Simulation of reaction diffusion processes over biologically relevant size and time scales using multi-GPU workstations

AbstractSimulation of in vivo cellular processes with the reaction–diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel efficiency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems

Approximation and inference methods for stochastic biochemical kinetics-a tutorial review

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics

Accelerated Algorithms for Stochastic Simulation of Chemically Reacting Systems

Stochastic models are widely used in the simulation of biochemical systems at a cellular level. For well mixed models, the system state can be represented by the population of each species. The probabilities for the system to be in each state are governed by the Chemical Master Equation (CME), which is generally a huge ordinary differential equation (ODE) system. The cost of solving the CME directly is generally prohibitive, due to its huge size.The Stochastic Simulation Algorithm (SSA) provides a kinetic Monte Carlo approach to obtain the solution to the CME. It does this by simulating every reaction event in the system. A great many stochastic realizations must be performed, to obtain accurate probabilities for the states. The SSA can generate a highly accurate result, however the computation of many SSA realizations may be expensive if there are many reaction events. Tau-leaping is an approximate algorithm that can speed up the simulation for many systems. It advances the system with a selected stepsize. In each step, it directly samples the number of reaction events in each reaction channel, which yields a faster simulation than SSA. The error in tau-leaping is controlled by selecting the stepsize properly.We have developed a new, accelerated tau-leaping algorithm for discrete stochastic simulation that make use of the fact that exact (time-dependent) solutions are known for some of the most common reaction motifs (subgraphs of the network of chemical species and reactants). This idea can be extended to spatial stochastic simulation, by treating the diffusion network as a special motif for which there is an exact time dependent solution. We describe the well-mixed and spatial stochastic time dependent solution algorithms, along with numerical experiments illustrating their effectiveness

Cell polarity under extreme morphological conditions

Cell polarity is an important phenomenon in a multitude of cellular and developmental processes. The cellular contexts that polarity occurs in include a wide array of morphological properties such as size, shape, and growth. An important, conserved system of cell polarity depends on the intracellular localisation of proteins that act as diffusive molecular switches. Since the localisation of these proteins depends on their reactive and diffusive properties, cell size and growth may alter polarity induced by localisation. My work contributes extensive analyses of an established protein localisation model under extreme morphological conditions such as extremely small and rapidly growing cells. My work also uncovers non-trivial, biologically relevant behaviour caused by the inclusion of these morphological properties and further discusses the mechanisms underlying the observed behaviour. In addition, I contribute and discuss a novel computational tool that can continue to aid the research community in understanding cell polarity under extreme morphological conditions

Accelerating Exact Stochastic Simulation of Biochemical Systems

The ability to accurately and efficiently simulate computer models of biochemical systems is of growing importance to the molecular biology and pharmaceutical research communities. Exact stochastic simulation is a popular approach for simulating such systems because it properly represents genetic noise and it accurately represents systems with small populations of chemical species. Unfortunately, the computational demands of exact stochastic simulation often limit its applicability. To enable next-generation whole-cell and multi-cell stochastic modeling, advanced tools and techniques must be developed to increase simulation efficiency. This work assesses the applicability of a variety of hardware and software acceleration approaches for exact stochastic simulation including serial algorithm improvements, parallel computing, reconfigurable computing, and cluster computing. Through this analysis, improved simulation techniques for biological systems are explored and evaluated