Equilibrium free energies from nonequilibrium measurements using maximum-likelihood methods

We present a maximum likelihood argument for the Bennett acceptance ratio method, and derive a simple formula for the variance of free energy estimates generated using this method. This derivation of the acceptance ratio method, using a form of logistic regression, a common statistical technique, allows us to shed additional light on the underlying physical and statistical properties of the method. For example, we demonstrate that the acceptance ratio method yields the lowest variance for any estimator of the free energy which is unbiased in the limit of large numbers of measurements.     

Second order elastic effects in a homogeneous isotropic compressible infinite medium with an elliptic hole and acted upon by a tensile force at infinity

Analytic expressions for the second order elasticity case of the problem of an isotropic, infinite medium of compressible material having an elliptic hole and acted upon by a tensile force at infinity are obtained. These results are improvements on the classical elasticity theory in which the elastic constants do not play any role for determination of the stresses. The expressions for the second order effects in the cases of a circular hole and a slit along the major axis have been obtained as particular cases.     

Mathematical analysis of coupled parallel simulations

A set of parallel replicas of a single simulation can be statistically coupled to closely approximate long trajectories. In many cases, this produces nearly linear speedup over a single simulation ( M times faster with M simulations), rendering previously intractable problems within reach of large computer clusters. Interestingly, by varying the coupling of the parallel simulations, it is possible in some systems to obtain greater than linear speedup. The methods are generalizable to any search algorithm with long residence times in intermediate states.     

Synthesis of a trimeric gp120 epitope mimic conjugated to a T-helper peptide to improve antigenicity

A fully synthetic trivalent mimotope of gp120 conjugated to pan allelic HLA DR binding epitope was prepared using solid-phase peptide synthesis and optimized copper-catalyzed azide-alkyne cycloaddition. The methodology efficiently provides chemically uniform heteromultimeric peptide constructs with enhanced binding, avidity, and specificity toward an established HIV-neutralizing human antibody, MAb b12. The versatile synthetic strategy serves as a powerful platform for the development of synthetic peptides as potential HIV-1 vaccine candidates.     

Atomistic folding simulations of the five-helix bundle protein λ(6−85)

Protein folding is a classic grand challenge that is relevant to numerous human diseases, such as protein misfolding diseases like Alzheimer’s disease. Solving the folding problem will ultimately require a combination of theory, simulation, and experiment, with theory and simulation providing an atomically detailed picture of both the thermodynamics and kinetics of folding and experimental tests grounding these models in reality. However, theory and simulation generally fall orders of magnitude short of biologically relevant time scales. Here we report significant progress toward closing this gap: an atomistic model of the folding of an 80-residue fragment of the λ repressor protein with explicit solvent that captures dynamics on a 10 milliseconds time scale. In addition, we provide a number of predictions that warrant further experimental investigation. For example, our model’s native state is a kinetic hub, and biexponential kinetics arises from the presence of many free-energy basins separated by barriers of different heights rather than a single low barrier along one reaction coordinate (the previously proposed incipient downhill folding scenario).