Estimates of marker-associated QTL effects in Monte Carlo backcross generations using multiple regression

Summary The decision of whether or not to use QTLassociated markers in breeding programs needs further information about the magnitude of the additive and dominance effects that can be estimated. The objectives of this paper are (1) to apply some of the Moreno-Gonzalez (1993) genetic models to backcross simulation data generated by the Monte Carlo method, and (2) to get simulation information about the number of testing progenies and mapping density in relation to the magnitude of gene effect estimates. Results of the Monte Carlo study show that the stepwise regression analysis was able to detect relatively small additive and dominance effects when the QTL are independently segregating. When testing selfed families derived from backcross individuals, dominance effects had a larger error standard deviation and were estimated at a lower frequency. Linked QTL require a higher marker mapping density on the genome and a larger number of progenies to detect small genetic effects. Reduction of the environmental error variance by evaluating selfed backcross families in replicate experiments increased the power of the test. Expressions of the number of progenies for detecting significant additive effects were developed for some genetic situations. The ratio of the within-backcross genetic variance to the square of a gene effect estimate is a function of the number of progenies, the heritability of the trait, the marker map density and the portion of the genetic variance explained by the model. Different values (from 0 to 1) assigned to (relative position of the QTL in the marker segment) did not cause a large shift in the residual mean square of the model.     

On the Sampling Method for Grand Canonical Monte Carlo Simulations

Abstract

A bulk Lennard-Jones fluid was simulated using the grand canonical Monte Carlo method. Three different sampling methods were used in the transition matrix, namely the Metropolis, Barker and a third novel method. While it can be shown that the Metropolis method will give the most accurate ensemble averages in the limit of an infinitely long run, the new method termed “Modified Barker Sampling” (MBS), is shown to be superior for the runs of practical length for the particular system studied.     

Taboo-based Monte Carlo Search as a Method to Improve Sampling Efficiency

Abstract

Taboo-based Monte Carlo search which restricts the sampling of the region near an old configuration, is developed. In this procedure, Monte Carlo simulation and random search method are combined to improve the sampling efficiency. The feasibility of this method is tested on global optimization of a continuous model function, melting of the 256 Lennard-Jones particles at T? = 0.680 and ρ? = 0.850 and polypeptides (alanine dipeptide and Metenkephalin). From the comparison of results for the model function between our method and other methods, we find the increase of convergence rate and the high possibility of escaping from the local energy minima. The results of the Lennard-Jones solids and polypeptides show that the convergence property to reach the equilibrium state is better than that of others. It is also found that no significant bias in ensemble distribution is detected, though taboo-based Monte Carlo search does not sample the correct ensemble distribution owing to the restriction of the sampling of the region near an old configuration.     

A General Monte Carlo Method for Mapping Multiple Quantitative Trait Loci

In this paper we address the mapping of multiple quantitative trait loci (QTLs) in line crosses for which the genetic data are highly incomplete. Such complicated situations occur, for instance, when dominant markers are used or when unequally informative markers are used in experiments with outbred populations. We describe a general and flexible Monte Carlo expectation-maximization (Monte Carlo EM) algorithm for fitting multiple-QTL models to such data. Implementation of this algorithm is straightforward in standard statistical software, but computation may take much time. The method may be generalized to cope with more complex models for animal and human pedigrees. A practical example is presented, where a three-QTL model is adopted in an outbreeding situation with dominant markers. The example is concerned with the linkage between randomly amplified polymorphic DNA (RAPD) markers and QTLs for partial resistance to Fusarium oxysporum in lily.     

Monte Carlo simulation of pathogen behavior during the sprout production process

Food-borne disease outbreaks linked to the consumption of raw sprouts have become a concern over the past decade. A Monte Carlo simulation model of the sprout production process was created to determine the most-effective points for pathogen control. Published literature was reviewed, and relevant data were compiled. Appropriate statistical distributions were determined and used to create the Monte Carlo model with Analytica software. Factors modeled included initial pathogen concentration and prevalence, seed disinfection effectiveness, and sampling of seeds prior to sprouting, sampling of irrigation water, or sampling of the finished product. Pathogen concentration and uniformity of seed contamination had a large effect on the fraction of contaminated batches predicted by the simulation. The model predicted that sprout sampling and irrigation water sampling at the end of the sprouting process would be more effective in pathogen detection than seed sampling prior to production. Day of sampling and type of sample (sprout or water) taken had a minimal effect on rate of detection. Seed disinfection reduced the proportion of contaminated batches, but in some cases it also reduced the ability to detect the pathogen when it was present, because cell numbers were reduced below the detection limit. Both the amount sampled and the pathogen detection limit were shown to be important variables in determining sampling effectiveness. This simulation can also be used to guide further research and compare the levels of effectiveness of different risk reduction strategies.     

In Silico Generation of Peptides by Replica Exchange Monte Carlo: Docking-Based Optimization of Maltose-Binding-Protein Ligands

Short peptides can be designed in silico and synthesized through automated techniques, making them advantageous and versatile protein binders. A number of docking-based algorithms allow for a computational screening of peptides as binders. Here we developed ex-novo peptides targeting the maltose site of the Maltose Binding Protein, the prototypical system for the study of protein ligand recognition. We used a Monte Carlo based protocol, to computationally evolve a set of octapeptides starting from a polialanine sequence. We screened in silico the candidate peptides and characterized their binding abilities by surface plasmon resonance, fluorescence and electrospray ionization mass spectrometry assays. These experiments showed the designed binders to recognize their target with micromolar affinity. We finally discuss the obtained results in the light of further improvement in the ex-novo optimization of peptide based binders.     

A Monte Carlo simulation of plasmid replication during the bacterial division cycle

Plasmids have cell cycle replication patterns that need to be considered in models of their replication dynamics. To compare current theories for control of plasmid replication with experimental data for timing of plasmid replication with the cell cycle, a Monte Carlo simulation of plasmid replication and partition was developed. High-copy plasmid replication was simulated by incorporating equations previously developed from the known molecular biology of ColE1-type plasmids into the cell-cycle simulation. Two types of molecular mechanisms for low-copy plasmid replication were tested: accumulation of an initiator protein in proportion to cell mass and binding of the plasmid origin to the cell membrane. The low-copy plasmids were partitioned actively, with a specific mechanism to mediate the transfer from mother to daughter cells, whereas the high-copy plasmids were partitioned passively with cell mass.The simulation results and experimental data demonstrate cell-cycle-specific replication for the low-copy F plasmid and cell-cycle-independent replication for the high-copy pBR322, ColBM, and R6K plasmids. The simulation results indicate that synchronous replication at multiple plasmid origins is critical for the cell-cycle-specific pattern observed in rapidly growing cells. Variability in the synchrony of initiation of multiple plasmid origins give rise to a cell-cycle-independent pattern and is offered as a plausible explanation for the controversy surrounding the replication pattern of the low-copy plasmids. A comparison of experimental data and simulation results for the low-copy F plasmid at several growth rates indicates that either initiation mechanism would be sufficient to explain the timing of replication with the cell cycle. The simulation results also demonstrate that, although cell-cycle-specific and cell-cycle independent replication patterns give rise to very different gene-expression patterns during short induction periods in age-selected populations, long-term expression of genes encoded on low-copy and high-copy plasmids in exponentially growing cells have nearly the same patterns. These results may be important for the future use of low-copy plasmids as expression vectors and validate the use of simpler models for high-copy plasmids that do not consider cell-cycle phenomena. (c) 1996 John Wiley & Sons, Inc.     

Computer Simulation of Two-Dimensional Continuum Flows by the Direct Simulation Monte Carlo Method

Abstract

Computer simulations using particles are an attractive method to extract microscopic information of flow phenomena [1]. The molecular dynamics (MD) method, in which Newton's equations of motions are integrated, gives the temporal development of the system. In the MD simulation of fluid flows, the computational region is limited to atomistic scales [2]. On the other hand, the direct simulation Monte Carlo (DSMC) method, in which collisions of particles are made on a probabilistic basis, has a potential of treating a realistic system with a macroscopic scale length retaining the atomistic details. The DSMC method provides an efficient way to integrate the Boltzmann equation from the rarefied gas to the near-continuum region. Bird clarified the validity of the DSMC method in the near-continuum flow region [3]. However, the DSMC method has not been applied to the continuum region and compared with the continuum hydrodynamics.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic treesusing DNA sequence data. The birth-death process with species sampling isused to specify the prior distribution of phylogenies and ancestralspeciation times, and the posterior probabilities of phylogenies are usedto estimate the maximum posterior probability (MAP) tree. Monte Carlointegration is used to integrate over the ancestral speciation times forparticular trees. A Markov Chain Monte Carlo method is used to generate theset of trees with the highest posterior probabilities. Methods aredescribed for an empirical Bayesian analysis, in which estimates of thespeciation and extinction rates are used in calculating the posteriorprobabilities, and a hierarchical Bayesian analysis, in which theseparameters are removed from the model by an additional integration. TheMarkov Chain Monte Carlo method avoids the requirement of our earliermethod for calculating MAP trees to sum over all possible topologies (whichlimited the number of taxa in an analysis to about five). The methods areapplied to analyze DNA sequences for nine species of primates, and the MAPtree, which is identical to a maximum-likelihood estimate of topology, hasa probability of approximately 95%.     

Fast Protein Loop Sampling and Structure Prediction Using Distance-Guided Sequential Chain-Growth Monte Carlo Method

Loops in proteins are flexible regions connecting regular secondary structures. They are often involved in protein functions through interacting with other molecules. The irregularity and flexibility of loops make their structures difficult to determine experimentally and challenging to model computationally. Conformation sampling and energy evaluation are the two key components in loop modeling. We have developed a new method for loop conformation sampling and prediction based on a chain growth sequential Monte Carlo sampling strategy, called Distance-guided Sequential chain-Growth Monte Carlo (DiSGro). With an energy function designed specifically for loops, our method can efficiently generate high quality loop conformations with low energy that are enriched with near-native loop structures. The average minimum global backbone RMSD for 1,000 conformations of 12-residue loops is Å, with a lowest energy RMSD of Å, and an average ensemble RMSD of Å. A novel geometric criterion is applied to speed up calculations. The computational cost of generating 1,000 conformations for each of the x loops in a benchmark dataset is only about cpu minutes for 12-residue loops, compared to ca cpu minutes using the FALCm method. Test results on benchmark datasets show that DiSGro performs comparably or better than previous successful methods, while requiring far less computing time. DiSGro is especially effective in modeling longer loops (– residues).     

Algorithm and data structures for efficient energy maintenance during Monte Carlo simulation of proteins.

Monte Carlo simulation (MCS) is a common methodology to compute pathways and thermodynamic properties of proteins. A simulation run is a series of random steps in conformation space, each perturbing some degrees of freedom of the molecule. A step is accepted with a probability that depends on the change in value of an energy function. Typical energy functions sum many terms. The most costly ones to compute are contributed by atom pairs closer than some cutoff distance. This paper introduces a new method that speeds up MCS by exploiting the facts that proteins are long kinematic chains and that few degrees of freedom are changed at each step. A novel data structure, called the ChainTree, captures both the kinematics and the shape of a protein at successive levels of detail. It is used to efficiently detect self-collision (steric clash between atoms) and/or find all atom pairs contributing to the energy. It also makes it possible to identify partial energy sums left unchanged by a perturbation, thus allowing the energy value to be incrementally updated. Computational tests on four proteins of sizes ranging from 68 to 755 amino acids show that MCS with the ChainTree method is significantly faster (as much as 10 times faster for the largest protein) than with the widely used grid method. They also indicate that speed-up increases with larger proteins.     

Design Space Development for the Extraction Process of Danhong Injection Using a Monte Carlo Simulation Method

A design space approach was applied to optimize the extraction process of Danhong injection. Dry matter yield and the yields of five active ingredients were selected as process critical quality attributes (CQAs). Extraction number, extraction time, and the mass ratio of water and material (W/M ratio) were selected as critical process parameters (CPPs). Quadratic models between CPPs and CQAs were developed with determination coefficients higher than 0.94. Active ingredient yields and dry matter yield increased as the extraction number increased. Monte-Carlo simulation with models established using a stepwise regression method was applied to calculate the probability-based design space. Step length showed little effect on the calculation results. Higher simulation number led to results with lower dispersion. Data generated in a Monte Carlo simulation following a normal distribution led to a design space with a smaller size. An optimized calculation condition was obtained with 10000 simulation times, 0.01 calculation step length, a significance level value of 0.35 for adding or removing terms in a stepwise regression, and a normal distribution for data generation. The design space with a probability higher than 0.95 to attain the CQA criteria was calculated and verified successfully. Normal operating ranges of 8.2-10 g/g of W/M ratio, 1.25-1.63 h of extraction time, and two extractions were recommended. The optimized calculation conditions can conveniently be used in design space development for other pharmaceutical processes.     

A Modified Valley Restrained Monte Carlo Method to Efficiently Search the Low Energy Structures of Peptides

Abstract

A new Monte Carlo sampling scheme, namely the Modified Valley Restrained Monte Carlo procedure, is used to obtain the global energy minimum conformations for polypeptides, such as Met-enkephalin and Melittin. For each peptide, we found close agreement with previous results from both theoretical and experimental studies. The simple idea for controlling the step size according to the Valley Function, provides useful suggestions in searching the global energy minimum structures, and furthermore helps solve the multiple minima problem.     

A New Version of the Insertion Particle Method for Determining the Chemical Potential by Monte Carlo Simulation

A new version of the test particle method for determining the chemical potential by Monte Carlo simulations is proposed. The method, applicable to any fluid at any density, combines the Widom's test particle insertion method with the ideas of the scaled particle theory, gradual insertion method and multistage sampling. Its applicability is exemplified by evaluating the chemical potential of the hard sphere fluid at a very high density in semi-grand-canonical and grand-canonical ensembles. A theory estimating the efficiency (i.e. statistical errors) of the method is proposed and the results are compared with the Widom's and gradual insertion methods, and the analytic results.     

Prediction of Plausible Bacterial Composition Based on Terminal Restriction Fragment Length Polymorphisms using a Monte Carlo Method

We have developed a new approach for the estimation of bacterial proportional compositions in microbiota based on terminal restriction length polymorphism (T-RFLP) data and a Monte Carlo algorithm. This program estimates proportional compositions by minimizing distances between peak values and the relative abundance of each group, containing several species, estimated from peak areas of capillary electrophoresis for T-RFLP analysis. Oral bacteria in 36 saliva samples obtained from three individuals were analyzed using the program. Upon comparison, the estimated proportional composition obtained from one of the samples matched that from a clone library. Additionally, comparisons among the bacterial proportional compositions of saliva samples obtained from three individuals four times per day for 3 days revealed that the types of microbiota present in each individual did not change within each 24-h time period and were distinguishable from those in other individuals.     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

A Concerted Molecular Design Method by Temperature-Guided Monte Carlo Search / Potential Applications for ab initio Ligand Design

This work demonstrates the conceptual feasibility of a method for systematic and concerted design of a molecular structure with a favorable interaction toward a prescribed target. Since a semi-empirical QM hamiltonian is used to calculate energies, the method described here allows the continual atomic change and reassessment of molecular structure with respect to its own internal energy and its target interaction energy. Modelling the ligand molecular structure on an atomistic basis, in contrast to a fragment basis, permits the construction of higher energy transitional structures which bridge between viable ligand structures. This allows a most thorough way to accomplish meticulous configurational sampling. The use of two examples, the creation of an ammonia molecule to interact with a formic acid target, and a formic acid molecule to form a dimer with a target, more clearly illustrates the features of a temperature guided Monte Carlo simulation which was developed to allow thorough configurational sampling. This is accomplished by appropriately varying the temperature of the MC simulation. A series of random starting configurations underwent this systematic MC sampling procedure to locate various structural and interaction energy minima. The results of these simulations demonstrate thorough configurational sampling and convergence.     

Study of Clustering in Nonideal Ion Plasma by a Combined Open Ensemble Monte Carlo - Cluster Expansion Method

The chemical potential and Gibbs free energy of ion clusters are obtained by Monte Carlo method combined with a cluster expansion in a wide range of pressures. Gibbs free energy and configurational energy of the symmetric ion plasma is calculated by Frenkel-Band cluster expansion. The energy is compared with Monte Carlo data for a periodic system.     

Genomewide Multipoint Linkage Analysis of Seven Extended Palauan Pedigrees with Schizophrenia, by a Markov-Chain Monte Carlo Method

Palauans are an isolated population in Micronesia with lifetime prevalence of schizophrenia (SCZD) of 2%, compared to the world rate of approximately 1%. The possible enrichment for SCZD genes, in conjunction with the potential for reduced etiological heterogeneity and the opportunity to ascertain statistically powerful extended pedigrees, makes Palauans a population of choice for the mapping of SCZD genes. We have used a Markov-chain Monte Carlo method to perform a genomewide multipoint analysis in seven extended pedigrees from Palau. Robust multipoint parametric and nonparametric linkage (NPL) analyses were performed under three nested diagnostic classifications-core, spectrum, and broad. We observed four regions of interest across the genome. Two of these regions-on chromosomes 2p13-14 (for which, under core diagnostic classification, NPL=6.5 and parametric LOD=4.8) and 13q12-22 (for which, under broad diagnostic classification, parametric LOD=3.6, and, under spectrum diagnostic classification, parametric LOD=3.5)-had evidence for linkage with genomewide significance, after correction for multiple testing; with the current pedigree resource and genotyping, these regions are estimated to be 4.3 cM and 19.75 cM in size, respectively. A third region, with intermediate evidence for linkage, was identified on chromosome 5q22-qter (for which, under broad diagnostic classification, parametric LOD=2.5). The fourth region of interest had only borderline suggestive evidence for linkage (on 3q24-28; for this region, under broad diagnostic classification, parametric LOD=2.0). All regions exhibited evidence for genetic heterogeneity. Our findings provide significant evidence for susceptibility loci on chromosomes 2p13-14 and 13q12-22 and support both a model of genetic heterogeneity and the utility of a broader set of diagnostic classifications in the population from Palau.     

A New Monte Carlo Method for Direct Calculation of the Critical Size and the Formation Work of a Microdrop

New Monte Carlo procedures in open ensembles are proposed. Non-stationary Markov chain procedure in the μl;pT - ensemble provides a direct estimation for the critical size of a condensation nucleus at given p and T. A stationary procedure in the μlpT ensemble with two allowed particle numbers n and n + 1 provides the direct way to calculate the chemical potential and Gibbs free energy of a cluster; in the grand canonical (μlVT) ensemble the same approach gives μl and the Helmholtz free energy. The same procedures are readily applicable to periodic systems representing bulk phases.