Kinetic models for peptide-induced leakage from vesicles and cells

In this article analytical expressions for peptide-induced membrane leakage are presented. Two different models for time-dependent leakage have been developed. In the first, the leakage is assumed to be coupled by pores formed by the peptides. In the second model the peptide is assumed to induce a stress/perturbation in the membrane, and in order to reduce the stress, rearrangements in the membrane are induced. The leakage is coupled to these rearrangements, and when equilibrium is achieved no more leakage occurs. From the kinetic models simple fitting routines have been developed involving only two fitting parameters, and these have been used to fit experimental data for two prion protein-derived peptides as well as the honey bee toxin melittin in both vesicles and erythrocytes with good results. The fitted parameters provide both a quantitative and a qualitative basis for interpreting the experimental results. In addition a model for the peptide concentration-dependent leakage is presented, which was used to fit experimental data for leakage induced by the prion protein-derived peptides. The models presented in this article are compared with other models for peptide-induced membrane leakage.     

Mathematical and kinetic modeling of biofilm reactor based on ant colony optimization

Inverse estimation of model parameters via mathematical modeling route, known as inverse modeling (IM), is an attractive alternative approach to the experimental methods. This approach makes use of efficient optimization techniques in the course of solution of an inverse problem with the aid of measured data. In this study, a novel optimization method based on ant colony optimization (ACO), denoted by ACO-IM, is presented for inverse estimation of kinetic and film thickness parameters of biofilm models that describe an experimental fixed bed anaerobic reactor. The proposed optimization method for parameter estimation emulates the fact that ants are capable of finding the shortest path from a food source to their nest by depositing a trial of pheromone during their walk. The efficacy of the ACO-IM for numerical estimation of bio-kinetic parameters is demonstrated through its application for the anaerobic treatment of industry wastewater in a fixed bed biofilm process. The results explain the rigorousness of mathematical models, the form of kinetic and film thickness models and the type of packing to be used with the biofilm process for accurate determination of kinetic and film thickness parameters so as to ensure reliable predictive performance of the biofilm reactor models.     

Analysis of some nonrandom mating models

In this paper a few asymmetric models are presented taking account of the effects of assortative mating on an autosomal trait controlled by a single locus possibly with multiple alleles. The models are developed by specifying the intensities for preference mating for various phenotypes. The analysis is confined to the case in which preference is exercised by the individuals of one sex only. It is assumed that males possess unlimited fertility.The dynamics of the population and its equilibrium distribution are discussed. The gene frequency usually changes with time and equilibrium distribution in most cases depends only on the assortment parameters. Expressions are obtained giving the additive and dominance components of variance, and covariances for relatives for populations in equilibrium for some of the models.     

Maximum likelihood and Bayesian methods for estimating the distribution of selective effects among classes of mutations using DNA polymorphism data

Maximum likelihood and Bayesian approaches are presented for analyzing hierarchical statistical models of natural selection operating on DNA polymorphism within a panmictic population. For analyzing Bayesian models, we present Markov chain Monte-Carlo (MCMC) methods for sampling from the joint posterior distribution of parameters. For frequentist analysis, an Expectation-Maximization (EM) algorithm is presented for finding the maximum likelihood estimate of the genome wide mean and variance in selection intensity among classes of mutations. The framework presented here provides an ideal setting for modeling mutations dispersed through the genome and, in particular, for the analysis of how natural selection operates on different classes of single nucleotide polymorphisms (SNPs).     

A community model of ciliateTetrahymena and bacteriaE. coli: Part I. Individual-based models ofTetrahymena andE. coli populations

The dynamics of a microbial community consisting of a eucaryotic ciliateTetrahymena pyriformis and procaryoticEscherichia coli in a batch culture is explored by employing an individual-based approach. In this portion of the article, Part I, population models are presented. Because both models are individual-based, models of individual organisms are developed prior to construction of the population models. The individual models use an energy budget method in which growth depends on energy gain from feeding and energy sinks such as maintenance and reproduction. These models are not limited by simplifying assumptions about constant yield, constant energy sinks and Monod growth kinetics as are traditional models of microbal organisms. Population models are generated from individual models by creating distinct individual types and assigning to each type the number of real individuals they represent. A population is a compilation of individual types that vary in a phase of cell cycle and physiological parameters such as filtering rate for ciliates and maximum anabolic rate for bacteria. An advantage of the developed models is that they realistically describe the growth of the individual cells feeding on resource which varies in density and composition. Part II, the core of the project, integrates models into a dynamic microbial community and provides model analysis based upon available data.     

Parameter Estimation of Some Epidemic Models. The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus

The research presented in this paper addresses the problem of fitting a mathematical model to epidemic data. We propose an implementation of the Landweber iteration to solve locally the arising parameter estimation problem. The epidemic models considered consist of suitable systems of ordinary differential equations. The results presented suggest that the inverse problem approach is a reliable method to solve the fitting problem. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters against real data sets for the case of recurrent epidemics caused by the respiratory syncytial virus in children.     

Uninformative Parameters and Model Selection Using Akaike's Information Criterion

Abstract: As use of Akaike's Information Criterion (AIC) for model selection has become increasingly common, so has a mistake involving interpretation of models that are within 2 AIC units (ΔAIC ≤ 2) of the top-supported model. Such models are <2 ΔAIC units because the penalty for one additional parameter is +2 AIC units, but model deviance is not reduced by an amount sufficient to overcome the 2-unit penalty and, hence, the additional parameter provides no net reduction in AIC. Simply put, the uninformative parameter does not explain enough variation to justify its inclusion in the model and it should not be interpreted as having any ecological effect. Models with uninformative parameters are frequently presented as being competitive in the Journal of Wildlife Management, including 72% of all AIC-based papers in 2008, and authors and readers need to be more aware of this problem and take appropriate steps to eliminate misinterpretation. I reviewed 5 potential solutions to this problem: 1) report all models but ignore or dismiss those with uninformative parameters, 2) use model averaging to ameliorate the effect of uninformative parameters, 3) use 95% confidence intervals to identify uninformative parameters, 4) perform all-possible subsets regression and use weight-of-evidence approaches to discriminate useful from uninformative parameters, or 5) adopt a methodological approach that allows models containing uninformative parameters to be culled from reported model sets. The first approach is preferable for small sets of a priori models, whereas the last 2 approaches should be used for large model sets or exploratory modeling.     

Regression Models for Clinical Trials with Correlated Categorical Responses

Regression models for correlated categorical data are presented in which the covariance is a function of measured effects. The regression and covariance parameters are estimated by extended least square methods. A numerical example of a clinical trial comparing two antiemetic treatment regimes for patients receiving chemotherapy is given to illustrate the approach.     

Statistical estimation of statistical mechanical models: helix-coil theory and peptide helicity prediction.

Analysis of biopolymer sequences and structures generally adopts one of two approaches: use of detailed biophysical theoretical models of the system with experimentally-determined parameters, or largely empirical statistical models obtained by extracting parameters from large datasets. In this work, we demonstrate a merger of these two approaches using Bayesian statistics. We adopt a common biophysical model for local protein folding and peptide configuration, the helix-coil model. The parameters of this model are estimated by statistical fitting to a large dataset, using prior distributions based on experimental data. L(1)-norm shrinkage priors are applied to induce sparsity among the estimated parameters, resulting in a significantly simplified model. Formal statistical procedures for evaluating support in the data for previously proposed model extensions are presented. We demonstrate the advantages of this approach including improved prediction accuracy and quantification of prediction uncertainty, and discuss opportunities for statistical design of experiments. Our approach yields a 39% improvement in mean-squared predictive error over the current best algorithm for this problem. In the process we also provide an efficient recursive algorithm for exact calculation of ensemble helicity including sidechain interactions, and derive an explicit relation between homo- and heteropolymer helix-coil theories and Markov chains and (non-standard) hidden Markov models respectively, which has not appeared in the literature previously.     

Stochastic epidemic models: A survey

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.     

Epidemic growth rate and household reproduction number in communities of households,schools and workplaces

In this paper we present a novel and coherent modelling framework for the characterisation of the real-time growth rate in SIR models of epidemic spread in populations with social structures of increasing complexity. Known results about homogeneous mixing and multitype models are included in the framework, which is then extended to models with households and models with households and schools/workplaces. Efficient methods for the exact computation of the real-time growth rate are presented for the standard SIR model with constant infection and recovery rates (Markovian case). Approximate methods are described for a large class of models with time-varying infection rates (non-Markovian case). The quality of the approximation is assessed via comparison with results from individual-based stochastic simulations. The methodology is then applied to the case of influenza in models with households and schools/workplaces, to provide an estimate of a household-to-household reproduction number and thus asses the effort required to prevent an outbreak by targeting control policies at the level of households. The results highlight the risk of underestimating such effort when the additional presence of schools/workplaces is neglected. Our framework increases the applicability of models of epidemic spread in socially structured population by linking earlier theoretical results, mainly focused on time-independent key epidemiological parameters (e.g. reproduction numbers, critical vaccination coverage, epidemic final size) to new results on the epidemic dynamics.     

Phase diagrams for impure lipid systems. Application to lipid/anaesthetic mixtures

A physical model is presented to describe theoretically the temperature-dependent interactions of lipid bilayers with small molecules such as anaesthetics. Based on an earlier model, a triangular lattice in which each site is occupied by a single lipid chain is constructed and the small (anaesthetic) molecules are assumed to occupy interstitial sites in the centre of each lattice triangle. The phase characteristics of such lipid/anaesthetic mixtures are described in terms of the interaction parameters between lipid-lipid, lipid-anaesthetic and anaesthetic-anaesthetic molecules. Depending on the chemical nature of the interacting species the following three models are formulated: Model I. An interstitial model in which the only perturbation is in the head-group region of the bilayer and direct interactions between neighbouring anaesthetic molecules are taken into account. Model II. Here, only hydrophobic interactions between anaesthetics and lipids are considered. Model III. Both van der Waals' and coulombic interactions are taken into account. Phase diagrams for the three models are obtained by numerical calculation over a wide range of interaction parameters. It is shown that in all three models, lateral phase separation takes place due to the presence of anaesthetics. The heat of transition, however, is found to be virtually independent of the anaesthetic concentration.     

Model choice and influential cases for survival studies

Deletion diagnostics are developed for identifying observations that influence the estimates of regression parameters and the mixture parameter in the families of relative risk functions for failure time data. The diagnostic for the regression parameters is a generalization of Cain and Lange's (1984, Biometrics 40, 493-499) measure of individual influence. The generalizations of martingale residuals, Schoenfeld's partial residuals (1982, Biometrika 69, 239-241), and score residuals by Therneau, Grambsch, and Fleming (1990, Biometrika 77, 147-160) are also obtained. The influence of some observations on regression parameters can be drastically modified as the mixture parameter changes, even for a very small change. In addition, adding or deleting some observations might result in choosing different models. The diagnostics are applied to a family proposed by Guerrero and Johnson (1982, Biometrika 69, 309-314). One illustrative example is presented.     

A new method for non-destructive measurement of biomass, growth rates, vertical biomass distribution and dry matter content based on digital image analysis

BACKGROUND AND AIMS: Biomass is an important trait in functional ecology and growth analysis. The typical methods for measuring biomass are destructive. Thus, they do not allow the development of individual plants to be followed and they require many individuals to be cultivated for repeated measurements. Non-destructive methods do not have these limitations. Here, a non-destructive method based on digital image analysis is presented, addressing not only above-ground fresh biomass (FBM) and oven-dried biomass (DBM), but also vertical biomass distribution as well as dry matter content (DMC) and growth rates. METHODS: Scaled digital images of the plants silhouettes were taken for 582 individuals of 27 grass species (Poaceae). Above-ground biomass and DMC were measured using destructive methods. With image analysis software Zeiss KS 300, the projected area and the proportion of greenish pixels were calculated, and generalized linear models (GLMs) were developed with destructively measured parameters as dependent variables and parameters derived from image analysis as independent variables. A bootstrap analysis was performed to assess the number of individuals required for re-calibration of the models. KEY RESULTS: The results of the developed models showed no systematic errors compared with traditionally measured values and explained most of their variance (R(2) > or = 0.85 for all models). The presented models can be directly applied to herbaceous grasses without further calibration. Applying the models to other growth forms might require a re-calibration which can be based on only 10-20 individuals for FBM or DMC and on 40-50 individuals for DBM. CONCLUSIONS: The methods presented are time and cost effective compared with traditional methods, especially if development or growth rates are to be measured repeatedly. Hence, they offer an alternative way of determining biomass, especially as they are non-destructive and address not only FBM and DBM, but also vertical biomass distribution and DMC.     

Molecular Mechanics Studies of Molybdenum Disulphide Catalysts Parameterisation of Molybdenum and Sulphur

Abstract

A method for the parameterisation of molybdenum disulphide is presented which reproduces the crystal structure accurately. The method involves calculating parameters such that there is no net force contribution from any individual term of the potential on any atom. Ideal bond lengths and bond angles are taken from the X-ray crystal structure; stretching and bending force constants are calculated from a combination of spectroscopic data and quantum mechanics calculations, whereby the energy function with bond length or bond angle is calculated and fitted with an harmonic potential. For the non-bonded Lennard-Jones parameters, the dispersion coefficient C was calculated by an interpolation of existing published parameters using a multiple regression and then the crystal energy was minimised with respect to the van der Waals radius r₀ using a fixed crystal fragment.

These parameters were tested for various models of the hexagonal and rhombohedral forms of MoS₂. RMS fits between structures minimised with molecular mechanics and experimental models ranged from 0.006 Å to 0.012 Å.     

A spatial model of cellular molecular trafficking including active transport along microtubules

We consider models of Ran-driven nuclear transport of molecules such as proteins in living cells. The mathematical model presented is the first to take into account for the active transport of molecules along the cytoplasmic microtubules. All parameters entering the models are thoroughly discussed. The model is tested by numerical simulations based on discontinuous Galerkin finite element methods. The numerical experiments are compared to the behavior observed experimentally.