GneimoSim: a modular internal coordinates molecular dynamics simulation package

Molecular Modeling is an Enabling Approach to Complement and Enhance Channelopathy Research

Hundreds of human membrane proteins form channels that transport necessary ions and compounds, including drugs and metabolites, yet details of their normal function or how function is altered by genetic variants to cause diseases are often unknown. Without this knowledge, researchers are less equipped to develop approaches to diagnose and treat channelopathies. High-resolution computational approaches such as molecular modeling enable researchers to investigate channelopathy protein function, facilitate detailed hypothesis generation, and produce data that is difficult to gather experimentally. Molecular modeling can be tailored to each physiologic context that a protein may act within, some of which may currently be difficult or impossible to assay experimentally. Because many genomic variants are observed in channelopathy proteins from high-throughput sequencing studies, methods with mechanistic value are needed to interpret their effects. The eminent field of structural bioinformatics integrates techniques from multiple disciplines including molecular modeling, computational chemistry, biophysics, and biochemistry, to develop mechanistic hypotheses and enhance the information available for understanding function. Molecular modeling and simulation access 3D and time-dependent information, not currently predictable from sequence. Thus, molecular modeling is valuable for increasing the resolution with which the natural function of protein channels can be investigated, and for interpreting how genomic variants alter them to produce physiologic changes that manifest as channelopathies. © 2022 American Physiological Society. Compr Physiol 12:3141-3166, 2022.

High-performance transformation of protein structure representation from internal to Cartesian coordinates

We present a highly parallel algorithm to convert internal coordinates of a polymeric molecule into Cartesian coordinates. Traditionally, converting the structures of polymers (e.g., proteins) from internal to Cartesian coordinates has been performed serially, due to an inherent linear dependency along the polymer chain. We show this dependency can be removed using a tree-based concatenation of coordinate transforms between segments, and then parallelized efficiently on graphics processing units (GPUs). The conversion algorithm is applicable to protein engineering and fitting protein structures to experimental data, and we observe an order of magnitude speedup using parallel processing on a GPU compared to serial execution on a CPU.

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.

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.

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.