Thermodynamic parameters for the helix-coil transition of oligopeptides: molecular dynamics simulation with the peptide growth method.

The helix-coil transition equilibrium of polypeptides in aqueous solution was studied by molecular dynamics simulation. The peptide growth simulation method was introduced to generate dynamic models of polypeptide chains in a statistical (random) coil or an alpha-helical conformation. The key element of this method is to build up a polypeptide chain during the course of a molecular transformation simulation, successively adding whole amino acid residues to the chain in a predefined conformation state (e.g., alpha-helical or statistical coil). Thus, oligopeptides of the same length and composition, but having different conformations, can be incrementally grown from a common precursor, and their relative conformational free energies can be calculated as the difference between the free energies for growing the individual peptides. This affords a straightforward calculation of the Zimm-Bragg sigma and s parameters for helix initiation and helix growth. The calculated sigma and s parameters for the polyalanine alpha-helix are in reasonable agreement with the experimental measurements. The peptide growth simulation method is an effective way to study quantitatively the thermodynamics of local protein folding.

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.

On a psychophysical transformed-rule up and down method converging on a 75% level of correct responses

Tranformed-rule up and down psychophysical methods have gained great popularity, mainly because they combine criterion-free responses with an adaptive procedure allowing rapid determination of an average stimulus threshold at various criterion levels of correct responses. The statistical theory underlying the methods now in routine use is based on sets of consecutive responses with assumed constant probabilities of occurrence. The response rules requiring consecutive responses prevent the possibility of using the most desirable response criterion, that of 75% correct responses. The earliest transformed-rule up and down method, whose rules included nonconsecutive responses, did not contain this limitation but failed to become generally accepted, lacking a published theoretical foundation. Such a foundation is provided in this article and is validated empirically with the help of experiments on human subjects and a computer simulation. In addition to allowing the criterion of 75% correct responses, the method is more efficient than the methods excluding nonconsecutive responses in their rules.

Progress toward chemical accuracy in the computer simulation of condensed phase reactions.

We describe a procedure for the generation of chemically accurate computer-simulation models to study chemical reactions in the condensed phase. The process involves (i) the use of a coupled semiempirical quantum and classical molecular mechanics method to represent solutes and solvent, respectively; (ii) the optimization of semiempirical quantum mechanics (QM) parameters to produce a computationally efficient and chemically accurate QM model; (iii) the calibration of a quantum/classical microsolvation model using ab initio quantum theory; and (iv) the use of statistical mechanical principles and methods to simulate, on massively parallel computers, the thermodynamic properties of chemical reactions in aqueous solution. The utility of this process is demonstrated by the calculation of the enthalpy of reaction in vacuum and free energy change in aqueous solution for a proton transfer involving methanol, methoxide, imidazole, and imidazolium, which are functional groups involved with proton transfers in many biochemical systems. An optimized semiempirical QM model is produced, which results in the calculation of heats of formation of the above chemical species to within 1.0 kcal/mol (1 kcal = 4.18 kJ) of experimental values. The use of the calibrated QM and microsolvation QM/MM (molecular mechanics) models for the simulation of a proton transfer in aqueous solution gives a calculated free energy that is within 1.0 kcal/mol (12.2 calculated vs. 12.8 experimental) of a value estimated from experimental pKa values of the reacting species.