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.

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.

In situ isolation of mRNA from individual plant cells: creation of cell-specific cDNA libraries.

A method for isolating and cloning mRNA populations from individual cells in living, intact plant tissues is described. The contents of individual cells were aspirated into micropipette tips filled with RNA extraction buffer. The mRNA from these cells was purified by binding to oligo(dT)-linked magnetic beads and amplified on the beads using reverse transcription and PCR. The cell-specific nature of the isolated mRNA was verified by creating cDNA libraries from individual tomato leaf epidermal and guard cell mRNA preparations. In testing the reproducibility of the method, we discovered an inherent limitation of PCR amplification from small amounts of any complex template. This phenomenon, which we have termed the "Monte Carlo" effect, is created by small and random differences in amplification efficiency between individual templates in an amplifying cDNA population. The Monte Carlo effect is dependent upon template concentration: the lower the abundance of any template, the less likely its true abundance will be reflected in the amplified library. Quantitative assessment of the Monte Carlo effect revealed that only rare mRNAs (< or = 0.04% of polyadenylylated mRNA) exhibited significant variation in amplification at the single-cell level. The cDNA cloning approach we describe should be useful for a broad range of cell-specific biological applications.