Equipartition Principle for Internal Coordinate Molecular Dynamics

The <i>principle of equipartition of (kinetic) energy</i> for all-atom Cartesian molecular dynamics states that each momentum phase space coordinate on the average has <i>kT</i>/2 of kinetic energy in a canonical ensemble. This principle is used in molecular dynamics simulations to initialize velocities, and to calculate statistical properties such as entropy. Internal coordinate molecular dynamics (ICMD) models differ from Cartesian models in that the overall kinetic energy depends on the generalized coordinates and includes cross-terms. Due to this coupled structure, no such equipartition principle holds for ICMD models. In this paper, we introduce noncanonical <i>modal coordinates</i> to recover some of the structural simplicity of Cartesian models and develop a new equipartition principle for ICMD models. We derive low-order recursive computational algorithms for transforming between the modal and physical coordinates. The equipartition principle in modal coordinates provides a rigorous method for initializing velocities in ICMD simulations, thus replacing the <i>ad hoc</i> methods used until now. It also sets the basis for calculating conformational entropy using internal coordinates

Conserved Mechanism of Conformational Stability and Dynamics in G‑Protein-Coupled Receptors

G-protein-coupled receptors (GPCRs) are transmembrane receptors involved in diverse biological functions. Despite the diversity in their amino acid sequences, class A GPCRs exhibit a conserved structural topology and possibly a common mechanism of receptor activation. To understand how this high sequence diversity translates to a conserved functional mechanism, we have compared the dynamic behavior of eight class A GPCRs comprised of six biogenic amine receptors, adenosine A_2A, and the peptide receptor protease-activated receptor 1. Starting from the crystal structures of the inactive state of these receptors bound to inverse agonists or antagonists, we have performed multiple all-atom MD simulations adding up to several microseconds of simulation. We elucidated the similarities and differences in the dynamic behavior and the conformational ensembles sampled by these eight class A GPCRs. Among the six biogenic amine receptors studied here, β₂-adrenergic receptor shows the highest level of fluctuation in the sixth and seventh transmembrane helices, possibly explaining its high basal activity. In contrast, the muscarinic acetylcholine receptors show the lowest fluctuations as well as tight packing and low hydration of the transmembrane domain. All eight GPCRs show several conserved allosteric communication pipelines from the residues in the agonist binding site with the G-protein interface. Positions of the residues along these pipelines that serve as major hubs of allosteric communication are conserved in their respective structures. These findings have important implications in understanding the dynamics and allosteric mechanism of communication in class A GPCRs and hence are useful for designing conformation-specific drugs

Structural Dynamics and Thermostabilization of Neurotensin Receptor 1

The neurotensin receptor NTSR1 binds the peptide agonist neurotensin (NTS) and signals preferentially via the G_q protein. Recently, Grisshammer and co-workers reported the crystal structure of a thermostable mutant NTSR1-GW5 with NTS bound. Understanding how the mutations thermostabilize the structure would allow efficient design of thermostable mutant GPCRs for protein purification, and subsequent biophysical studies. Using microsecond scale molecular dynamics simulations (4 μs) of the thermostable mutant NTSR1-GW5 and wild type NTSR1, we have elucidated the structural and energetic factors that affect the thermostability and dynamics of NTSR1. The thermostable mutant NTSR1-GW5 is found to be less flexible and less dynamic than the wild type NTSR1. The point mutations confer thermostability by improving the interhelical hydrogen bonds, hydrophobic packing, and receptor interactions with the lipid bilayer, especially in the intracellular regions. During MD, NTSR1-GW5 becomes more hydrated compared to wild type NTSR1, with tight hydrogen bonded water clusters within the transmembrane core of the receptor, thus providing evidence that water plays an important role in improving helical packing in the thermostable mutant. Our studies provide valuable insights into the stability and functioning of NTSR1 that will be useful in future design of thermostable mutants of other peptide GPCRs

Role of Specific Cations and Water Entropy on the Stability of Branched DNA Motif Structures

DNA three-way junctions (TWJs) are important intermediates in various cellular processes and are the simplest of a family of branched nucleic acids being considered as scaffolds for biomolecular nanotechnology. Branched nucleic acids are stabilized by divalent cations such as Mg²⁺, presumably due to condensation and neutralization of the negatively charged DNA backbone. However, electrostatic screening effects point to more complex solvation dynamics and a large role of interfacial waters in thermodynamic stability. Here, we report extensive computer simulations in explicit water and salt on a model TWJ and use free energy calculations to quantify the role of ionic character and strength on stability. We find that enthalpic stabilization of the first and second hydration shells by Mg²⁺ accounts for 1/3 and all of the free energy gain in 50% and pure MgCl₂ solutions, respectively. The more distorted DNA molecule is actually destabilized in pure MgCl₂ compared to pure NaCl. Notably, the first shell, interfacial waters have very low translational and rotational entropy (i.e., mobility) compared to the bulk, an entropic loss that is overcompensated by increased enthalpy from additional electrostatic interactions with Mg²⁺. In contrast, the second hydration shell has anomalously high entropy as it is trapped between an immobile and bulklike layer. The nonmonotonic entropic signature and long-range perturbations of the hydration shells to Mg²⁺ may have implications in the molecular recognition of these motifs. For example, we find that low salt stabilizes the parallel configuration of the three-way junction, whereas at normal salt we find antiparallel configurations deduced from the NMR. We use the 2PT analysis to follow the thermodynamics of this transition and find that the free energy barrier is dominated by entropic effects that result from the decreased surface area of the antiparallel form which has a smaller number of low entropy waters in the first monolayer

Protein Structure Refinement of CASP Target Proteins Using GNEIMO Torsional Dynamics Method

A longstanding challenge in using computational methods for protein structure prediction is the refinement of low-resolution structural models derived from comparative modeling methods into highly accurate atomistic models useful for detailed structural studies. Previously, we have developed and demonstrated the utility of the internal coordinate molecular dynamics (MD) technique, generalized Newton–Euler inverse mass operator (GNEIMO), for refinement of small proteins. Using GNEIMO, the high-frequency degrees of freedom are frozen and the protein is modeled as a collection of rigid clusters connected by torsional hinges. This physical model allows larger integration time steps and focuses the conformational search in the low frequency torsional degrees of freedom. Here, we have applied GNEIMO with temperature replica exchange to refine low-resolution protein models of 30 proteins taken from the continuous assessment of structure prediction (CASP) competition. We have shown that GNEIMO torsional MD method leads to refinement of up to 1.3 Å in the root-mean-square deviation in coordinates for 30 CASP target proteins without using any experimental data as restraints in performing the GNEIMO simulations. This is in contrast with the unconstrained all-atom Cartesian MD method performed under the same conditions, where refinement requires the use of restraints during the simulations

Dynamic Behavior of the Active and Inactive States of the Adenosine A_2A Receptor

The adenosine A_2A receptor (A_2AR) belongs to the superfamily of membrane proteins called the G-protein-coupled receptors (GPCRs) that form one of the largest superfamilies of drug targets. Deriving thermostable mutants has been one of the strategies used for crystallization of A_2AR in both the agonist and antagonist bound conformational states. The crystal structures do not reveal differences in the activation mechanism of the mutant receptors compared to the wild type receptor, that have been observed experimentally. These differences stem from the dynamic behavior of the mutant receptors. Furthermore, it is not understood how the mutations confer thermostability. Since these details are difficult to obtain from experiments, we have used atomic level simulations to elucidate the dynamic behavior of the agonist and antagonist bound mutants as well the wild type A_2AR. We found that significant enthalpic contribution leads to stabilization of both the inactive state (StaR2) and active-like state (GL31) thermostable mutants of A_2AR. Stabilization resulting from mutations of bulky residues to alanine is due to the formation of interhelical hydrogen bonds and van der Waals packing that improves the transmembrane domain packing. The thermostable mutant GL31 shows less movement of the transmembrane helix TM6 with respect to TM3 than the wild type receptor. While restricted dynamics of GL31 is advantageous in its purification and crystallization, it could also be the reason why these mutants are not efficient in activating the G proteins. We observed that the calculated stress on each residue is higher in the wild type receptor compared to the thermostable mutants, and this stress is required for activation to occur. Thus, reduced dynamic behavior of the thermostable mutants leading to lowered activation of these receptors originates from reduced stress on each residue. Finally, accurate calculation of the change in free energy for single mutations shows good correlation with the change in the measured thermostability. These results provide insights into the effect of mutations that can be incorporated in deriving thermostable mutants for other GPCRs

Structure Refinement of Protein Low Resolution Models Using the GNEIMO Constrained Dynamics Method

The challenge in protein structure prediction using homology modeling is the lack of reliable methods to refine the low resolution homology models. Unconstrained all-atom molecular dynamics (MD) does not serve well for structure refinement due to its limited conformational search. We have developed and tested the constrained MD method, based on the generalized Newton–Euler inverse mass operator (GNEIMO) algorithm for protein structure refinement. In this method, the high-frequency degrees of freedom are replaced with hard holonomic constraints and a protein is modeled as a collection of rigid body clusters connected by flexible torsional hinges. This allows larger integration time steps and enhances the conformational search space. In this work, we have demonstrated the use of torsional GNEIMO method without using any experimental data as constraints, for protein structure refinement starting from low-resolution decoy sets derived from homology methods. In the eight proteins with three decoys for each, we observed an improvement of ∼2 Å in the rmsd in coordinates to the known experimental structures of these proteins. The GNEIMO trajectories also showed enrichment in the population density of native-like conformations. In addition, we demonstrated structural refinement using a “freeze and thaw” clustering scheme with the GNEIMO framework as a viable tool for enhancing localized conformational search. We have derived a robust protocol based on the GNEIMO replica exchange method for protein structure refinement that can be readily extended to other proteins and possibly applicable for high throughput protein structure refinement

Computational Method To Identify Druggable Binding Sites That Target Protein–Protein Interactions

Protein–protein interactions are implicated in the pathogenesis of many diseases and are therefore attractive but challenging targets for drug design. One of the challenges in development is the identification of potential druggable binding sites in protein interacting interfaces. Identification of interface surfaces can greatly aid rational drug design of small molecules inhibiting protein–protein interactions. In this work, starting from the structure of a free monomer, we have developed a ligand docking based method, called “<i>FindBindSite</i>” (FBS), to locate protein–protein interacting interface regions and potential druggable sites in this interface. <i>FindBindSite</i> utilizes the results from docking a small and diverse library of small molecules to the entire protein structure. By clustering regions with the highest docked ligand density from FBS, we have shown that these high ligand density regions strongly correlate with the known protein–protein interacting surfaces. We have further predicted potential druggable binding sites on the protein surface using FBS, with druggability being defined as the site with high density of ligands docked. FBS shows a hit rate of 71% with high confidence and 93% with lower confidence for the 41 proteins used for predicting druggable binding sites on the protein–protein interface. Mining the regions of lower ligand density that are contiguous with the high scoring high ligand density regions from FBS, we were able to map 70% of the protein–protein interacting surface in 24 out of 41 structures tested. We also observed that FBS has limited sensitivity to the size and nature of the small molecule library used for docking. The experimentally determined hotspot residues for each protein–protein complex cluster near the best scoring druggable binding sites identified by FBS. These results validate the ability of our technique to identify druggable sites within protein–protein interface regions that have the maximal possibility of interface disruption

Thermostabilization of the β₁‑Adrenergic Receptor Correlates with Increased Entropy of the Inactive State

The dynamic nature of GPCRs is a major hurdle in their purification and crystallization. Thermostabilization can facilitate GPCR structure determination, as has been shown by the structure of the thermostabilized β₁-adrenergic receptor (β₁AR) mutant, m23-β₁AR, which has been thermostabilized in the inactive state. However, it is unclear from the structure how the six thermostabilizing mutations in m23-β₁AR affect receptor dynamics. We have used molecular dynamics simulations in explicit solvent to compare the conformational ensembles for both wild type β₁AR (wt-β₁AR) and m23-β₁AR. Thermostabilization results in an increase in the number of accessible microscopic conformational states within the inactive state ensemble, effectively increasing the side chain entropy of the inactive state at room temperature, while suppressing large-scale main chain conformational changes that lead to activation. We identified several diverse mechanisms of thermostabilization upon mutation. These include decrease of long-range correlated movement between residues in the G-protein coupling site to the extracellular region (Y227A^5.58, F338M^7.48), formation of new hydrogen bonds (R68S), and reduction of local stress (Y227^5.58, F327^7.37, and F338^7.48). This study provides insights into microscopic mechanisms underlying thermostability that leads to an understanding of the effect of these mutations on the structure of the receptor

How Do Short Chain Nonionic Detergents Destabilize G‑Protein-Coupled Receptors?

Stability of detergent-solubilized G-protein-coupled receptors (GPCRs) is crucial for their purification in a biologically relevant state, and it is well-known that short chain detergents such as octylglucoside are more denaturing than long chain detergents such as dodecylmaltoside. However, the molecular basis for this phenomenon is poorly understood. To gain insights into the mechanism of detergent destabilization of GPCRs, we used atomistic molecular dynamics simulations of thermostabilized adenosine receptor (A_2AR) mutants embedded in either a lipid bilayer or detergent micelles of alkylmaltosides and alkylglucosides. A_2AR mutants in dodecylmaltoside or phospholipid showed low flexibility and good interhelical packing. In contrast, A_2AR mutants in either octylglucoside or nonylglucoside showed decreased α-helicity in transmembrane regions, decreased α-helical packing, and the interpenetration of detergent molecules between transmembrane α-helices. This was not observed in octylglucoside containing phospholipid. Cholesteryl hemisuccinate in dodecylmaltoside increased the energetic stability of the receptor by wedging into crevices on the hydrophobic surface of A_2AR, increasing packing interactions within the receptor and stiffening the detergent micelle. The data suggest a three-stage process for the initial events in the destabilization of GPCRs by octylglucoside: (i) highly mobile detergent molecules form small micelles around the receptor; (ii) loss of α-helicity and decreased interhelical packing interactions in transmembrane regions are promoted by increased receptor thermal motion; (iii) transient separation of transmembrane helices allowed penetration of detergent molecules into the core of the receptor. The relative hydration of the headgroup and alkyl chain correlates with detergent harshness and suggests new avenues to develop milder versions of octylglucoside for receptor crystallization