Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.     

A formulation of the lifetime distribution and the existence of its moments

Summary The lifetime distribution is formulated in terms of g(t), defined as the ratio of the hazard function to the tail probability function, to study the properties of the lifetime distribution. A criterion is provided for the asymptotic behaviour of g(t) and the hazard function. Criteria for the existence and non-existence of the moments of any probability distribution of a non-negative random variable are obtained in terms of the derivatives of g(t). Examples are given to illustrate the use of the criteria and applications made to stochastic models of population growth as well as other lifetime distributions.This research was supported under National Health Research and Development Project No. 605-7-434 (22)(48) of the Department of National Health and Welfare of Canada.     

In situ classification and image cytometry of pelagic bacteria from a high mountain lake (gossenkollesee, austria)

We describe a procedure to measure the cell sizes of pelagic bacteria after determinative hybridization with rRNA-targeted fluorescently labeled oligonucleotide probes. Our approach is based on established image analysis techniques modified for objects simultaneously stained with two fluorescent dyes. It allows the estimation of biomass and cell size distribution and the morphological characterization of different bacterial taxa in plankton samples. The protocol was tested in a study of the bacterioplankton community of a high mountain lake during and after the ice break period. Cells that hybridized with a probe for the domain Bacteria accounted for 70% of the bacterial abundance (range, 49 to 83%) as determined by 4(prm1),6(prm1)-diamidino-2-phenylindole staining (K. G. Porter and Y. S. Feig, Limnol. Oceanogr. 25:943-948, 1980), but for >85% of the total biomass (range, 78 to 99%). The size distribution for members of the beta subclass of the Proteobacteria shifted toward larger cells and clearly distinguished this group from the total bacterial assemblage. In the surface water layer beneath the winter cover, bacteria belonging to the beta 1 subgroup constituted about one-half of the beta subclass abundance. The mean cell volume of the beta 1 subgroup bacteria was significantly less than that of the beta subclass proteobacteria, and the beta 1 subgroup accounted for less than 30% of the total beta subclass biovolume. Two weeks later, the biovolume of the beta Proteobacteria had decreased to the level of the beta 1 subgroup, and both the biovolume size distributions and cell morphologies of the beta Proteobacteria and the beta 1 subgroup were very similar. We could thus quantify the disappearance of large, morphologically distinct beta subclass proteobacteria which were not members of the beta 1 subgroup during the ice break period. Our results demonstrate that changes in biovolumes and cell size distributions of different bacterial taxa, and eventually of individual populations, reveal hitherto unknown processes within aquatic bacterial assemblages and may open new perspectives for the study of microbial food webs.     

Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.     

New Better than Used and Other Concepts for a Class of Life Distributions

It is well-known that the inequalities used in the definition of the New Better than Used (N. B. U.) and the New Better than Used in Expectation (N.B.U.E.) concepts, see BARLOW and PROSCHAN (1965, 1975) become equalities if, and only if, the life length of an organism follows an exponential distribution. It is proved in the present paper that these inequalities also reduce to equalities for the class of life distributions that have the “setting the clock back to zero” property. Simple examples of these distributions include the exponential, the linear hazard exponential and the Gompertz distributions. The General Krane distributions (Krane 1963) belong to this class, as well as a recent model introduced by CHIANG and CONFORTI (1989) of a survival distribution in which the hazard rate is a function of the accumulated effect of an individual's continuous exposure to the toxic material in the environment and his biological reaction to the toxin absorbed. As a simple application of the result proved in the paper, the life expectancy of an organism at age γ₀ involved in the N.B.U.E. concept is evaluated for the Gompertzian growth process and for the Chiang and Conforti model.     

The size of epidemics in populations with heterogeneous susceptibility

We formulate and study a general epidemic model allowing for an arbitrary distribution of susceptibility in the population. We derive the final-size equation which determines the attack rate of the epidemic, somewhat generalizing previous work. Our main aim is to use this equation to investigate how properties of the susceptibility distribution affect the attack rate. Defining an ordering among susceptibility distributions in terms of their Laplace transforms, we show that a susceptibility distribution dominates another in this ordering if and only if the corresponding attack rates are ordered for every value of the reproductive number R0. This result is used to prove a sharp universal upper bound for the attack rate valid for any susceptibility distribution, in terms of R0 alone, and a sharp lower bound in terms of R0 and the coefficient of variation of the susceptibility distribution. We apply some of these results to study two issues of epidemiological interest in a population with heterogeneous susceptibility: (1) the effect of vaccination of a fraction of the population with a partially effective vaccine, (2) the effect of an epidemic of a pathogen inducing partial immunity on the possibility and size of a future epidemic. In the latter case, we prove a surprising '50% law': if infection by a pathogen induces a partial immunity reducing susceptibility by less than 50%, then, whatever the value of R0>1 before the first epidemic, a second epidemic will occur, while if susceptibility is reduced by more than 50%, then a second epidemic will only occur if R0 is larger than a certain critical value greater than 1.     

Cumulative Damage Survival Models for the Randomized Complete Block Design

A continuous time discrete state cumulative damage process {X(t), t ≥ 0} is considered, based on a non‐homogeneous Poisson hit‐count process and discrete distribution of damage per hit, which can be negative binomial, Neyman type A, Polya‐Aeppli or Lagrangian Poisson. Intensity functions considered for the Poisson process comprise a flexible three‐parameter family. The survival function is S(t) = P(X(t) ≤ L) where L is fixed. Individual variation is accounted for within the construction for the initial damage distribution {P(X(0) = x) | x = 0, 1, …,}. This distribution has an essential cut‐off before x = L and the distribution of L – X(0) may be considered a tolerance distribution. A multivariate extension appropriate for the randomized complete block design is developed by constructing dependence in the initial damage distributions. Our multivariate model is applied (via maximum likelihood) to litter‐matched tumorigenesis data for rats. The litter effect accounts for 5.9 percent of the variance of the individual effect. Cumulative damage hazard functions are compared to nonparametric hazard functions and to hazard functions obtained from the PVF‐Weibull frailty model. The cumulative damage model has greater dimensionality for interpretation compared to other models, owing principally to the intensity function part of the model.     

Beta and gamma actin mRNAs are differentially located within myoblasts

Actin is of fundamental importance to all eukaryotic cells. Of the six mammalian actins, beta (beta) and gamma (gamma) cytoplasmic are the isoforms found in all nonmuscle cells and differ by only four amino acids at the amino-terminal region. Both genes are regulated temporally and spatially, though no differences in protein function have been described. Using fluorescent double in situ hybridization we describe the simultaneous intracellular localization of both beta and gamma actin mRNA. This study shows that myoblasts differentially segregate the beta and gamma actin mRNAs. The distribution of gamma actin mRNA, only to perinuclear and nearby cytoplasm, suggests a distribution based on diffusion or restriction to nearby cytoplasm. The distribution of beta actin mRNA, perinuclear and at the cell periphery, implicates a peripheral localizing signal which is unique to the beta isoform. The peripheral beta actin mRNA corresponded to cellular morphologies, extending processes, and ruffling edges that reflect cell movement. Total actin and gamma actin protein steady-state distributions were identified by specific antibodies. gamma actin protein was found in both stress fibers and at the cell plasma membrane and does not correspond to its mRNA distribution. We suggest that localized protein synthesis rather than steady-state distribution functionally differentiates between the actin isoforms.     

On measures of association among genetic variables

Systems involving many variables are important in population and quantitative genetics, for example, in multi-trait prediction of breeding values and in exploration of multi-locus associations. We studied departures of the joint distribution of sets of genetic variables from independence. New measures of association based on notions of statistical distance between distributions are presented. These are more general than correlations, which are pairwise measures, and lack a clear interpretation beyond the bivariate normal distribution. Our measures are based on logarithmic (Kullback-Leibler) and on relative 'distances' between distributions. Indexes of association are developed and illustrated for quantitative genetics settings in which the joint distribution of the variables is either multivariate normal or multivariate-t, and we show how the indexes can be used to study linkage disequilibrium in a two-locus system with multiple alleles and present applications to systems of correlated beta distributions. Two multivariate beta and multivariate beta-binomial processes are examined, and new distributions are introduced: the GMS-Sarmanov multivariate beta and its beta-binomial counterpart.     

Creep function of a single living cell

We used a novel uniaxial stretching rheometer to measure the creep function J(t) of an isolated living cell. We show, for the first time at the scale of the whole cell, that J(t) behaves as a power-law J(t) = At(alpha). For N = 43 mice myoblasts (C2-7), we find alpha = 0.24 +/- 0.01 and A = (2.4 +/- 0.3) 10(-3) Pa(-1) s(-alpha). Using Laplace Transforms, we compare A and alpha to the parameters G(0) and beta of the complex modulus G*(omega) = G(0)omega(beta) measured by other authors using magnetic twisting cytometry and atomic force microscopy. Excellent agreement between A and G(0) on the one hand, and between alpha and beta on the other hand, indicated that the power-law is an intrinsic feature of cell mechanics and not the signature of a particular technique. Moreover, the agreement between measurements at very different size scales, going from a few tens of nanometers to the scale of the whole cell, suggests that self-similarity could be a central feature of cell mechanical structure. Finally, we show that the power-law behavior could explain previous results first interpreted as instantaneous elasticity. Thus, we think that the living cell must definitely be thought of as a material with a large and continuous distribution of relaxation time constants which cannot be described by models with a finite number of springs and dash-pots.     

Regression models for infant mortality data in Norwegian siblings, using a compound Poisson frailty distribution with random scale

The power variance function distributions, which include the gamma and compound Poisson (CP) distributions among others, are commonly used in frailty models for family data. In a previous paper, we presented a frailty model constructed by randomizing the scale parameter in a CP distribution. When combined with a parametric baseline hazard, this yields a model with heterogeneity on both the individual and the family level and a subgroup with zero frailty, corresponding to people not experiencing the event. In this paper, we discuss covariates in the model. Depending on where the covariates are inserted in the model, one may have proportional hazards at the individual level, the family level, and a larger group level (for covariates shared by many families, e.g. ethnic groups) or get accelerated failure times. Each of these alternatives gives a specific interpretation of the covariate effects. An application to data infant mortality in siblings from the Medical Birth Registry of Norway is included. We compare the results for some of the different covariate modeling options.     

Bayesian regularization for flexible baseline hazard functions in Cox survival models

Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi‐parametric choices allow for more flexible patterns but they can suffer from overfitting and instability. Regularization methods through prior distributions with correlated structures usually give reasonable answers to these types of situations. We discuss Bayesian regularization for Cox survival models defined via flexible baseline hazards specified by a mixture of piecewise constant functions and by a cubic B‐spline function. For those “semi‐parametric” proposals, different prior scenarios ranging from prior independence to particular correlated structures are discussed in a real study with microvirulence data and in an extensive simulation scenario that includes different data sample and time axis partition sizes in order to capture risk variations. The posterior distribution of the parameters was approximated using Markov chain Monte Carlo methods. Model selection was performed in accordance with the deviance information criteria and the log pseudo‐marginal likelihood. The results obtained reveal that, in general, Cox models present great robustness in covariate effects and survival estimates independent of the baseline hazard specification. In relation to the “semi‐parametric” baseline hazard specification, the B‐splines hazard function is less dependent on the regularization process than the piecewise specification because it demands a smaller time axis partition to estimate a similar behavior of the risk.     

Survival and hazard functions for progressive diseases using saddlepoint approximations

Saddlepoint approximations for the computation of survival and hazard functions are introduced in the context of parametric survival analysis. Although these approximations are computationally fast, accurate, and relatively straightforward to implement, their use in survival analysis has been lacking. We approximate survival functions using the Lugannani and Rice saddlepoint approximation to the distribution function or by numerically integrating the saddlepoint density approximation. The hazard function is approximated using the saddlepoint density and distribution functions. The approximations are especially useful for consideration of survival and hazard functions for waiting times in complicated models. Examples include total or partial waiting times for a disease that progresses through various stages (convolutions of distributions).     

Reversal time distribution in the perception of visual ambiguous stimuli

Reversal of perspective for ambiguous optical stimuli (Necker cube, Schröder staircase, honeycomb) has been studied, determining the statistical distribution of time intervals spent on each percept. The experimental distributions can be fitted with the gamma function, characterized by two parameters n, b. The two parameters are not independent, showing a correlatiomn = 0.74.Subsequent intervals appear to be largely independent; from the beta distribution for the fraction of time spent on a given percept, one can show that the subjects differ only in regard to the variance of this variable.     

Biological growth and spread modeled by systems of recursions. I. Mathematical theory

We study the asymptotic behavior of solutions to a system of recursions u in+1 = Qi[mu n], i = 1, ..., k. The vector operator Q has the origin theta and a positive vector beta as fixed points and is defined for vector-valued functions bounded between theta and gamma where gamma greater than or equal to beta. In addition, Q is order-preserving, commutes with translation, and is continuous in the topology of uniform convergence on compact subsets. Let theta less than or equal to pi much less than beta, and suppose that for all pi much less than alpha much less than beta, Q(n) alpha]----beta as n----infinity. If u0 much greater than pi on a sufficiently large ball and has bounded support, then un propagates with a speed c*(xi) in the direction of the unit vector xi as n----infinity. In certain cases, c*(xi) can be calculated explicitly. The results generalize those of a scalar equation studied by Weinberger.     

A note on QTL detecting for censored traits

Most existing statistical methods for mapping quantitative trait loci (QTL) assume that the phenotype follows a normal distribution and that it is fully observed. However, some phenotypes have skewed distributions and may be censored. This note proposes a simple and efficient approach to QTL detecting for censored traits with the Cox PH model without estimating the baseline hazard function which is "nuisance".     

Molecular Dynamics Investigation of Bond Ordering of Unsaturated Lipids in Monolayers

Molecular dynamics simulations of three model lipid monolayers of 2,3-diacyl-D-glycerolipids, that contained stearoyl (18:0) in the position 3 and oleoyl (18:9cis), linoleoyl (18:26cis), or linolenoyl (18:33cis) in the position 2, have been carried out. The simulation systems consisted of 24 lipid molecules arranged in a rectangular simulation cell, with periodic boundary conditions in the surface plane. 1 nanosecond simulations were performed at T = 295 K. C-C and C-H bond order parameter profiles and the bond orientation distributions about the monolayer normal have been calculated. The relation of the distributions to the order parameters was analyzed in terms of maxima and widths of the distributions. The cis double bond order parameter is found to be higher than those of adjacent single C-C bonds. The widths of the two distributions of C-H bonds of the cis double bond segment in di- and triunsaturated molecules are much smaller than that obtained for methylene group located between the double bonds. The bond orientation distribution function widths depend on both the segment location in the chain and the segment chemical structure.     

Polypeptide growth factors augment interleukin 1-induced release of prostaglandin E2 by rheumatoid arthritis synovial cells in vitro

When stimulated with increasing amounts of interleukin 1 beta (IL 1 beta) rheumatoid arthritis (RA), as compared with osteoarthritis (OA), synovial cells grown in RPMI plus fetal bovine serum (FBS), released significantly more prostaglandin E2 (PGE2) (p less than 0.05; paired t test, two-tailed). PGE2 release by IL 1 beta-stimulated RA synovial cells grown for 14 days in serum-free RPMI was significantly less than that released by the same cells grown in medium plus 10% FBS (p less than 0.03; two-tailed). Since these data suggest that growth factors present in FBS may augment the effects of IL 1 beta, experiments were conducted to study the influence of four polypeptide growth factors--transforming growth factor-beta (TGF-beta), platelet-derived growth factor (PDGF), epidermal growth factor (EGF), and basic fibroblast growth factor (bFGF), on IL 1 beta-induced release of PGE2 by cultured RA synovial cells. Both EGF and bFGF significantly enhanced IL 1 beta-induced release of PGE2 (p less than 0.05; paired t test, one-tailed), while PDGF was synergistic with IL 1 beta, significantly increasing release of PGE2 by these cultured cells (p less than 0.02; two-tailed). No such effect was seen when TGF-beta was added to the culture medium. Taken together, these data lend support to the concept that within the synovial micro-environment small quantities of individual growth factors may potentiate the effects of IL 1 beta to amplify intra-articular inflammation.     

A stochastic-covariate failure model with an application to case-control analysis

A stochastic process X(t) is periodically stationary (and ergodic) if, for every k> or =1 and every (t(1),ellipsis,t(k)) in R(k), the sequence of random vectors (X(t(1)+n),ellipsis,X(t(k)+n))n=0,+1, ellipsis, is stationary (and ergodic). For such an ergodic process, let T be a positive random variable defined on the sample space of the process, representing a time of failure. The local failure-rate function is assumed to be of the form up(x),-infinity0 is a small number, tending to 0; and, for each u,T=T(u) is the corresponding failure-time. It is shown that X(T(u)) and uT(u) have, for u-->0, a limiting joint distribution and are, in fact, asymptotically independent. The marginal distributions are explicitly given. Let Y be a random variable whose distribution is the limit of that of X(T(u)). Under the hypothesis that p(x) is unknown or of known functional form but with unknown parameters, it is shown how p(x) can be estimated on the basis of independent copies of the random variable Y. The results are applied to the analysis of a case-control study featuring a 'marker' process X(t) and an 'event-time' T. The event in the study is considered to be particularly rare, and this is reflected in the assumption u-->0. The control-distribution is identified with the average marginal distribution of the (periodically stationary) marker process X(t), and the case-distribution is identified with that of Y. The particular application is a biomedical trial to determine the risk of stroke in terms of the level of an anticoagulant in the blood of the patient.