Search

Understanding the dynamics of biomolecular complexes, e.g., of protein-ligand (un)binding, requires the comprehension of paths such systems take between metastable states. In MD simulations, paths are usually not observable per se, but they need to be inferred from simulation trajectories. Here, we present a novel approach to cluster trajectories based on a community detection algorithm that necessitates only the definition of a single parameter. The unbinding of the streptavidin-biotin complex is used as a benchmark system and the A 2a adenosine receptor in complex with the inhibitor ZM241385 as an elaborate application. We demonstrate how such clusters of trajectories correspond to pathways and how the approach helps in the identification of reaction coordinates for a considered (un)binding process.

Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled, nonequilibrium processes can be associated with a biased energy landscape, which accounts for finite sampling effects and external driving. When the data-driven Langevin equation (dLE) approach [ Phys . Rev . Lett . 2015 , 115 , 050602] is extended to the modeling of nonequilibrium processes, an efficient way to calculate multidimensional Langevin fields is outlined. The dLE is shown to correctly account for various nonequilibrium processes, including the enforced dissociation of sodium chloride in water, the pressure-jump induced nucleation of a liquid of hard spheres, and the conformational dynamics of a helical peptide sampled from nonstationary short trajectories.

As standard unbiased molecular dynamics (MD) simulations become impractical for sampling rare events, "targeted MD" employs a moving distance constraint to enforce rare transitions along some reaction coordinate x. To calculate free energy profiles from these nonequilibrium simulations via Δ G( x) = W( x) - W diss ( x), apart from the (readily obtained) work W( x) performed on the system, the dissipated work W diss ( x) is also required. By employing a second-order cumulant expansion of Jarzynski's equality combined with an analysis within Langevin theory, the dissipated work can be expressed via a nonequilibrium friction coefficient Γ NEQ ( x) that may be calculated on-the-fly from constraint force fluctuations. Adopting the ion dissociation of NaCl in water as a test system, this friction correction is shown to result in accurate free energy profiles, even for a modest number of simulations and at high constraint velocities. As a bonus, the analysis of Γ NEQ ( x) may yield valuable insight into the microscopic mechanism of friction.

While adequately chosen reaction coordinates are expected to reveal the mechanism of a dynamical process, it proves to be notoriously difficult to model the complex structural rearrangements of a macromolecule by a low-dimensional collective coordinate. Adopting the hinge-bending motion of T4 lysozyme (T4L) as a prominent example and performing a 50 μs long unbiased molecular dynamics (MD) simulation of T4L, a general strategy to identify reaction coordinates of protein functional dynamics is developed. As a systematic method to reduce the dimensionality of the dynamics, first various types of principal component analyses are employed, and it is shown that the applicability and outcome of the approach crucially depends on the type of input coordinates used. In a second step, prospective candidates for a reaction coordinate are tested by studying the molecule's response to external pulling along the coordinate, using targeted MD simulations. While trying to directly enforce the open-closed transition does not recover the two-state behavior of T4L, this transition is triggered by a locking mechanism, by which the side chain of Phe4 changes from a solvent-exposed to a hydrophobically buried state. The mechanism is found to stabilize the open and closed states of T4L and thereby causes their relatively long lifetime of ∼10 μs. In extension of the usual two-state picture, a four-state model of the functional motion of T4L is proposed, which describes a hierarchical coupling of the fast nanosecond opening-closing motion and the slow microsecond locking transition.