Internal coordinate molecular dynamics (ICMD) methods provide a more natural description of a protein by using bond, angle and torsional coordinates instead of a Cartesian coordinate representation. Freezing high frequency bonds and angles in the ICMD model gives rise to constrained ICMD (CICMD) models. There are several theoretical aspects that need to be developed in order to make the CICMD method robust and widely usable. In this paper we have designed a new framework for 1) initializing velocities for non-independent CICMD coordinates, 2) efficient computation of center of mass velocity during CICMD simulations, 3) using advanced integrators such as Runge-Kutta, Lobatto and adaptive CVODE for CICMD simulations, and 4) cancelling out the “flying ice cube effect” that sometimes arises in Nosé-Hoover dynamics. The Generalized Newton-Euler Inverse Mass Operator (GNEIMO) method is an implementation of a CICMD method that we have developed to study protein dynamics. GNEIMO allows for a hierarchy of coarse-grained simulation models based on the ability to rigidly constrain any group of atoms. In this paper, we perform tests on the Lobatto and Runge-Kutta integrators to determine optimal simulation parameters. We also implement an adaptive coarse graining tool using the GNEIMO Python interface. This tool enables the secondary structure-guided “freezing and thawing” of degrees of freedom in the molecule on the fly during MD simulations, and is shown to fold four proteins to their native topologies. With these advancements we envision the use of the GNEIMO method in protein structure prediction, structure refinement, and in studying domain motion.

The focus of this paper is to examine whether conformational search using constrained molecular dynamics (MD) method is more enhanced and enriched towards “native-like” structures compared to all-atom MD for the protein folding as a model problem. Constrained MD methods provide an alternate MD tool for protein structure prediction and structure refinement. It is computationally expensive to perform all-atom simulations of protein folding because the processes occur on a timescale of microseconds. Compared to the all-atom MD simulation, constrained MD methods have the advantage that stable dynamics can be achieved for larger time steps and the number of degrees of freedom is an order of magnitude smaller, leading to a decrease in computational cost. We have developed a generalized constrained MD method that allows the user to “freeze and thaw” torsional degrees of freedom as fit for the problem studied. We have used this method to perform all-torsion constrained MD in implicit solvent coupled with the replica exchange method to study folding of small proteins with various secondary structural motifs such as, α-helix (polyalanine, WALP16), β-turn (1E0Q), and a mixed motif protein (Trp-cage). We demonstrate that constrained MD replica exchange method exhibits a wider conformational search than all-atom MD with increased enrichment of near native structures. “Hierarchical” constrained MD simulations, where the partially formed helical regions in the initial stretch of the all-torsion folding simulation trajectory of Trp-cage were frozen, showed a better sampling of near native structures than all-torsion constrained MD simulations. This is in agreement with the zipping-and-assembly folding model put forth by Dill and coworkers for folding proteins. The use of hierarchical “freeze and thaw” clustering schemes in constrained MD simulation can be used to sample conformations that contribute significantly to folding of proteins.

Recent experiments to derive a thermally stable mutant of turkey beta-1-adrenergic receptor (beta1AR) have shown that a combination of six single point mutations resulted in a 20 degrees C increase in thermal stability in mutant beta1AR. Here we have used the all-atom force-field energy function to calculate a stability score to detect stabilizing point mutations in G-protein coupled receptors. The calculated stability score shows good correlation with the measured thermal stability for 76 single point mutations and 22 multiple mutants in beta1AR. We have demonstrated that conformational sampling of the receptor for various mutants improve the prediction of thermal stability by 50%. Point mutations Y227A5.58, V230A5.61, and F338M7.48 in the thermally stable mutant m23-beta1AR stabilizes key microdomains of the receptor in the inactive conformation. The Y227A5.58 and V230A5.61 mutations stabilize the ionic lock between R139(3.50) on transmembrane helix3 and E285(6.30) on transmembrane helix6. The mutation F338M7.48 on TM7 alters the interaction of the conserved motif NPxxY(x)5,6F with helix8 and hence modulates the interaction of TM2-TM7-helix8 microdomain. The D186-R317 salt bridge (in extracellular loops 2 and 3) is stabilized in the cyanopindolol-bound wild-type beta1AR, whereas the salt bridge between D184-R317 is preferred in the mutant m23. We propose that this could be the surrogate to a similar salt bridge found between the extracellular loop 2 and TM7 in beta2AR reported recently. We show that the binding energy difference between the inactive and active states is less in m23 compared to the wild-type, which explains the activation of m23 at higher norepinephrine concentration compared to the wild-type. Results from this work throw light into the mechanism behind stabilizing mutations. The computational scheme proposed in this work could be used to design stabilizing mutations for other G-protein coupled receptors.

We present a critical assessment of the performance of our homology model refinement method for G-protein coupled receptors (GPCRs), called LITICon, that led to top ranking structures in a recent structure prediction assessment GPCRDOCK2010. GPCRs form the largest class of drug targets for which only a few crystal structures are currently available. Therefore accurate homology models are essential for drug design in these receptors. We submitted five models each for human chemokine CXCR4 (bound to small molecule IT1t and peptide CVX15) and dopamine D3DR (bound to small molecule eticlopride) before the crystal structures were published. Our models in both CXCR4/IT1t and D3/eticlopride assessments were ranked first and second respectively by ligand RMSD to the crystal structures. For both receptors, we developed two types of protein models: homology models based on known GPCR crystal structures, and ab initio models based on the prediction method MembStruk. The homology based models compared better to the crystal structures than the ab initio models. However a robust refinement procedure for obtaining high accuracy structures is needed. We demonstrate that optimization of the helical tilt, rotation and translation are vital for GPCR homology model refinement. As a proof of concept, our in-house refinement program LITiCon captured the distinct orientation of TM2 in CXCR4, which differs from that of adrenoreceptors. These findings would be critical for refining GPCR homology models in future.

A self-consistent model for a finite-size non-neutral ultracold plasma is obtained by extending a conventional model of globular star clusters. This model describes the dynamics of electrons at quasi-equilibrium trapped within the potential created by a cloud of stationary ions. A random sample of electron positions and velocities can be generated with the statistical properties defined by this model.