Enhanced conformational sampling in Monte Carlo simulations of proteins: application to a constrained peptide.

A Monte Carlo simulation method for globular proteins, called extended-scaled-collective-variable (ESCV) Monte Carlo, is proposed. This method combines two Monte Carlo algorithms known as entropy-sampling and scaled-collective-variable algorithms. Entropy-sampling Monte Carlo is able to sample a large configurational space even in a disordered system that has a large number of potential barriers. In contrast, scaled-collective-variable Monte Carlo provides an efficient sampling for a system whose dynamics is highly cooperative. Because a globular protein is a disordered system whose dynamics is characterized by collective motions, a combination of these two algorithms could provide an optimal Monte Carlo simulation for a globular protein. As a test case, we have carried out an ESCV Monte Carlo simulation for a cell adhesive Arg-Gly-Asp-containing peptide, Lys-Arg-Cys-Arg-Gly-Asp-Cys-Met-Asp, and determined the conformational distribution at 300 K. The peptide contains a disulfide bridge between the two cysteine residues. This bond mimics the strong geometrical constraints that result from a protein's globular nature and give rise to highly cooperative dynamics. Computation results show that the ESCV Monte Carlo was not trapped at any local minimum and that the canonical distribution was correctly determined.

A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

A potential mediator of collagenous block copolymer gradients in mussel byssal threads

Mussel byssal threads contain unusual block copolymer-like proteins that combine collagen with flanking domains that resemble silk-fibroin (preCol-D) or elastin (preCol-P). These are distributed in complementary gradients along the length of the threads and as precursors in the mussel foot. We discuss a 76-kDa precursor, preCol-NG, from a cDNA library of the foot where it has no gradient but rather is distributed evenly along the distal to proximal axis. A pepsin-resistant fragment of preCol-NG has been confirmed in byssal threads. Like preCol-D and -P, this protein has a central collagenous domain, flanking domains, an acidic patch, and histidine-rich termini. The flanking domains of preCol-NG resemble the glycine-rich proteins of plant cell walls with tandem XGlyn repeats where X denotes alanine, leucine, or asparagine but not proline. Similarity with the (glycine–alanine) repeats and poly(alanine) runs of arthropod silks also exists. Based on available evidence, a model of preCol axial assembly is proposed in which preCol-NG functions as a mediator between preCol-D/-P molecules. This is consistent with the observed progression of mechanical properties in byssal threads.