Virtual Cell modelling and simulation software environment.

The Virtual Cell (VCell; http://vcell.org/) is a problem solving environment, built on a central database, for analysis, modelling and simulation of cell biological processes. VCell integrates a growing range of molecular mechanisms, including reaction kinetics, diffusion, flow, membrane transport, lateral membrane diffusion and electrophysiology, and can associate these with geometries derived from experimental microscope images. It has been developed and deployed as a web-based, distributed, client-server system, with more than a thousand world-wide users. VCell provides a separation of layers (core technologies and abstractions) representing biological models, physical mechanisms, geometry, mathematical models and numerical methods. This separation clarifies the impact of modelling decisions, assumptions and approximations. The result is a physically consistent, mathematically rigorous, spatial modelling and simulation framework. Users create biological models and VCell will automatically (i) generate the appropriate mathematical encoding for running a simulation and (ii) generate and compile the appropriate computer code. Both deterministic and stochastic algorithms are supported for describing and running non-spatial simulations; a full partial differential equation solver using the finite volume numerical algorithm is available for reaction-diffusion-advection simulations in complex cell geometries including 3D geometries derived from microscope images. Using the VCell database, models and model components can be reused and updated, as well as privately shared among collaborating groups, or published. Exchange of models with other tools is possible via import/export of SBML, CellML and MatLab formats. Furthermore, curation of models is facilitated by external database binding mechanisms for unique identification of components and by standardised annotations compliant with the MIRIAM standard. VCell is now open source, with its native model encoding language (VCML) being a public specification, which stands as the basis for a new generation of more customised, experiment-centric modelling tools using a new plug-in based platform.

Modeling of transcellular Ca transport in rat duodenum points to coexistence of two mechanisms of apical entry.

Employing realistic parameters, we have demonstrated that a relatively simple mathematical model can reproduce key features of steady-state Ca2+ transport with the assumption of two mechanisms of Ca2+ entry: a channel-like flux and a carrier-mediated transport. At low luminal [Ca2+] (1-5 mM), facilitated entry dominates and saturates with Km = 0.4 mM. At luminal [Ca2+] of tens of millimolar, apical permeability is dominated by the channel flux that in turn is regulated by cytosolic Ca2+. The model reproduces the linear relationship between maximum Ca2+ transport rate and intestinal calbindin D9K (CaBP) content. At luminal [Ca2+] > 50 mM, local sensitivity analysis shows transcellular transport to be most sensitive to variations in CaBP. At low luminal [Ca2+], transport becomes sensitive to apical entry regulation. The simulations have been run within the Virtual Cell modeling environment, yielding the time course of external Ca2+ and spatiotemporal distributions of both intracellular Ca2+ and CaBP. Coexistence of two apical entry mechanisms accords with the properties of the duodenal Ca2+ transport protein CaT1 and the epithelial Ca2+ channel ECaC.

A new model for nuclear envelope breakdown.

Nuclear envelope breakdown was investigated during meiotic maturation of starfish oocytes. Fluorescent 70-kDa dextran entry, as monitored by confocal microscopy, consists of two phases, a slow uniform increase and then a massive wave. From quantitative analysis of the first phase of dextran entry, and from imaging of green fluorescent protein chimeras, we conclude that nuclear pore disassembly begins several minutes before nuclear envelope breakdown. The best fit for the second phase of entry is with a spreading disruption of the membrane permeability barrier determined by three-dimensional computer simulations of diffusion. We propose a new model for the mechanism of nuclear envelope breakdown in which disassembly of the nuclear pores leads to a fenestration of the nuclear envelope double membrane.

Topology of the mitochondrial inner membrane: dynamics and bioenergetic implications.

Electron tomography indicates that the mitochondrial inner membrane is not normally comprised of baffle-like folds as depicted in textbooks. In actuality, this membrane is pleomorphic, with narrow tubular regions connecting the internal compartments (cristae) to each other and to the membrane periphery. The membrane topologies observed in condensed (matrix contracted) and orthodox (matrix expanded) mitochondria cannot be interconverted by passive folding and unfolding. Instead, transitions between these morphological states likely involve membrane fusion and fission. Formation of tubular junctions in the inner membrane appears to be energetically favored, because they form spontaneously in yeast mitochondria following large-amplitude swelling and recontraction. However, aberrant, unattached, vesicular cristae are also observed in these mitochondria, suggesting that formation of cristae junctions depends on factors (such as the distribution of key proteins and/or lipids) that are disrupted during extreme swelling. Computer modeling studies using the "Virtual Cell" program suggest that the shape of the inner membrane can influence mitochondrial function. Simulations indicate that narrow cristae junctions restrict diffusion between intracristal and external compartments, causing depletion of ADP and decreased ATP output inside the cristae.

Physiological modeling with virtual cell framework.

This article describes a computational framework for cell biological modeling and simulation that is based on the mapping of experimental biochemical and electrophysiological data onto experimental images. The framework is designed to enable the construction of complex general models that encompass the general class of problems coupling reaction and diffusion.

An image-based model of calcium waves in differentiated neuroblastoma cells.

Calcium waves produced by bradykinin-induced inositol-1,4, 5-trisphosphate (InsP(3))-mediated release from endoplasmic reticulum (ER) have been imaged in N1E-115 neuroblastoma cells. A model of this process was built using the "virtual cell," a general computational system for integrating experimental image, biochemical, and electrophysiological data. The model geometry was based on a cell for which the calcium wave had been experimentally recorded. The distributions of the relevant cellular components [InsP(3) receptor (InsP(3)R)], sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pumps, bradykinin receptors, and ER] were based on 3D confocal immunofluorescence images. Wherever possible, known biochemical and electrophysiological data were used to constrain the model. The simulation closely matched the spatial and temporal characteristics of the experimental calcium wave. Predictions on different patterns of calcium signals after InsP(3) uncaging or for different cell geometries were confirmed experimentally, thus helping to validate the model. Models in which the spatial distributions of key components are altered suggest that initiation of the wave in the center of the neurite derives from an interplay of soma-biased ER distribution and InsP(3) generation biased toward the neurite. Simulations demonstrate that mobile buffers (like the indicator fura-2) significantly delay initiation and lower the amplitude of the wave. Analysis of the role played by calcium diffusion indicated that the speed of the wave is only slightly dependent on the ability of calcium to diffuse to and activate neighboring InsP(3) receptor sites.

Morphological control of inositol-1,4,5-trisphosphate-dependent signals.

Inositol-1,4,5-trisphosphate (InsP(3))-mediated calcium signals represent an important mechanism for transmitting external stimuli to the cell. However, information about intracellular spatial patterns of InsP(3) itself is not generally available. In particular, it has not been determined how the interplay of InsP(3) generation, diffusion, and degradation within complex cellular geometries can control the patterns of InsP(3) signaling. Here, we explore the spatial and temporal characteristics of [InsP(3)](cyt) during a bradykinin-induced calcium wave in a neuroblastoma cell. This is achieved by using a unique image-based computer modeling system, Virtual Cell, to integrate experimental data on the rates and spatial distributions of the key molecular components of the process. We conclude that the characteristic calcium dynamics requires rapid, high-amplitude production of [InsP(3)](cyt) in the neurite. This requisite InsP(3) spatiotemporal profile is provided, in turn, as an intrinsic consequence of the cell's morphology, demonstrating how geometry can locally and dramatically intensify cytosolic signals that originate at the plasma membrane. In addition, the model predicts, and experiments confirm, that stimulation of just the neurite, but not the soma or growth cone, is sufficient to generate a calcium response throughout the cell.

Determination of time-dependent inositol-1,4,5-trisphosphate concentrations during calcium release in a smooth muscle cell.

The level of [InsP3]cyt required for calcium release in A7r5 cells, a smooth muscle cell line, was determined by a new set of procedures using quantitative confocal microscopy to measure release of InsP3 from cells microinjected with caged InsP3. From these experiments, the [InsP3]cyt required to evoke a half-maximal calcium response is 100 nM. Experiments with caged glycerophosphoryl-myo-inositol 4, 5-bisphosphate (GPIP2), a slowly metabolized analogue of InsP3, gave a much slower recovery and a half-maximal response of an order of magnitude greater than InsP3. Experimental data and highly constrained variables were used to construct a mathematical model of the InsP3-dependent [Ca2+]cyt changes; the resulting simulations show high fidelity to experiment. Among the elements considered in constructing this model were the mechanism of the InsP3-receptor, InsP3 degradation, calcium buffering in the cytosol, and refilling of the ER stores via sarcoplasmic endoplasmic reticulum ATPase (SERCA) pumps. The model predicts a time constant of 0.8 s for InsP3 degradation and 13 s for GPIP2. InsP3 degradation was found to be a prerequisite for [Ca2+]cyt recovery to baseline levels and is therefore critical to the pattern of the overall [Ca2+]cyt signal. Analysis of the features of this model provides insights into the individual factors controlling the amplitude and shape of the InsP3-mediated calcium signal.

A general computational framework for modeling cellular structure and function.

The "Virtual Cell" provides a general system for testing cell biological mechanisms and creates a framework for encapsulating the burgeoning knowledge base comprising the distribution and dynamics of intracellular biochemical processes. It approaches the problem by associating biochemical and electrophysiological data describing individual reactions with experimental microscopic image data describing their subcellular localizations. Individual processes are collected within a physical and computational infrastructure that accommodates any molecular mechanism expressible as rate equations or membrane fluxes. An illustration of the method is provided by a dynamic simulation of IP3-mediated Ca2+ release from endoplasmic reticulum in a neuronal cell. The results can be directly compared to experimental observations and provide insight into the role of experimentally inaccessible components of the overall mechanism.