The intricate machinery of a living cell must function even when subjected to thermal fluctuations. The effect of thermal fluctuations on a molecule is best described as random time dependent perturbations. Cellular processes are modeled by stochastic processes. While thermal fluctuations can be disruptive, it is more often the case that a cell uses the resulting randomness to its advantage. One example is Brownian motion, or diffusion, used to transport small molecules throughout the cell. The central motivation of my research is to understand how cells harness their intrinsic stochasticity.
JN. and M. Schwemmer. Effects of moderate noise on a limit cycle oscillator: Counterrotation and bistability. Phys. Rev. Lett., 112:114101, 2014.preprintabstract
JN, P. C. Bressloff, and J. P. Keener. Breakdown of fast-slow analysis in an excitable system with channel noise. Phys. Rev. Lett., 111:128121, 2013.preprintabstract
S. Isaacson and JN. Uniform asymptotic approximation of diffusion to a small target. Phys. Rev. E, 88:012820, 2013.preprintabstract
JN and J. Chapman. Metastable behavior in Markov processes with internal states. J. Math. Biol., 2013.preprintabstract
P. C. Bressloff and JN. Stochastic models of intracellular transport. Rev. Mod. Phys., 85:135-196, 2013.preprintabstract
JN. Isolating intrinsic noise sources in a stochastic genetic switch. Physical Biol.,