Parallel simulation of multiple proteins through a bioreactor coupled with biochemical reactions

This paper presents a parallel numerical solution to investigate multiple growth factors competitive binding within a bioreactor, an in vitro flow cell culture system. Since we assume all the species have the same flow, thus the multiphysics of fluid flow is modeled by the same incompressible Navier-Stokes equations. The kinetics of biochemical reactions happens in the fluid and on the cell surfaces as well, thus they are modeled by two separate sets of coupled nonlinear ordinary differential equations (ODEs). The mass transport of different species in the fluid is modeled by a distinctive set of coupled nonlinear partial differential equations (PDEs) for each of them. To solve this computational intensive system efficiently, a novel parallel algorithm is devised, in which all the numerical computations are solved in parallel, including parallel discretization of those mass transport equations PDEs and parallel linear system solver. A novel parallel strongly implicit procedure (SIP) solver is designed. For solving binding equations ODEs in the whole domain efficiently, a parallel scheme combined with a sequential CVODE solver is used for the purpose of high performance and simplicity. Overall, our parallel algorithms show good performance and stability. Preliminary simulation results are obtained. We have found that heparin or possibly other solution binding agents can effectively prevent fibroblast growth factor-2 (FGF-2) capture under flow, but only at high concentrations, and FGF-2 cross regulating receptor binding agents, such as heparin-binding epidermal growth factor-like growth factor (HB-EGF) or possibly other proteoglycan-competitors, has little effect on FGF-2 capture in single pass flow even at high concentration. Further experiments need to be conducted to verify the predictions of our parallel simulation system. This parallel modeling system can be used to any biochemical reaction analysis in a similar flow environment.