Exploring the Origin of Power Law Distribution in Single-Molecule Conformation Dynamics: Energy Landscape Perspectives

We explored the origin of power law distribution observed in single-molecule conformational dynamics experiments. By establishing a kinetic master equation approach to study statistically the microscopic state dynamics, we show that the underlying landscape with exponentially distributed density of states leads to power law distribution of kinetics. The exponential density of states emerges when the system becomes glassy and landscape becomes rough with significant trapping.

Robustness and Coherence of a Three-Protein Circadian Oscillator: Landscape and Flux Perspectives

Three-protein circadian oscillations in cyanobacteria sustain for weeks. To understand how cellular oscillations function robustly in stochastic fluctuating environments, we used a stochastic model to uncover two natures of circadian oscillation: the potential landscape related to steady-state probability distribution of protein concentrations; and the corresponding flux related to speed of concentration changes which drive the oscillations. The barrier height of escaping from the oscillation attractor on the landscape provides a quantitative measure of the robustness and coherence for oscillations against intrinsic and external fluctuations. The difference between the locations of the zero total driving force and the extremal of the potential provides a possible experimental probe and quantification of the force from curl flux. These results, correlated with experiments, can help in the design of robust oscillatory networks.

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.

Quantifying robustness and dissipation cost of yeast cell cycle network: The funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio ( RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.

Dominant kinetic paths on biomolecular binding-folding energy landscape

The identification of kinetic pathways is a central issue in understanding the nature of flexible binding. A new approach is proposed here to study the dynamics of this binding-folding process through the establishment of a path integral framework on the underlying energy landscape. The dominant kinetic paths of binding and folding can be determined and quantified. In this case, the corresponding kinetic paths of binding are shown to be intimately correlated with those of folding and the dynamics becomes quite cooperative. The kinetic time can be obtained through the contributions from the dominant paths and has a U-shape dependence on temperature.

Funneled landscape leads to robustness of cellular networks: MAPK signal transduction

We uncover the underlying potential energy landscape for a cellular network. We find that the potential energy landscape of the mitogen-activated protein-kinase signal transduction network is funneled toward the global minimum. The funneled landscape is quite robust against random perturbations. This naturally explains robustness from a physical point of view. The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network. Funneled landscape is a realization of the Darwinian principle of natural selection at the cellular network level. It provides an optimal criterion for network connections and design. Our approach is general and can be applied to other cellular networks.

Diffusion and single molecule dynamics on biomolecular interface binding energy landscape

We propose a new approach to study the diffusion dynamics on biomolecular interface binding energy landscape. The resulting mean first passage time (MFPT) has 'U'curve dependence on the temperature. It is shown that the large specificity ratio of gap to roughness of the underlying binding energy landscape not only guarantees the thermodynamic stability and the specificity [P.A. Rejto, G.M. Verkhivker, in: Proc. Natl. Acad. Sci. 93 (1996) 8945; C.J. Tsai, S. Kumar, B. Ma, R. Nussinov, Protein Sci. 8 (1999) 1181; G.A. Papoian, P.G. Wolynes, Biopolymers 68 (2003) 333; J. Wang, G.M. Verkhivker, Phys. Rev. Lett. 90 (2003) 198101] but also the kinetic accessibility. The complex kinetics and the associated fluctuations reflecting the structures of the binding energy landscape emerge upon temperature changes. The theory suggests a way of connecting the models/simulations with single molecule experiments by analysing the kinetic trajectories.

Energy landscape theory, funnels, specificity, and optimal criterion of biomolecular binding

We study the nature of biomolecular binding. We found that in general there exists several thermodynamic phases: a native binding phase, a non-native phase, and a glass or local trapping phase. The quantitative optimal criterion for the binding specificity is found to be the maximization of the ratio of the binding transition temperature versus the trapping transition temperature, or equivalently the ratio of the energy gap of binding between the native state and the average non-native states versus the dispersion or variance of the non-native states. This leads to a funneled binding energy landscape.

Diffusion dynamics, moments, and distribution of first-passage time on the protein-folding energy landscape, with applications to single molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We found that the first passage-time (FPT) distribution undergoes a dynamic transition at a temperature below which the FPT distribution develops a power-law tail, a signature of the intermittent nonexponential kinetic phenomena for the folding dynamics. Possible applications to single-molecule dynamics experiments are discussed.

Permanent Genetic Resources added to Molecular Ecology Resources Database 1 May 2009-31 July 2009

This article documents the addition of 512 microsatellite marker loci and nine pairs of Single Nucleotide Polymorphism (SNP) sequencing primers to the Molecular Ecology Resources Database. Loci were developed for the following species: Alcippe morrisonia morrisonia, Bashania fangiana, Bashania fargesii, Chaetodon vagabundus, Colletes floralis, Coluber constrictor flaviventris, Coptotermes gestroi, Crotophaga major, Cyprinella lutrensis, Danaus plexippus, Fagus grandifolia, Falco tinnunculus, Fletcherimyia fletcheri, Hydrilla verticillata, Laterallus jamaicensis coturniculus, Leavenworthia alabamica, Marmosops incanus, Miichthys miiuy, Nasua nasua, Noturus exilis, Odontesthes bonariensis, Quadrula fragosa, Pinctada maxima, Pseudaletia separata, Pseudoperonospora cubensis, Podocarpus elatus, Portunus trituberculatus, Rhagoletis cerasi, Rhinella schneideri, Sarracenia alata, Skeletonema marinoi, Sminthurus viridis, Syngnathus abaster, Uroteuthis (Photololigo) chinensis, Verticillium dahliae, Wasmannia auropunctata, and Zygochlamys patagonica. These loci were cross-tested on the following species: Chaetodon baronessa, Falco columbarius, Falco eleonorae, Falco naumanni, Falco peregrinus, Falco subbuteo, Didelphis aurita, Gracilinanus microtarsus, Marmosops paulensis, Monodelphis Americana, Odontesthes hatcheri, Podocarpus grayi, Podocarpus lawrencei, Podocarpus smithii, Portunus pelagicus, Syngnathus acus, Syngnathus typhle,Uroteuthis (Photololigo) edulis, Uroteuthis (Photololigo) duvauceli and Verticillium albo-atrum. This article also documents the addition of nine sequencing primer pairs and sixteen allele specific primers or probes for Oncorhynchus mykiss and Oncorhynchus tshawytscha; these primers and assays were cross-tested in both species.

Genetic diversity of the subterranean Gansu zokor in a semi-natural landscape

We studied the relationship between genetic diversity of the subterranean Gansu zokor Myospalax cansus and habitat variability in the Loess Plateau, Qinghai Province, China. We used a combination of geographic information systems and molecular techniques to assess the impact of habitat composition and human activities on the genetic diversity of zokor populations in this semi-natural landscape. Although they occurred relatively infrequently in the landscape, woodland and high-coverage grassland habitats were the main positive contributors to the genetic diversity of zokor populations. Rural residential land, plain agricultural land and low-coverage grassland had a negative effect on genetic diversity. Hilly agricultural land and middle-coverage grassland had little impact on zokor genetic diversity. There were also interactions between some habitat types, that is, habitat types with relatively better quality together promoted conservation of genetic diversity, while the interaction between (among) bad habitat types made situations worse. Finally, habitat diversity, measured as patch richness and Shannon's diversity index, was positively correlated with the genetic diversity. These results demonstrated that: (1) different habitat types had different effects on the genetic diversity of zokor populations and (2) habitat quality and habitat heterogeneity were important in maintaining genetic diversity. Habitat composition was closely related to land use thus emphasizing the importance of human activities on the genetic diversity of subterranean rodent populations in this semi-natural landscape. Although the Gansu zokor was considered to be a pest species in the Loess Plateau, our study provides insights for the management and conservation of other subterranean rodent species.

Mitochondrial and chloroplast phylogeography of Picea crassifolia Kom. (Pinaceae) in the Qinghai-Tibetan Plateau and adjacent highlands

The disjunct distribution of forests in the Qinghai-Tibetan Plateau (QTP) and adjacent Helan Shan and Daqing Shan highlands provides an excellent model to examine vegetation shifts, glacial refugia and gene flow of key species in this complex landscape region in response to past climatic oscillations and human disturbance. In this study, we examined maternally inherited mitochondrial DNA (nad1 intron b/c and nad5 intron 1) and paternally inherited chloroplast DNA (trnC-trnD) sequence variation within a dominant forest species, Picea crassifolia Kom. We recovered nine mitotypes and two chlorotypes in a survey of 442 individuals from 32 populations sampled throughout the species' range. Significant mitochondrial DNA population subdivision was detected (G(ST) = 0.512; N-ST = 0.679), suggesting low levels of recurrent gene flow through seeds among populations and significant phylogeographical structure (N-ST > GST, P < 0.05). Plateau haplotypes differed in sequence from those in the adjacent highlands, suggesting a long period of allopatric fragmentation between the species in the two regions and the presence of independent refugia in each region during Quaternary glaciations. On the QTP platform, all but one of the disjunct populations surveyed were fixed for the same mitotype, while most populations at the plateau edge contained more than one haplotype with the mitotype that was fixed in plateau platform populations always present at high frequency. This distribution pattern suggests that present-day disjunct populations on the QTP platform experienced a common recolonization history. The same phylogeographical pattern, however, was not detected for paternally inherited chloroplast DNA haplotypes. Two chlorotypes were distributed throughout the range of the species with little geographical population differentiation (G(ST) = N-ST = 0.093). This provides evidence for highly efficient pollen-mediated gene flow among isolated forest patches, both within and between the QTP and adjacent highland populations. A lack of isolation to pollen-mediated gene flow between forests on the QTP and adjacent highlands is surprising given that the Tengger Desert has been a geographical barrier between these two regions for approximately the last 1.8 million years.

Reproductive ecology of the Qinghai-Tibet Plateau endemic Gentiana straminea (Gentianaceae), a hermaphrodite perennial characterized by herkogamy and dichogamy

The combined occurrence of both herkogamy and dichogamy in a hermaphrodite species has been considered to strongly favour outcrossing. In this study, we investigated in detail the reproductive ecology of Gentiana straminea Maxim. (Gentianaceae), a hermaphrodite perennial endemic to the Qinghai-Tibet Plateau. In a series of observations and experiments over four consecutive years, we examined whether the combination of dichogamy and herkogamy in individual flowers completely prevents geitonogamous pollen transfer in this species. The mode of floral development clearly indicates that autonomous self-pollination is completely avoided through herkogamy and dichogamy in individual flowers. This implication was confirmed by the breeding experiments, since no seed was produced when flowers were isolated. However, this gentian proved to be highly self-compatible when geitonogamous selfing was artificially induced. Many flowers opened simultaneously on individual plants, the ratio of male to female phase flowers was close to 2:1 in each inflorescence, at the full anthesis phase, and they were randomly distributed amongst the upper, middle and lower parts of each stem's inflorescence. On average, Bombus sushikini Skorikov, the most frequent visitor and only legitimate pollinator of G. straminea, visited nearly two flowers per inflorescence, and four flowers per plant. Among the pollinators' foraging bouts, the proportions of geitonogamous visits to inflorescences or flowers within an individual plant were 29% and 37%, respectively. Therefore, despite the strict dichogamous and herkogamous characteristics of the individual flowers, geitonogamous selfing might still prevail in G. straininea because of the size of its floral displays and the continuous visiting behavior of B. sushkini. (C) 2005 Elsevier SAS. All rights reserved.