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.     

Monte Carlo studies in Gold Nanoparticles enhanced radiotherapy: The impact of modelled parameters in dose enhancement

PurposeOver the last decades, Gold Nanoparticles (AuNPs) have been presented as an innovative approach in radiotherapy (RT) enhancement. Several studies have proven that the irradiation of tumors containing AuNPs could lead to more effective tumor control than irradiation alone. Studies with low kV photons and AuNPs conclude in encouraging results regarding the level of radioenhancement. However, experimental and theoretical studies with MV photons report controversial findings concerning the correlation between dose enhancement effect and tumor cell killing. The great variation in the experimental protocols and simulations complicates the comparison of their outcomes and depicts the need for limiting the variety of investigated parameters. Our purpose is to point out a possible direction for building realistic Monte Carlo (MC) models that could end up with promising results in MV photons RT enhancement.MethodsWe explored published in silico studies concerning AuNPs enhanced RT from 2010 to 2019. In this review, we discuss the different AuNPs and MV photon beams characteristics that have been reported and their effect in dose enhancement.ResultsAuNPs size, concentration, type of distribution along with photon beams energy and the presence of flattening filter in linear accelerators seem to be the major parameters that determine AuNPs radioenhancement in silico.ConclusionsPrior to AuNPs clinical translation in photon radiotherapy, in silico studies should emphasize on nanodosimetry and track structure codes than condensed history ones. Toxicity estimation and biological aspects should be implemented in MC simulations so as to achieve accurate and realistic modelling of AuNPs driven RT.     

Minimum sample sizes for identifying chromosomal fragile sites from individuals: Monte Carlo estimation

A Monte Carlo simulation procedure was used to estimate the exact level of the standardized X ² test statistic (X _s ²) for randomness in the FSM methodology for the identification of fragile sites from chromosomal breakage data for single individuals. A random-number generator was used to simulate 10 000 chromosomal breakage data sets, each corresponding to the null hypothesis of no fragile sites for numbers of chromosomal breaks (n) from 1 to 2000 and at three levels of chromosomal band resolution (k). The reliability of the test was assessed by comparisons of the empirical and nominal α levels for each of the corresponding values of n and k. These analyses indicate that the sparse and discrete nature of chromosomal breakage data results in large and unpredictable discrepancies between the empirical and nominal α levels when fragile site identifications are based on small numbers of breaks (n < 0.5 k). With n≥ 0.5 k, the distribution of X _s ² appears to be stable and non-significant differences in the empirical and nominal α levels are generally obtained. These results are inherent to the nature of the data and are, therefore, relevant to any statistical model for the identification of fragile sites from chromosomal breakage data. For FSM identification of fragile sites at α = 0.05, we suggest that n≥ 0.5 k is the minimum reliable number of mapped chromosomal breaks per individual. Received: 28 April 1997 / Accepted: 1 July 1997     

Monte Carlo studies of lipid / water interfaces

The results of a series of numerical simulations of the aqueous interface near several types of lipid bilayer headgroups are presented. The Monte Carlo method was used to study 172 water molecules located between two lipid bilayers separated by 24.5 Å. The types of headgroups used in the studies include phosphorylcholine, -ethanolamine and -serine. The quantities calculated were molecular density, dipolar orientation and number of hydrogen bonds as functions of the distance from the interfacial regions. The data point out important differences in the organization of the interfacial water for each of the three different lipids.     

Anomalous diffusion due to binding: a Monte Carlo study.

In classical diffusion, the mean-square displacement increases linearly with time. But in the presence of obstacles or binding sites, anomalous diffusion may occur, in which the mean-square displacement is proportional to a nonintegral power of time for some or all times. Anomalous diffusion is discussed for various models of binding, including an obstruction/binding model in which immobile membrane proteins are represented by obstacles that bind diffusing particles in nearest-neighbor sites. The classification of binding models is considered, including the distinction between valley and mountain models and the distinction between singular and nonsingular distributions of binding energies. Anomalous diffusion is sensitive to the initial conditions of the measurement. In valley models, diffusion is anomalous if the diffusing particles start at random positions but normal if the particles start at thermal equilibrium positions. Thermal equilibration leads to normal diffusion, or to diffusion as normal as the obstacles allow.     

Monte Carlo studies of the hydrocarbon region of lipid bilayers

We present the results of a Monte Carlo study of systems of hydrocarbon chains attached to a plane interface and interacting through hard core repulsive forces only. The chain-order parameters which we find in our studies are compared to experimental results (NMR and ESR). The role of “kink” states and the relevance of our studies to theoretical models are also discussed.     

Hamiltonian Monte Carlo methods for efficient parameter estimation in steady state dynamical systems

Background

Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system’s states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes.

Results

We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions.

Conclusion

Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-253) contains supplementary material, which is available to authorized users.     

Optimising muscle parameters in musculoskeletal models using Monte Carlo simulation

The use of musculoskeletal simulation software has become a useful tool for modelling joint and muscle forces during human activity, including in reduced gravity because direct experimentation is difficult. Knowledge of muscle and joint loads can better inform the design of exercise protocols and exercise countermeasure equipment. In this study, the LifeModeler? (San Clemente, CA, USA) biomechanics simulation software was used to model a squat exercise. The initial model using default parameters yielded physiologically reasonable hip-joint forces but no activation was predicted in some large muscles such as rectus femoris, which have been shown to be active in 1-g performance of the activity. Parametric testing was conducted using Monte Carlo methods and combinatorial reduction to find a muscle parameter set that more closely matched physiologically observed activation patterns during the squat exercise. The rectus femoris was predicted to peak at 60.1% activation in the same test case compared to 19.2% activation using default parameters. These results indicate the critical role that muscle parameters play in joint force estimation and the need for exploration of the solution space to achieve physiologically realistic muscle activation.     

Monte Carlo studies of a model for lipid-gramicidin A bilayers.

This paper presents results of Monte Carlo simulations of a full bilayer of 200 lipid chains and one gramicidin A dimer. Simulations are described for systems with lipid chains of 14, 16, and 18 carbons, respectively. Using accepted potential functions to calculate interactions between all non-hydrogen atoms a Monte Carlo configuration sampling is generated from which order parameter profiles are calculated and specific configurations are displayed. Results are compared with experimental data for lipid-gramicidin bilayers.     

Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods

Hodgkin–Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron’s electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known.     

Monte Carlo simulation of protein folding in the presence of residue-specific binding sites

Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residue-specific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.     

Radiation shielding parameters of some antioxidants using Monte Carlo method

In this paper, radiation shielding parameters such as mass attenuation coefficients and half value layer (HVL) of some antioxidants are investigated using MCNPX (version 2.4.0). The validation of the generated MCNPX simulation geometry for antioxidant structures is provided by comparing the results with standard WinXcom data for radiation mass attenuation coefficients of antioxidants. Very good agreement between W?NXCOM and MCNPX was obtained. The results from the validated geometry were used to calculate the shielding parameters of different antioxidants. The radiation attenuation properties of each antioxidant were compared with each other. The results showed that, on average, the highest and the lowest radiation mass attenuation coefficients were observed on hesperidin and delphinidin chloride, respectively. It can be concluded that Monte Carlo simulation is a strong tool and an alternate method where experimental investigations are not possible and a standard simulation setup can be used in further studies for different biological structures. It can also be concluded that the obtained results from this study are very useful for radiology and radiotherapy applications where antioxidants are frequently used.     

Aqueous hydration of nucleic acid constituents: Monte Carlo computer simulation studies

Monte Carlo computer simulations were performed on dilute aqueous solutions of thymine, cytosine, uracil, adenine, guanine, the dimethyl phosphate anion in the gauche-gauche conformation and a ribose and deoxyribose derivative. The aqueous hydration of each molecule was analysed in terms of quasi-component distribution functions based on the Proximity Criterion, and partitioned into hydrophobic, hydrophilic and ionic contributions. Color stereo views of selected hydration complexes are also presented. A preliminary discussion of the transferability of functional group coordination numbers is given. The results enable to comment on two current problems related to the hydration of nucleic acids: a) the theory of Dickerson and coworkers on the role of water in the relative stability of the A and B form of DNA and b) the idea of water bridges and filaments emerging from the computer simulation results on the hydration of DNA fragments by Clementi.     

Monte Carlo studies of folding, dynamics, and stability in alpha-helices

Folding simulations of polyalanine peptides were carried out using an off-lattice Monte Carlo simulation technique. The peptide was represented as a chain of residues, each of which contains two interaction sites: one corresponding to the C(alpha) atom and the other to the side chain. A statistical potential was used to describe the interaction between these sites. The preferred conformations of the peptide chain on the energy surface, starting from several initial conditions, were searched by perturbations on its generalized coordinates with the Metropolis criterion. We observed that, at low temperatures, the effective energy was low and the helix content high. The calculated helix propagation (s) and nucleation (sigma) parameters of the Zimm-Bragg model were in reasonable agreement with the empirical data. Exploration of the energy surface of the alanine-based peptides (AAQAA)(3) and AAAAA(AAARA)(3)A demonstrated that their behavior is similar to that of polyalanine, in regard to their effective energy, helix content, and the temperature-dependence of their helicity. In contrast, stable secondary structures were not observed for (Gly)(20) at similar temperatures, which is consistent with the nonfolder nature of this peptide. The fluctuations in the slowest dynamics mode, which describe the elastic behavior of the chain, showed that as the temperature decreases, the polyalanine peptides become stiffer and retain conformations with higher helix content. Clustering of conformations during the folding phase implied that polyalanine folds into a helix through fewer numbers of intermediate conformations as the temperature decreases.     

Kinetics of cooperative ligand–lattice binding: Fast Monte Carlo integration

A fast Monte Carlo integration algorithm with varying time step is described for cooperative binding of ligands of arbitrary length to a one-dimensional lattice. This algorithm is particularly suitable for strongly cooperative or anticooperative systems, i.e., when the time scales for different kinetic events are very different. As an application, the kinetics of a bimodal two-ligand system are briefly discussed.     

Monte Carlo studies on water in the dCpG/proflavin crystal hydrate

The extensive water network identified in the crystallographic studies of the dCpG/Proflavin hydrate by Neidle, Berman and Shieh (Nature 288, 129, 1980) forms an ideal test case for a) assessing the accuracy of theoretical calculations on nucleic acid--water systems based on statistical thermodynamic computer simulation, and b) the possible use of computer simulation in predicting the water positions in crystal hydrates for use in the further refinement and interpretation of diffraction data. Monte Carlo studies have been carried out on water molecules in the unit cell of dCpG/proflavin, with the nucleic acid complex fixed and the condensed phase environment of the system treated by means of periodic boundary conditions. Intermolecular interactions are described by potential functions representative of quantum mechanical calculations developed by Clementi and coworkers, and widely used in recent studies of the aqueous hydration of various forms of DNA fragments. The results are analyzed in terms of hydrogen bond topology, hydrogen bond distances and energies, mean water positions, and water crystal probability density maps. Detailed comparison of calculated and experimentally observed results are given, and the sensitivity of results to choice of potential is determined by comparison with simulation results based on a set of empirical potentials.