The Virtual Cell: a software environment for computational cell biology

The newly emerging field of computational cell biology requires software tools that address the needs of a broad community of scientists. Cell biological processes are controlled by an interacting set of biochemical and electrophysiological events that are distributed within complex cellular structures. Computational modeling is familiar to researchers in fields such as molecular structure, neurobiology and metabolic pathway engineering, and is rapidly emerging in the area of gene expression. Although some of these established modeling approaches can be adapted to address problems of interest to cell biologists, relatively few software development efforts have been directed at the field as a whole. The Virtual Cell is a computational environment designed for cell biologists as well as for mathematical biologists and bioengineers. It serves to aid the construction of cell biological models and the generation of simulations from them. The system enables the formulation of both compartmental and spatial models, the latter with either idealized or experimentally derived geometries of one, two or three dimensions.     

Virtual NEURON: a strategy for merged biochemical and electrophysiological modeling

Because of its highly branched dendrite, the Purkinje neuron requires significant computational resources if coupled electrical and biochemical activity are to be simulated. To address this challenge, we developed a scheme for reducing the geometric complexity; while preserving the essential features of activity in both the soma and a remote dendritic spine. We merged our previously published biochemical model of calcium dynamics and lipid signaling in the Purkinje neuron, developed in the Virtual Cell modeling and simulation environment, with an electrophysiological model based on a Purkinje neuron model available in NEURON. A novel reduction method was applied to the Purkinje neuron geometry to obtain a model with fewer compartments that is tractable in Virtual Cell. Most of the dendritic tree was subject to reduction, but we retained the neuron’s explicit electrical and geometric features along a specified path from spine to soma. Further, unlike previous simplification methods, the dendrites that branch off along the preserved explicit path are retained as reduced branches. We conserved axial resistivity and adjusted passive properties and active channel conductances for the reduction in surface area, and cytosolic calcium for the reduction in volume. Rallpacks are used to validate the reduction algorithm and show that it can be generalized to other complex neuronal geometries. For the Purkinje cell, we found that current injections at the soma were able to produce similar trains of action potentials and membrane potential propagation in the full and reduced models in NEURON; the reduced model produces identical spiking patterns in NEURON and Virtual Cell. Importantly, our reduced model can simulate communication between the soma and a distal spine; an alpha function applied at the spine to represent synaptic stimulation gave similar results in the full and reduced models for potential changes associated with both the spine and the soma. Finally, we combined phosphoinositol signaling and electrophysiology in the reduced model in Virtual Cell. Thus, a strategy has been developed to combine electrophysiology and biochemistry as a step toward merging neuronal and systems biology modeling.     

Common pathways for growth and for plasticity

Cell growth and differentiation in developing tissues are, at first impression, quite different endeavors from readjusting synaptic strength during activity-dependent synaptic plasticity in mature neurons. Nevertheless, it is becoming increasingly clear that these two distinct processes share multiple intracellular signaling events. How these common pathways result in cell division (during proliferation), large-scale cellular remodeling (during differentiation) or synapse-specific changes (during synaptic plasticity) is only starting to be elucidated. Here we review the latest findings on two prototypical examples of these shared mechanisms: the Ras-PI3K pathway and the intracellular signaling elicited by neural cell adhesion molecules interacting with growth factor receptors.     

Spermatozoa and Plasmodium zoites: the same way to invade oocyte and host cells?

Cell movement or motility is essential for a large variety of processes. Fertilization and host cells invasion by parasites are among the mostly studied models so far. Body of evidences into the literature raises the question that common mechanisms may be found in the sequential events that lead to cell motility in these two particular models. This short review aims at highlighting these common features by comparing knowledge on motile forms of Plasmodium falciparum and one of the best known motile cell namely the spermatozoa. Emphasis will be done on the substantial changes affecting the biochemical, electrophysiological and functional properties of both models.     

An Open Model of Actin Dendritic Nucleation

The availability of quantitative experimental data on the kinetics of actin assembly has enabled the construction of many mathematical models focused on explaining specific behaviors of this complex system. However these ad hoc models are generally not reusable or accessible by the large community of actin biologists. In this work, we present a comprehensive model that integrates and unifies much of the in vitro data on the components of the dendritic nucleation mechanism for actin dynamics. More than 300 simulations have been run based on compartmental and three-dimensional spatial versions of this model. Several key findings are highlighted, including an explanation for the sharp boundary between actin assembly and disassembly in the lamellipodia of migrating cells. Because this model, with the simulation results, is “open source”, in the sense that it is publicly available and editable through the Virtual Cell database (http://vcell.org), it can be accessed, analyzed, modified, and extended.     

Computer evaluation of network dynamics models with application to cell cycle control in budding yeast

Cellular processes are governed by complex networks of interacting genes and proteins. Theoretical molecular biologists attempt to describe these processes via mathematical models by writing biochemical reaction equations. Modellers are building increasingly larger and complex mathematical models to describe these cellular processes, making model evaluation a time consuming and difficult task. The authors describe an automatable process for model evaluation and a software system that implements this process. The software is adaptable to many types of models and is freely available along with all needed data files. The cell cycle control system for budding yeast is known in fine detail and constrained by more than 100 phenotypic observations in mutant strains. As an example, the authors apply their process to a model of cell cycle control in budding yeast containing dozens of regulatory equations and explaining nearly all of the known mutant phenotypes.     

A web platform for the network analysis of high-throughput data in melanoma and its use to investigate mechanisms of resistance to anti-PD1 immunotherapy

Cellular phenotypes are established and controlled by complex and precisely orchestrated molecular networks. In cancer, mutations and dysregulations of multiple molecular factors perturb the regulation of these networks and lead to malignant transformation. High-throughput technologies are a valuable source of information to establish the complex molecular relationships behind the emergence of malignancy, but full exploitation of this massive amount of data requires bioinformatics tools that rely on network-based analyses.In this report we present the Virtual Melanoma Cell, an online tool developed to facilitate the mining and interpretation of high-throughput data on melanoma by biomedical researches. The platform is based on a comprehensive, manually generated and expert-validated regulatory map composed of signaling pathways important in malignant melanoma. The Virtual Melanoma Cell is a tool designed to accept, visualize and analyze user-generated datasets. It is available at: https://www.vcells.net/melanoma. To illustrate the utilization of the web platform and the regulatory map, we have analyzed a large publicly available dataset accounting for anti-PD1 immunotherapy treatment of malignant melanoma patients.     

UML as a cell and biochemistry modeling language

The systems biology community is building increasingly complex models and simulations of cells and other biological entities, and are beginning to look at alternatives to traditional representations such as those provided by ordinary differential equations (ODE). The lessons learned over the years by the software development community in designing and building increasingly complex telecommunication and other commercial real-time reactive systems, can be advantageously applied to the problems of modeling in the biology domain. Making use of the object-oriented (OO) paradigm, the unified modeling language (UML) and Real-Time Object-Oriented Modeling (ROOM) visual formalisms, and the Rational Rose RealTime (RRT) visual modeling tool, we describe a multi-step process we have used to construct top–down models of cells and cell aggregates. The simple example model described in this paper includes membranes with lipid bilayers, multiple compartments including a variable number of mitochondria, substrate molecules, enzymes with reaction rules, and metabolic pathways. We demonstrate the relevance of abstraction, reuse, objects, classes, component and inheritance hierarchies, multiplicity, visual modeling, and other current software development best practices. We show how it is possible to start with a direct diagrammatic representation of a biological structure such as a cell, using terminology familiar to biologists, and by following a process of gradually adding more and more detail, arrive at a system with structure and behavior of arbitrary complexity that can run and be observed on a computer. We discuss our CellAK (Cell Assembly Kit) approach in terms of features found in SBML, CellML, E-CELL, Gepasi, Jarnac, StochSim, Virtual Cell, and membrane computing systems.     

Lessons from genetics: interpreting complex phenotypes in RNAi screens

Mammalian cell biology is witnessing a new era in which cellular processes are explained through dynamic networks of interacting cellular components. In this fast-pacing field, where image-based RNAi screening is taking a central role, there is a strong need to improve ways to capture such interactions in space and time. Cell biologists traditionally depict these events by confining themselves to the level of a single cell, or to many population-averaged cells. Similarly, classical geneticists observe and interpret phenotypes in a single organism to delineate signaling processes, but have also described genetic phenomena in populations of organisms. The analogy in the two approaches inspired us to draw parallels with, and take lessons from concepts in classical genetics.     

Cell division in the CNS: protective response or lethal event in post-mitotic neurons?

Cell cycle events have been documented to be associated with several human neurodegenerative diseases. This review focuses on two diseases--Alzheimer's disease and ataxia telangiectasia--as well as their mouse models. Cell cycle studies have shown that ectopic expression of cell cycle markers is spatially and regional correlated well with neuronal cell death in both disease conditions. Further evidence of ectopic cell cycling is found in both human diseases and in its mouse models. These findings suggest that loss of cell cycle control represents a common pathological root of disease, which underlies the defects in the affected brain tissues in both human and mouse. Loss of cell cycle control is a unifying hypothesis for inducing neuronal death in CNS. In the disease models we have examined, cell cycle markers appear before the more well-recognized pathological changes and thus could serve as early stress markers--outcome measures for preclinical trials of potential disease therapies. As a marker these events could serve as a new criterion in human pathological diagnosis. The evidence to date is compatible with the requirement for a second "hit" for a neuron to progress cell cycle initiation and DNA replication to death. If this were true, any intervention of blocking 'second' processes might prevent or slow the neuronal cell death in the process of disease. What is not known is whether, in an adult neuron, the cell cycle event is part of the pathology or rather a desperate attempt of a neuron under stress to protect itself.     

Spatio-temporal dependence of the signaling response in immune-receptor trafficking networks regulated by cell density: a theoretical model

Cell signaling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signaling pathways. In most experimental systems, ligand concentration and cell density vary within a wide range of values. Dependence of the signal response on cell density is related with the extracellular volume available per cell. This dependence has previously been studied using non-spatial models which assume that signaling components are well mixed and uniformly distributed in a single compartment. In this paper, a mathematical model that shows the influence exerted by cell density on the spatio-temporal evolution of ligands, cell surface receptors, and intracellular signaling molecules is developed. To this end, partial differential equations were used to model ligand and receptor trafficking dynamics through the different domains of the whole system. This enabled us to analyze several interesting features involved with these systems, namely: a) how the perturbation caused by the signaling response propagates through the system; b) receptor internalization dynamics and how cell density affects the robustness of dose-response curves upon variation of the binding affinity; and c) that enhanced correlations between ligand input and system response are obtained under conditions that result in larger perturbations of the equilibrium ligand + surface receptor [Please see text] ligand - receptor complex. Finally, the results are compared with those obtained by considering that the above components are well mixed in a single compartment.     

Biochemical and statistical network models for systems biology

The normal and abnormal behavior of a living cell is governed by complex networks of interacting biomolecules. Models of these networks allow us to make predictions about cellular behavior under a variety of environmental cues. In this review, we focus on two broad classes of such models: biochemical network models and statistical inference models. In particular, we discuss a number of modeling approaches in the context of the assumptions that they entail, the types of data required for their inference, and the range of their applicability.     

Collective modes and wavelike solutions to cellular control equations

A living cell is viewed as a system of biochemical reaction pathways which are self- and mutually-regulating. A matrix differential equation is proposed which governs the system behavior. A periodic boundary condition is introduced which allows the equation to be solved for its eigenvalues and eigenvectors. The nature of the solution is such that a set of coordinates representing strongly interacting chemical populations is converted into a set of collective coordinates representing weakly interacting oscillatory modes. The modes are travelling waves which transport matter through an open loop and information through a closed loop. The validity of the model is examined, as is the relation to other models of the cellular regulatory apparatus. An experiment is outlined which should detect these modes if they are present in living cells. The main impediment to their detection is nonlinearity, which produces decay of the modes. Several predictions of the model may be associated with specific cellular attributes. The “growth mode” belongs to zero frequency. An unstable mode acts like a switch causing a cell to enter a new phase. Cell division is seen as such a phase transition. Although there is discontinuity in the global aspect (one cell becoming two), there is still a slow variation in chemical concentrations, in keeping with biochemical evidence.     

Modeling regulatory networks at Virginia Tech

The life of a cell is governed by the physicochemical properties of a complex network of interacting macromolecules (primarily genes and proteins). Hence, a full scientific understanding of and rational engineering approach to cell physiology require accurate mathematical models of the spatial and temporal dynamics of these macromolecular assemblies, especially the networks involved in integrating signals and regulating cellular responses. The Virginia Tech Consortium is involved in three specific goals of DARPA's computational biology program (Bio-COMP): to create effective software tools for modeling gene-protein-metabolite networks, to employ these tools in creating a new generation of realistic models, and to test and refine these models by well-conceived experimental studies. The special emphasis of this group is to understand the mechanisms of cell cycle control in eukaryotes (yeast cells and frog eggs). The software tools developed at Virginia Tech are designed to meet general requirements of modeling regulatory networks and are collected in a problem-solving environment called JigCell.     

Electrophoretic Properties, Cell Surface Morphology and Calcium in Amphibian Gastrulation

The process of gastrulation is characterized by extensive morphogeneticmovements, cell shape changes and intercellular rearrangements.This paper presents the results and inferences of experimentalanalysis of these events. Cell electrokinetic mobility, whichis a measure of net cell surface charge density, cell surfacemorphological changes, and the role of calcium are aspects ofgastrular events which we believe play a significant role. Ourhypothesis is that these parameters are interrelated and weoffer suggestions with respect to the interrelationships andhow these aspects mediate morphogenetic movements.     

Unraveling cell division mechanisms with small-molecule inhibitors

Cell division is the process by which a cell creates two genetically identical daughter cells. To maintain genomic integrity, a complex and highly regulated sequence of events ensures that the replicated chromosomes are equally partitioned between the daughter cells. For more than 50 years, strategies designed around small-molecule inhibitors have been critical in advancing our understanding of this essential process. Here we introduce a series of questions on the biology of cell division and illustrate how small molecules have been used to design experiments to address these questions. Because of the highly dynamic nature of cell division, the temporal control over protein function that is possible with small molecules has been particularly valuable in dissecting biological mechanisms.     

The cellular basis of cell sorting kinetics

Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis.The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However, the model dynamics at the cellular scale are defined implicitly and are not well-justified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear.It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.     

Phenotypic characterization of telomerase-immortalized primary non-malignant and malignant tumor-derived human prostate epithelial cell lines

In vitro human prostate cell culture models are critical for clarifying the mechanism of prostate cancer progression and for testing preventive and therapeutic agents. Cell lines ideal for the study of human primary prostate tumors would be those derived from spontaneously immortalized tumor cells; unfortunately, explanted primary prostate cells survive only short-term in culture, and rarely immortalize spontaneously. Therefore, we recently have generated five immortal human prostate epithelial cell cultures derived from both the benign and malignant tissues of prostate cancer patients with telomerase, a gene that prevents cellular senescence. Examination of these cell lines for their morphologies and proliferative capacities, their abilities to grow in low serum, to respond to androgen stimulation, to grow above the agar layer, to form tumors in SCID mice, suggests that they may serve as valid, useful tools for the elucidation of early events in prostate tumorigenesis. Furthermore, the chromosome alterations observed in these immortalized cell lines expressing aspects of the malignant phenotypes imply that these cell lines accurately recapitulate the genetic composition of primary tumors. These novel in vitro models may offer unique models for the study of prostate carcinogenesis and also provide the means for testing both chemopreventive and chemotherapeutic agents.     

Protein kinase C epsilon in cell division: Control of abscission

Cell division requires the separation and partitioning of sister chromatids to opposite ends of the cell before an actomyosin ring contracts the membrane in between during cytokinesis. The final irreversible step occurs during abscission when the ring breaks down and the membrane is sealed in its place. The physical mechanics of contraction depend on RhoA which is stimulated by a centralspindlin complex around the cell equator. However exactly how these events are reversed to allow actomyosin breakdown and abscission were not well understood. Here we will discuss new findings which implicate Protein Kinase C epsilon (PKCε) as a regulator of RhoA signalling required for abscission.