Yu-Pin Luo

Fluctuations in gene regulatory networks as Gaussian colored noise

The study of fluctuations in gene regulatory networks is extended to the case of Gaussian colored noise. First, the solution of the corresponding Langevin equation with colored noise is expressed in terms of an Ito integral. Then, two important lemmas concerning the variance of an Ito integral and the covariance of two Ito integrals are shown. Based on the lemmas, we give the general formulas for the variances and covariance of molecular concentrations for a regulatory network near a stable equilibrium explicitly. Two examples, the gene autoregulatory network and the toggle switch, are presented in details. In general, it is found that the finite correlation time of noise reduces the fluctuations and enhances the correlation between the fluctuations of the molecular components.

A generalized integral fluctuation theorem for general jump processes

Using the Feynman-Kac and Cameron-Martin-Girsanov formulae, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Unlike the latter approach that has been extensively employed in the existing literature, our approach can naturally bring out the definition of a time reversal of a Markovian stochastic system. Additionally, we find that the robust GIFT usually does not result in a detailed fluctuation theorem.

Steady-state work fluctuations for an overdamped Brownian particle driven by external stochastic force

The steady-state work fluctuations for an overdamped Brownian particle driven by an external stochastic force are analyzed by using the Langevin approach. The first two moments of the work distribu...

Characterization of Vacancy Defect Interaction on the Electric Properties of Zigzag Single-Walled Carbon Nanotubes

Characterization of the interaction between vacancy defects in zigzag single-walled carbon nanotubes (SWCNTs) was carried out through geometric and bandstructure analyses with density functional theory (DFT). This interaction depends on the detail orientation between the defects and, in turns, influences the electric properties of the defective zigzag SWCNTs if any two defects are within the defect influencing range. Our results shed some light on the origin of the instability found in the electric properties of SWCNTs.