Orientational oscillations of the peptide groups of an α-helix

The low-energy orientational oscillations of the peptide groups of an -helix are considered and the value of the frequency is estimated to be in agreement with experiments. Approximate formulae are derived for the projection of a dipole moment on the helix axis and for the helix parameters. Within the framework of a three-chain model, the asymptotics of the soliton solution is obtained using a discrete approach.The analysis of -helix geometry exhibits two types of low-frequency oscillations of the -helix. The first one is connected with atom movements along the helix axis with the peptide groups twisting around the helix axis. Accordingly, it changes the hydrogen bond lengths between neighbouring peptide groups. In the second case, the slopes of the peptide groups to the helix axis oscillate without the helix parameters changing. Here, the energy of interactions between peptide-group dipoles is changed and, as a result, the oscillations have an optical nature. The frequency of the optical orientational oscillations is approximately 100 cm^-1.     

Lattice population dynamics for plants with dispersing seeds and Vegetative propagation

The population dynamics of plants in a lattice structured habitat are studied theoretically. Plants are assumed to propagate both by producing seeds that scatter over the population and by vegetative reproduction by extending runners, rhizomes, or roots, to neighboring vacant sites. In addtion, the seed production rate may be dependent on the local density in the neighborhood, indicating beneficial or harmful crowding effects. Two sets of population dynamical equation(s) are derived: one based onmean-field approximation and the other based onpair approximation (tracing both global and local densities simultaneously). We examine the accuracy of these approximate dynamics by comparing them with direct computer simulation of the stochastic lattice model. Pair approximation is much more accurate than mean-field approximation. Mean-field approximation overestimates the parameter range for persistence if crowding effects on seed production are harmful or weakly beneficial, but underestimates it if crowding effects are highly beneficial. Dynamics may show bistability (both population persistence and extinction) if the effect of crowding is strongly beneficial. If there is a linear trade-off between seed production and vegetative reproduction, the equilibrium abundance of the population may be maximised by a mixture of seed production and vegetative reproduction, rather than by pure seed production or by pure vegetative reproduction. This result is correctly predicted by pair approximation but not by mean-field approximation.     

Functional data analysis with covariate-dependent mean and covariance structures

Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interesting results.     

Analyses of spatial patterns and population processes of clonal plants

The nonrandom spatial structure of terrestrial plants is formed by ecological interactions and reproduction with a limited dispersal range, and in turn this may strongly affect population dynamics and population genetics. The traditional method of modelling in population ecology is either to neglect spatial pattern (e.g. in transition matrix models) or to do straightforward computer simulation. We review here three analytical mothods to deal with plant populations in a lattice-structured habitat, which propagate both by seeds that scatter over the whole habitat and by vegetative reproduction (producing runners, rhizomes, etc.) to neighboring vacant sites. [1]Dynamics of global and local densities: Dynamical equations of population density considering nearest-neighbor correlation (spatial clumping) are developed as the joint dynamics of global average density and local density (comparable to mean crowding) based onpair approximation. If there is a linear trade-off between seed production and vegetative reproduction, the equilibrium abundance of the population may be maximized by engaging both means of reproduction. This result is accurately predicted by the pair approximation method, but not by mean-field approximation (neglect of spatial structure). [2]Cluster size distributions: Using global and local densities obtained by pair approximation, we predicted cluster size distribution, i.e. the number of clusters of occupied sites of various sizes. [3]Clonal identity probability decreasing with distance: Multi-locus measurement of allozymes or other neutral molecular markers tells us whether or not a given pair of individuals belong to the same clone. From the pattern of clonal identity probability decreasing with the distance between ramets, we can estimate the relative importance of two modes of reproduction: vegetative propagation and sexual seed production.     

Derivation and testing of pair potentials for protein folding. When is the quasichemical approximation correct?

Many existing derivations of knowledge-based statistical pair potentials invoke the quasichemical approximation to estimate the expected side-chain contact frequency if there were no amino acid pair-specific interactions. At first glance, the quasichemical approximation that treats the residues in a protein as being disconnected and expresses the side-chain contact probability as being proportional to the product of the mole fractions of the pair of residues would appear to be rather severe. To investigate the validity of this approximation, we introduce two new reference states in which no specific pair interactions between amino acids are allowed, but in which the connectivity of the protein chain is retained. The first estimates the expected number of side-chain contracts by treating the protein as a Gaussian random coil polymer. The second, more realistic reference state includes the effects of chain connectivity, secondary structure, and chain compactness by estimating the expected side-chain contrast probability by placing the sequence of interest in each member of a library of structures of comparable compactness to the native conformation. The side-chain contact maps are not allowed to readjust to the sequence of interest, i.e., the side chains cannot repack. This situation would hold rigorously if all amino acids were the same size. Both reference states effectively permit the factorization of the side-chain contact probability into sequence-dependent and structure-dependent terms. Then, because the sequence distribution of amino acids in proteins is random, the quasichemical approximation to each of these reference states is shown to be excellent. Thus, the range of validity of the quasichemical approximation is determined by the magnitude of the side-chain repacking term, which is, at present, unknown. Finally, the performance of these two sets of pair interaction potentials as well as side-chain contact fraction-based interaction scales is assessed by inverse folding tests both without and with allowing for gaps.     

Simplified neuron model as a principal component analyzer

A simple linear neuron model with constrained Hebbian-type synaptic modification is analyzed and a new class of unconstrained learning rules is derived. It is shown that the model neuron tends to extract the principal component from a stationary input vector sequence.     

Parameter estimation for discretely observed linear birth‐and‐death processes

Birth‐and‐death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, as the likelihood can become numerically unstable when data arise from the most common sampling schemes, such as annual population censuses. A further difficulty arises when the discrete observations are not equi‐spaced, for example, when census data are unavailable for some years. We present two approaches to estimating the birth, death, and growth rates of a discretely observed linear birth‐and‐death process: via an embedded Galton‐Watson process and by maximizing a saddlepoint approximation to the likelihood. We study asymptotic properties of the estimators, compare them on numerical examples, and apply the methodology to data on monitored populations.