Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models

Inference for Dirichlet process hierarchical models is typicallyperformed using Markov chain Monte Carlo methods, which canbe roughly categorized into marginal and conditional methods.The former integrate out analytically the infinite-dimensionalcomponent of the hierarchical model and sample from the marginaldistribution of the remaining variables using the Gibbs sampler.Conditional methods impute the Dirichlet process and updateit as a component of the Gibbs sampler. Since this requiresimputation of an infinite-dimensional process, implementationof the conditional method has relied on finite approximations.In this paper, we show how to avoid such approximations by designingtwo novel Markov chain Monte Carlo algorithms which sample fromthe exact posterior distribution of quantities of interest.The approximations are avoided by the new technique of retrospectivesampling. We also show how the algorithms can obtain samplesfrom functionals of the Dirichlet process. The marginal andthe conditional methods are compared and a careful simulationstudy is included, which involves a non-conjugate model, differentdatasets and prior specifications.     

The stability and folding process of amyloidogenic mutant human lysozymes.

Amyloid deposits are frequently formed by mutant proteins that have a lower stability than the wild-type proteins. Some reports, however, have shown that mutant-induced thermodynamic destabilization is not always a general mechanism of amyloid formation. To obtain a better understanding of the mechanism of amyloid fibril formation, we show in this study that equilibrium and kinetic refolding-unfolding reaction experiments with two amyloidogenic mutant human lysozymes (I56T and D67H) yield folding pathways that can be drawn as Gibbs energy diagrams. The equilibrium stabilities between the native and denatured states of both mutant proteins were decreased, but the degrees of instability were different. The Gibbs energy diagrams of the folding process reveal that the Gibbs energy change between the native and folding intermediate states was similar for both proteins, and also that the activation Gibbs energy change from the native state to the transition state decreased. Our results confirm that the tendency to favor the intermediate of denaturation facilitates amyloid formation by the mutant human lysozymes more than equilibrium destabilization between the native and completely denatured states does.     

Fixed and random effects selection in linear and logistic models

We address the problem of selecting which variables should be included in the fixed and random components of logistic mixed effects models for correlated data. A fully Bayesian variable selection is implemented using a stochastic search Gibbs sampler to estimate the exact model-averaged posterior distribution. This approach automatically identifies subsets of predictors having nonzero fixed effect coefficients or nonzero random effects variance, while allowing uncertainty in the model selection process. Default priors are proposed for the variance components and an efficient parameter expansion Gibbs sampler is developed for posterior computation. The approach is illustrated using simulated data and an epidemiologic example.     

Bayesian estimation of dominance merits in noninbred populations by using Gibbs sampling with two reduced sets of mixed model equations

Henderson's mixed model equations system is generally required in a Gibbs sampling application. In two previous studies, we proposed two indirect solving approaches that give dominance values in an animal model context with no need to process all this system. The first one does not require D-1 and the second is based on processing the additive animal model residuals. In the present work, we show that these two methods can be handled iteratively. Since the Bayesian approach is now a widely used tool in estimation of genetic parameters, the main part of this work is devoted to a Gibbs sampling application that can be accelerated by means of the aforementioned indirect solving methods. Three replicates of a population data set are simulated in the paper to compare the applications and estimates. This shows effectively that the estimates given by implementing a Gibbs sampler with each of the two suggested solving methods are obtained with less computational time and are comparable to those given by considering the integral system, particularly when priors are more weighted.     

Determination of the thermodynamic parameters of the complex formation between malvidin-3-O-glucoside and polyphenols. Copigmentation effect in red wines

The thermodynamics of the molecular association process between the malvidin-3-O-glucoside and a series of polyphenol derivatives (called 'copigmentation' in food chemistry) were studied in aqueous media. The Gibbs free energy, enthalpy and entropy values were determined by the fluorometric method. A combination of the Job's method with the van't Hoff theory was applied for data evaluation. The results show the exothermic character of the copigmentation process. The change of the enthalpy seems to be the same in every complexation step. However, the decreasing of the entropy term is higher at higher stoichiometries. As a result, the Gibbs free energy changes and, thus, the complex stability decreases quickly with increasing stoichiometry. Quantum-chemical investigation reveals the complexity of molecular interactions between malvidin and polyphenols, which is preferably based on pi-pi and OH-pi interaction moderated by repulsive Coulomb-type interactions.     

Interactions of two amphiphilic penicillins with myoglobin in aqueous buffered solutions: a thermodynamic and spectroscopy study

The interactions and complexation process of the amphiphilic penicillins sodium cloxacillin and sodium dicloxacillin with horse myoglobin in aqueous buffered solutions of pH 4.5 and 7.4 have been examined by equilibrium dialysis, zeta-potential, isothermal titration calorimetry (ITC) and UV-Vis absorbance techniques. A more opened structure of the protein molecules is detected as a consequence of the reduction of pH from 7.4 to 4.5. Binding isotherms and derived Hill coefficients reflect a cooperative binding behavior. Gibbs energies of binding per mole of drug were obtained from equilibrium dialysis data and compared with those derived from the zeta potential taking into account cooperativity. DeltaGads degrees values so obtained are large and negative at low concentrations where binding to the "high-energy" sites occurs and decreases with the drug concentration. The enthalpies of binding have been obtained from ITC and are small and exothermic so that the Gibbs energies of binding are dominated by large increases in entropy consistent with hydrophobic interactions. Other thermodynamic quantities of the binding mechanism, that is, entropy, DeltaSITCi, Gibbs energy, DeltaGITCi, the binding constant, KITCi, and the number of binding sites, ni, were also obtained, confirming the above results. From ITC data and following a theoretical model, the number of bound and free penicillin molecules was calculated, being higher at pH 4.5 than at pH 7.4. The binding of penicillin causes a conformational transition on protein structure as a consequence of the resulting intramolecular repulsion between the penicillin molecules bound to the protein. Thermodynamic quantites (the Gibbs energy of the transition in water, DeltaGw degrees , and in a hydrophobic environment, DeltaGhc degrees) of the denaturation process were calculated, indicating that at pH 4.5 some of the histidine residues are protonated, becoming accessible to solvent and giving rise to a more opened protein structure.     

Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.     

Energetics and conformational changes upon complexation of a phenothiazine drug with human serum albumin

The interactions and complexation process of the amphiphilic phenothiazine fluphenazine hydrochloride with human serum albumin in aqueous buffered solutions of pH 3.0 and 7.4 have been examined by zeta-potential, isothermal titration calorimetry (ITC), UV-vis spectroscopy, and dynamic light scattering (DLS) techniques with the aim of analyzing the effect of hydrophobic and electrostatic forces on the complexation process and the alteration of protein conformation upon binding. Thus, the energetics and stoichiometry of the binding process were derived from ITC data. The enthalpies of binding obtained are small and exothermic, so the Gibbs energies of binding are dominated by large increases in entropy, consistent with hydrophobic interactions at a acidic pH. However, at physiological pH, binding to the first class of binding sites is dominated by an enthalpic contribution due to the existence of electrostatic interactions and probably some hydrogen bonding. Binding isotherms were obtained from microcalorimetric data by using a theoretical model based on the Langmuir isotherm. zeta-Potential data showed a reversal in the sign of the protein charge at pH 7.4, as a consequence of the binding of the drug to the protein. Gibbs energies of drug binding per mole of drug were also derived from zeta-potential data. On the other hand, binding of the phenothiazine that causes a conformational transition on the protein structure was followed as a function of drug concentration using UV-vis spectroscopy, and the data were analyzed to obtain the Gibbs energy of the transition in water (deltaG(degree)w) and in a hydrophobic environment (deltaG(degree)hc). Finally, the population distribution of the different species in solution and the size of the complexes were analyzed through dynamic light scattering. The existence of an aggregation process of drug/protein complexes, as a consequence of the expanded structure of the protein induced by the drug and subsequent further binding, is in agreement with ITC data. In addition, detection of drug aggregates at concentrations below the drug critical micelle concentration was also detected by this technique.     

Does microbial life always feed on negative entropy? Thermodynamic analysis of microbial growth.

Schr?dinger stated in his landmark book, What is Life?, that life feeds on negative entropy. In this contribution, the validity of this statement is discussed through a careful thermodynamic analysis of microbial growth processes. In principle, both feeding on negative entropy, i.e. yielding products of higher entropy than the substrates, and generating heat can be used by microorganisms to rid themselves of internal entropy production resulting from maintenance and growth processes. Literature data are reviewed in order to compare these two mechanisms. It is shown that entropy-neutral, entropy-driven, and entropy-retarded growth exist. The analysis of some particularly interesting microorganisms shows that enthalpy-retarded microbial growth may also exist, which would signify a net uptake of heat during growth. However, the existence of endothermic life has never been demonstrated in a calorimeter. The internal entropy production in live cells also reflects itself in the Gibbs energy dissipation accompanying growth, which is related quantitatively to the biomass yield. An empirical correlation of the Gibbs energy dissipation in terms of the physico-chemical nature of the growth substrate has been proposed in the literature and can be used to predict the biomass yield approximately. The ratio of enthalpy change and Gibbs energy change can also be predicted since it is shown to be approximately equal to the same ratio of the relevant catabolic process alone.     

Equilibrium calculations on systems of biochemical reactions at specified pH and pMg.

The use of G' in discussing the thermodynamics of biochemical reactions at a specified pH and pMg is justified by use of a Legendre transform of the Gibbs energy G. When several enzymatic reactions occur simultaneously in a system, the standard transformed Gibbs energies of reaction delta rG'0 can be used in a computer program to calculate the equilibrium composition that minimizes the transformed Gibbs energy at the specified pH and pMg. The calculation of standard transformed Gibbs energies of formation of reactants at pH 7 and pMg 3 is described. In addition a method for calculating the equilibrium concentrations of reactants is illustrated for a system with steady state concentrations of some reactants like ATP and NAD.     

Electroporation of curved lipid membranes in ionic strength gradients

A thermodynamic theory for the membrane electroporation of curved membranes such as those of lipid vesicles and cylindrical membrane tubes has been developed. The theory covers in particular the observation that electric pore formation and shape deformation of vesicles and cells are dependent on the salt concentration of the suspending solvent. It is shown that transmembrane salt gradients can appreciably modify the electrostatic part of Helfrich's spontaneous curvature, elastic bending rigidity and Gaussian curvature modulus of charged membranes. The Gibbs reaction energy of membrane electroporation can be explicitely expressed in terms of salt gradient-dependent contributions of bending, the ionic double layers and electric surface potentials and dielectric polarisation of aqueous pores. In order to cover the various physical contribution to the chemical process of electroporation-resealing, we have introduced a generalised chemophysical potential covering all generalised forces and generalised displacements in terms of a transformed Gibbs energy formalism. Comparison with, and analysis of, the data of electrooptical relaxation kinetic studies show that the Gibbs reaction energy terms can be directly determined from turbidity dichroism (Planck's conservative dichroism). The approach also quantifies the electroporative cross-membrane material exchange such as electrolyte release, electrohaemolysis of red blood cells or uptake of drugs and dyes and finally gene DNA by membrane electroporation.     

iGibbs: improving Gibbs motif sampler for proteins by sequence clustering and iterative pattern sampling

The motif prediction problem is to predict short, conserved subsequences that are part of a family of sequences, and it is a very important biological problem. Gibbs is one of the first successful motif algorithms and it runs very fast compared with other algorithms, and its search behavior is based on the well-studied Gibbs random sampling. However, motif prediction is a very difficult problem and Gibbs may not predict true motifs in some cases. Thus, the authors explored a possibility of improving the prediction accuracy of Gibbs while retaining its fast runtime performance. In this paper, the authors considered Gibbs only for proteins, not for DNA binding sites. The authors have developed iGibbs, an integrated motif search framework for proteins that employs two previous techniques of their own: one for guiding motif search by clustering sequences and another by pattern refinement. These two techniques are combined to a new double clustering approach to guiding motif search. The unique feature of their framework is that users do not have to specify the number of motifs to be predicted when motifs occur in different subsets of the input sequences since it automatically clusters input sequences into clusters and predict motifs from the clusters. Tests on the PROSITE database show that their framework improved the prediction accuracy of Gibbs significantly. Compared with more exhaustive search methods like MEME, iGibbs predicted motifs more accurately and runs one order of magnitude faster.     

Combining the meiosis Gibbs sampler with the random walk approach for linkage and association studies with a general complex pedigree and multimarker loci

A linkage analysis for finding inheritance states and haplotype configurations is an essential process for linkage and association mapping. The linkage analysis is routinely based upon observed pedigree information and marker genotypes for individuals in the pedigree. It is not feasible for exact methods to use all such information for a large complex pedigree especially when there are many missing genotypic data. Proposed Markov chain Monte Carlo approaches such as a single-site Gibbs sampler or the meiosis Gibbs sampler are able to handle a complex pedigree with sparse genotypic data; however, they often have reducibility problems, causing biased estimates. We present a combined method, applying the random walk approach to the reducible sites in the meiosis sampler. Therefore, one can efficiently obtain reliable estimates such as identity-by-descent coefficients between individuals based on inheritance states or haplotype configurations, and a wider range of data can be used for mapping of quantitative trait loci within a reasonable time.     

Multivariate survival analysis with positive stable frailties

In this paper, we describe Bayesian modeling of dependent multivariate survival data using positive stable frailty distributions. A flexible baseline hazard formulation using a piecewise exponential model with a correlated prior process is used. The estimation of the stable law parameter together with the parameters of the (conditional) proportional hazards model is facilitated by a modified Gibbs sampling procedure. The methodology is illustrated on kidney infection data (McGilchrist and Aisbett, 1991).     

Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops.

We apply the method of "blocking Gibbs" sampling to a problem of great importance and complexity-linkage analysis. Blocking Gibbs sampling combines exact local computations with Gibbs sampling, in a way that complements the strengths of both. The method is able to handle problems with very high complexity, such as linkage analysis in large pedigrees with many loops, a task that no other known method is able to handle. New developments of the method are outlined, and it is applied to a highly complex linkage problem in a human pedigree.     

Inference for discretely observed stochastic kinetic networks with applications to epidemic modeling

We present a new method for Bayesian Markov Chain Monte Carlo-based inference in certain types of stochastic models, suitable for modeling noisy epidemic data. We apply the so-called uniformization representation of a Markov process, in order to efficiently generate appropriate conditional distributions in the Gibbs sampler algorithm. The approach is shown to work well in various data-poor settings, that is, when only partial information about the epidemic process is available, as illustrated on the synthetic data from SIR-type epidemics and the Center for Disease Control and Prevention data from the onset of the H1N1 pandemic in the United States.     

Improved techniques for sampling complex pedigrees with the Gibbs sampler

Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler.     

The combination of transformed and constrained Gibbs energies

Gibbs free energy is the thermodynamic potential representing the fundamental equation at constant temperature, pressure, and molar amounts. Transformed Gibbs energies are important for biochemical systems because the local concentrations within cell compartments cannot yet be determined accurately. The method of Constrained Gibbs Energies adds kinetic reaction extent limitations to the internal constraints of the system thus extending the range of applicability of equilibrium thermodynamics from predefined constraints to dynamic constraints, e.g., adding time-dependent constraints of irreversible chemical change. In this article, the implementation and use of Transformed Gibbs Energies in the Gibbs energy minimization framework is demonstrated with educational examples. The combined method has the advantage of being able to calculate transient thermodynamic properties during dynamic simulation.     

Temperature dependence of the nucleation constant rate in beta amyloid fibrillogenesis

Beta-amyloid peptide (A beta), in fibrillar form, is the primary constituent of senile plaques, a defining feature of Alzheimer's disease (AD). In solution assays, fibrils form with a lag time, interpreted as a nucleation/condensation-dependent process. The kinetics of fibrillogenesis is controlled by two key parameters: nucleation and elongation rate constants. We report here the study of the temperature dependence of the nucleation rate constant on an A beta monomer concentration of 18.4 microM at pH 7.4 and at temperatures ranging from 302 to 318 K. We found that the nucleation constant varied as in the Arrhenius law, giving an activation energy of 311.2 kJ mol(-1). The corresponding values of enthalpy of activation (deltaH*), entropy of activation (deltaS*) and Gibbs energy of activation (deltaG*) were evaluated by Eyring's equation of absolute reaction rate. A Gibbs energy of activation of approximately 110 kJ mol(-1) was obtained.     

Improved prediction of MHC class I and class II epitopes using a novel Gibbs sampling approach

MOTIVATION: Prediction of which peptides will bind a specific major histocompatibility complex (MHC) constitutes an important step in identifying potential T-cell epitopes suitable as vaccine candidates. MHC class II binding peptides have a broad length distribution complicating such predictions. Thus, identifying the correct alignment is a crucial part of identifying the core of an MHC class II binding motif. In this context, we wish to describe a novel Gibbs motif sampler method ideally suited for recognizing such weak sequence motifs. The method is based on the Gibbs sampling method, and it incorporates novel features optimized for the task of recognizing the binding motif of MHC classes I and II. The method locates the binding motif in a set of sequences and characterizes the motif in terms of a weight-matrix. Subsequently, the weight-matrix can be applied to identifying effectively potential MHC binding peptides and to guiding the process of rational vaccine design. RESULTS: We apply the motif sampler method to the complex problem of MHC class II binding. The input to the method is amino acid peptide sequences extracted from the public databases of SYFPEITHI and MHCPEP and known to bind to the MHC class II complex HLA-DR4(B1*0401). Prior identification of information-rich (anchor) positions in the binding motif is shown to improve the predictive performance of the Gibbs sampler. Similarly, a consensus solution obtained from an ensemble average over suboptimal solutions is shown to outperform the use of a single optimal solution. In a large-scale benchmark calculation, the performance is quantified using relative operating characteristics curve (ROC) plots and we make a detailed comparison of the performance with that of both the TEPITOPE method and a weight-matrix derived using the conventional alignment algorithm of ClustalW. The calculation demonstrates that the predictive performance of the Gibbs sampler is higher than that of ClustalW and in most cases also higher than that of the TEPITOPE method.