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.

Low-compressibility and hard materials ReB2 and WB2: Prediction from first-principles study

First-principle calculations are performed to investigate the structural, elastic, and electronic properties of ReB2 and WB2. The calculated equilibrium structural parameters of ReB2 are consistent with the available experimental data. The calculations indicate that WB2 in the P6(3)/mmc space group is more energetically stable under the ambient condition than in the P6/mmm. Based on the calculated bulk modulus, shear modulus of polycrystalline aggregate, ReB2 and WB2 can be regarded as potential candidates of ultra-incompressible and hard materials. Furthermore, the elastic anisotropy is discussed by investigating the elastic stiffness constants. Density of states and electron density analysis unravel the covalent bonding between the transition metal atoms and the boron atoms as the driving force of the high bulk modulus and high shear modulus as well as small Poisson's ratio.

First-passage time distribution and non-Markovian diffusion dynamics of protein folding

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a Levy-type distribution with power-law tails, indicating a nonself-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (Levy) distribution of the relaxation time of the underlined protein energy landscape is observed.

Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Toughening mechanism of polymer blends: Influence of voiding ability of dispersed-phase particles

The parameters which effect the cavitation strain of polymer blends toughened with a shear yield mechanism have been studied by analysis of the stress acted on the equatorial plane of dispersed-phase particles. As a result, the cavitation strain of polymer blends depends on the Young's modulus and the Poisson's ratio of the dispersed-phase particles and the matrix and also on the break stress of dispersed-phase particles. We tried to provide a criterion for selecting the materials used as dispersed-phase particles which can effectively enhance the toughness of polymer blends. (C) 1996 John Wiley & Sons, Inc.

THE APPLICATION OF THE MPB4 THEORY TO THE INTERFACE BETWEEN 2 IMMISCIBLE ELECTROLYTE-SOLUTIONS .2. THE DIFFERENTIAL CAPACITANCE OF THE WATER 1,2-DICHLOROETHANE INTERFACE

The MPB4 theory is used to calculate the differential capacitance of the interface between LiCl in water and TBATPB in 1,2-dichloroethane at electrolyte concentrations of 0.005, 0.01 and 0.02 M. The effects of the ion size and the image force, and the influence of the electrolyte concentration, the surface charge density and the solvent effect on the inner layer potential drop are considered simultaneously. These effects can be ascribed to the ionic penetration into the opposite solution and ion-ion correlations across the interface. Our results are in better agreement with experimental data than those obtained using Gouy-Chapman theory. This indicates that the MPB4 theory may also describe the structure of the water \1,2-dichloroethane interface provided that the influence of the electrolyte concentration, the surface charge density and the solvent effect on the inner layer potential distribution are included in the calculation. Comparison of the theoretical results with those of the water \nitrobenzene interface shows that the structure of the water \1,2-dichloroethane interface is similar to that of the water \nitrobenzene interface, except that in the former case the inner-layer potential drop is much higher and the effects of the image force and the ion size are more pronounced.

THE APPLICATION OF THE MPB4 THEORY TO THE INTERFACE BETWEEN 2 IMMISCIBLE ELECTROLYTE-SOLUTIONS .1. THE DIFFERENTIAL CAPACITANCE OF THE WATER NITROBENZENE INTERFACE

We use the MPB4 theory to calculate the differential capacitance of the interface between NaBr + water and tetrabutylammoniumtetraphenyl borate (TBATPB) + nitrobenzene at electrolyte concentrations of 0.01 M, 0.02 M and 0.05 M. In addition to the effects

Photosynthesis-irradiance response at physiological level: A mechanistic model

A mechanistic model is developed to present the photosynthetic response of phytoplankton to irradiance at the physiological level. The model is operated on photosynthetic units (PSU), and each PSU is assumed to have two states: reactive and activated. Light absorption that drives a reactive PSU into the activated state results from the effective absorption of the PSU. Transitions between the two states are asymmetrical in rate. A PSU in the reactive state becomes activated much faster than it recovers from the activated state to the reactive one. The turnover time for an activated PSU to transit into the reactive one is defined by the turnover time of the electron transport chain. The present model yields a photosynthesis-irradiance curve (PE-curve) in a hyperbola, which is described by three physiological parameters: effective cross-section (sigma (PSII)), turnover time of electron transport chain (tau) and number of PSUs (N). The PE-curve has an initial slope of sigma (PSII) x N, a half-saturated irradiance of 1/(sigma (PSII)), and a maximal photosynthetic rate of Nlc at the saturated irradiance. The PE-curve from the present model is comparable to the empirical function based on the target theory described by the Poisson distribution. (C) 2001 Academic Press.

广义预测控制方法在网络遥操作机器人系统中的应用

Internet网络的时变时延及网络数据丢包严重影响了遥操作机器人系统的操作性能,甚至造成系统不稳定。为了解决这一问题,提出一种新的基于Internet的遥操作机器人系统控制结构。通过在主端对给定信息加入时间标签获得过去的系统回路时延,采用多元线性回归算法,预测下一时刻系统回路时延,然后在从端设计一个广义预测控制器控制远端机器人,从而改善时变时延对系统性能的影响。应用广义预测控制器产生的冗余控制信息,降低了网络数据丢包对系统的影响。最后根据预测控制稳定性定理,推导出系统的稳定性条件。仿真试验结果表明,该方法能有效解决时变时延以及网络数据丢包引起的性能下降问题。

基于介电泳的电极阵列电场仿真研究

介电泳方法被广泛地应用于微纳颗粒的分离和操纵中,实现介电泳操作的关键是设计满足所需电场分布的电极阵列。针对目前在微电极阵列设计中尚缺乏简单有效的电场解析方法的现状,提出一种基于格林公式的电极阵列电场的解析方法。首先介绍了传统介电泳和行波介电泳的概念和计算模型,分析了介电泳过程与电极上所施加的交变电压的频率和幅度的关系,然后在确立电极电势的边界条件的基础上,采用基于格林公式的电场解析方法,建立了非均匀电场的解析模型,得出不同条件下的电极阵列电场分布的仿真结果,最后利用FEMLAB有限元仿真软件对解析模型进行了对比仿真,验证了该解析模型的可行性。基于格林公式的电场解析求解方法能够有效地提高电极阵列设计中的针对性以及缩短电极设计的时间。