GPU-Accelerated Steady-State Computation of Large Probabilistic Boolean Networks

Computation of steady-state probabilities is an important aspect of analysing biological systems modelled as probabilistic Boolean networks (PBNs). For small PBNs, efficient numerical methods can be successfully applied to perform the computation with the use of Markov chain state transition matrix underlying the studied networks. However, for large PBNs, numerical methods suffer from the state-space explosion problem since the state-space size is exponential in the number of nodes in a PBN. In fact, the use of statistical methods and Monte Carlo methods remain the only feasible approach to address the problem for large PBNs. Such methods usually rely on long simulations of a PBN. Since slow simulation can impede the analysis, the efficiency of the simulation procedure becomes critical. Intuitively, parallelising the simulation process can be an ideal way to accelerate the computation. Recent developments of general purpose graphics processing units (GPUs) provide possibilities to massively parallelise the simulation process. In this work, we propose a trajectory-level parallelisation framework to accelerate the computation of steady-state probabilities in large PBNs with the use of GPUs. To maximise the computation efficiency on a GPU, we develop a dynamical data arrangement mechanism for handling different size PBNs with a GPU, and a specific way of storing predictor functions of a PBN and the state of the PBN in the GPU memory. Experimental results show that our GPU-based parallelisation gains a speedup of approximately 400 times for a real-life PBN.