On the Thermodynamic Hypothesis of Protein Folding Govindarajan, Sridhar; Goldstein, Richard A.
Proceedings of the National Academy of Sciences - PNAS,
05/1998, Letnik:
95, Številka:
10
Journal Article
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The validity of the thermodynamic hypothesis of protein folding was explored by simulating the evolution of protein sequences. Simple models of lattice proteins were allowed to evolve by random point ...mutations subject to the constraint that they fold into a predetermined native structure with a Monte Carlo folding algorithm. We employed a simple analytical approach to compute the probability of violation of the thermodynamic hypothesis as a function of the size of the protein, the fraction of the total number of possible conformations which are kinetically accessible, and the roughness of the free-energy landscape. It was found that even if the folding is under kinetic control, the sequence will evolve so that the native state is most often the state of minimum free energy.
I provide a brief introduction to the concept of spatial autocorrelation and its incorporation into regression-type models. Spatial autocorrelation occurs when the response variable is correlated ...with itself at other locations in the region of interest. The autocorrelation usually takes a specific form where observations close in space are more correlated than those farther apart, and the rate of decay of the correlation is a function of the distance separating 2 locations. I present 2 commonly used models: 1) geostatistical modeling in which data are collected at points in the study region and 2) conditional autoregression (lattice) models in which data are aggregated over small nonoverlapping sub-areas of the study region. I also describe incorporation of explanatory covariates, such as habitat or physico-chemical attributes. I emphasize frequentist methods, but I briefly describe Bayesian approaches. I also provide some advantages, such as obtaining correct standard errors for estimators, and disadvantages, such as requirements for larger sample sizes, of incorporating spatial autocorrelation into the modeling effort. This information can aid researchers in designing and analyzing models of the relationships between species distributions and habitat. As a result, more informative models can be developed which further aid in management of wildlife.
Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and ...q-anyonic models as well as nonlinear Schrödinger equation (NLS) and the derivative NLS quantum field models involving anyonic operators, N-particle sectors of which yield the well known anyon gases, interacting through ? and derivative ?-function potentials.
Habitat destruction is one of the primary causes of species extinction in recent history. Even if the destruction is restricted to a local area, its accumulation increases the risk of extinction. To ...investigate the effect of local habitat destruction, we studied two- and three-species model systems. The former contains prey (
X) and predator (
Y), while the latter is composed of
X,
Y and a top predator (
Z). If the species
Z goes extinct, then the latter becomes the former. Species dynamics are modeled within the lattice applying local and global interactions. Local interaction occurs between neighboring lattice points. In contrast, global interaction is allowed between any pair of lattice points, and its dynamics can be represented by the mean-field theory that is equivalent to Lotka-Volterra equation. Barriers, representing habitat loss, are randomly located between adjacent lattice points with the probability
p. The barrier interrupts the reproduction of the prey
X, but the predators
Y and
Z suffer no direct damage from the barriers. It is found that the effects of barriers on both species
X and
Y in the two-species model are usually opposite to those in the three-species model. Namely, if extinction occurs, the influence of habitat destruction on surviving species changes dramatically. We also find that when the density
p of barriers increases the two models exhibit different extinction patterns: sometimes species
X goes extinct, but sometimes the predator or top predator become extinct depending on the level of barrier density. The mean-field theory adequately predicts such species extinction, but it cannot explain some of the results. We interpret the results as an indirect relation between habitat destruction and species extinction.
Many simulations of plant or animal dispersal across landscapes fragmented by human activity have represented the environment as habitat or non-habitat. Here, the consequences of representing habitat ...on grids as a continuous surface (0–1) versus as binary (0, 1) are examined for such models. Simulated landscapes with mean habitat quality of 0.5, with different variance, and with 50% each of habitat and non-habitat are compared. Random and non-random patterns are simulated. Dispersal can be directionally biased. Dispersal across continuous landscapes is more frequent and faster than across binary landscapes. On continuous landscapes, pattern matters, with success and speed reduced as local heterogeneity increases. Increased variance also reduces success and speed. The degree to which a species uses the landscape as a continuum of habitat, versus as either/or, will improve its response to forces that require increased movement for survival, such as habitat fragmentation and climatic change. The range of representations from binary to continuous will affect models including spread of disturbances, but the importance of heterogeneity will vary with the species or phenomena being modeled.
An individual-based, spatially explicit stochastic lattice model, CAPS, was designed to examine multiple processes responsible for spatial patterns of abundance and diversity of sessile species in ...heterogeneous landscapes. Species simulated by CAPS differ in habitat preferences (niche width), dispersal of propagules, and relative fecundity. The spatial distribution of habitat types are represented as heterogeneous gridded landscapes. The outcome of competition and establishment processes in successive generations is determined locally via a seed lottery. A series of 200 year-long simulations was performed to investigate the effects of variation in species characteristics and competition, landscape heterogeneity, and disturbance on patterns of species abundances. The outcome of competition was most sensitive to differences in fecundity between species, the spatial distribution of suitable habitat and the initial distribution of species. Species with a narrow niche were confined to a single habitat type and remained at or near their initialization sites. Broader niches resulted in increasing niche overlap and competition but enhanced species mobility, allowing abundance levels to approach expected values determined by map resources. Even so, initial distributions still affected the spatial patterns of species distributions at year 200. Disturbance regimes were simulated by varying the frequency, extent and spatial pattern of disturbances. Disturbance events removed species from affected sites but did not otherwise alter habitat characteristics. Results showed that disturbances may lead to a reversal in competition and establishment, dependent on species-specific differences in fecundity and dispersal. Although intermediate levels of disturbance frequency and extent increased the probability of species coexistence, the spatial pattern of disturbance played an unexpectedly important role in the tradeoff between dispersal and fecundity. The ability to simulate multiple factors affecting patterns of persistence, abundance and spatial distribution of species provided by CAPS allows new insight into the temporal and spatial patterns of community development.
Particle methods such as the meso-particle method or the method of movable cellular automata provide new possibilities for the simulation of wear, mass-transfer, plastic deformation and melting ...processes. One crucial point, however, is to ensure that in the continuum limit macroscopic isotropy is guaranteed. We show how this can be done in two- and three-dimensional lattices.
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