We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the weighted likelihood ratios hit stochastic boundaries depending on the current observations. The proof is based on the reduction of the initial problems into appropriate three-dimensional optimal stopping problems and the analysis of the associated parabolic-type free-boundary problems. We provide closed-form estimates for the value functions and the boundaries, under certain nontrivial relations between the coefficients of the observable diffusion.

The factors that influence the enhanced stability observed experimentally of human rhinovirus 14 (HRV14) upon binding a hydrophobic antiviral drug have been investigated by molecular dynamics. Simulations centered about the HRV14 drug-binding pocket allow the reliable assessment of differences in capsid protein motions of HRV14 and drug-bound HRV14. We propose that the experimentally observed stabilization of the ligated virus arises from higher entropy, rather than enthalpy. Time-averaged interaction energies between the viral protein and molecules occupying the pocket are less favorable in the presence of the drug, consistent with the proposal that the observed stability arises from entropic effects. Interaction energies characterizing subunit–subunit contacts within one viral protomer are found to be substantially stronger than those between two protomers. Such distinction in subunit interaction would have clear implications on assembly and disassembly. Drug binding is found to affect large-scale, collective properties, while leaving local atomic properties unperturbed. Specifically, the simulations reveal a weakening of long-range correlations in atomic motions upon drug binding. On the other hand, neither the fast time scale RMS fluctuations of individual atomic positions nor the fluctuation build-up curves from the capsid β-sandwich forming the drug-binding pocket show a consistent distinction between the drug-bound and drug-free viral simulations. Collectively, the detailed description available from the simulations provides an understanding of the experimental observations on the drug-induced changes in thermal stability and protease sensitivity reported for picornaviruses. The predicted significance of binding entropy can be explored experimentally and should be considered in the design of new antiviral compounds.