Protein structure refinement of CASP target proteins using GNEIMO torsional dynamics method

Kinase inhibitors allosterically disrupt a regulatory interaction to enhance PKCα membrane translocation

The eukaryotic kinase domain has multiple intrinsically disordered regions whose conformation dictates kinase activity. Small molecule kinase inhibitors (SMKIs) rely on disrupting the active conformations of these disordered regions to inactivate the kinase. While SMKIs are selected for their ability to cause this disruption, the allosteric effects of conformational changes in disordered regions is limited by a lack of dynamic information provided by traditional structural techniques. In this study, we integrated multiscale molecular dynamics simulations with FRET sensors to characterize a novel allosteric mechanism that is selectively triggered by SMKI binding to the protein kinase Cα domain. The indole maleimide inhibitors BimI and sotrastaurin were found to displace the Gly-rich loop (G-loop) that normally shields the ATP-binding site. Displacement of the G-loop interferes with a newly identified, structurally conserved binding pocket for the C1a domain on the N lobe of the kinase domain. This binding pocket, in conjunction with the N-terminal regulatory sequence, masks a diacylglycerol (DAG) binding site on the C1a domain. SMKI-mediated displacement of the G-loop released C1a and exposed the DAG binding site, enhancing protein kinase Cα translocation both to synthetic lipid bilayers and to live cell membranes in the presence of DAG. Inhibitor chemotype determined the extent of the observed allosteric effects on the kinase domain and correlated with the extent of membrane recruitment. Our findings demonstrate the allosteric effects of SMKIs beyond the confines of kinase catalytic conformation and provide an integrated computational-experimental paradigm to investigate parallel mechanisms in other kinases.

Methods for the Refinement of Protein Structure 3D Models

The refinement of predicted 3D protein models is crucial in bringing them closer towards experimental accuracy for further computational studies. Refinement approaches can be divided into two main stages: The sampling and scoring stages. Sampling strategies, such as the popular Molecular Dynamics (MD)-based protocols, aim to generate improved 3D models. However, generating 3D models that are closer to the native structure than the initial model remains challenging, as structural deviations from the native basin can be encountered due to force-field inaccuracies. Therefore, different restraint strategies have been applied in order to avoid deviations away from the native structure. For example, the accurate prediction of local errors and/or contacts in the initial models can be used to guide restraints. MD-based protocols, using physics-based force fields and smart restraints, have made significant progress towards a more consistent refinement of 3D models. The scoring stage, including energy functions and Model Quality Assessment Programs (MQAPs) are also used to discriminate near-native conformations from non-native conformations. Nevertheless, there are often very small differences among generated 3D models in refinement pipelines, which makes model discrimination and selection problematic. For this reason, the identification of the most native-like conformations remains a major challenge.

Experimental accuracy in protein structure refinement via molecular dynamics simulations

Refinement is the last step in protein structure prediction pipelines to convert approximate homology models to experimental accuracy. Protocols based on molecular dynamics (MD) simulations have shown promise, but current methods are limited to moderate levels of consistent refinement. To explore the energy landscape between homology models and native structures and analyze the challenges of MD-based refinement, eight test cases were studied via extensive simulations followed by Markov state modeling. In all cases, native states were found very close to the experimental structures and at the lowest free energies, but refinement was hindered by a rough energy landscape. Transitions from the homology model to the native states require the crossing of significant kinetic barriers on at least microsecond time scales. A significant energetic driving force toward the native state was lacking until its immediate vicinity, and there was significant sampling of off-pathway states competing for productive refinement. The role of recent force field improvements is discussed and transition paths are analyzed in detail to inform which key transitions have to be overcome to achieve successful refinement.

Distinct structural mechanisms determine substrate affinity and kinase activity of protein kinase Cα

Protein kinase Cα (PKCα) belongs to the family of AGC kinases that phosphorylate multiple peptide substrates. Although the consensus sequence motif has been identified and used to explain substrate specificity for PKCα, it does not inform the structural basis of substrate-binding and kinase activity for diverse substrates phosphorylated by this kinase. The transient, dynamic, and unstructured nature of this protein-protein interaction has limited structural mapping of kinase-substrate interfaces. Here, using multiscale MD simulation-based predictions and FRET sensor-based experiments, we investigated the conformational dynamics of the kinase-substrate interface. We found that the binding strength of the kinase-substrate interaction is primarily determined by long-range columbic interactions between basic (Arg/Lys) residues located N-terminally to the phosphorylated Ser/Thr residues in the substrate and by an acidic patch in the kinase catalytic domain. Kinase activity stemmed from conformational flexibility in the region C-terminal to the phosphorylated Ser/Thr residues. Flexibility of the substrate-kinase interaction enabled an Arg/Lys two to three amino acids C-terminal to the phosphorylated Ser/Thr to prime a catalytically active conformation, facilitating phosphoryl transfer to the substrate. The structural mechanisms determining substrate binding and catalytic activity formed the basis of diverse binding affinities and kinase activities of PKCα for 14 substrates with varying degrees of sequence conservation. Our findings provide insight into the dynamic properties of the kinase-substrate interaction that govern substrate binding and turnover. Moreover, this study establishes a modeling and experimental method to elucidate the structural dynamics underlying substrate selectivity among eukaryotic kinases.

Hamiltonian Monte Carlo with Constrained Molecular Dynamics as Gibbs Sampling

Compared to fully flexible molecular dynamics, simulations of constrained systems can use larger time steps and focus kinetic energy on soft degrees of freedom. Achieving ergodic sampling from the Boltzmann distribution, however, has proven challenging. Using recent generalizations of the equipartition principle and Fixman potential, here we implement Hamiltonian Monte Carlo based on constrained molecular dynamics as a Gibbs sampling move. By mixing Hamiltonian Monte Carlo based on fully flexible and torsional dynamics, we are able to reproduce free energy landscapes of simple model systems and enhance sampling of macrocycles.

Computational protein structure refinement: Almost there, yet still so far to go

Protein structures are essential in modern biology yet experimental methods are far from being able to catch up with the rapid increase in available genomic data. Computational protein structure prediction methods aim to fill the gap while the role of protein structure refinement is to take approximate initial template-based models and bring them closer to the true native structure. Current methods for computational structure refinement rely on molecular dynamics simulations, related sampling methods, or iterative structure optimization protocols. The best methods are able to achieve moderate degrees of refinement but consistent refinement that can reach near-experimental accuracy remains elusive. Key issues revolve around the accuracy of the energy function, the inability to reliably rank multiple models, and the use of restraints that keep sampling close to the native state but also limit the degree of possible refinement. A different aspect is the question of what exactly the target of high-resolution refinement should be as experimental structures are affected by experimental conditions and different biological questions require varying levels of accuracy. While improvement of the global protein structure is a difficult problem, high-resolution refinement methods that improves local structural quality such as favorable stereochemistry and the avoidance of atomic clashes are much more successful.

Overcoming potential energy distortions in constrained internal coordinate molecular dynamics simulations

The Internal Coordinate Molecular Dynamics (ICMD) method is an attractive molecular dynamics (MD) method for studying the dynamics of bonded systems such as proteins and polymers. It offers a simple venue for coarsening the dynamics model of a system at multiple hierarchical levels. For example, large scale protein dynamics can be studied using torsional dynamics, where large domains or helical structures can be treated as rigid bodies and the loops connecting them as flexible torsions. ICMD with such a dynamic model of the protein, combined with enhanced conformational sampling method such as temperature replica exchange, allows the sampling of large scale domain motion involving high energy barrier transitions. Once these large scale conformational transitions are sampled, all-torsion, or even all-atom, MD simulations can be carried out for the low energy conformations sampled via coarse grained ICMD to calculate the energetics of distinct conformations. Such hierarchical MD simulations can be carried out with standard all-atom forcefields without the need for compromising on the accuracy of the forces. Using constraints to treat bond lengths and bond angles as rigid can, however, distort the potential energy landscape of the system and reduce the number of dihedral transitions as well as conformational sampling. We present here a two-part solution to overcome such distortions of the potential energy landscape with ICMD models. To alleviate the intrinsic distortion that stems from the reduced phase space in torsional MD, we use the Fixman compensating potential. To additionally alleviate the extrinsic distortion that arises from the coupling between the dihedral angles and bond angles within a force field, we propose a hybrid ICMD method that allows the selective relaxing of bond angles. This hybrid ICMD method bridges the gap between all-atom MD and torsional MD. We demonstrate with examples that these methods together offer a solution to eliminate the potential energy distortions encountered in constrained ICMD simulations of peptide molecules.

Protein structure refinement via molecular-dynamics simulations: What works and what does not?

Protein structure refinement during CASP11 by the Feig group was described. Molecular dynamics simulations were used in combination with an improved selection and averaging protocol. On average, modest refinement was achieved with some targets improved significantly. Analysis of the CASP submission from our group focused on refinement success versus amount of sampling, refinement of different secondary structure elements and whether refinement varied as a function of which group provided initial models. The refinement of local stereochemical features was examined via the MolProbity score and an updated protocol was developed that can generate high-quality structures with very low MolProbity scores for most starting structures with modest computational effort. Proteins 2016; 84(Suppl 1):282-292. © 2015 Wiley Periodicals, Inc.

Significant Refinement of Protein Structure Models Using a Residue-Specific Force Field

An important application of all-atom explicit-solvent molecular dynamics (MD) simulations is the refinement of protein structures from low-resolution experiments or template-based modeling. A critical requirement is that the native structure is stable with the force field. We have applied a recently developed residue-specific force field, RSFF1, to a set of 30 refinement targets from recent CASP experiments. Starting from their experimental structures, 1.0 μs unrestrained simulations at 298 K retain most of the native structures quite well except for a few flexible terminals and long internal loops. Starting from each homology model, a 150 ns MD simulation at 380 K generates the best RMSD improvement of 0.85 Å on average. The structural improvements roughly correlate with the RMSD of the initial homology models, indicating possible consistent structure refinement. Finally, targets TR614 and TR624 have been subjected to long-time replica-exchange MD simulations. Significant structural improvements are generated, with RMSD of 1.91 and 1.36 Å with respect to their crystal structures. Thus, it is possible to achieve realistic refinement of protein structure models to near-experimental accuracy, using accurate force field with sufficient conformational sampling.

Internal coordinate molecular dynamics: a foundation for multiscale dynamics

Internal coordinates such as bond lengths, bond angles, and torsion angles (BAT) are natural coordinates for describing a bonded molecular system. However, the molecular dynamics (MD) simulation methods that are widely used for proteins, DNA, and polymers are based on Cartesian coordinates owing to the mathematical simplicity of the equations of motion. However, constraints are often needed with Cartesian MD simulations to enhance the conformational sampling. This makes the equations of motion in the Cartesian coordinates differential-algebraic, which adversely impacts the complexity and the robustness of the simulations. On the other hand, constraints can be easily placed in BAT coordinates by removing the degrees of freedom that need to be constrained. Thus, the internal coordinate MD (ICMD) offers an attractive alternative to Cartesian coordinate MD for developing multiscale MD method. The torsional MD method is a special adaptation of the ICMD method, where all the bond lengths and bond angles are kept rigid. The advantages of ICMD simulation methods are the longer time step size afforded by freezing high frequency degrees of freedom and performing a conformational search in the more important low frequency torsional degrees of freedom. However, the advancements in the ICMD simulations have been slow and stifled by long-standing mathematical bottlenecks. In this review, we summarize the recent mathematical advancements we have made based on spatial operator algebra, in developing a robust long time scale ICMD simulation toolkit useful for various applications. We also present the applications of ICMD simulations to study conformational changes in proteins and protein structure refinement. We review the advantages of the ICMD simulations over the Cartesian simulations when used with enhanced sampling methods and project the future use of ICMD simulations in protein dynamics.

GneimoSim: a modular internal coordinates molecular dynamics simulation package

The generalized Newton-Euler inverse mass operator (GNEIMO) method is an advanced method for internal coordinates molecular dynamics (ICMD). GNEIMO includes several theoretical and algorithmic advancements that address longstanding challenges with ICMD simulations. In this article, we describe the GneimoSim ICMD software package that implements the GNEIMO method. We believe that GneimoSim is the first software package to include advanced features such as the equipartition principle derived for internal coordinates, and a method for including the Fixman potential to eliminate systematic statistical biases introduced by the use of hard constraints. Moreover, by design, GneimoSim is extensible and can be easily interfaced with third party force field packages for ICMD simulations. Currently, GneimoSim includes interfaces to LAMMPS, OpenMM, and Rosetta force field calculation packages. The availability of a comprehensive Python interface to the underlying C++ classes and their methods provides a powerful and versatile mechanism for users to develop simulation scripts to configure the simulation and control the simulation flow. GneimoSim has been used extensively for studying the dynamics of protein structures, refinement of protein homology models, and for simulating large scale protein conformational changes with enhanced sampling methods. GneimoSim is not limited to proteins and can also be used for the simulation of polymeric materials.

Evaluation of unrestrained replica-exchange simulations using dynamic walkers in temperature space for protein structure refinement

A central problem of computational structural biology is the refinement of modeled protein structures taken from either comparative modeling or knowledge-based methods. Simulations are commonly used to achieve higher resolution of the structures at the all-atom level, yet methodologies that consistently yield accurate results remain elusive. In this work, we provide an assessment of an adaptive temperature-based replica exchange simulation method where the temperature clients dynamically walk in temperature space to enrich their population and exchanges near steep energetic barriers. This approach is compared to earlier work of applying the conventional method of static temperature clients to refine a dataset of conformational decoys. Our results show that, while an adaptive method has many theoretical advantages over a static distribution of client temperatures, only limited improvement was gained from this strategy in excursions of the downhill refinement regime leading to an increase in the fraction of native contacts. To illustrate the sampling differences between the two simulation methods, energy landscapes are presented along with their temperature client profiles.