GPU-based Linear Algebra for Calculating Steady-State Probability and Dynamics of Molecular Networks

In this thesis we present a GPU-based implementation for the linear algebra kernels necessary to perform steady-state and dynamics study of biochemical reaction networks. The underlying goal is to provide a practical implementation for the Chemical Master Equation framework, a stochastic and discrete-state continuos-time formulation that provides a fundamental framework for biochemical reaction networks in the cell. In general, the study of CME may provide some deeper understanding of the issues involved through concrete biological network. The CME framework provides an exact representation of the microscopical state by considering the detailed chemical amount of each and every molecular species. This leads to an exponentially growing microstate space and, hence, to a computational challenge. From these premises it follows that we need a more efficient implementation for the linear algebra methods used by the theoretical framework to calculate steady-state and dynamics. A viable solution to accelerate linear algebra kernels is the use of Graphic Processing Units (GPUs), an emerging highly parallel computer architecture available on a single chip. This technology is well suited for dense linear algebra due to its high floating point instruction throughput and due to its large memory bandwidth. Therefore, we design a GPU-based implementation of a steady-state probability landscape solver (based on Jacobi iteration) and a dynamics simulation (based on Arnoldi) According to experimental results, it is now possible to efficiently deal with more realistic biochemical networks, up to 56 million microscopic states and 99x faster for steady-state analysis and up to 18 million states and 28x faster for dynamics analysis, allowing a close comparison between theoretical predictions and laboratory experiments.