Single molecule dynamics and statistical fluctuations of gene regulatory networks: A repressilator

The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between similar to 10(-3) and similar to 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

With the aid of thermodynamics of Gibbs, the expression of the spinodal was derived for the polydisperse polymer-solvent system in the framework of Sanchez-Lacombe Lattice Fluid Theory (SLLFT). For convenience, we considered that a model polydisperse polymer contains three sub-components. According to our calculation, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights of the polydisperse polymer, but the z-average molecular weight ((M) over bar (z)) dependence on the spinodal is invisible. The dependence of free volume on composition, temperature, molecular weight, and its distribution results in the effect of (M) over bar (n) on the spinodal. Moreover, it has been found that the effect of changing (M) over bar (w) on the spinodal is much bigger than that of changing (M) over bar (n) and the extrema of the spinodal increases with the rise of the weight-average molecular weight of the polymer in the solutions with upper critical solution temperature (UCST). However, the effect of polydispersity on the spinodal can be neglected for the polymer with a considerably high weight-average molecular weight. A more simple expression of the spinodal for the polydisperse polymer solution in the framework of SLLFT was also derived under the assumption of upsilon(*)=upsilon(1)(*)=upsilon(2)(*) and (1/r(1)(0))-(1/r(2i)(0))-->(1/r(1)(0)).

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .1. POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION

The Gibbs free energies and equations of state of polymers with special molar mass distributions, e.g., Flory distribution, uniform distribution and Schulz distribution, are derived based on a lattice fluid model. The influence of the polydispersity (or t

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .2. BINARY MIXTURE OF POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION

In this paper, the Gibbs free energy, the equation of state and the chemical potentials of polydisperse multicomponent polymer mixtures are derived. For general binary mixtures of polydisperse polymers, we also give the Gibbs free energy, the equation of

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .3. BINARY MIXTURE OF POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION WITH STRONG-INTERACTIONS

For a binary mixture of polydisperse polymers with strong interactions, the free energy, the equation of state, the chemical potentials and the spinodal are formulated on the basis of the lattice fluid model. Further, the spinodal curves for the system wi

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER MIXTURES

A statistical thermodynamics theory of polydisperse polymer blends based on a lattice model description of a fluid is formulated. Characterization of a binary polydisperse polymer mixture requires a knowledge of the pure polymer system and the interaction energy. It is assumed that the intrinsic and interactive properties of polymer (for example, T*, P*, rho*, and epsilon(ij)*) are independent of molecular size. Thermodynamic properties of ternary and higher order mixtures are completely defined in terms of the pure fluid polymer parameters and the binary interaction energies. Thermodynamic stability criteria for the phase transitions of a binary mixture are shown. The binodal and spinodal of general binary systems and of special binary systems are discussed.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER BLENDS WITH STRONG INTERACTION

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMERS

A statistical thermodynamics theory of polydisperse polymers based on a lattice model of fluids is formulated. Pure polydisperse polymer can be completely characterized by three scale factors and the molecular weight distribution of the system. The equation of state does not satisfy a simple corresponding-states principle, except for a polymer fluid of sufficiently high molecular weight. The relationships between thermal expansion coefficient alpha and isothermal compressibility beta with reduced variables are also predicted.

STATISTICAL THERMODYNAMICS OF A LATTICE FLUID - PURE POLYMER

A statistical thermodynamics theory of a polydisperse polymer based on a lattice model of a fluid is formulated. The pure polydisperse polymer is completely characterized by three scale factors and the distribution law of the system. The equation of state does not satisfy a simple corresponding state principle, except for the polymer fluid with sufficiently high molecular weight.

Substrate induction and statistical optimization for the production of chitosanase from Microbacterium sp OU01

The chitosanase production was markedly enhanced by substrate induction, statistical optimization of medium composition and culture conditions by Microbacteritan sp. OU01 in shake-flask. A significant influence of (NH4)(2)SO4, MgSO4 center dot 7H(2)O and initial pH on chitosanase production was noted with Plackett-Burman design. It was then revealed with the method of steepest ascent and response surface methodology (RSM) that 19.0 g/L (NH4)(2)SO4, 1.3 g/L MgSO4 and an initial pH of 2.0 were optimum for the production of chitosanase; colloidal chitosan appeared to be the best inducer for chitosanase production by Microbacterium sp. OU01. This optimization strategy led to the enhancement of chitosanase from 3.6 U/mL to 118 U/mL. (c) 2006 Elsevier Ltd. All rights reserved.

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Outer wave number spectrum and statistical distribution of apparent wave number vector

Based on the ray theory and Longuet-Higgins's linear,model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper. (C) 2002 Elsevier Science Ltd. All rights reserved.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.