Parallel Load Balancing Strategies for Ensembles of Stochastic Biochemical Simulations

The evolution of biochemical systems where some chemical species are present with only a small number of molecules, is strongly influenced by discrete and stochastic effects that cannot be accurately captured by continuous and deterministic models. The budding yeast cell cycle provides an excellent example of the need to account for stochastic effects in biochemical reactions. To obtain statistics of the cell cycle progression, a stochastic simulation algorithm must be run thousands of times with different initial conditions and parameter values. In order to manage the computational expense involved, the large ensemble of runs needs to be executed in parallel. The CPU time for each individual task is unknown before execution, so a simple strategy of assigning an equal number of tasks per processor can lead to considerable work imbalances and loss of parallel efficiency. Moreover, deterministic analysis approaches are ill suited for assessing the effectiveness of load balancing algorithms in this context. Biological models often require stochastic simulation. Since generating an ensemble of simulation results is computationally intensive, it is important to make efficient use of computer resources. This paper presents a new probabilistic framework to analyze the performance of dynamic load balancing algorithms when applied to large ensembles of stochastic biochemical simulations. Two particular load balancing strategies (point-to-point and all-redistribution) are discussed in detail. Simulation results with a stochastic budding yeast cell cycle model confirm the theoretical analysis. While this work is motivated by cell cycle modeling, the proposed analysis framework is general and can be directly applied to any ensemble simulation of biological systems where many tasks are mapped onto each processor, and where the individual compute times vary considerably among tasks

Application of a stochastic name-­passing calculus to representation and simulation of molecular processes

We describe a novel application of a stochastic name passing calculus for the study of biomolecular systems. We specify the structure and dynamics of biochemical networks in a variant of the stochastic P-­calculus, yielding a model which is mathematically well­defined and biologically faithful. We adapt the operational semantics of the calculus to account for both the time and probability of biochemical reactions, and present a computer implementation of the calculus for biochemical simulations

CRANKITE: a fast polypeptide backbone conformation sampler

Background: CRANKITE is a suite of programs for simulating backbone conformations of polypeptides and proteins. The core of the suite is an efficient Metropolis Monte Carlo sampler of backbone conformations in continuous three-dimensional space in atomic details. Methods: In contrast to other programs relying on local Metropolis moves in the space of dihedral angles, our sampler utilizes local crankshaft rotations of rigid peptide bonds in Cartesian space. Results: The sampler allows fast simulation and analysis of secondary structure formation and conformational changes for proteins of average length

Accurate implementation of leaping in space: The spatial partitioned-leaping algorithm

There is a great need for accurate and efficient computational approaches that can account for both the discrete and stochastic nature of chemical interactions as well as spatial inhomogeneities and diffusion. This is particularly true in biology and nanoscale materials science, where the common assumptions of deterministic dynamics and well-mixed reaction volumes often break down. In this article, we present a spatial version of the partitioned-leaping algorithm (PLA), a multiscale accelerated-stochastic simulation approach built upon the tau-leaping framework of Gillespie. We pay special attention to the details of the implementation, particularly as it pertains to the time step calculation procedure. We point out conceptual errors that have been made in this regard in prior implementations of spatial tau-leaping and illustrate the manifestation of these errors through practical examples. Finally, we discuss the fundamental difficulties associated with incorporating efficient exact-stochastic techniques, such as the next-subvolume method, into a spatial-leaping framework and suggest possible solutions.Comment: 15 pages, 9 figures, 2 table

Reduction of dynamical biochemical reaction networks in computational biology

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to backward pruning machine learning techniques

Design and Implementation of a Stand-Alone Tool for Metabolic Simulations

In this thesis, we present the design and implementation of a stand-alone tool for metabolic simulations. This system is able to integrate custom-built SBML models along with external user’s input information and produces the estimation of any reactants participating in the chain of the reactions in the provided model, e.g., ATP, Glucose, Insulin, for the given duration using numerical analysis and simulations. This tool offers the food intake arguments in the calculations to consider the personalized metabolic characteristics in the simulations. The tool has also been generalized to take into consideration of temporal genomic information and be flexible for simulation of any given biochemical model. After implementation, experimental results have demonstrated the numerical effectiveness of optimization for model selection and the feasibility of the proposed tool for the given metabolic simulation. The proof of concept analysis on the energy metabolism and insulin-glucose metabolism revealed this tool can be promising for a variety of healthcare applications

A Framework to Analyze the Performance of Load Balancing Schemes for Ensembles of Stochastic Simulations

Ensembles of simulations are employed to estimate the statistics of possible future states of a system, and are widely used in important applications such as climate change and biological modeling. Ensembles of runs can naturally be executed in parallel. However, when the CPU times of individual simulations vary considerably, a simple strategy of assigning an equal number of tasks per processor can lead to serious work imbalances and low parallel efficiency. This paper presents a new probabilistic framework to analyze the performance of dynamic load balancing algorithms for ensembles of simulations where many tasks are mapped onto each processor, and where the individual compute times vary considerably among tasks. Four load balancing strategies are discussed: most-dividing, all-redistribution, random-polling, and neighbor-redistribution. Simulation results with a stochastic budding yeast cell cycle model is consistent with the theoretical analysis. It is especially significant that there is a provable global decrease in load imbalance for the local rebalancing algorithms due to scalability concerns for the global rebalancing algorithms. The overall simulation time is reduced by up to 25%, and the total processor idle time by 85%