A Monte Carlo study of the amylosic chain conformation

Monte Carlo studies of the unperturbed amylosic chain conformation have been carried out in the approximation of separable chain configuration energies. Sample chains of arbitrary chain length have been generated so as to be distributed consistent with refined estimates of the configuration energy and thus suitable for evaluation of averages of the desired configuration-dependent properties. Perspective drawings of representative chains from the Monte Carlo sample have been made for comparison with standard idealizations of amylosic chain conformation. He molecular model employed generates a randomly coiling chain possessing perceptible regions of left-handed pseudohelical backbone trajectory. Distribution functions for the end-to-end distance of short amylosic chains disclose some propensity for the chain to suffer self-intersections at sort range in the chain sequence, which may vitiate the usual amylosic chain models based on the assumed independence of sets of glycosidic linkage torsion angles. The amylosic persistence vector and persistence length have been calculated as a function of chain length for the chain model employed.     

Monte Carlo study of cycloamylose: chain conformation, radius of gyration, and diffusion coefficient

Cyclic (1 --> 4)-alpha-D-glucan chains with or without excluded volume have been collected from a huge number (about 10(7)) of linear amylosic chains generated by the Monte Carlo method with a conformational energy map for maltose, and their mean-square radii of gyration and translational diffusion coefficients D (based on the Kirkwood formula) have been computed as functions of x (the number of glucose residues in a range from 7 to 300) and the excluded-volume strength represented by the effective hard-core radius. Both /x and D in the unperturbed state weakly oscillate for x < 30 and the helical nature of amylose appears more pronouncedly in cyclic chains than in linear chains. As x increases, these properties approach the values expected for Gaussian rings. Though excluded-volume effects on them are always larger in cycloamylose than in the corresponding linear amylose, the ratios of and the hydrodynamic radius of the former to the respective properties of the latter in good solvents can be slightly lower than or comparable to the (asymptotic) Gaussian-chain values when x is not sufficiently large. An interpolation expression is constructed for the relation between the gyration-radius expansion factors for linear and cyclic chains from the present Monte Carlo data and the early proposed asymptotic relation with the aid of the first-order perturbation theories.     

A study of deleterious gene structure in plants using Markov chain Monte Carlo

The characteristics of deleterious genes have been of great interest in both theory and practice in genetics. Because of the complex genetic mechanism of these deleterious genes, most current studies try to estimate the overall magnitude of mortality effects on a population, which is characterized classically by the number of lethal equivalents. This number is a combination of several parameters, each of which has a distinct biological effect on genetic mortality. In conservation and breeding programs, it is important to be able to distinguish among different combinations of these parameters that lead to the same number of lethal equivalents, such as a large number of mildly deleterious genes or a few lethal genes, The ability to distinguish such parameter combinations requires more than one generation of mating. We propose a model for survival data from a two-generation mating experiment on the plant species Brassica rapa, and we enable inference with Markov chain Monte Carlo. This computational strategy is effective because a vast amount of missing genotype information must be accounted for. In addition to the lethal equivalents, the two-generation data provide separate information on the average intensity of mortality and the average number of deleterious genes carried by an individual. In our Markov chain Monte Carlo algorithm, we use a vector proposal distribution to overcome inefficiency of a single-site Gibbs sampler. Information about environmental effects is obtained from an outcrossing experiment conducted in parallel with the two-generation mating experiments.     

A Monte Carlo simulation study of the influence of internal motions on the molecular conformation deduced from two-dimensional NMR experiments

Monte Carlo methods have been used to simulate internal motions of aromatic protons of an oligonucleotide at the nanosecond time scale. Each proton is allowed to fluctuate about its equilibrium position. The longitudinal cross-relaxation rates of such a system of spins have been determined by computing the appropriate correlation functions. Then the interproton distances have been deduced according to the procedure generally used in two-dimensional nmr techniques (nuclear Overhauser effect spectroscopy--NOESY) and compared to the true values. The influence of the amplitude A and of the internal rotational diffusion constant Dint characterizing the dynamics of the system has been checked for in-phase and for uncorrelated motions. It is shown that for the investigated models the distances deduced from NOESY experiments may be under- or overestimated, depending strongly on the values of A and Dint. Furthermore, the cross-relaxation rate of a couple of protons is very sensitive to the correlation level of the motions of both protons.     

A Monte Carlo study of the self-assembly of bacteriorhodopsin

Bacteriorhodopsin (BR) and specific lipid molecules self-assemble into a quasi two-dimensional lattice structure known as the purple membrane (PM). In the PM, BR molecules exist in a trimeric form with lipid molecules present in the space enclosed by each trimeric unit and in the inter-trimer space. These trimeric units, which have a roughly circular cross-section, are arranged in hexagonal patterns with long-ranged crystalline order. In this work, we investigate the self-assembly of BR in the PM via Monte Carlo simulations of a two-dimensional model of the membrane and proteins. The protein molecules are modeled as 120 degrees sectors of a circle and the lipid molecules enter into the model through effective protein-protein interactions. The sectors cannot overlap with each other, and in addition to this excluded volume interaction there are site-site attractive interactions between specific points of the proteins to mimic interactions between helices on the proteins and lipid-induced interactions. At low values of the attractive well depth, the proteins are found in the monomeric form at all concentrations. At moderate and high values of the attractive well depth, trimers are formed as the concentration increases, and with a further increase in concentration the trimers organize into a hexagonal lattice. The interactions between the proteins and those induced by the intra-trimer lipids play an equally important role in the formation of trimers and the lattice. The lipids in the inter-trimer space cause the trimers to orient in a specific direction in the hexagonal crystal lattice.     

The Monte Carlo simulation of pearl chain formation

Summary The phenomenon of pearl chain formation (PCF) is investigated by means of a statistical model using the Monte Carlo method. Fifteen particles (cells) interacting with simple dipole-dipole potential are shown to form chains under the influence of an external field with a threshold potential significantly lower than the two particle estimate. A possible overlap between PCF and the thermal effects of an electric field is suggested.     

Monte Carlo simulations of a polymer chain conformation. The effectiveness of local moves algorithms and estimation of entropy

A linear chain on a simple cubic lattice was simulated by the Metropolis Monte Carlo method using a combination of local and non-local chain modifications. Kink-jump, crankshaft, reptation and end-segment moves were used for local changes of the chain conformation, while for non-local chain rearrangements the "cut-and-paste" algorithm was employed. The statistics of local micromodifications was examined. An approximate method for estimating the conformational entropy of a polymer chain, based on the efficiency of the kink-jump motion respecting chain continuity and excluded volume constraints, was proposed. The method was tested by calculating the conformational entropy of the undisturbed chain, the chain under tension and in different solvent conditions (athermal, theta and poor) and also of the chain confined in a slit. The results of these test calculations are qualitatively consistent with expectations. Moreover, the obtained values of the conformational entropy of self avoiding chain with ends fixed over different separations, agree very well with the available literature data.

A Monte Carlo study of the dynamics of G-protein activation.

To link quantitatively the cell surface binding of ligand to receptor with the production of cellular responses, it may be necessary to explore early events in signal transduction such as G-protein activation. Two different model frameworks relating receptor/ligand binding to G-protein activation are examined. In the first framework, a simple ordinary differential equation model is used to describe receptor/ligand binding and G-protein activation. In the second framework, the events leading to G-protein activation are simulated using a dynamic Monte Carlo model. In both models, reactions between ligand-bound receptors and G-proteins are assumed to be diffusion-limited. The Monte Carlo model predicts two regimes of G-protein activation, depending upon whether the lifetime of a receptor/ligand complex is long or short compared with the time needed for diffusional encounters of complexes and G-proteins. When the lifetime of a complex is relatively short compared with the diffusion time, the movement of ligand among free receptors by binding and unbinding ("switching") significantly enhances G-protein activation. Receptor antagonists dramatically reduce G-protein activation and, thus, signal transduction in this case, and significant clustering of active G-proteins near receptor/ligand complexes results. The simple ordinary differential equation model poorly predicts G-protein activation for this situation. In the alternative case, when diffusion is relatively fast, ligand movement among receptors is less important and the simple ordinary differential equation model and Monte Carlo model results are similar. In this case, there is little clustering of active G-proteins near receptor/ligand complexes. Results also indicate that as the GTPase activity of the alpha-subunit decreases, the steady-state level of alpha-GTP increases, although temporal sensitivity is compromised.     

Calculation of the structure of the serotonin-antibiotic lasalocid A complex by conformation analysis and the Monte Carlo method

The conformational aspects of interaction of the antibiotic X537A at complexation with serotonin, hydration of molecules and their complex were studied by the methods of theoretical conformational analysis and Monte-Carlo.     

Searching for convergence in phylogenetic Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) is a methodology that is gaining widespread use in the phylogenetics community and is central to phylogenetic software packages such as MrBayes. An important issue for users of MCMC methods is how to select appropriate values for adjustable parameters such as the length of the Markov chain or chains, the sampling density, the proposal mechanism, and, if Metropolis-coupled MCMC is being used, the number of heated chains and their temperatures. Although some parameter settings have been examined in detail in the literature, others are frequently chosen with more regard to computational time or personal experience with other data sets. Such choices may lead to inadequate sampling of tree space or an inefficient use of computational resources. We performed a detailed study of convergence and mixing for 70 randomly selected, putatively orthologous protein sets with different sizes and taxonomic compositions. Replicated runs from multiple random starting points permit a more rigorous assessment of convergence, and we developed two novel statistics, delta and epsilon, for this purpose. Although likelihood values invariably stabilized quickly, adequate sampling of the posterior distribution of tree topologies took considerably longer. Our results suggest that multimodality is common for data sets with 30 or more taxa and that this results in slow convergence and mixing. However, we also found that the pragmatic approach of combining data from several short, replicated runs into a "metachain" to estimate bipartition posterior probabilities provided good approximations, and that such estimates were no worse in approximating a reference posterior distribution than those obtained using a single long run of the same length as the metachain. Precision appears to be best when heated Markov chains have low temperatures, whereas chains with high temperatures appear to sample trees with high posterior probabilities only rarely.     

Bayesian phylogenetic inference via Markov chain Monte Carlo methods

We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees close to the current tree in the chain. We illustrate the algorithm with restriction site data on 9 plant species, then extend to DNA sequences from 32 species of fish. The algorithm mixes well in both examples from random starting trees, generating reproducible estimates and credible sets for the path of evolution.     

A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics

In quantitative genetics, Markov chain Monte Carlo (MCMC) methods are indispensable for statistical inference in non-standard models like generalized linear models with genetic random effects or models with genetically structured variance heterogeneity. A particular challenge for MCMC applications in quantitative genetics is to obtain efficient updates of the high-dimensional vectors of genetic random effects and the associated covariance parameters. We discuss various strategies to approach this problem including reparameterization, Langevin-Hastings updates, and updates based on normal approximations. The methods are compared in applications to Bayesian inference for three data sets using a model with genetically structured variance heterogeneity.     

The effect of sonication on the hydrocarbon chain conformation in model membrane systems: A Raman spectroscopic study

Raman spectra are presented for egg lecithin above and below the gel-liquid crystal phase transition, and several regions of the Raman spectrum are shown to be sensitive to conformational changes in the hydrocarbon chains. These regions are used to investigate the effect of sonication on the structure of egg lecithin and dipalmitoyl lecithin vesicles.Sonication of both egg lecithin above T_m, and dipalmitoyl lecithin above and below T_m produces no change in the relative population of trans and gauche isomers in any of the systems studied. Sonication does however appear to effect interchain interactions, a possible consequence of imperfect packing towards the center of the bilayers in vesicle systems.     

Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters

Accurate and fast estimation of genetic parameters that underlie quantitative traits using mixed linear models with additive and dominance effects is of great importance in both natural and breeding populations. Here, we propose a new fast adaptive Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of genetic parameters in the linear mixed model with several random effects. In the learning phase of our algorithm, we use the hybrid Gibbs sampler to learn the covariance structure of the variance components. In the second phase of the algorithm, we use this covariance structure to formulate an effective proposal distribution for a Metropolis-Hastings algorithm, which uses a likelihood function in which the random effects have been integrated out. Compared with the hybrid Gibbs sampler, the new algorithm had better mixing properties and was approximately twice as fast to run. Our new algorithm was able to detect different modes in the posterior distribution. In addition, the posterior mode estimates from the adaptive MCMC method were close to the REML (residual maximum likelihood) estimates. Moreover, our exponential prior for inverse variance components was vague and enabled the estimated mode of the posterior variance to be practically zero, which was in agreement with the support from the likelihood (in the case of no dominance). The method performance is illustrated using simulated data sets with replicates and field data in barley.     

A unified Markov chain Monte Carlo framework for mapping multiple quantitative trait loci

In this article, a unified Markov chain Monte Carlo (MCMC) framework is proposed to identify multiple quantitative trait loci (QTL) for complex traits in experimental designs, based on a composite space representation of the problem that has fixed dimension. The proposed unified approach includes the existing Bayesian QTL mapping methods using reversible jump MCMC algorithm as special cases. We also show that a variety of Bayesian variable selection methods using Gibbs sampling can be applied to the composite model space for mapping multiple QTL. The unified framework not only results in some new algorithms, but also gives useful insight into some of the important factors governing the performance of Gibbs sampling and reversible jump for mapping multiple QTL. Finally, we develop strategies to improve the performance of MCMC algorithms.     

Monte Carlo study of sI hydrogen hydrates

In this study, we perform grand canonical Monte Carlo simulations to evaluate the hydrogen storage capacity of structure I (sI) hydrogen hydrates at pressures up to 500 MPa. Initially, we calculate the upper limit of H₂ content of sI hydrates by studying the hypothetical sI hydrate, where H₂ is the single guest component. It is found that the storage capacity of the hypothetical pure H₂ sI hydrate could reach 3.5 wt% at 500 MPa and 274 K. Depending on pressure, the large cavities of the pure H₂ hydrate can accommodate up to three H₂ molecules while the small ones are singly occupied at most, even at pressures as high as 500 MPa, without any double occupancy being observed. Subsequently, the binary H₂–ethylene oxide (EO) hydrate is examined. In this case, the large cavities are occupied by a single EO molecule while the small cavities can accommodate at most a single H₂ molecule. Such configuration results in a maximum H₂ content of only 0.37 wt%. The hydrogen storage capacity does not improve significantly even in case when EO is replaced by a component with smaller molecular weight.