Complexes++: Efficient and versatile coarse-grained simulations of protein complexes and their dense solutions.

The interior of living cells is densely filled with proteins and their complexes, which perform multitudes of biological functions. We use coarse-grained simulations to reach the system sizes and time scales needed to study protein complexes and their dense solutions and to interpret experiments. To take full advantage of coarse-graining, the models have to be efficiently implemented in simulation engines that are easy to use, modify, and extend. Here, we introduce the Complexes++ simulation software to simulate a residue-level coarse-grained model for proteins and their complexes, applying a Markov chain Monte Carlo engine to sample configurations. We designed a parallelization scheme for the energy evaluation capable of simulating both dilute and dense systems efficiently. Additionally, we designed the software toolbox pycomplexes to easily set up complex topologies of multi-protein complexes and their solutions in different thermodynamic ensembles and in replica-exchange simulations, to grow flexible polypeptide structures connecting ordered protein domains, and to automatically visualize structural ensembles. Complexes++ simulations can easily be modified and they can be used for efficient explorations of different simulation systems and settings. Thus, the Complexes++ software is well suited for the integration of experimental data and for method development.

MDBenchmark: A toolkit to optimize the performance of molecular dynamics simulations.

Despite the impending flattening of Moore's law, the system size, complexity, and length of molecular dynamics (MD) simulations keep on increasing, thanks to effective code parallelization and optimization combined with algorithmic developments. Going forward, exascale computing poses new challenges to the efficient execution and management of MD simulations. The diversity and rapid developments of hardware architectures, software environments, and MD engines make it necessary that users can easily run benchmarks to optimally set up simulations, both with respect to time-to-solution and overall efficiency. To this end, we have developed the software MDBenchmark to streamline the setup, submission, and analysis of simulation benchmarks and scaling studies. The software design is open and as such not restricted to any specific MD engine or job queuing system. To illustrate the necessity and benefits of running benchmarks and the capabilities of MDBenchmark, we measure the performance of a diverse set of 23 MD simulation systems using GROMACS 2018. We compare the scaling of simulations with the number of nodes for central processing unit (CPU)-only and mixed CPU-graphics processing unit (GPU) nodes and study the performance that can be achieved when running multiple simulations on a single node. In all these cases, we optimize the numbers of message passing interface (MPI) ranks and open multi-processing (OpenMP) threads, which is crucial to maximizing performance. Our results demonstrate the importance of benchmarking for finding the optimal system and hardware specific simulation parameters. Running MD simulations with optimized settings leads to a significant performance increase that reduces the monetary, energetic, and environmental costs of MD simulations.

Quantifying Protein-Protein Interactions in Molecular Simulations.

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants Kd, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B2. As a measure of nonspecific binding and stickiness, B2 is receiving renewed attention in the context of so-called liquid-liquid phase separation in protein and nucleic acid solutions. We show that Kd is fully determined by B2 and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B2. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B2 from insertion and removal energies by applying Bennett's acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B2 from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for Kd and B2 allow us to separate out the contributions of nonbinding interactions to B2. Comparison of calculated and measured values of Kd and B2 can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of Kd and B2 calculations make them well suited for high-throughput studies of large interactomes.

Dynamic cluster formation determines viscosity and diffusion in dense protein solutions.

We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the Kd ≈ 10-mM regime.

Rotational Diffusion Depends on Box Size in Molecular Dynamics Simulations.

We show that the rotational dynamics of proteins and nucleic acids determined from molecular dynamics simulations under periodic boundary conditions suffer from significant finite-size effects. We remove the box-size dependence of the rotational diffusion coefficients by adding a hydrodynamic correction kB T/6 ηV with kB Boltzmann's constant, T the absolute temperature, η the solvent shear viscosity, and V the box volume. We show that this correction accounts for the finite-size dependence of the rotational diffusion coefficients of horse-heart myoglobin and a B-DNA dodecamer in aqueous solution. The resulting hydrodynamic radii are in excellent agreement with experiment.

Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

Propranolol restricts the mobility of single EGF-receptors on the cell surface before their internalization.

The epidermal growth factor receptor is involved in morphogenesis, proliferation and cell migration. Its up-regulation during tumorigenesis makes this receptor an interesting therapeutic target. In the absence of the ligand, the inhibition of phosphatidic acid phosphohydrolase activity by propranolol treatment leads to internalization of empty/inactive receptors. The molecular events involved in this endocytosis remain unknown. Here, we quantified the effects of propranolol on the mobility of single quantum-dot labelled receptors before the actual internalization took place. The single receptors showed a clear stop-and-go motion; their diffusive tracks were continuously interrupted by sub-second stalling events, presumably caused by transient clustering. In the presence of propranolol we found that: i) the diffusion rate reduced by 22 %, which indicates an increase in drag of the receptor. Atomic force microscopy measurements did not show an increase of the effective membrane tension, such that clustering of the receptor remains the likely mechanism for its reduced mobility. ii) The receptor got frequently stalled for longer periods of multiple seconds, which may signal the first step of the internalization process.