Fundamental limitations between noise and back-action in bio-molecular networks

Abstract

In an interconnection of two components in a bio-molecular network, noise in the downstream component can be reduced by increasing the magnitude of the down-stream signal. However, this method of reducing noise increases the back-effect to the upstream system, called 'retroactivity', thereby increasing the perturbation to the upstream system. In this thesis, we seek to quantify the total error in the system caused by the perturbations due to retroactivity and noise, and to analyze the trade-off between the two errors. We model the system as a set of non-linear chemical Langevin equations and quantify the trade-off for two different approximations of this non-linear model. First we consider a system linearized about a fixed point and quantify the trade-off using transfer functions. Next we use a linear approximation of the propensity functions in the Langevin equation and quantify the error by calculating upper bounds using contraction theory for deterministic and stochastic systems. Future research directions in improving the upper bounds are discussed.