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A Fokker-Planck Approach For Modeling Integrated NanoBio Systems

J. W. Jenkins, S. Sundaram

Keywords: Fokker Plank Master Equation Multiscale Biosystems

Physics-based, high-fidelity simulations have emerged as indispensable tools in the design of complex, microfluidic devices (lab-on-chip). However, ab-initio analysis becomes increasingly complicated as the dimensions of the device approach nanoscales and molecular information/interactions must be considered (Integrated Nanobiosystems). The information exchange between the nanoscale and the microscale is difficult for two reasons. First, device/component level simulations are traditionally continuum based while molecular physics is resolved using a variety of methods (e.g. Molecular Dynamics (MD)). Integrating the two schemes to yield a self consistent calculation of biomolecular reactions in a microfluidic device, is a formidable task. Secondly, the time scale differences between nanoscale (relaxation phenomena in pico/nano seconds) and microscale (response in milliseconds) poses serious challenges in active coupling between the molecular and continuum aspects of any integrated simulation. The Master Equation (ME), Fokker-Planck Equation (FPE) or the Langevin Equation (LE) offer a unique advantage of being based on partial differential equation, which facilitates integration with continuum approach. At CFDRC we have successfully coupled a FPE-based description of biomolecular events with a continuum-based convective-diffusive-reactive treatment of biosystems (CFD-ACE+). The goal of this work is to be able to simulate nano-resolved, biomolecular reactions (DNA hybridization, Ag-Ab interactions) in spatially inhomogeneous systems with convective(drift)-diffusive transport. FPE formulation and boundary conditions, along with their relationships to ME transition probabilities will be discussed. The method will be illustrated with two specific examples (a) modeling of the rotation rate of a molecular motor and (b) shear influenced ligand binding.

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