Size Nc Research Articles

New method for determining size of critical nucleus of fibril formation of polypeptide chains

A new method for determining the size of critical nucleus of fibril formation of polypeptide chains is proposed. Based on the hypothesis that the fibril grows by addition of a nascent peptide to the preformed template, the nucleus size N(c) is defined as the number of forming template peptides above which the time to add a new monomer becomes independent of the template size. Using lattice models one can show that our method and the standard method which is based on calculation of the free energy, provide the same result for N(c).

Fractal structure of the crystalline-nuclei boundaries in 2D colloidal crystallization: Computer simulations

By performing 2D kinetic Monte Carlo simulations of colloidal crystallization we found that the boundaries of the crystalline nuclei are not only rough, as obtained by experimentalists, but fractal, whose value (df) we calculated. The corresponding boundary for the crystals, above the critical size (Nc), is also fractal but smoother. A knowledge of the particles coordinates during the crystallization process allows us to calculate the Nc, the line tension (γ) and the chemical potential difference (Δμ) between the two phases. However, different from the experimentalists procedure, we found that the boundary fractalities are needed to derive γ and Δμ.

Wet granular rafts: aggregation in two dimensions under shear flow

The aggregation and fragmentation of cohesive granular particles trapped at an air–liquid interface under shear flow are investigated by experiments and compared with numerical simulations. The cohesion owing to the formation of capillary bridges from a thin oil film covering the particles is found to dominate other particle–particle interactions. In the steady state the radius of gyration Rg of an N particle cluster follows a power law Rg ∝ N1/δ. The fractal dimension δ of the clusters lies in the range between 1.5 and 1.6 and depends only weakly on the shear rate . The probability to find a cluster of N particles or larger P(N) displays an exponential tail P(N) ∝ exp(−N/Nc) with a characteristic cluster size Nc. A power law Nc ∝ −β with an exponent β = 0.65 ± 0.06 (β = 0.68 ± 0.02) is found in our experiments (simulations). The fractal dimension of the clusters and the value of β are consistent with an estimate of the largest stable cluster based on the balance between the capillary force and the viscous drag force.

Low effective population size and survivorship in a grassland grouse

Assessments of census size (Nc) and effective population size (Ne) are necessary for the conservation of species exhibiting population declines. We examined two populations (Oklahoma and New Mexico) of the lesser prairie-chicken (Tympanuchus pallidicinctus), a declining lek-breeding bird, in which one population (Oklahoma) has larger clutch size and more nesting attempts per year but lower survival caused by human changes to the landscape. We estimated demographic and genetic estimates of Ne for each population and found that both populations have low Ne estimates with a risk of inbreeding depression. Although Oklahoma females produce a larger number of offspring, the proportion of females successfully reproducing is not higher than in New Mexico. Higher reproductive effort has likely reached a physiological limit in Oklahoma prairie-chickens but has not led to a higher Ne or even a larger Nc than New Mexico. We propose that future conservation efforts focus on maximizing survivorship and decreasing the variance in reproductive success because these factors are more likely than increasing reproductive output alone to yield population persistence in lek-breeding species.

Critical behavior of XY spin chain with Dzyaloshinsky–Moriya interaction studied in terms of Loschmidt echo

In this paper, the critical behavior of the general XY spin chain with the Dzyaloshinsky–Moriya (DM) interaction is studied by means of a Loschmidt Echo (LE) calculation. LE presents a Gauss decay in the region of magnetic field intensity |λ|<1 and an exponential decay in the region of |λ|>1. There exists a critical spin chain size NC. When spin chain size is larger than NC, the value of λ corresponding to the minimum value of LE (λm) is independent of the spin chain size and keeps a stable value. In the region of λ<0, the stable value is same for different DM interactions. In the region of λ>0, the stable value varies with changing DM interaction.

Kinetic Monte Carlo simulation of shape transition of strained quantum dots

The pyramid-to-dome transition in GexSi1−x on Si(100) initiated by step formation on pyramidal quantum dots is atomistically simulated using a multistate lattice model in two-dimensions incorporating effective surface reconstructions. Under quasiequilibrium growth conditions associated with low deposition rates, the transition occurs at island size nc following nc∼x−1.69 independent of temperature and deposition rate. The shape transition is found to be an activated process. Results are explained by a theory based on simple forms of facet energies and elastic energies estimated using a shallow island approximation. An asymptotic scaling relation nc1/d∼x−2 for x→0 applicable to d=2 or 3 dimensions is derived. The shape transition energy barrier can be dominated by the interface energy between steep and shallow facets.

Sulcal set optimization for cortical surface registration

Flat mapping based cortical surface registration constrained by manually traced sulcal curves has been widely used for inter subject comparisons of neuroanatomical data. Even for an experienced neuroanatomist, manual sulcal tracing can be quite time consuming, with the cost increasing with the number of sulcal curves used for registration. We present a method for estimation of an optimal subset of size NC from N possible candidate sulcal curves that minimizes a mean squared error metric over all combinations of NC curves. The resulting procedure allows us to estimate a subset with a reduced number of curves to be traced as part of the registration procedure leading to optimal use of manual labeling effort for registration. To minimize the error metric we analyze the correlation structure of the errors in the sulcal curves by modeling them as a multivariate Gaussian distribution. For a given subset of sulci used as constraints in surface registration, the proposed model estimates registration error based on the correlation structure of the sulcal errors. The optimal subset of constraint curves consists of the NC sulci that jointly minimize the estimated error variance for the subset of unconstrained curves conditioned on the NC constraint curves. The optimal subsets of sulci are presented and the estimated and actual registration errors for these subsets are computed.

A vector model of associative memory with clipped synapses

The influence of a clipping procedure on the properties of vector associative memory is investigated. The analysis is performed for the particular case of a phase model of a parametric neural network with 2q-state neurons. The critical network size Nc is found. It is shown that, for small network sizes (N Nc) leads to a deterioration of the recognition ability and reduces the storage capacity.

Effective size closely approximates the census size in the heavily exploited western Atlantic population of the sandbar shark, Carcharhinus plumbeus

The sandbar shark, Carcharhinus plumbeus, is a long-lived species with low lifetime fecundity that is heavily fished in the western North Atlantic. Inshore nursery grounds increase survivorship of sandbar shark pups and the principal nurseries are in the mid-Atlantic region. We calculated effective number of breeders (Nb) and effective population size (Ne) for adults utilizing the nursery grounds of the Delaware Bay and the Eastern Shore of Virginia by genotyping 902 animals across five cohorts at eight microsatellite loci. Estimates of Nb and Ne were compared to estimates of census size (Nc) of cohorts obtained from Delaware Bay. The estimated Ne/Nc and Nb/Nc ratios were 0.45 or higher whether the Delaware Bay cohorts were considered as distinct year classes or combined. This is in contrast to estimated Ne/Nc ratios in other exploited marine fishes, which are several orders of magnitude smaller. Instead, the Ne/Nc ratio of sandbar sharks is similar to that found in marine and terrestrial mammals.

A travelling cluster approximation for lattice fermions strongly coupled to classical degrees of freedom

We suggest and implement a new Monte Carlo strategy for correlated models involving fermions strongly coupled to classical degrees of freedom, with accurate handling of quenched disorder as well. Current methods iteratively diagonalise the full Hamiltonian for a system of N sites with computation time τN ∼N4. This limits achievable sizes to N ∼100. In our method the energy cost of a Monte Carlo update is computed from the Hamiltonian of a cluster, of size Nc, constructed around the reference site, and embedded in the larger system. As MC steps sweep over the system, the cluster Hamiltonian also moves, being reconstructed at each site where an update is attempted. In this method τN,Nc ∼NNc3. Our results are obviously exact when Nc=N, and converge quickly to this asymptote with increasing Nc, particularly in the presence of disorder. We provide detailed benchmarks on the Holstein model and the double exchange model. The `locality' of the energy cost, as evidenced by our results, suggests that several important but inaccessible problems can now be handled with control. This method forms the basis of our studies in Europhys. Lett. 68, 564 (2004), Phys. Rev. Lett. 94, 136601 (2005), and Phys. Rev. Lett. 96, 016602 (2006).

Evolution of Human Immunodeficiency Virus Under Selection and Weak Recombination

To predict emergence of drug resistance in patients undergoing antiretroviral therapy, we study accumulation of preexisting beneficial alleles in a haploid population of N genomes. The factors included in the model are selection with the coefficient s and recombination with the small rate per genome r (r << s sqrt of k, where k is the average number of less-fit loci per genome). Mutation events are neglected. To describe evolution at a large number of linked loci, we generalize the analytic method we developed recently for an asexual population. We show that the distribution of genomes over the deleterious allele number moves in time as a "solitary wave" that is quasi-deterministic in the middle (on the average) but has stochastic edges. We arrive at a single-locus expression for the average accumulation rate, in which the effects of linkage, recombination, and random drift are all accounted for by the effective selection coefficient s lnNr/lnNs(2)k/r. At large N, the effective selection coefficient approaches the single-locus value s. Below the critical size N(c) approximately 1/r, a population eventually becomes a clone, recombination cannot produce new sequences, and virus evolution stops. Taking into account finite mutation rate predicts a small, finite rate of evolution at N < N(c). We verify the accuracy of the results analytically and by Monte Carlo simulation. On the basis of our findings, we predict that partial depletion of the HIV population by combined anti-retroviral therapy can suppress emergence of drug-resistant strains.

EFFECTIVE POPULATION SIZES AND TEMPORAL STABILITY OF GENETIC STRUCTURE IN RANA PIPIENS, THE NORTHERN LEOPARD FROG

Although studies of population genetic structure are very common, whether genetic structure is stable over time has been assessed for very few taxa. The question of stability over time is particularly interesting for frogs because it is not clear to what extent frogs exist in dynamic metapopulations with frequent extinction and recolonization, or in stable patches at equilibrium between drift and gene flow. In this study we collected tissue samples from the same five populations of leopard frogs, Rana pipiens, over a 22-30 year time interval (11-15 generations). Genetic structure among the populations was very stable, suggesting that these populations were not undergoing frequent extinction and colonization. We also estimated the effective size of each population from the change in allele frequencies over time. There exist few estimates of effective size for frog populations, but the data available suggest that ranid frogs may have much larger ratios of effective size (Ne) to census size (Nc) than toads (bufonidae). Our results indicate that R. pipiens populations have effective sizes on the order of hundreds to at most a few thousand frogs, and Ne/Nc ratios in the range of 0.1-1.0. These estimates of Ne/Nc are consistent with those estimated for other Rana species. Finally, we compared the results of three temporal methods for estimating Ne. Moment and pseudolikelihood methods that assume a closed population gave the most similar point estimates, although the moment estimates were consistently two to four times larger. Wang and Whitlock's new method that jointly estimates Ne and the rate of immigration into a population (m) gave much smaller estimates of Ne and implausibly large estimates of m. This method requires knowing allele frequencies in the source of immigrants, but was thought to be insensitive to inexact estimates. In our case the method may have failed because we did not know the true source of immigrants for each population. The method may be more sensitive to choice of source frequencies than was previously appreciated, and so should be used with caution if the most likely source of immigrants cannot be identified clearly.

Inflorescence Sampling Improves Effective Population Size of Grasses

Variation in seed production per plant leads to reductions in effective population size (Ne), which is a major factor promoting genetic drift of heterogenetic populations during seed collection and regeneration. The objectives of this study were (i) to compare Ne to the census population size (Nc) among different seed harvest methods; (ii) use inflorescence sampling to determine Ne/Nc for numerous heterogenetic grass species, and (iii) to predict the optimum number of inflorescences per plant to most efficiently increase Ne Estimates of Ne/Nc from rubbing whole plants, cutting whole plants, and from sampling a constant two inflorescences per plant were made on Festuca pratensis Huds., Lolium perenne L., and Pseudoroegneria spicata (Pursh) Á. Löve accessions. Inflorescence sampling was also completed on four accessions of Bromus inermis Leyss., Dactylis glomerata L., F arundinacea Schreb., L. perenne, Pseudoroegneria spicata, and Phalaris aquatica L. The mean Ne/Nc for the inflorescence method was 0.78, significantly higher then the 0.64 average for the cut or rub methods. For all species and entries, the slope of the curves describing Ne/Nc to inflorescence number was initially steep from 1 to 3 inflorescences and then leveled off asymptotically. Thus, most of the benefit occurs after sampling only a few inflorescences. The results show that sampling a constant number of inflorescences per plant promotes Ne and reduces the potential for genetic drift associated with collection and regeneration of heterogenetic grass populations.

EFFECTIVE POPULATION SIZES AND TEMPORAL STABILITY OF GENETIC STRUCTURE IN RANA PIPIENS, THE NORTHERN LEOPARD FROG

Although studies of population genetic structure are very common, whether genetic structure is stable over time has been assessed for very few taxa. The question of stability over time is particularly interesting for frogs because it is not clear to what extent frogs exist in dynamic metapopulations with frequent extinction and recolonization, or in stable patches at equilibrium between drift and gene flow. In this study we collected tissue samples from the same five populations of leopard frogs, Rana pipiens, over a 22–30 year time interval (11–15 generations). Genetic structure among the populations was very stable, suggesting that these populations were not undergoing frequent extinction and colonization. We also estimated the effective size of each population from the change in allele frequencies over time. There exist few estimates of effective size for frog populations, but the data available suggest that ranid frogs may have much larger ratios of effective size (Ne) to census size (Nc) than toads (bufonidae). Our results indicate that R. pipiens populations have effective sizes on the order of hundreds to at most a few thousand frogs, and Ne/Nc ratios in the range of 0.1–1.0. These estimates of Ne/Nc are consistent with those estimated for other Rana species. Finally, we compared the results of three temporal methods for estimating Ne. Moment and pseudolikelihood methods that assume a closed population gave the most similar point estimates, although the moment estimates were consistently two to four times larger. Wang and Whitlock's new method that jointly estimates Ne and the rate of immigration into a population (m) gave much smaller estimates of Ne and implausibly large estimates of m. This method requires knowing allele frequencies in the source of immigrants, but was thought to be insensitive to inexact estimates. In our case the method may have failed because we did not know the true source of immigrants for each population. The method may be more sensitive to choice of source frequencies than was previously appreciated, and so should be used with caution if the most likely source of immigrants cannot be identified clearly.

Monte Carlo Simulations Investigating the Threading of Cyclic Poly(ethylene oxide) by Linear Chains in the Melt

A coarse-grained Monte Carlo algorithm on a modified diamond lattice has been used to study the dependence of threading of cyclic poly(ethylene oxide) molecules by linear poly(ethylene oxide) chains in the melt on the mass fraction (Xc) and the size (Nc) of the cyclics. Both short-range interactions based on the rotational isomeric state model and long-range interactions from a discretized form of the Lennard-Jones (LJ) potential energy function are included. LJ parameters σ and e/kB of 3.76 A and 154 K, respectively, are estimated for the coarse-grained model. In addition, a method is presented for detecting threading of cyclics that have instantaneous conformations that significantly differ from a circle. The percentage of cyclic molecules threaded can be described as a linear function of Xc. When the cyclics consist of 10 or less coarse-grained monomer units, the percentage of cyclic molecules threaded falls to less than 1%, which suggests that spontaneous threading of cyclics smaller than 30-crown-10 ...

Spatial homogeneity and temporal heterogeneity of red drum (Sciaenops ocellatus) microsatellites: effective population sizes and management implications.

The red drum (Sciaenops ocellatus) is one of a number of species that occupy estuarine waters as juveniles and migrate to open ocean waters as adults. This species has experienced dramatic declines in population numbers over the past 2 decades, which has prompted increasing fishery restriction. In addition, hatchery augmentation has been initiated by several states to increase the abundance of juveniles in local areas. In South Carolina hatchery-reared fish have made significant (20%) contributions to the juvenile population on very local scales. As hatchery-reared fish are typically produced by a small number of individuals, the genetic consequences of augmentation programs are of concern. In this article we assess genetic variation at 5 microsatellite loci in S. ocellatus. The data indicate little geographic differentiation among samples collected along the Atlantic Coast of the United States, but substantial differences among year classes taken from South Carolina. The gene frequency differences among year classes were used to estimate the effective population size (Nc) of S. ocellatus in South Carolina and suggested that Ne was less than 300 from 1990 to 1993 and increased to about 1000 in 1994 and 1995. Whether this increase reflects the effectiveness of management regulations or simply a random fluctuation in S. ocellatus populations is not clear. The data suggest that a limited number of individuals produce the bulk of a given year class and support the sweepstakes hypothesis. Given the small Ne and estimates of the contribution of hatchery-reared fish to the wild stock, it is suggested that programs have the potential to increase, rather than decrease; Ne in the wild.

Energy barrier effect on transient nucleation kinetics: Nucleation flux and lag-time calculation

Energy barrier effect on the transient nucleation kinetics is studied. For a high barrier case an advanced interpolation of the “boundary-layer” type is suggested that is valid for the entire time interval. The nucleation kinetics for the “nucleated cluster” size nc is described, the lag time estimate for n=nc is given. For a low barrier case a new “similarity” solution is reported. It is shown that analytical results provide an adequate description of the transient nucleation kinetics (in comparison with numerical solution of governing equation) for both high-barrier and low-barrier conditions.

Structural transitions in nitrogen molecular clusters: Experiment and simulation

The structure of (N2)n clusters is investigated up to the size of several hundred molecules with means of electron diffraction experiments and numerical simulations. The comparison relies on the calculated diffraction patterns. The structures extracted numerically are obtained with a global optimization procedure. Two transformations are observed. The first one is the transition from polyicosahedral to multilayer icosahedral. It is seen from simulations to occur near the crossover size n*∼40 molecules, but is hardly seen in the experiment. The second one is the transition from icosahedral to cubic. In this case, both approaches indicate a crystalline crossover size nc located near 150–200 molecules. However, while the structures resulting from global optimization clearly show the enhanced stability of perfect cubic structures at zero temperature above nc, the information obtained from experimental diffraction functions at finite temperature and pressure exhibits a more progressive appearance of the crystalline features. This suggests the presence of significant defects in the real structure of nitrogen molecular clusters as they undergo their transformation toward the bulk face-centered-cubic geometry.

Two-stage procedures for approximating the expected reward: The negative exponential case

Let X 1, X 2, … be i.i.d. random variables with two-parameter exponential distribution, and suppose that given a sample of size n, the reward is Y n=max {X 1, …, X n}−c n. When the scale parameter is unknown, the optimal fixed sample size n c * for maximizing the expected reward E (Y n) cannot be found. This paper deals with the problem of approximating the optimal fixed sample size expected reward R nc* through a two-stage procedure and shows that the difference between the expected reward using the proposed procedure and R nc* vanishes as c approaches zero.

Review of DNA‐based census and effective population size estimators

AbstractThe detection of reductions in effective population size (Ne) or census size (Nc) is essential for conservation. Recent developments allow wildlife researchers to obtain genetic material via non‐invasive sampling techniques that may provide the large sample sizes necessary for precise estimates of Ne and Nc. Population genetic theory provides several methods to estimate Ne from allele frequency data: including temporal change in allele frequencies, gametic disequilibrium and heterozygote excess methods. Modification of capture–mark–recapture methods for use with multi‐locus genotype data provides new means for estimating Nc. The combination of new DNA sampling techniques, polymerase chain reaction‐based DNA markers and analytical methods may provide unprecedented power to detect reductions in Ne and Nc of endangered populations. However, these genetic methods are largely untested in the field. We review some relatively unexplored, but promising ways that multi‐locus genetic data can be used to provide important genetic and demographic information and suggest avenues for further research in this area.