Potential energy landscape and robustness of a gene regulatory network: Toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers.

Theoretical investigation of 5D-metal monocarbide

Bond distances, vibrational frequencies, electron affinities, ionization potentials and dissociation energies of the title molecules in neutral, positively and negatively charged ions were studied by use of density functional method. The calculated results were compared with previous theoretical and experimental studies. Ground states for each molecule were assigned. It was found that for some molecules, low-lying state, in which the energy is much close to the ground state, was obtained. In this case, further studies both experimentally and theoretically are necessary in order to find the true global minimum.

Chemical bonding and electronic structure of 4d-metal monocarbides

Bond distances, vibrational frequencies, dissociation energies, electron affinities, ionization potentials and dipole moments of the title molecules in neutral and charged ions were studied by use of density functional method. Ground states for each molecule were assigned. For neutral and cationic molecules, the bond distance decreases from YC (YC+) to RhC (RhC+), then increases, while for anionic molecules, the bond distance decreases from YC- to RuC-, then increases. Opposite trend was observed for vibrational frequency. The bond ionic character decreases from ZrC to PdC for neutral molecules. The bonding patterns are discussed and compared with the available studies.

Ab initio configuration-interaction study of the ground and low-lying electronic states of NiI

For the first time, we have studied the potential-energy curves, spectroscopic terms, vibrational levels, and the spectroscopic constants of the ground and low-lying excited states of NiI by employing the complete active space self-consistent-field method with relativistic effective core potentials followed by multireference configuration-interaction calculations. We have identified six low-lying electronic states of NiI with doublet spin multiplicities, including three states of Delta symmetry and three states of Pi symmetry of the molecule within 15 000 cm(-1). The lowest (2)Delta state is identified as the ground state of NiI, and the lowest (2)Pi state is found at 2174.56 cm(-1) above it. These results fully support the previous conclusion of the observed spectra although our computational energy separation of the two states is obviously larger than that of the experimental values. The present calculations show that the low-lying excited states [13.9] (2)Pi and [14.6] (2)Delta are 3 (2)Pi and 3 (2)Delta electronic states of NiI, respectively. Our computed spectroscopic terms, vibrational levels, and spectroscopic constants for them are in good agreement with the experimental data available at present. In the present work we have not only suggested assignments for the observed states but also computed more electronic states that are yet to be observed experimentally. (c) 2005 American Institute of Physics.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

A surface energy model and application to mechanical behavior analysis of single crystals at sub-micron scale

Size effects of mechanical behaviors of materials are referred to the variation of the mechanical behavior due to the sample sizes changing from macroscale to micro-/nanoscales. At the micro-/nanoscale, since sample has a relatively high specific surface area (SSA) (ratio of surface area to volume), the surface although it is often neglected at the macroscale, becomes prominent in governing the energy effect, although it is often neglected at the macroscale, becomes prominent in governing the mechanical behavior. In the present research, a continuum model considering the surface energy effect is developed through introducing the surface energy to total potential energy. Simultaneously, a corresponding finite element method is developed. The model is used to analyze the axial equilibrium strain problem for a Cu nanowire at the external loading-free state. As another application of the model, from dimensional analysis, the size effects of uniform compression tests on the microscale cylinder specimens for Ni and Au single crystals are analyzed and compared with experiments in literatures. (C) 2009 Elsevier B.V. All rights reserved.

Separation of potential and kinetic electron emission from Si and W induced by multiply charged neon and argon ions

T he total secondary electron emission yields, gamma(T), induced by impact of the fast ions Neq+ (q = 2-8) and Arq+ (q = 3-12) on Si and Neq+ (q = 2-8) on W targets have been measured. It was observed that for a given impact energy, gamma(T) increases with the charge of projectile ion. By plotting gamma(T) as a function of the total potential energy of the respective ion, true kinetic and potential electron yields have been obtained. Potential electron yield was proportional to the total potential energy of the projectile ion. However, decrease in potential electron yield with increasing kinetic energy of Neq+ impact on Si and W was observed. This decrease in potential electron yield with kinetic energy of the ion was more pronounced for the projectile ions having higher charge states. Moreover, kinetic electron yield to energy-loss ratio for various ion-target combinations was calculated and results were in good agreement with semi-empirical model for kinetic electron emission.

Nuclear potential and fusion cross sections for synthesizing super-heavy elements in di-nuclear systems

A double folding method with simplified Skyreme-type nucleon-nucleon interaction is used to calculate the nuclear interaction potential between two nuclei. The calculation is performed in tip-to-tip orientation of the two nuclei if they are deformed. Based on this methods, the potential energy surfaces, the fusion probabilities and the evaporation residue cross sections for some cold fusion reactions leading to super-heavy elements within di-nuclear system model are evaluated. It is indicated that after the improvement, the exponential decreasing systematics of the fusion probability with increasing charge number of projectile on the Pb based target become better and the evaporation residue cross sections are in better agreement with the experimental data.