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.

Mechanocellular models of epithelial morphogenesis

“…A similar approach has been taken to describe the role of Myosin II patterning in driving intercalation during germband extension (80). Such biological detail is rarer in the more complex mechanocellular models described above; though recent examples include (44,69). Further development of increasingly detailed mechanocellular models will require the careful derivation of key relationships between the fluorescence intensity of relevant proteins and mechanical properties from liveimaging datasets.…”

Simulation Frameworks for Morphogenetic Problems

“…The inter-cellular interaction described by the second term takes all pair-interactions between the elements β j of other cells j and the elements α i of cell i into account. Numerically, the forward Euler and a two-step Runge-Kutta scheme have been used to integrate Equation (11) [92]. Similar to the inter-atomic interaction potentials in molecular dynamics simulations, the phenomenological potentials V intra , V inter are chosen such that the subcellular elements prefer to be in an equilibrium distance to their neighbouring elements, i.e., that the subcellular elements repel each other when the distance between two cells is low, and attract each other when the distance is large.…”

“…However, due to its algorithmic simplicity borrowed from molecular dynamics, efficient library implementations can be used [92,93]. It has been reported that the SEM is suitable to study problems with up to 10,000 cells [91].…”

Computational Modeling of Inflammation and Wound Healing

“…However, most of these ABMs have been focused on delineating intracellular detail as an adjunct to basic research. [24][25][26][27] We propose that ABMs are also well suited to a translational role to bridge basic science knowledge and the rational development of clinically applicable strategies. 14,23,28,29 We have developed a series of ABMs with this specific goal in mind.…”