Modeling - Approaches
Cell migration is a superb example of biological complexity, as it intertwines biochemical signaling networks with biophysical locomotory processes. The challenge is to integrate the myriad of molecular components and interactions that are continually being identified, into the process of cell migration as a dynamical system. By analogy to other complex systems, this integration will be enabled by casting of the interrelationships in terms of mathematical models.
Why Model Migration?
To understand why mathematical models can be useful to defining the complexities of a biological process such as cell migration consider for a moment their application to the engineering of human-made technologies. The Boeing 777 jet aircraft possesses millions of parts, organized into roughly 150,000 distinct subsystems most of which are complicated networks comprising many thousands of components; effective and safe operation of this aircraft could not have been achieved without appropriate mathematical modeling efforts. This is also the case with other complex engineered technologies such as the internal combustion engine and VLSI chips. In none of these examples could one hope to understand the effect of any particular component or even subsystem without formulating mathematical models representative of the various physico-chemical processes involved. As components and subsystems underlying living cells continue to be identified, the need to develop computational models describing these parts is evident. With appropriate modeling it should be possible to interpret and even predict results from experimental studies on molecular-level interventions in cell migration - whether by genetic alterations, pharmacological treatment, or materials presentation. The modeling of cell migration requires a deep understanding of each of the component processes and their integration into a physiological phenomenon. Consequently it is implicit that a dynamic and reciprocal interaction is needed, with those investigators generating the information about these component processes and their integration. The application of data to these models figures prominently in the process of refining and developing the models themselves.
Modeling Approaches
Until a completely comprehensive physico-chemical model of cell migration in its entirety is feasible, there is a need to make available to investigators diverse categories of models that are useful for different purposes. One approach is that of detailed physico-chemical models for the various individual biophysical processes involved in locomotion: e.g., lamellipodial/filopodial membrane extension, formation of cell/substratum attachments, generation of intracellular contractile forces, and force transmission to the cell/substratum attachments. Eventually, a comprehensive physico-chemical model for cell locomotion overall could incorporate all these processes in a coordinated manner, and would connect them to regulatory signaling pathways (as well as gene expression dynamics). In the meantime, however, we believe that the most productive road to this ultimate model will be to move forward simultaneously along three avenues: one focuses on relational models with special emphasis on how intracellular signals govern cell migration behavior, a second address physicochemical models, with emphasis on cell membrane and cytoskeleton processes involved in lamellipod extension, adhesion, and force generation, and the third incorporates both biochemical signals and biophysical processes into the interactive, Virtual Cell Web site.
Cue-Signal-Response Analysis in Cell Migration
A useful framework for parsing the effects of extracellular cues (e.g., diffusible ligands, substratum-bound ligands, mechanical stresses, etc.) on cell migration responses via the intracellular signals generated by the cues and governing the responses as illustrated.
At least certain aspects of mechanistic information concerning the physico-chemical reaction and transport events involved in signal generation following cell stimulation by cues is certainly available for some systems, and for such computational analysis by means of differential equation models for the signaling pathways can be gainfully employed; this is the approach being taken in the Virtual Cell facet of the Consortium Computational Modeling Initiative under the direction of Les Loew. For systems in which physico-chemical detail is not available, computational analysis of how key signaling activities depend on various cue stimuli can be performed using relational models of the sort that are now familiar as bioinformatics approaches to genomic data. While the downstream phenomena of signaling activities govern the biophysical processes underlying cell motility, relatively little is known concerning the critical physico-chemical reaction and transport mechanisms so that differential equation models are at this point in time highly premature; accordingly, relational or informatics models are especially appropriate for computational analysis.
We are undertaking development of informatics-based, relational models for computational analysis of cue-signal and signal-response dependences. Foremost among these are two diverse methodologies: [A] Principal Components / Partial Least Square analysis; and [B] Bayesian Network analysis.
Principal Components / Partial Least Squares analysis involves casting cue-signal or signal-response data as output (signal or response, respectively) vectors in the multi-dimensional space of input (cue or signal, respectively) vectors. Mathematically, this permits the cue-signal or signal-response data to be cast in terms of matrix algebra. A useful feature of this casting is that a new set of modified "input" vectors can be determined which most effectively predict the output vectors, even when the number of vectors is drastically reduced (see Figure 2 below). Interestingly, the modified "input" vectors comprise combinations of the original input variables, enabling identification of how complex networks integrate to generate particular outputs from a wide range of inputs.
Bayesian Network
Bayesian Network analysis involves elucidation of connections between inputs and outputs (cues and signals, or signals and responses) that most effectively represent apparent directional influences of one upon the other according to the experimental data at hand. Here the influence relationships can be thought of as representing "circuit logic", with downstream activities being dependent in complicated ways upon combinations of upstream activities (see Figure 3 below) (Sachs et al., 2002). It is important to note that in Bayesian Network analysis, model effectiveness with respect to the experimental data can be calculated in relative terms comparatively to alternative models.
The types of experimental data most useful for these two classes of computational analysis are different in general. Bayesian Network models are most powerfully determined from a very large number of replicates, even if of only a small number of conditions. Principal Components / Partial Least Squares models are most powerfully determined from a large number of conditions, even if with only a small number of replicates. Thus, the kind of computational model chosen for data analysis should be considered in context of the type of data available. We are thus also pursuing efforts to develop experimental methodologies directly aimed toward data-generating capabilities for our cue-signal-response computational modeling methods. One key data type is enzymatic activity of kinases involved in intracellular signaling networks, and we have had some initial "proof of concept" success with a 96-well plate high-throughput format for a set of protein kinases of interest in cell migration regulation as well as other cell behavioral functions (see Figure 4 below) (Janes et al., 2003).
Force-Based Computational Model for Cell Migration in 3-Dimensional Matrices
While computational models for cell migration on two-dimensional substrata (DiMilla et al., 1991) have described how diverse molecular properties and mechanisms are integrated in cell movement, the same issues might contribute differently to a model for migration within three-dimensional matrices. To address this more complicated situation, we have developed a computational model for cell migration in three-dimensional matrices using a force-based dynamics approach. This model determines an overall locomotion velocity vector, comprising speed and direction, for individual cells based on internally-generated forces transmitted into external traction forces and considering a time-scale during which attachment and detachment events occur. Key parameters characterizing cell and matrix properties, including cell/matrix adhesion, mechanical properties of the matrix, and proteolytic matrix degradation, are taken into account. The model shows good agreement with experimental results for the limiting case of migration on two-dimensional substrata as well as recent experiments in three-dimensional natural tissues and synthetic gels. Certain predicted features for three-dimensional migration are qualitatively similar to their two-dimensional counterparts, but new effects generally absent in two-dimensional systems are now predicted to arise in many three-dimensional situations.
Physico-Chemical Models
Cell movement is a mechanical phenomenon. Two of the main barriers hindering studies of cell movements are: lack of computational models and limited quantitative data. Without the former, many existing qualitative models of cell behavior remain static and unsubstantiated. Without the latter, modeling is but guesswork. The best way to elucidate general principles of cell motility is to choose a specific model system, 'dissect' it and to attempt a very complete understanding of its working. Among a great variety of possible approaches, one is detailed physico-chemical modeling, when a lot of quantitative data is available. An excellent example of such a model, focusing on mechanics (and neglecting molecular pathways) is the recently described finite element model (Herant et al., 2003) that considers the cytoskeleton of neutrophil as two inter penetrative fluids - one actually fluid part of the cytoplasm, and another being contractile actin gel. The role of computational modeling of this kind in understanding increasing volume of quantitative data (Roy et al., 2001) is crucial and will continue to increase.
One approach is to develop detailed physico-chemical models of cell movements, which can account for particular biophysical processes in terms of the physics and chemistry of the molecular interactions involved. In particular, we focus on lamellipodia of simple shaped rapidly migrating cells, like keratocytes and nematode sperm. Equations of mechanics of actin/myosin networks and couple with reaction-diffusion-drift equations governing actin turnover and biochemical regulatory pathways. (Ultimately, this will include equations of dynamic graded adhesion system and of 'steering' microtubule system.) These equations comprise deterministic continuous models, which can be simulated using sophisticated finite element methods on free boundary domains. Quantitative data of image analyses can be used to derive the model equations. Predictions of the model simulations about shapes, movements and densities are compared to the corresponding experimental results. The models also allow generating specific suggestions for new experiments.
As an example, compare
the movies of the moving
nematode sperm cell and keratocyte
cell with corresponding 'virtual
cells' based on our models:
http://www.math.ucdavis.edu/~mogilner/Normal_motility.mov
http://www.math.ucdavis.edu/~mogilner/CompKerat4.mpg
A microscopic
model of protrusion force at the leading edge of the cell (Mogilner
et al., 2003), a model of actin organization at the leading edge
(Grimm et al., 2003), a model of actin turnover
in migrating cell (Mogilner & Edelstein-Keshet,
2002), and models of locomotion of the simplest migrating cell
- sperm of nematode Ascaris suum have already been developed (Bottino
et al., 2002; Mogliner & Verzi,
2003; Wolgemuth et al., 2003).
Physico-chemical model of actin dynamics regulated by the Rac-PAK signaling pathway
Using the image analysis approaches and the statistical analyses described below we investigate the role of Rac1 – PAK (p21-activated kinase) signaling in mediating cell protrusion. In Ponti et al., 2004, we identified two spatially overlapping, yet molecularly distinct actin modules mediating epithelial cell migration: the lamellipodium being the protrusive module and the lamella being the adhesive/contractile module.
In this context, PAK is a particularly interesting enzyme because of its potential function as a linker of lamellipodium assembly and lamella contraction (Fig. 5). PAK is upstream of a signaling cascade that regulates cofilin, a protein which promotes F-actin cycling through its F-actin-nucleating, -severing, and -depolymerizing activity. How the manifold actions of cofilin modulate cell protrusion has been unclear. Localized activation of cofilin has been shown to promote local edge advancement (Ghosh et al., 2004), and pathways have been identified which link cofilin activation to growth factor stimulation in chemotactic protrusion (Chan et al., 2000; Zebda et al., 2000). However, the depolymerizing and severing activities of cofilin may actually weaken the structure of the lamellipodial network to destabilize the links between lamellipodium, lamella, and/or the cytoplasmic domain of adhesion complexes. These links are required to convert the work of polymerization-induced forces in the lamellipodium into edge movement. Thus, global increases in cofilin activity might also be expected to reduce cell protrusivity.
In a collaborative study with Dr. Gary Bokoch at TSRI we used quantitative Fluorescent Speckle Microscopy to examine the functional implications of cofilin on the regulation of lamellipodium and lamella dynamics, and in particular the structural interactions of these two actin modules, by variation of the global activation level of cofilin (Delorme et al. 2007). Enhancement of cofilin activity accelerates F-actin turnover and retrograde flow, resulting in widening of the lamellipodium. This is accompanied by increased spatial overlap of the lamellipodium and lamella networks and reduced cell edge protrusion efficiency. We proposed a model in which cofilin functions as a regulator of cell protrusion by modulating the structural coupling of lamellipodium and lamella and thus the efficiency of the transduction of protrusive forces, in response to PAK-mediated signals. In parallel we are investigating with the same tools the function of tropomyosin as a functional switch between lamellipodium and lamella assembly, of the relationship between lamella contraction and lamella and lamellipodium dynamics.
These data are being compiled in a physico-chemical modelto test the pathway hypothesis in Fig.5 mechanistically and quantitatively. The model conjectures mechanical feedback from PAK-initiated lamellipodium assembly and lamella contraction into Rac1 – PAK signaling. Such feedback could explain the periodicity of cell protrusion illustrated in Fig. 2. Both assembly and contraction generate forces that may be transduced through the actin network to integrins in adhesion complexes (Geiger and Bershadsky, 2001). Force-activated integrins in turn may reactivate Rac1 (Schwartz and Shattil, 2000).On the one hand, the physico-chemical model will allow us to integrate and study the effect of the time constants of integrin-Rac1 signaling, the Rac1-PAK signaling pathways, lamellipodium assembly and disassembly, and recycling of dissociated actin monomers into re-polymerizable ones, and thus predict the periodicity of protrusion. On the other hand, by measuring the periodicity of protrusion, actin turnover and flow in control cells and cells in which specific signaling nodes are perturbed it will be possible to estimate the time constants of these signaling pathways in situ.
Statistical Analysis
Statistical Analysis of the causality between cytoskeleton dynamics and cell protrusion
The goal of this modeling effort is to exploit time-resolved high resolution measurements of cell protrusion dynamics and cytoskeleton assembly, disassembly and flow to establish the causality and timing of the earliest molecular events in the cell migration cycle.
To measure protrusion dynamics image tracking algorithms have been developed, which establish the homomorphism of cell outlines between consecutive frames of a light microscopy time-lapse sequence. The algorithms rely on evolutionary equations (Sethian, 1999) that describe the most likely paths of the cell boundary between the first and the second time point in the frame pair considered (Machacek and Danuser, 2006 ) (Fig. 1). Underlying the evolutionary equations are either simple phenomenological models or advanced mechanical models that predict the local displacement of the plasma membrane as a function of the local cell shape or forces acting upon the cell boundary. It turns out that the choice of the model plays a minor role in the edge displacement solution if the image sampling in the time-lapse sequence is sufficient (Machacek and Danuser, 2006 ). The use of evolutionary equations bears the advantage that edge displacements at any length scale and degree of edge deformation are accurately represented without need for fiduciary marks in the plasma membrane. Thus, the algorithm can simultaneously track, for instance, the rapid expansion of a micro-spike next to minute movements of a quiescent edge.
 |
Fig.1 Tracking cell boundary displacements using evolutionary equations. (A) Modeled boundary evolution between two consecutive time points (T and T+1) in a movie of a migrating cell. (B) Modeled paths of virtual fiduciary marks on the plasma membrane. Path lengths provide a local measure of the edge displacement between the two time points. The zoom up of marker paths indicates the robustness of the method in tracking large boundary deformations while preserving the topology of the boundary. |
By visualizing edge displacements in space-time maps, where
the vertical axis denotes the position of the measurement
point along the cell edge and the horizontal axis denotes
time, it is straight
forward to determine if and how cell protrusion and retraction
is coordinated spatially and over time (Fig. 2A) (Machacek
and Danuser, 2006 ). The displays
in Fig.2B-C indicate
that cell protrusion and retraction obey a high spatial
and temporal organization, although the edge movements
observed with the migration
of a cell appear to be random. The organization was found
to depend on the activation state of the molecular machinery
near the cell edge.
For example, we discovered that in migrating epithelial
cells the activation level of the Rac1 GTPase controls
the velocity with which protrusion
waves propagate transversally along the cell edge (Fig.
2B versus Fig. 2C). Multiple and randomly induced transversal
protrusion waves, visible
as linear rims in Fig. 2B, crisscross, generating complex
super-position patterns of edge movement in two dimensions.
In Fig. 2C the rims run
vertically, i.e. the entire active cell edge protrudes
and retracts in synchrony. The persistence of the transversal
wave has been found
to depend on the concentration of activatable actin filament
nucleating protein Arp2/3. Such pattern analysis will be
invaluable for identifying
further molecular factors involved in protrusion regulation.
The edge tracking and pattern analysis software will be
released via the CMC
software portal after further Beta-testing of the package
and upon publication of the paper describing the method.
Early requests can
be directed to Gaudenz Danuser.
A second critical observation emerging from the displays
refers to the intrinsic heterogeneity of protrusion in
many cell types. Regions of net advancement can be found
next to regions of net withdrawal
and these states continuously alter over time. One would
expect that the states of molecules involved in driving
protrusion change accordingly.
Therefore, by probing heterogeneity in the activation states
of molecules and mechanical cues near the edge and by correlating
them with the
heterogeneity of protrusion it will be possible to establish
the exact relationships and timing between the dynamic
action of the protrusion
machinery and its output in terms of cell edge movement.
To extract these relationships and influences, statistical
models of the kinds
described in “Cue-Signal-Response Analysis
in Cell Migration” are
developed. The natural variation in system states, which
can be captured by precise and comprehensive image analysis,
allows us to determine
the coupling between molecular components and derive mechanisms
of protrusion control without need for acute cell perturbation.
This approach is currently exploited by the Danuser lab
to establish the functional linkage between actin cytoskeleton
dynamics and protrusion and between the activation of Rho family GTPases and protrusion.
Initial results from these studies
are shown in Figs 3 and 4.
 |
| Fig. 3 Coupling cell protrusion dynamics and actin assembly dynamics by statistical models. (A) Comparison of protrusion pattern (top) and assembly pattern (bottom). Visually the heterogeneous patterns display similarity. Regions of fast protrusion coincide with regions of elevated actin network assembly. (B) The simplest approach to quantitate the coupling between the two variables is by cross-correlation of the two activity maps in A. More advanced methods are available which separate the random, heterogeneous activity pattern from random measurement noise. The significant correlation peak at -10 s suggests a coupling between actin assembly and protrusion, as expected. Surprisingly, however, peak assembly lags peak protrusion. Several models that could explain this phenomenon are under investigation. |
 |
| Fig. 4 Coupling of cell protrusion and RhoA activation. (A) Protrusion activity pattern. (B) RhoA activity pattern, indicating that the modulation of this Rho GTPase at the leading edge is similar to the modulation of protrusion. (C) Cross-correlation between the two variables indicating that RhoA activation and protrusion are synchronous. |
To measure actin cytoskeleton dynamics quantitative Fluorescent Speckle Microscopy is used, which reports the rates of assembly, disassembly, and the flow state of the actin cytoskeleton (Danuser & Waterman-Storer 2006). Correlation analysis of actin network assembly and protrusion, for example, revealed that protrusion and polymerization are coupled. However, the peak assembly lags the peak protrusion by ~10 - 20 s (Fig. 3B; unpublished data). This finding challenges the dogma that protrusion is directly controlled by the efficiency of actin assembly at the leading edge. There are several models that may explain this phenomenon. These are currently scrutinized experimentally and theoretically inside and outside the Consortium
To analyze the timing of Rho family GTPase activation relative
to heterogeneous edge movements the activation states of
the Rho GTPases (Cdc42, Rac1, and RhoA) were visualized
by biosensors in Dr. Hahn’s
group at UNC (Biosensor Initiative) (Kraynov et al., 2000; Nalbant
et al., 2004, Pertz et al., 2006).
All three GTPases exhibit space and time modulations that
correlate with the modulation of protrusion activity. This
allows us to identify the timing between the activation
of a specific Rho GTPase and the initiation of a protrusion
event. Since
all the activation
events of one Rho GTPase are recorded relative to protrusion
events, it is also possible to merge the recordings of
two Rho GTPases and
analyze their timing indirectly. Therefore, these analyses
deliver not only information on the causality and timing
of system variables
observed simultaneously, but they may be used to reveal
the relations and influences of variables that are probed
in different experiments.
Our current results (preliminary and unpublished data)
suggest a causality between RhoA activation and protrusion
(Fig. 4) while Rac1 and Cdc42
lag the protrusion by 10 – 30
s.
One of the fundamental problems in reconstructing large regulatory networks in cells is the superposition of multiple, nested feedback mechanisms of different signals. In cell migration, this is further complicated by the intimate interaction of mechanical and chemical signals which are distributed in space at various length scales. Conventional approaches for cue-signal-response analysis, which mostly focus on the inference of linear, spatially invariant signaling cascades, provide limited power to the reconstruction of spatially variant and feedback-coupled processes. One of the main goals of the Danuser lab contribution to the Consortium is the development of an entirely new set of mathematical tools to infer from live cell image data cause-and-effect relationships between feedback- and feedforward-coupled signaling and mechanical activities.
Continuum Mechanical Model
Continuum mechanical model of integrated adhesion and contraction forces in lamella of migrating cells
Fig. 5 purports a model of protrusion regulation which relies on a subtle spatial and temporal balance of chemical signaling and force generation in contractile and adhesive modules. While adhesion forces can be measured by traction force mapping or extracellular tension biosensors, contraction forces are less accessible. Biosensor development for probing intracellular tension is underway in the Signaling Initiative. Alternatively, force generation can also be reconstructed from the deformation of the cytoskeleton using inverse dynamics. The idea of inverse dynamics is illustrated very easily based on force application on a linear spring. If the spring constant is known, it is straightforward to deduce the force increase from the extension of the spring observed between two time points (Fig. 6). The same idea is applicable to 2D and 3D materials, if they can be considered as a continuum. For the actin cytoskeleton this seems to hold true at micron length scales, i.e. for a scale several times larger than the mesh size of the filamentous network (Gardel et al., 2004). Cytoskeleton deformation can be probed precisely with techniques such as Fluorescent Speckle Microscopy (Fig. 7). While absolute values of cytoskeleton elasticity (equivalent to the spring constant in the 1D case) will be very difficult to assess, several micro-rheological methods are becoming available to map out the spatial modulation in actin network elasticity inside cells (Crocker et al., 2000; Kole et al., 2005). Given experimental data of cytoskeleton deformation and elasticity modulation, the theory of continuum-mechanics provides equations to describe the relationship between the unknown forces and the observed cytoskeleton deformation. Mathematical approaches are developed in this modeling effort to invert these equations and back out the deformation-generating force field from measurements of cytoskeleton deformation (Fig. 7A). In a second step, these inverse dynamics approaches are expanded to distinguish between force components associated with the coupling of the actin cytoskeleton to adhesion complexes (equivalent to traction force maps probed extracellularly) and those associated with actin cytoskeleton contraction (Fig. 7B).
Quantitative Fluorescent Speckle Microscopy analysis of actin-adhesion coupling
Complementary to adhesion force reconstruction is the investigation of the transient direct and indirect coupling of the actin cytoskeleton to components of adhesion complexes. This information will also support the testing of the physico-chemical model of non-steady state protrusion (Fig. 5), as it will reveal how much of the contraction forces transduced through the actin cytoskeleton are coupled to integrins and the extracellular matrix. To asses the degree of coupling multi-color fluorescent speckle microscopy has been developed in the laboratory of Dr. Clare Waterman-Storer. The Danuser lab developed image analysis methods and a statistical model of the adhesion – actin interface to quantify and interpret the flow coupling of two speckle populations, the first probing actin cytoskeleton flow, the second probing the movement of any of the proteins within adhesion complexes. Results of this work have been published (Hu et al., 2007) and highlighted on the CMC update (Feb2007 Update).
The Virtual Cell
 |
The "Virtual Cell" is a unique computational environment that is being developed by the National Resource for Cell Analysis and Modeling (http://www.nrcam.uchc.edu) at the University of Connecticut Health Center (Farmington, CT, USA). It provides a sophisticated framework for analyzing, modeling, and simulating cellular function that can range from metabolic pathways to signaling networks to membrane transport and electrophysiology. The software environment can also be used to analyze microscope-based experiments such as FRAP, photo release, and probe translocation. |
It is a general software system to allow biologists with little training in physics and mathematics to engage in computational cell biology. A biology-oriented graphical user interface provides for the assembly of models by specifying the molecules, reactions and structures involved. By providing a structured environment for pulling together related pieces of quantitative data, it enables the construction of complex spatial models of biological processes. Simulations are then produced by the software from these models and the predictions of these simulations can be directly compared with experimental data. If the simulation does not match the experiment, the model must be an incomplete or faulty description of the cell biology and must be modified. If the simulations are consistent with the experiment, new simulations with different conditions can be used to predict the results of new experiments that can further test the limits of the applicability of the model. This cycle, depicted in the Figure, is simply a restatement of the classical scientific method for the case of a complex set of cell biological hypotheses - a cell biological model (Slepchenko et al., 2003).
The Virtual Cell has been specifically designed to be a tool for a wide range of scientists - from experimental cell biologists to theoretical biophysicists. On the one hand, models of cell biological processes can be easily created, allowing quick testing of simple models to evaluate hypotheses or to interpret experimental data. On the other hand, the Virtual Cell provides an integrated framework that facilitates building of large, multi-layered models to probe the predicted behavior of complex, highly non-linear systems (e.g. spatial oscillatory calcium waves, cell cycle regulation by intracellular signaling networks). One of the unique strengths of the Virtual Cell is that models can be based on both experimental data (biochemistry, molecular biology, imaging, etc.) and purely theoretical assumptions by using a very general conceptual structure of a model as a collection of arbitrary processes. These are defined in terms of which molecules are involved (ranging from elemental species such as sodium or calcium, to large protein complexes), where they are located (defined areas within a tissue, cell, organelle, etc., or well mixed compartments), and how they interact with each other (simple kinetic reactions, membrane transport fluxes, diffusion, etc.). The user can build complex models with the web browser-based interface to specify compartmental topology and geometry, molecular characteristics, and relevant interaction parameters; the Virtual Cell then automatically converts the specified biological mechanisms to a corresponding mathematical system of ordinary and/or partial differential equations. The mathematics-savvy user may directly specify the complete mathematical description of the model, bypassing the schematic interface. The system will automatically solve the equations by applying numerical solvers and generate appropriate software code to perform and analyze simulations. The simulations are run on a powerful multi-node, multi-processor computer cluster that is used as a dedicated server for computationally intensive applications. Results of the simulations can be displayed and analyzed on-line or downloaded to the user's computer in a variety of formats, from raw data to Quicktime movie files. The models and their applications and simulations are all stored in a secure database that maintains user privacy. Moreover, the database provides mechanisms for sharing models for collaborations and publishing of specific versions. Links to external databases (KEGG or SwissProt) facilitate incorporation of existing data when building models. A powerful set of tools based on XML technology is also available to compare and edit models; the XML representation also facilitates the use of other tools - we support both emerging standards for biological modeling languages, SBML (http://sbml.org/documents/) and CellML (http://www.cellml.org/public/about/what_is_cellml.html) for either import or export into/from the Virtual Cell.
Access to the Virtual Cell is free but requires registration by filling out a simple web-based form (http://www.nrcam.uchc.edu/vcellR3/login/newuser.jsp). A User Guide (http://www.nrcam.uchc.edu/vcellR3/login/userguide.jsp) and several tutorials (http://www.nrcam.uchc.edu/vcellR3/login/tutorial.jsp) are available for self-instruction. A free annual short course is offered each June for hands on instruction at UCHC. Registered users can access any models that have been 'published' by other users. In addition, a public account, entitled CMC, has been established for the Cell Migration Consortium and the scientific community at large. It currently contains several models related to PIP2 turnover, calcium release, and analysis of FRAP experiments; within these, several applications illustrate how to use the Virtual Cell to model fluorescent probe translocation and photorelease experiments. As new CMC-related models are developed they will be deposited in the CMC account.
General References on the Virtual Cell Computational Cell Biology Software
Schaff et al., 1997A general computational framework for modeling cellular structure and function.
Slepchenko et al., 2000 Numerical approach to fast reaction-diffusion systems: application to buffered calcium waves in bistable models.
Schaff et al., 2001 Analysis of non-linear dynamics on arbitrary geometries with the Virtual Cell.
Loew & Schaff, 2001The Virtual Cell: A software environment for computational cell biology.
Slepchenko et al., 2002 Computational cell biology: spatiotemporal simulation of cellular events.
References to the Application of the Virtual Cell
Fink et al., 1999a Morphological control of inositol-1,4,5-trisphosphate-dependent signals.
Fink et al., 1999b Determination of time-dependent inositol-1,4,5-trisphosphate concentrations during calcium release in a smooth muscle cell.
Fink et al., 2000 An image-based model of calcium waves in differentiated neuroblastoma cells.
Mannella et al., 2001 Topology of the mitochondrial inner membrane: dynamics and bioenergetic implications.
Hinkle et al., 2002 Chromosomal association of Ran during meiotic and mitotic divisions.
Johenning et al., 2002 Distinct intracellular calcium transients in neurites and somata integrate neuronal signals.
Fridlyand et al., 2003 Modeling of Ca2+ flux in pancreatic {beta}-cells: role of the plasma membrane and intracellular stores.
Rolls et al., 2002 Targeting of rough endoplasmic reticulum membrane proteins and ribosomes in invertebrate neurons.
Roy et al., 2001 Local photorelease of caged thymosin ß4 in locomoting keratocytes causes cell turning.
Slepchenko et al., 2001 Modeling of transcellular Ca transport in rat duodenum points to coexistence of two mechanisms of apical entry.
Smith et al., 2002 Systems analysis of Ran transport.
Terasaki et al., 2001 A new model for nuclear envelope breakdown.
Xu et al., 2003 Kinetic analysis of receptor-activated phosphoinositide turnover.
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