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.

Direct measurement of salt-bridge solvation energies using a peptide model system: implications for protein stability.

The solvation energies of salt bridges formed between the terminal carboxyl of the host pentapeptide AcWL- X-LL and the side chains of Arg or Lys in the guest (X) position have been measured. The energies were derived from octanol-to-buffer transfer free energies determined between pH 1 and pH 9. 13C NMR measurements show that the salt bridges form in the octanol phase, but not in the buffer phase, when the side chains and the terminal carboxyl group are charged. The free energy of salt-bridge formation in octanol is approximately -4 kcal/mol (1 cal = 4.184 J), which is equal to or slightly larger than the sum of the solvation energies of noninteracting pairs of charged side chains. This is about one-half the free energy that would result from replacing a charge pair in octanol with a pair of hydrophobic residues of moderate size. Therefore, salt bridging in octanol can change the favorable aqueous solvation energy of a pair of oppositely charged residues to neutral or slightly unfavorable but cannot provide the same free energy decrease as hydrophobic residues. This is consistent with recent computational and experimental studies of protein stability.