Stochastic modeling of reaction kinetics in biosensors using the Fokker Planck equation

The discrete-state continuous-time processes occurring in binding and release of analytes in affinity-based biosensors are formulated using stochastic differential equations (SDEs). The Fokker Planck (FP) equation is used to solve for the governing probability density function (pdf) of the number of captured analytes. A derivation method from the Markovian Master equation to the Fokker Planck equation is also given, which provides an alternative approach to the conventionally used Monte Carlo simulation methods, which has advantages in systems where the state space is large. Using FP equation, the time evolution of pdfs of the captured analytes in typical biosensor settings can be analyzed and subsequently be used to compute the expected behaviour and uncertainty of the detection and also be implemented in the design of optimal estimators.