Integrative multicellular biological modeling: a case study of 3D epidermal development using GPU algorithms

Abstract

Background: Simulation of sophisticated biological models requires considerable computational power. These models typically integrate together numerous biological phenomena such as spatially-explicit heterogeneous cells, cell-cell interactions, cell-environment interactions and intracellular gene networks. The recent advent of programming for graphical processing units (GPU) opens up the possibility of developing more integrative, detailed and predictive biological models while at the same time decreasing the computational cost to simulate those models.

Results: We construct a 3D model of epidermal development and provide a set of GPU algorithms that executes significantly faster than sequential central processing unit (CPU) code. We provide a parallel implementation of the subcellular element method for individual cells residing in a lattice-free spatial environment. Each cell in our epidermal model includes an internal gene network, which integrates cellular interaction of Notch signaling together with environmental interaction of basement membrane adhesion, to specify cellular state and behaviors such as growth and division. We take a pedagogical approach to describing how modeling methods are efficiently implemented on the GPU including memory layout of data structures and functional decomposition. We discuss various programmatic issues and provide a set of design guidelines for GPU programming that are instructive to avoid common pitfalls as well as to extract performance from the GPU architecture.

Conclusions: We demonstrate that GPU algorithms represent a significant technological advance for the simulation of complex biological models. We further demonstrate with our epidermal model that the integration of multiple complex modeling methods for heterogeneous multicellular biological processes is both feasible and computationally tractable using this new technology. We hope that the provided algorithms and source code will be a starting point for modelers to develop their own GPU implementations, and encourage others to implement their modeling methods on the GPU and to make that code available to the wider community.

Figure 1

Diagram of cell-cell and cell-environment interactions coupled with an intracellular gene network within each cell in a model of epidermal development. Not all interactions have experimental confirmation.

Figure 2

Data structure memory layout. (A) An example data structure containing three variables to hold 3D spatial coordinates. (B) Memory layout of the variables when N data structures are allocated together in a CPU program. The variables for each data structure are grouped together in sequential memory locations. (C) Preferable memory layout of N data structures for a GPU program. Each variable in the data structure are grouped together in sequential memory locations, and each variable group is padded to value A to insure alignment requirements. Alignment can be handled automatically, such as with CUDA's cudaMallocPitch function, and the alignment value must be used when calculating array indexes.

Figure 3

Single layer of epidermal cells. 3D visualization of 100 cells each with 20 subcellular elements and periodic boundary conditions forming a single layer of the epidermis. The greenish-yellow plane under the cells represents the basement membrane. Red subcellular elements have an adhesive force term with the basement membrane, and blue subcellular elements indicate the basal cellular state.

Figure 4

Multiple layers of epidermal cells. 3D visualization of full model after running for 130000 iterations showing 535 cells forming multiple layers of the epidermis. The model started with 100 cells in a single layer as shown in Figure 3 and proceeded through about three cell divisions. The greenish-yellow plane under the cells represents the basement membrane. Red subcellular elements have an adhesive force term with the basement membrane, while blue subcellular elements indicate the basal cellular state and yellow subcellular elements indicate the suprabasal cellular state.