2004 10 12

Spatial Modeling in BioSpice: 

Spatial Modeling in BioSpice P. Colella, J. Grcar, P. Schwartz, CRD/LBNL D. Adalsteinsson, UNC Arkin*, E. Alm, S. Andrews, K. Erickson*, A. Gilman, K. Koster, M. Onsum*, PBD/LBNL, *DBE/UCB

Research Problem: 

Research Problem Goal: a software platform to investigate problems in intracellular communication. Develop tools for spatial modeling. Reaction-diffusion systems in cytosol, cell membranes, surface-volume coupling, multi-compartment models. Support of: Moving boundaries to represent cell growth, division. Realistic cell shapes obtained by processing experimental images of cells into level set data. Verification and validation of software by reproducing results of existing literature that model, for example, sporulation, chemotaxis, calcium waves, etc. Integration into BioSpice software infrastructure.

Current Approaches and Major Results: 

Current Approaches and Major Results Chombo software library for solving applied PDEs Cartesian grid embedded boundary methods Adaptive mesh refinement (AMR) capable C++ / FORTRAN implementation Parallel capable via MPI I/O via HDF5 file format ChomboVis integrated visualization tool Applied Numerical Algorithm Group, Lawrence Berkeley National Laboratory,

Current Approaches and Major Results: 

Current Approaches and Major Results

Current Approaches and Major Results: 

Current Approaches and Major Results ChomboVis image of cut-cell model of San Francisco Bay

Current Approaches and Major Results: 

Current Approaches and Major Results ChomboVis image of cut-cell model of San Francisco Bay

Current Approaches and Major Results: 

Current Approaches and Major Results Cartesian grid embedded boundary methods for reaction-diffusion problems on deforming domains. Cut-cell spatial discretization makes for easy grid generation. Implicit temporal discretization, unconditionally stable, second-order accurate in space and time.

Current Approaches and Major Results: 

Current Approaches and Major Results Reaction-diffusion processes on cell surfaces. Level set method determines membrane as thin cut-cell region. Membrane motion obtained by modifying the level set function. Leverages Cartesian grid embedded boundary method (reaction-diffusion algorithms, software infrastructure, graphics engine). Level sets produced from tiff stacks of electron microscope images enable realistic cell geometries.

Current Approaches and Major Results: 

Current Approaches and Major Results Gradient sensing and amplification in chemotaxing neutrophils. Migration toward chemoattractants with as little as 2% gradients. Mechanisms responsible for cell motility subject of ongoing study. Complex biochemical feedback mechanism coupled with spatial transport. Polarization, amplification and adaptation of the sensing network. Extend 1D model (Lvechenko and Iglesias) to investigate 3D spatial effects of diffusing components. Surface activation and cytoplasmic diffusion (PI3K, PTEN SGP). Surface diffusion (P1P, P2, P3).

Current Approaches and Major Results: 

Current Approaches and Major Results Gradient sensing and amplification in chemotaxing neutrophils, cont. 1D simulation duplicating the model validation calculations performed by Lvechenko and Iglesias, Biophys. J. 82:50-63. time length P3

Current Approaches and Major Results: 

Current Approaches and Major Results Gradient sensing and amplification in chemotaxing neutrophils, cont. P3 in the membrane compartment of a 2D simulation representing the cell as a disk or a single tiff slice. 1 compartment 2 compartment P3 in a 2D simulation representing the cell as a disk or a single tiff slice.

Current Approaches and Major Results: 

Current Approaches and Major Results Gradient sensing and amplification in chemotaxing neutrophils, cont. P3 on the surface of a 3D, two-compartment model based on level set reconstruction of the cell from SEM tiff stack data.

Current Approaches and Major Results: 

Current Approaches and Major Results Calcium waves in neuroblastoma cells Model parameters based, in part, on fitting reaction rates in a simulation to extensive experimental data (Fink, Slepchenko, et al.) Fittings performed using Virtual Cell Necessitates introducing “effective” areas and volumes so 2D simulation mimics 3D Finding: neuronal morphology plays a key role in the wave dynamics in response to external signal

Current Approaches and Major Results: 

Current Approaches and Major Results Spatial Modeling in Dashboard Level set description of cell geometry (currently limited to 1 compartment models) Archive file contains complete specification of geometry, boundary conditions, and solver parameters (grid spacing, diffusive time step) Solver acquires reaction pathways through C-code evaluation of rates 3D graphical output to HDF5 files for viewing with ChomboVis

6 and 12 month 2004-5 Milestones: 

6 and 12 month 2004-5 Milestones (9/04) Protoype spatial model in Dashboard 3D, two-compartment spatial models demonstrated Gradient sensing and amplification in chemotaxing neutrophils Cell geometry specification standard (D. Adalsteinsson) (3/05) Two-compartment spatial models in Dashboard Calcium waves in neuroblastoma cells Comparison of 3D realization with original 2D model in the literature (9/05) Verification and validation of software including benchmarking against models realized under Virtual Cell Demonstrate geometrical / dimensional impact on 1D and 2D models when implemented in 3D. Implement these spatial models as templates for use by other researchers through the Dashboad.

Team 2004-5: 

Team 2004-5 CRD/LBNL Spatial Modeling: P. Colella (10%), J. Grcar (25%), P. Schwartz (100%) UNC: D. Adalsteinsson PBD/LBNL BioSpice: A. Arkin, A. Gilman, K. Koster