Fast simulation of stochastic biochemical reaction networks on cytomorphic chips

Abstract

The large-scale simulation of biochemical reaction networks in cells is important in pathway discovery in medicine, in analyzing complex cell function in systems biology, and in the design of synthetic biological circuits in living cells. However, cells can undergo many trillions of reactions over just an hour with multi-scale interacting feedback loops that manifest complex dynamics; their pathways exhibit non-modular behavior or loading; they exhibit high levels of stochasticity (noise) that require ex- pensive Gillespie algorithms and random-number generation for accurate simulations; and, they routinely operate with nonlinear statics and dynamics. Hence, such simulations are extremely computationally intensive and have remained an important bottleneck in computational biology over decades. By exploiting common mathematical laws between electronics and chemistry, this thesis demonstrates that digitally programmable analog integrated-circuit 'cytomorphic' chips can efficiently run stochastic simulations of complex molecular reaction networks in cells. In a proof-of-concept demonstration, we show that 0.35 [mu]m BiC- MOS cytomorphic gene and protein chips that interact via molecular data packets with FPGAs (Field Programmable Gate Arrays) to simulate networks involving up to 1,400 biochemical reactions can achieve a 700x speedup over COPASI, an efficient bio- chemical network simulator. They can also achieve a 30,000x speedup over MATLAB. The cytomorphic chips operate over five orders of magnitude of input concentration; they enable low-copy-number stochastic simulations by amplifying analog thermal noise that is consistent with Gillespie simulations; they represent non-modular load- ing effects and complex dynamics; and, they simulate zeroth, first, and second-order linear and nonlinear gene-protein networks with arbitrary parameters and network connectivity that can be flexibly digitally programmed. We demonstrate successful stochastic simulation of a p53 cancer pathway and glycolytic oscillations that are consistent with results obtained from conventional digital computer simulations, which are based on experimental data. We show that unlike conventional digital solutions, an increase in network scale or molecular population size does not compromise the simulation speed and accuracy of our completely parallel cytomorphic system. Thus, commonly used circuit improvements to future chips in our digital-to-analog converters, noise generators, and biasing circuits can enable further orders of magnitude of speedup, estimated to be a million fold for large-scale networks.