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Allostery refers to the puzzling phenomenon of long-range communication between distant sites in proteins. Despite its importance in biomolecular regulation and signal transduction, the underlying dynamical process is not well understood. This study introduces a dynamical model of allosteric communication based on "contact clusters"-localized groups of highly correlated contacts that facilitate interactions between secondary structures. The model shows that allostery involves a multi-step process with cooperative contact changes within clusters and communication between distant clusters mediated by rigid secondary structures. Considering time-dependent experiments on a photoswitchable PDZ3 domain, extensive (in total $\sim 500\,\mu$s) molecular dynamics simulations are conducted that directly monitor the photoinduced allosteric transition. The structural reorganization is illustrated by the time evolution of the contact clusters and the ligand, which affects the nonlocal coupling between distant clusters. A timescale analysis reveals dynamics from nano- to microseconds, which are in excellent agreement with the experimentally measured timescales.

While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates. Avoiding any assumption about the underlying data, the mutual information $I(X, Y)$ does account for multidimensional correlations. However, unlike the normalized Pearson correlation, it has no upper bound ($I \in [0, \infty)$), i.e., it is not clear if say, $I = 0.4$ corresponds to a low or a high correlation. Moreover, the mutual information (MI) involves the estimation of high-dimensional probability densities (e.g., six-dimensional for Cartesian coordinates), which requires a k-nearest neighbor algorithm, such as the estimator by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)]. As existing methods to normalize the MI cannot be used in connection with this estimator, a new approach is presented, which uses an entropy estimation method that is invariant under variable transformations. The algorithm is numerically efficient and does not require more effort than the calculation of the (un-normalized) MI. After validating the method by applying it to various toy models, the normalized MI between the $C_{\alpha}$ -coordinates of T4 lysozyme is considered and compared to a correlation analysis of inter-residue contacts.

A novel mixed quantum-classical approach to simulating nonadiabatic dynamics of molecules at metal surfaces is presented. The method combines the numerically exact hierarchical equations of motion approach for the quantum electronic degrees of freedom with Langevin dynamics for the classical degrees of freedom, namely, low-frequency vibrational modes within the molecule. The approach extends previous mixed quantum-classical methods based on Langevin equations to models containing strong electron-electron or quantum electronic-vibrational interactions, while maintaining a nonperturbative and non-Markovian treatment of the molecule-metal coupling. To demonstrate the approach, nonequilibrium transport observables are calculated for a molecular nanojunction containing strong interactions.