUT1, preventing sucrose recovery from the apoplastic space in the fungus/plant interface.

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.

Subcellular protein expression models for microsatellite instability in colorectal adenocarcinoma tissue images

Background

New bioimaging techniques capable of visualising the co-location of numerous proteins within individual cells have been proposed to study tumour heterogeneity of neighbouring cells within the same tissue specimen. These techniques have highlighted the need to better understand the interplay between proteins in terms of their colocalisation.

Results

We recently proposed a cellular-level model of the healthy and cancerous colonic crypt microenvironments. Here, we extend the model to include detailed models of protein expression to generate synthetic multiplex fluorescence data. As a first step, we present models for various cell organelles learned from real immunofluorescence data from the Human Protein Atlas. Comparison between the distribution of various features obtained from the real and synthetic organelles has shown very good agreement. This has included both features that have been used as part of the model input and ones that have not been explicitly considered. We then develop models for six proteins which are important colorectal cancer biomarkers and are associated with microsatellite instability, namely MLH1, PMS2, MSH2, MSH6, P53 and PTEN. The protein models include their complex expression patterns and which cell phenotypes express them. The models have been validated by comparing distributions of real and synthesised parameters and by application of frameworks for analysing multiplex immunofluorescence image data.

Conclusions

The six proteins have been chosen as a case study to illustrate how the model can be used to generate synthetic multiplex immunofluorescence data. Further proteins could be included within the model in a similar manner to enable the study of a larger set of proteins of interest and their interactions. To the best of our knowledge, this is the first model for expression of multiple proteins in anatomically intact tissue, rather than within cells in culture.

Reproducibility in Computational Neuroscience Models and Simulations

OBJECTIVE

Like all scientific research, computational neuroscience research must be reproducible. Big data science, including simulation research, cannot depend exclusively on journal articles as the method to provide the sharing and transparency required for reproducibility.

METHODS

Ensuring model reproducibility requires the use of multiple standard software practices and tools, including version control, strong commenting and documentation, and code modularity.

RESULTS

Building on these standard practices, model-sharing sites and tools have been developed that fit into several categories: 1) standardized neural simulators; 2) shared computational resources; 3) declarative model descriptors, ontologies, and standardized annotations; and 4) model-sharing repositories and sharing standards.

CONCLUSION

A number of complementary innovations have been proposed to enhance sharing, transparency, and reproducibility. The individual user can be encouraged to make use of version control, commenting, documentation, and modularity in development of models. The community can help by requiring model sharing as a condition of publication and funding.

SIGNIFICANCE

Model management will become increasingly important as multiscale models become larger, more detailed, and correspondingly more difficult to manage by any single investigator or single laboratory. Additional big data management complexity will come as the models become more useful in interpreting experiments, thus increasing the need to ensure clear alignment between modeling data, both parameters and results, and experiment.

In silico spatial simulations reveal that MCC formation and excess BubR1 are required for tight inhibition of the anaphase-promoting complex

In response to the activation of the mitotic spindle assembly checkpoint (SAC), distinct inhibitory pathways control the activity of the anaphase-promoting complex (APC/C). It remains unclear whether the different regulatory mechanisms function in separate pathways or as part of an integrated signalling system. Here, five variant models of APC/C regulation were constructed and analysed. The simulations showed that all variant models were able to reproduce the wild type behaviour of the APC. However, only one model, which included both the mitotic checkpoint complex (MCC) as well as BubR1 as direct inhibitors of the APC/C, was able to reproduce both wild and mutant type behaviour of APC/C regulation. Interestingly, in this model, the MCC as well as the BubR1 binding rate to the APC/C was comparable to the known Cdc20-Mad2 binding rate and could not be made higher. Mad2 active transport towards the spindle mid-zone accelerated the inhibition speed of the APC/C but not its concentration level. The presented study highlights the principle that a systems biology approach is critical for the SAC mechanism and could also be used for predicting hypotheses to design future experiments. The presented work has successfully distinguished between five potent inhibitors of the APC/C using a systems biology approach. Here, the favoured model contains both BubR1 and MCC as direct inhibitors of the APC/C.

Point process models for localization and interdependence of punctate cellular structures

Accurate representations of cellular organization for multiple eukaryotic cell types are required for creating predictive models of dynamic cellular function. To this end, we have previously developed the CellOrganizer platform, an open source system for generative modeling of cellular components from microscopy images. CellOrganizer models capture the inherent heterogeneity in the spatial distribution, size, and quantity of different components among a cell population. Furthermore, CellOrganizer can generate quantitatively realistic synthetic images that reflect the underlying cell population. A current focus of the project is to model the complex, interdependent nature of organelle localization. We built upon previous work on developing multiple non-parametric models of organelles or structures that show punctate patterns. The previous models described the relationships between the subcellular localization of puncta and the positions of cell and nuclear membranes and microtubules. We extend these models to consider the relationship to the endoplasmic reticulum (ER), and to consider the relationship between the positions of different puncta of the same type. Our results do not suggest that the punctate patterns we examined are dependent on ER position or inter- and intra-class proximity. With these results, we built classifiers to update previous assignments of proteins to one of 11 patterns in three distinct cell lines. Our generative models demonstrate the ability to construct statistically accurate representations of puncta localization from simple cellular markers in distinct cell types, capturing the complex phenomena of cellular structure interaction with little human input. This protocol represents a novel approach to vesicular protein annotation, a field that is often neglected in high-throughput microscopy. These results suggest that spatial point process models provide useful insight with respect to the spatial dependence between cellular structures. © 2016 International Society for Advancement of Cytometry.

Rule-based modeling with Virtual Cell

Rule-based modeling is invaluable when the number of possible species and reactions in a model become too large to allow convenient manual specification. The popular rule-based software tools BioNetGen and NFSim provide powerful modeling and simulation capabilities at the cost of learning a complex scripting language which is used to specify these models. Here, we introduce a modeling tool that combines new graphical rule-based model specification with existing simulation engines in a seamless way within the familiar Virtual Cell (VCell) modeling environment. A mathematical model can be built integrating explicit reaction networks with reaction rules. In addition to offering a large choice of ODE and stochastic solvers, a model can be simulated using a network free approach through the NFSim simulation engine.

AVAILABILITY AND IMPLEMENTATION

Available as VCell (versions 6.0 and later) at the Virtual Cell web site (http://vcell.org/). The application installs and runs on all major platforms and does not require registration for use on the user's computer. Tutorials are available at the Virtual Cell website and Help is provided within the software. Source code is available at Sourceforge.

CONTACT

vcell_support@uchc.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

On the importance of modelling the internal spatial dynamics of biological cells

Spatial effects such as cell shape have very often been considered negligible in models of cellular pathways, and many existing simulation infrastructures do not take such effects into consideration. Recent experimental results are reversing this judgement by showing that very small spatial variations can make a big difference in the fate of a cell. This is particularly the case when considering eukaryotic cells, which have a complex physical structure and many subtle control mechanisms, but bacteria are also interesting for the huge variation in shape both between species and in different phases of their lifecycle. In this work we perform simulations that measure the effect of three common bacterial shapes on the behaviour of model cellular pathways. To perform these experiments we develop ReDi-Cell, a highly scalable GPGPU cell simulation infrastructure for the modelling of cellular pathways in spatially detailed environments. ReDi-Cell is validated against known-good simulations, prior to its use in new work. We then use ReDi-Cell to conduct novel experiments that demonstrate the effect that three common bacterial shapes (Cocci, Bacilli and Spirilli) have on the behaviour of model cellular pathways. Pathway wavefront shape, pathway concentration gradients, and chemical species distribution are measured in the three different shapes. We also quantify the impact of internal cellular clutter on the same pathways. Through this work we show that variations in the shape or configuration of these common cell shapes alter model cell behaviour.

Time-Dependent Model to Mimic Acetylcholine Induced Vasodilatation in Arterial Smooth Muscle Cells

Computational approaches for spatial modeling of dynamics of the intercellular distribution of molecules can parse, simplify, classify and organize the spatiotemporal richness of any biochemical pathway and demonstrate its impact on the cells function by simply coupling it with the downstream effecters. One such online system biology modeling package is Virtual cell that provides a unique open source software and it’s used for making mathematical models to simulate the cytoplasmic control of molecule that interact to produce certain cellular behavior. In our present study, a spatial model for time dependent acetylcholine induced relaxation of vascular endothelial cells lining the lumen of blood vessel that regulate the contractility of the arteries was generated. The time-dependent action of neurotransmitter acetylcholine for total time period for 1 second was studied on the endothelial cell at an interval of every 0.05 seconds. Such time simulated spatial models may be useful for testing and developing new hypotheses, interpretation of results and understand the dynamic behavior of cells.

Building cell models and simulations from microscope images

The use of fluorescence microscopy has undergone a major revolution over the past twenty years, both with the development of dramatic new technologies and with the widespread adoption of image analysis and machine learning methods. Many open source software tools provide the ability to use these methods in a wide range of studies, and many molecular and cellular phenotypes can now be automatically distinguished. This article presents the next major challenge in microscopy automation, the creation of accurate models of cell organization directly from images, and reviews the progress that has been made towards this challenge.

Time-Dependent Model to Mimic Acetylcholine Induced Vasodilatation in Arterial Smooth Muscle Cells

Computational approaches for spatial modeling of dynamics of the intercellular distribution of molecules can parse, simplify, classify and organize the spatiotemporal richness of any biochemical pathway and demonstrate its impact on the cells function by simply coupling it with the downstream effecters. One such online system biology modeling package is Virtual cell that provides a unique open source software and it’s used for making mathematical models to simulate the cytoplasmic control of molecule that interact to produce certain cellular behavior. In our present study, a spatial model for time dependent acetylcholine induced relaxation of vascular endothelial cells lining the lumen of blood vessel that regulate the contractility of the arteries was generated. The time-dependent action of neurotransmitter acetylcholine for total time period for 1 second was studied on the endothelial cell at an interval of every 0.05 seconds. Such time simulated spatial models may be useful for testing and developing new hypotheses, interpretation of results and understand the dynamic behavior of cells.

Cooperation through Competition-Dynamics and Microeconomics of a Minimal Nutrient Trade System in Arbuscular Mycorrhizal Symbiosis

In arbuscular mycorrhizal (AM) symbiosis, fungi and plants exchange nutrients (sugars and phosphate, for instance) for reciprocal benefit. Until now it is not clear how this nutrient exchange system works. Here, we used computational cell biology to simulate the dynamics of a network of proton pumps and proton-coupled transporters that are upregulated during AM formation. We show that this minimal network is sufficient to describe accurately and realistically the nutrient trade system. By applying basic principles of microeconomics, we link the biophysics of transmembrane nutrient transport with the ecology of organismic interactions and straightforwardly explain macroscopic scenarios of the relations between plant and AM fungus. This computational cell biology study allows drawing far reaching hypotheses about the mechanism and the regulation of nutrient exchange and proposes that the "cooperation" between plant and fungus can be in fact the result of a competition between both for the same resources in the tiny periarbuscular space. The minimal model presented here may serve as benchmark to evaluate in future the performance of more complex models of AM nutrient exchange. As a first step toward this goal, we included SWEET sugar transporters in the model and show that their co-occurrence with proton-coupled sugar transporters results in a futile carbon cycle at the plant plasma membrane proposing that two different pathways for the same substrate should not be active at the same time.

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.

PROKARYO: an illustrative and interactive computational model of the lactose operon in the bacterium Escherichia coli

Background

We are creating software for agent-based simulation and visualization of bio-molecular processes in bacterial and eukaryotic cells. As a first example, we have built a 3-dimensional, interactive computer model of an Escherichia coli bacterium and its associated biomolecular processes. Our illustrative model focuses on the gene regulatory processes that control the expression of genes involved in the lactose operon. Prokaryo, our agent-based cell simulator, incorporates cellular structures, such as plasma membranes and cytoplasm, as well as elements of the molecular machinery, including RNA polymerase, messenger RNA, lactose permease, and ribosomes.

Results

The dynamics of cellular ’agents’ are defined by their rules of interaction, implemented as finite state machines. The agents are embedded within a 3-dimensional virtual environment with simulated physical and electrochemical properties. The hybrid model is driven by a combination of (1) mathematical equations (DEQs) to capture higher-scale phenomena and (2) agent-based rules to implement localized interactions among a small number of molecular elements. Consequently, our model is able to capture phenomena across multiple spatial scales, from changing concentration gradients to one-on-one molecular interactions.

We use the classic gene regulatory mechanism of the lactose operon to demonstrate our model’s resolution, visual presentation, and real-time interactivity. Our agent-based model expands on a sophisticated mathematical E. coli metabolism model, through which we highlight our model’s scientific validity.

Conclusion

We believe that through illustration and interactive exploratory learning a model system like Prokaryo can enhance the general understanding and perception of biomolecular processes. Our agent-DEQ hybrid modeling approach can also be of value to conceptualize, illustrate, and—eventually—validate cell experiments in the wet lab.

Dynamical modeling of uncertain interaction-based genomic networks

BACKGROUND

Most dynamical models for genomic networks are built upon two current methodologies, one process-based and the other based on Boolean-type networks. Both are problematic when it comes to experimental design purposes in the laboratory. The first approach requires a comprehensive knowledge of the parameters involved in all biological processes a priori, whereas the results from the second method may not have a biological correspondence and thus cannot be tested in the laboratory. Moreover, the current methods cannot readily utilize existing curated knowledge databases and do not consider uncertainty in the knowledge. Therefore, a new methodology is needed that can generate a dynamical model based on available biological data, assuming uncertainty, while the results from experimental design can be examined in the laboratory.

RESULTS

We propose a new methodology for dynamical modeling of genomic networks that can utilize the interaction knowledge provided in public databases. The model assigns discrete states for physical entities, sets priorities among interactions based on information provided in the database, and updates each interaction based on associated node states. Whenever uncertainty in dynamics arises, it explores all possible outcomes. By using the proposed model, biologists can study regulation networks that are too complex for manual analysis.

CONCLUSIONS

The proposed approach can be effectively used for constructing dynamical models of interaction-based genomic networks without requiring a complete knowledge of all parameters affecting the network dynamics, and thus based on a small set of available data.

Multiscale modeling of mucosal immune responses

Computational modeling techniques are playing increasingly important roles in advancing a systems-level mechanistic understanding of biological processes. Computer simulations guide and underpin experimental and clinical efforts. This study presents ENteric Immune Simulator (ENISI), a multiscale modeling tool for modeling the mucosal immune responses. ENISI's modeling environment can simulate in silico experiments from molecular signaling pathways to tissue level events such as tissue lesion formation. ENISI's architecture integrates multiple modeling technologies including ABM (agent-based modeling), ODE (ordinary differential equations), SDE (stochastic modeling equations), and PDE (partial differential equations). This paper focuses on the implementation and developmental challenges of ENISI. A multiscale model of mucosal immune responses during colonic inflammation, including CD4+ T cell differentiation and tissue level cell-cell interactions was developed to illustrate the capabilities, power and scope of ENISI MSM.

Visualizing genome and systems biology: technologies, tools, implementation techniques and trends, past, present and future

"Α picture is worth a thousand words." This widely used adage sums up in a few words the notion that a successful visual representation of a concept should enable easy and rapid absorption of large amounts of information. Although, in general, the notion of capturing complex ideas using images is very appealing, would 1000 words be enough to describe the unknown in a research field such as the life sciences? Life sciences is one of the biggest generators of enormous datasets, mainly as a result of recent and rapid technological advances; their complexity can make these datasets incomprehensible without effective visualization methods. Here we discuss the past, present and future of genomic and systems biology visualization. We briefly comment on many visualization and analysis tools and the purposes that they serve. We focus on the latest libraries and programming languages that enable more effective, efficient and faster approaches for visualizing biological concepts, and also comment on the future human-computer interaction trends that would enable for enhancing visualization further.

Symmetry and scale orient Min protein patterns in shaped bacterial sculptures

The boundary of a cell defines the shape and scale of its subcellular organization. However, the effects of the cell's spatial boundaries as well as the geometry sensing and scale adaptation of intracellular molecular networks remain largely unexplored. Here, we show that living bacterial cells can be 'sculpted' into defined shapes, such as squares and rectangles, which are used to explore the spatial adaptation of Min proteins that oscillate pole-to-pole in rod-shaped Escherichia coli to assist cell division. In a wide geometric parameter space, ranging from 2 × 1 × 1 to 11 × 6 × 1 μm(3), Min proteins exhibit versatile oscillation patterns, sustaining rotational, longitudinal, diagonal, stripe and even transversal modes. These patterns are found to directly capture the symmetry and scale of the cell boundary, and the Min concentration gradients scale with the cell size within a characteristic length range of 3-6 μm. Numerical simulations reveal that local microscopic Turing kinetics of Min proteins can yield global symmetry selection, gradient scaling and an adaptive range, when and only when facilitated by the three-dimensional confinement of the cell boundary. These findings cannot be explained by previous geometry-sensing models based on the longest distance, membrane area or curvature, and reveal that spatial boundaries can facilitate simple molecular interactions to result in far more versatile functions than previously understood.

Spindle assembly checkpoint is sufficient for complete Cdc20 sequestering in mitotic control

The spindle checkpoint assembly (SAC) ensures genome fidelity by temporarily delaying anaphase onset, until all chromosomes are properly attached to the mitotic spindle. The SAC delays mitotic progression by preventing activation of the ubiquitin ligase anaphase-promoting complex (APC/C) or cyclosome; whose activation by Cdc20 is required for sister-chromatid separation marking the transition into anaphase. The mitotic checkpoint complex (MCC), which contains Cdc20 as a subunit, binds stably to the APC/C. Compelling evidence by Izawa and Pines (Nature 2014; 10.1038/nature13911) indicates that the MCC can inhibit a second Cdc20 that has already bound and activated the APC/C. Whether or not MCC per se is sufficient to fully sequester Cdc20 and inhibit APC/C remains unclear. Here, a dynamic model for SAC regulation in which the MCC binds a second Cdc20 was constructed. This model is compared to the MCC, and the MCC-and-BubR1 (dual inhibition of APC) core model variants and subsequently validated with experimental data from the literature. By using ordinary nonlinear differential equations and spatial simulations, it is shown that the SAC works sufficiently to fully sequester Cdc20 and completely inhibit APC/C activity. This study highlights the principle that a systems biology approach is vital for molecular biology and could also be used for creating hypotheses to design future experiments.

Local perturbation analysis: a computational tool for biophysical reaction-diffusion models

Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model's behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application.

COMBINE archive and OMEX format: one file to share all information to reproduce a modeling project

BACKGROUND

With the ever increasing use of computational models in the biosciences, the need to share models and reproduce the results of published studies efficiently and easily is becoming more important. To this end, various standards have been proposed that can be used to describe models, simulations, data or other essential information in a consistent fashion. These constitute various separate components required to reproduce a given published scientific result.

RESULTS

We describe the Open Modeling EXchange format (OMEX). Together with the use of other standard formats from the Computational Modeling in Biology Network (COMBINE), OMEX is the basis of the COMBINE Archive, a single file that supports the exchange of all the information necessary for a modeling and simulation experiment in biology. An OMEX file is a ZIP container that includes a manifest file, listing the content of the archive, an optional metadata file adding information about the archive and its content, and the files describing the model. The content of a COMBINE Archive consists of files encoded in COMBINE standards whenever possible, but may include additional files defined by an Internet Media Type. Several tools that support the COMBINE Archive are available, either as independent libraries or embedded in modeling software.

CONCLUSIONS

The COMBINE Archive facilitates the reproduction of modeling and simulation experiments in biology by embedding all the relevant information in one file. Having all the information stored and exchanged at once also helps in building activity logs and audit trails. We anticipate that the COMBINE Archive will become a significant help for modellers, as the domain moves to larger, more complex experiments such as multi-scale models of organs, digital organisms, and bioengineering.

Synthetic biology outside the cell: linking computational tools to cell-free systems

As mathematical models become more commonly integrated into the study of biology, a common language for describing biological processes is manifesting. Many tools have emerged for the simulation of in vivo synthetic biological systems, with only a few examples of prominent work done on predicting the dynamics of cell-free synthetic systems. At the same time, experimental biologists have begun to study dynamics of in vitro systems encapsulated by amphiphilic molecules, opening the door for the development of a new generation of biomimetic systems. In this review, we explore both in vivo and in vitro models of biochemical networks with a special focus on tools that could be applied to the construction of cell-free expression systems. We believe that quantitative studies of complex cellular mechanisms and pathways in synthetic systems can yield important insights into what makes cells different from conventional chemical systems.

Structural basis of thymosin-β4/profilin exchange leading to actin filament polymerization

Thymosin-β4 (Tβ4) and profilin are the two major sequestering proteins that maintain the pool of monomeric actin (G-actin) within cells of higher eukaryotes. Tβ4 prevents G-actin from joining a filament, whereas profilin:actin only supports barbed-end elongation. Here, we report two Tβ4:actin structures. The first structure shows that Tβ4 has two helices that bind at the barbed and pointed faces of G-actin, preventing the incorporation of the bound G-actin into a filament. The second structure displays a more open nucleotide binding cleft on G-actin, which is typical of profilin:actin structures, with a concomitant disruption of the Tβ4 C-terminal helix interaction. These structures, combined with biochemical assays and molecular dynamics simulations, show that the exchange of bound actin between Tβ4 and profilin involves both steric and allosteric components. The sensitivity of profilin to the conformational state of actin indicates a similar allosteric mechanism for the dissociation of profilin during filament elongation.

Active transport can greatly enhance Cdc20:Mad2 formation

To guarantee genomic integrity and viability, the cell must ensure proper distribution of the replicated chromosomes among the two daughter cells in mitosis. The mitotic spindle assembly checkpoint (SAC) is a central regulatory mechanism to achieve this goal. A dysfunction of this checkpoint may lead to aneuploidy and likely contributes to the development of cancer. Kinetochores of unattached or misaligned chromosomes are thought to generate a diffusible “wait-anaphase” signal, which is the basis for downstream events to inhibit the anaphase promoting complex/cyclosome (APC/C). The rate of Cdc20:C-Mad2 complex formation at the kinetochore is a key regulatory factor in the context of APC/C inhibition. Computer simulations of a quantitative SAC model show that the formation of Cdc20:C-Mad2 is too slow for checkpoint maintenance when cytosolic O-Mad2 has to encounter kinetochores by diffusion alone. Here, we show that an active transport of O-Mad2 towards the spindle mid-zone increases the efficiency of Mad2-activation. Our in-silico data indicate that this mechanism can greatly enhance the formation of Cdc20:Mad2 and furthermore gives an explanation on how the “wait-anaphase” signal can dissolve abruptly within a short time. Our results help to understand parts of the SAC mechanism that remain unclear.

Biocellion: accelerating computer simulation of multicellular biological system models

MOTIVATION

Biological system behaviors are often the outcome of complex interactions among a large number of cells and their biotic and abiotic environment. Computational biologists attempt to understand, predict and manipulate biological system behavior through mathematical modeling and computer simulation. Discrete agent-based modeling (in combination with high-resolution grids to model the extracellular environment) is a popular approach for building biological system models. However, the computational complexity of this approach forces computational biologists to resort to coarser resolution approaches to simulate large biological systems. High-performance parallel computers have the potential to address the computing challenge, but writing efficient software for parallel computers is difficult and time-consuming.

RESULTS

We have developed Biocellion, a high-performance software framework, to solve this computing challenge using parallel computers. To support a wide range of multicellular biological system models, Biocellion asks users to provide their model specifics by filling the function body of pre-defined model routines. Using Biocellion, modelers without parallel computing expertise can efficiently exploit parallel computers with less effort than writing sequential programs from scratch. We simulate cell sorting, microbial patterning and a bacterial system in soil aggregate as case studies.

AVAILABILITY AND IMPLEMENTATION

Biocellion runs on x86 compatible systems with the 64 bit Linux operating system and is freely available for academic use. Visit http://biocellion.com for additional information.

Plant systems biology: insights, advances and challenges

Plants dwelling at the base of biological food chain are of fundamental significance in providing solutions to some of the most daunting ecological and environmental problems faced by our planet. The reductionist views of molecular biology provide only a partial understanding to the phenotypic knowledge of plants. Systems biology offers a comprehensive view of plant systems, by employing a holistic approach integrating the molecular data at various hierarchical levels. In this review, we discuss the basics of systems biology including the various 'omics' approaches and their integration, the modeling aspects and the tools needed for the plant systems research. A particular emphasis is given to the recent analytical advances, updated published examples of plant systems biology studies and the future trends.

Understanding the sub-cellular dynamics of silicon transportation and synthesis in diatoms using population-level data and computational optimization

Controlled synthesis of silicon is a major challenge in nanotechnology and material science. Diatoms, the unicellular algae, are an inspiring example of silica biosynthesis, producing complex and delicate nano-structures. This happens in several cell compartments, including cytoplasm and silica deposition vesicle (SDV). Considering the low concentration of silicic acid in oceans, cells have developed silicon transporter proteins (SIT). Moreover, cells change the level of active SITs during one cell cycle, likely as a response to the level of external nutrients and internal deposition rates. Despite this topic being of fundamental interest, the intracellular dynamics of nutrients and cell regulation strategies remain poorly understood. One reason is the difficulties in measurements and manipulation of these mechanisms at such small scales, and even when possible, data often contain large errors. Therefore, using computational techniques seems inevitable. We have constructed a mathematical model for silicon dynamics in the diatom Thalassiosira pseudonana in four compartments: external environment, cytoplasm, SDV and deposited silica. The model builds on mass conservation and Michaelis-Menten kinetics as mass transport equations. In order to find the free parameters of the model from sparse, noisy experimental data, an optimization technique (global and local search), together with enzyme related penalty terms, has been applied. We have connected population-level data to individual-cell-level quantities including the effect of early division of non-synchronized cells. Our model is robust, proven by sensitivity and perturbation analysis, and predicts dynamics of intracellular nutrients and enzymes in different compartments. The model produces different uptake regimes, previously recognized as surge, externally-controlled and internally-controlled uptakes. Finally, we imposed a flux of SITs to the model and compared it with previous classical kinetics. The model introduced can be generalized in order to analyze different biomineralizing organisms and to test different chemical pathways only by switching the system of mass transport equations.

Exploring emergent properties in cellular homeostasis using OnGuard to model K+ and other ion transport in guard cells

It is widely recognized that the nature and characteristics of transport across eukaryotic membranes are so complex as to defy intuitive understanding. In these circumstances, quantitative mathematical modeling is an essential tool, both to integrate detailed knowledge of individual transporters and to extract the properties emergent from their interactions. As the first, fully integrated and quantitative modeling environment for the study of ion transport dynamics in a plant cell, OnGuard offers a unique tool for exploring homeostatic properties emerging from the interactions of ion transport, both at the plasma membrane and tonoplast in the guard cell. OnGuard has already yielded detail sufficient to guide phenotypic and mutational studies, and it represents a key step toward 'reverse engineering' of stomatal guard cell physiology, based on rational design and testing in simulation, to improve water use efficiency and carbon assimilation. Its construction from the HoTSig libraries enables translation of the software to other cell types, including growing root hairs and pollen. The problems inherent to transport are nonetheless challenging, and are compounded for those unfamiliar with conceptual 'mindset' of the modeler. Here we set out guidelines for the use of OnGuard and outline a standardized approach that will enable users to advance quickly to its application both in the classroom and laboratory. We also highlight the uncanny and emergent property of OnGuard models to reproduce the 'communication' evident between the plasma membrane and tonoplast of the guard cell.

Robustness analysis of stochastic biochemical systems

We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.

Meeting report from the fourth meeting of the Computational Modeling in Biology Network (COMBINE)

The Computational Modeling in Biology Network (COMBINE) is an initiative to coordinate the development of community standards and formats in computational systems biology and related fields. This report summarizes the topics and activities of the fourth edition of the annual COMBINE meeting, held in Paris during September 16-20 2013, and attended by a total of 96 people. This edition pioneered a first day devoted to modeling approaches in biology, which attracted a broad audience of scientists thanks to a panel of renowned speakers. During subsequent days, discussions were held on many subjects including the introduction of new features in the various COMBINE standards, new software tools that use the standards, and outreach efforts. Significant emphasis went into work on extensions of the SBML format, and also into community-building. This year’s edition once again demonstrated that the COMBINE community is thriving, and still manages to help coordinate activities between different standards in computational systems biology.

The role of low-grade inflammation and metabolic flexibility in aging and nutritional modulation thereof: a systems biology approach

Aging is a biological process characterized by the progressive functional decline of many interrelated physiological systems. In particular, aging is associated with the development of a systemic state of low-grade chronic inflammation (inflammaging), and with progressive deterioration of metabolic function. Systems biology has helped in identifying the mediators and pathways involved in these phenomena, mainly through the application of high-throughput screening methods, valued for their molecular comprehensiveness. Nevertheless, inflammation and metabolic regulation are dynamical processes whose behavior must be understood at multiple levels of biological organization (molecular, cellular, organ, and system levels) and on multiple time scales. Mathematical modeling of such behavior, with incorporation of mechanistic knowledge on interactions between inflammatory and metabolic mediators, may help in devising nutritional interventions capable of preventing, or ameliorating, the age-associated functional decline of the corresponding systems.

Decoding information in cell shape

Shape is an indicator of cell health. But how is the information in shape decoded? We hypothesize that decoding occurs by modulation of signaling through changes in plasma membrane curvature. Using analytical approaches and numerical simulations, we studied how elongation of cell shape affects plasma membrane signaling. Mathematical analyses reveal transient accumulation of activated receptors at regions of higher curvature with increasing cell eccentricity. This distribution of activated receptors is periodic, following the Mathieu function, and it arises from local imbalance between reaction and diffusion of soluble ligands and receptors in the plane of the membrane. Numerical simulations show that transient microdomains of activated receptors amplify signals to downstream protein kinases. For growth factor receptor pathways, increasing cell eccentricity elevates the levels of activated cytoplasmic Src and nuclear MAPK1,2. These predictions were experimentally validated by changing cellular eccentricity, showing that shape is a locus of retrievable information storage in cells.

Reaction-diffusion in the NEURON simulator

In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics) on the dynamics of neuronal response in health and disease, NEURON's Reaction-Diffusion (rxd) module in Python provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy's sparse linear algebra library.

A software architecture for multi-cellular system simulations on graphics processing units

The first aim of simulation in virtual environment is to help biologists to have a better understanding of the simulated system. The cost of such simulation is significantly reduced compared to that of in vivo simulation. However, the inherent complexity of biological system makes it hard to simulate these systems on non-parallel architectures: models might be made of sub-models and take several scales into account; the number of simulated entities may be quite large. Today, graphics cards are used for general purpose computing which has been made easier thanks to frameworks like CUDA or OpenCL. Parallelization of models may however not be easy: parallel computer programing skills are often required; several hardware architectures may be used to execute models. In this paper, we present the software architecture we built in order to implement various models able to simulate multi-cellular system. This architecture is modular and it implements data structures adapted for graphics processing units architectures. It allows efficient simulation of biological mechanisms.

Simulation of E. coli gene regulation including overlapping cell cycles, growth, division, time delays and noise

Due to the complexity of biological systems, simulation of biological networks is necessary but sometimes complicated. The classic stochastic simulation algorithm (SSA) by Gillespie and its modified versions are widely used to simulate the stochastic dynamics of biochemical reaction systems. However, it has remained a challenge to implement accurate and efficient simulation algorithms for general reaction schemes in growing cells. Here, we present a modeling and simulation tool, called ‘GeneCircuits’, which is specifically developed to simulate gene-regulation in exponentially growing bacterial cells (such as E. coli) with overlapping cell cycles. Our tool integrates three specific features of these cells that are not generally included in SSA tools: 1) the time delay between the regulation and synthesis of proteins that is due to transcription and translation processes; 2) cell cycle-dependent periodic changes of gene dosage; and 3) variations in the propensities of chemical reactions that have time-dependent reaction rates as a consequence of volume expansion and cell division. We give three biologically relevant examples to illustrate the use of our simulation tool in quantitative studies of systems biology and synthetic biology.

Visualizing time-related data in biology, a review

Time is of the essence in biology as in so much else. For example, monitoring disease progression or the timing of developmental defects is important for the processes of drug discovery and therapy trials. Furthermore, an understanding of the basic dynamics of biological phenomena that are often strictly time regulated (e.g. circadian rhythms) is needed to make accurate inferences about the evolution of biological processes. Recent advances in technologies have enabled us to measure timing effects more accurately and in more detail. This has driven related advances in visualization and analysis tools that try to effectively exploit this data. Beyond timeline plots, notable attempts at more involved temporal interpretation have been made in recent years, but awareness of the available resources is still limited within the scientific community. Here, we review some advances in biological visualization of time-driven processes and consider how they aid data analysis and interpretation.

A comparison of computational models for eukaryotic cell shape and motility

Eukaryotic cell motility involves complex interactions of signalling molecules, cytoskeleton, cell membrane, and mechanics interacting in space and time. Collectively, these components are used by the cell to interpret and respond to external stimuli, leading to polarization, protrusion, adhesion formation, and myosin-facilitated retraction. When these processes are choreographed correctly, shape change and motility results. A wealth of experimental data have identified numerous molecular constituents involved in these processes, but the complexity of their interactions and spatial organization make this a challenging problem to understand. This has motivated theoretical and computational approaches with simplified caricatures of cell structure and behaviour, each aiming to gain better understanding of certain kinds of cells and/or repertoire of behaviour. Reaction–diffusion (RD) equations as well as equations of viscoelastic flows have been used to describe the motility machinery. In this review, we describe some of the recent computational models for cell motility, concentrating on simulations of cell shape changes (mainly in two but also three dimensions). The problem is challenging not only due to the difficulty of abstracting and simplifying biological complexity but also because computing RD or fluid flow equations in deforming regions, known as a “free-boundary” problem, is an extremely challenging problem in applied mathematics. Here we describe the distinct approaches, comparing their strengths and weaknesses, and the kinds of biological questions that they have been able to address.

Evaluation of a genome-scale in silico metabolic model for Geobacter metallireducens by using proteomic data from a field biostimulation experiment

Accurately predicting the interactions between microbial metabolism and the physical subsurface environment is necessary to enhance subsurface energy development, soil and groundwater cleanup, and carbon management. This study was an initial attempt to confirm the metabolic functional roles within an in silico model using environmental proteomic data collected during field experiments. Shotgun global proteomics data collected during a subsurface biostimulation experiment were used to validate a genome-scale metabolic model of Geobacter metallireducens-specifically, the ability of the metabolic model to predict metal reduction, biomass yield, and growth rate under dynamic field conditions. The constraint-based in silico model of G. metallireducens relates an annotated genome sequence to the physiological functions with 697 reactions controlled by 747 enzyme-coding genes. Proteomic analysis showed that 180 of the 637 G. metallireducens proteins detected during the 2008 experiment were associated with specific metabolic reactions in the in silico model. When the field-calibrated Fe(III) terminal electron acceptor process reaction in a reactive transport model for the field experiments was replaced with the genome-scale model, the model predicted that the largest metabolic fluxes through the in silico model reactions generally correspond to the highest abundances of proteins that catalyze those reactions. Central metabolism predicted by the model agrees well with protein abundance profiles inferred from proteomic analysis. Model discrepancies with the proteomic data, such as the relatively low abundances of proteins associated with amino acid transport and metabolism, revealed pathways or flux constraints in the in silico model that could be updated to more accurately predict metabolic processes that occur in the subsurface environment.

Condor-COPASI: high-throughput computing for biochemical networks

Background

Mathematical modelling has become a standard technique to improve our understanding of complex biological systems. As models become larger and more complex, simulations and analyses require increasing amounts of computational power. Clusters of computers in a high-throughput computing environment can help to provide the resources required for computationally expensive model analysis. However, exploiting such a system can be difficult for users without the necessary expertise.

Results

We present Condor-COPASI, a server-based software tool that integrates COPASI, a biological pathway simulation tool, with Condor, a high-throughput computing environment. Condor-COPASI provides a web-based interface, which makes it extremely easy for a user to run a number of model simulation and analysis tasks in parallel. Tasks are transparently split into smaller parts, and submitted for execution on a Condor pool. Result output is presented to the user in a number of formats, including tables and interactive graphical displays.

Conclusions

Condor-COPASI can effectively use a Condor high-throughput computing environment to provide significant gains in performance for a number of model simulation and analysis tasks. Condor-COPASI is free, open source software, released under the Artistic License 2.0, and is suitable for use by any institution with access to a Condor pool. Source code is freely available for download at http://code.google.com/p/condor-copasi/, along with full instructions on deployment and usage.

OnGuard, a computational platform for quantitative kinetic modeling of guard cell physiology

Stomatal guard cells play a key role in gas exchange for photosynthesis while minimizing transpirational water loss from plants by opening and closing the stomatal pore. Foliar gas exchange has long been incorporated into mathematical models, several of which are robust enough to recapitulate transpirational characteristics at the whole-plant and community levels. Few models of stomata have been developed from the bottom up, however, and none are sufficiently generalized to be widely applicable in predicting stomatal behavior at a cellular level. We describe here the construction of computational models for the guard cell, building on the wealth of biophysical and kinetic knowledge available for guard cell transport, signaling, and homeostasis. The OnGuard software was constructed with the HoTSig library to incorporate explicitly all of the fundamental properties for transporters at the plasma membrane and tonoplast, the salient features of osmolite metabolism, and the major controls of cytosolic-free Ca²⁺ concentration and pH. The library engenders a structured approach to tier and interrelate computational elements, and the OnGuard software allows ready access to parameters and equations 'on the fly' while enabling the network of components within each model to interact computationally. We show that an OnGuard model readily achieves stability in a set of physiologically sensible baseline or Reference States; we also show the robustness of these Reference States in adjusting to changes in environmental parameters and the activities of major groups of transporters both at the tonoplast and plasma membrane. The following article addresses the predictive power of the OnGuard model to generate unexpected and counterintuitive outputs.

Computational analysis of calcium signaling and membrane electrophysiology in cerebellar Purkinje neurons associated with ataxia

Background

Mutations in the smooth endoplasmic reticulum (sER) calcium channel Inositol Trisphosphate Receptor type 1 (IP3R1) in humans with the motor function coordination disorders Spinocerebellar Ataxia Types 15 and 16 (SCA15/16) and in a corresponding mouse model, the IP3R1^{delta18/delta18} mice, lead to reduced IP3R1 levels. We posit that increasing IP3R1 sensitivity to IP3 in ataxias with reduced IP3R1 could restore normal calcium response. On the other hand, in mouse models of the human polyglutamine (polyQ) ataxias, SCA2, and SCA3, the primary finding appears to be hyperactive IP3R1-mediated calcium release. It has been suggested that the polyQ SCA1 mice may also show hyperactive IP3R1. Yet, SCA1 mice show downregulated gene expression of IP3R1, Homer, metabotropic glutamate receptor (mGluR), smooth endoplasmic reticulum Ca-ATP-ase (SERCA), calbindin, parvalbumin, and other calcium signaling proteins.

Results

We create a computational model of pathological alterations in calcium signaling in cerebellar Purkinje neurons to investigate several forms of spinocerebellar ataxia associated with changes in the abundance, sensitivity, or activity of the calcium channel IP3R1. We find that increasing IP3R1 sensitivity to IP3 in computational models of SCA15/16 can restore normal calcium response if IP3R1 abundance is not too low. The studied range in IP3R1 levels reflects variability found in human and mouse ataxic models. Further, the required fold increases in sensitivity are within experimental ranges from experiments that use IP3R1 phosphorylation status to adjust its sensitivity to IP3. Results from our simulations of polyglutamine SCAs suggest that downregulation of some calcium signaling proteins may be partially compensatory. However, the downregulation of calcium buffer proteins observed in the SCA1 mice may contribute to pathology. Finally, our model suggests that the calcium-activated voltage-gated potassium channels may provide an important link between calcium metabolism and membrane potential in Purkinje cell function.

Conclusion

Thus, we have established an initial platform for computational evaluation and prediction of ataxia pathophysiology. Specifically, the model has been used to investigate SCA15/16, SCA1, SCA2, and SCA3. Results suggest that experimental studies treating mouse models of any of these ataxias with appropriately chosen peptides resembling the C-terminal of IP3R1 could adjust receptor sensitivity, and thereby modulate calcium release and normalize IP3 response. In addition, the model supports the hypothesis of IP3R1 supersensitivity in SCA1.

Modeling of spatial intracellular signaling events in neurons

A neuron is able to seamlessly respond to a number of signals, in a timely and specific manner. This process, of integrating multiple inputs, relays on the orchestration of intracellular events by signaling networks. The inherent complexity of signaling networks has made computational modeling a useful approach to understand their underlying regulatory principles. Recent advances in imaging techniques have highlighted the nonhomogeneous nature of intracellular signaling and its significant contribution to the maintenance of signal specificity. Computational modeling can provide mechanistic insight into the origins of these inhomogeneous distributions of signaling components and their role in the integrative capabilities of the neuron.

In silico implementation of synthetic gene networks

Computational synthetic biology has borrowed methods, concepts, and techniques from systems biology and electrical engineering. Features of tools for the analysis of biochemical networks and the design of electric circuits have been combined to develop new software, where Standard Biological Parts (physically stored at the MIT Registry) have a mathematical description, based on mass action or Hill kinetics, and can be assembled into genetic networks in a visual, "drag & drop" fashion. Recent tools provide the user with databases, simulation environments, formal languages, and even algorithms for circuit automatic design to refine and speed up gene network construction. Moreover, advances in automation of DNA assembly indicate that synthetic biology software soon will drive the wet-lab implementation of DNA sequences.