Advanced Monte Carlo simulation techniques to study polymers under equilibrium conditions

The advances in materials and biological sciences have necessitated the use of molecular simulations to study polymers. The Markov chain Monte Carlo simulations enable the sampling of relevant microstates of polymeric systems by traversing paths that are impractical in molecular dynamics simulations. Several advances in applying Monte Carlo simulations to polymeric systems have been reported in recent decades. The proposed methods address sampling challenges encountered in studying different aspects of polymeric systems. Tracking the above advances has become increasingly challenging due to the extensive literature generated in the field. Moreover, the incorporation of new methods in the existing Monte Carlo simulation packages is cumbersome due to their complexity. Identifying the foundational algorithms that are common to different methods can significantly ease their implementation and make them accessible to the broader simulation community. The present chapter classifies the Monte Carlo methods for polymeric systems based on their objectives and standard features of their algorithms. We begin the article by providing an overview of advanced Monte Carlo techniques used for polymeric systems and their specific applications. We then classify the above techniques into two broad categories: 1) Monte Carlo moves and 2) Advanced sampling schemes. The former category is further divided to distinguish the Monte Carlo moves in the canonical and other ensembles. The advanced sampling schemes attempt to improve Monte Carlo sampling via approaches other than Monte Carlo moves. We use the above classification to identify common features of the methods and derive general expressions that explain their implementation. Such a strategy can help readers select the methods that are suitable for their study and develop computer programs that can be easily modified to implement new methods.Comment: 22 pages, 4 figures, 2 table

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94819/1/wrcr11621.pd

A pattern-search-based inverse method

Uncertainty in model predictions is caused to a large extent by the uncertainty in model parameters, while the identification of model parameters is demanding because of the inherent heterogeneity of the aquifer. A variety of inverse methods has been proposed for parameter identification. In this paper we present a novel inverse method to constrain the model parameters (hydraulic conductivities) to the observed state data (hydraulic heads). In the method proposed we build a conditioning pattern consisting of simulated model parameters and observed flow data. The unknown parameter values are simulated by pattern searching through an ensemble of realizations rather than optimizing an objective function. The model parameters do not necessarily follow a multi-Gaussian distribution, and the nonlinear relationship between the parameter and the response is captured by the multipoint pattern matching. The algorithm is evaluated in two synthetic bimodal aquifers. The proposed method is able to reproduce the main structure of the reference fields, and the performance of the updated model in predicting flow and transport is improved compared with that of the prior model.The authors gratefully acknowledge the financial support from the Ministry of Science and Innovation, project CGL2011-23295. The first author also acknowledges the scholarship provided by the China Scholarship Council (CSC [2007] 3020). The authors would like to thank Gregoire Mariethoz (University of New South Wales) and Philippe Renard (University of Neuchatel) for their enthusiastic help in answering questions about the direct sampling algorithm. Gregoire Mariethoz and two anonymous reviewers are also thanked for their comments during the reviewing process, which helped improving the final paper.Zhou ., H.; Gómez-Hernández, JJ.; Li ., L. (2012). A pattern-search-based inverse method. 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Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol

Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol

A Data-Analysis and Sensitivity-Optimization Framework for the KATRIN Experiment

Presently under construction, the Karlsruhe TRitium Neutrino (KATRIN) experiment is the next generation tritium beta-decay experiment to perform a direct kinematical measurement of the electron neutrino mass with an unprecedented sensitivity of 200 meV (90% C.L.). This thesis describes the implementation of a consistent data analysis framework, addressing technical aspects of the data taking process and statistical challenges of a neutrino mass estimation from the beta-decay electron spectrum

MOLNs: A cloud platform for interactive, reproducible and scalable spatial stochastic computational experiments in systems biology using PyURDME

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools, a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments