The use of a generalized born model for the analysis of protein conformational transitions: a comparative study with explicit solvent simulations for chemotaxis Y protein (CheY)

Enhancing backbone sampling in Monte Carlo simulations using internal coordinates normal mode analysis

Normal mode methods are becoming a popular alternative to sample the conformational landscape of proteins. In this study, we describe the implementation of an internal coordinate normal mode analysis method and its application in exploring protein flexibility by using the Monte Carlo method PELE. This new method alternates two different stages, a perturbation of the backbone through the application of torsional normal modes, and a resampling of the side chains. We have evaluated the new approach using two test systems, ubiquitin and c-Src kinase, and the differences to the original ANM method are assessed by comparing both results to reference molecular dynamics simulations. The results suggest that the sampled phase space in the internal coordinate approach is closer to the molecular dynamics phase space than the one coming from a Cartesian coordinate anisotropic network model. In addition, the new method shows a great speedup (∼5-7×), making it a good candidate for future normal mode implementations in Monte Carlo methods.

Evaluating the dynamics and electrostatic interactions of folded proteins in implicit solvents

Three implicit solvent models, namely GBMVII, FACTS, and SCPISM, were evaluated for their abilities to emulate an explicit solvent environment by comparing the simulated conformational ensembles, dynamics, and electrostatic interactions of the Src SH2 domain and the Lyn kinase domain. This assessment in terms of structural features in folded proteins expands upon the use of hydration energy as a metric for comparison. All-against-all rms coordinate deviation, average positional fluctuations, and ion-pair distance distribution were used to compare the implicit solvent models with the TIP3P explicit solvent model. Our study shows that the Src SH2 domains solvated with TIP3P, GBMVII, and FACTS sample similar global conformations. Additionally, the Src SH2 ion-pair distance distributions of solvent-exposed side chains corresponding to TIP3P, GBMVII, and FACTS do not differ substantially, indicating that GBMVII and FACTS are capable of modeling these electrostatic interactions. The ion-pair distance distributions of SCPISM are distinct from others, demonstrating that these electrostatic interactions are not adequately reproduced with the SCPISM model. On the other hand, for the Lyn kinase domain, a non-globular protein with bilobal structure and a large concavity on the surface, implicit solvent does not accurately model solvation to faithfully reproduce partially buried electrostatic interactions and lobe-lobe conformations. Our work reveals that local structure and dynamics of small, globular proteins are modeled well using FACTS and GBMVII. Nonetheless, global conformations and electrostatic interactions in concavities of multi-lobal proteins resulting from simulations with implicit solvent models do not match those obtained from explicit water simulations.

Free Energy Calculations for the Peripheral Binding of Proteins/Peptides to an Anionic Membrane. 1. Implicit Membrane Models

The binding of peptides and proteins to the surface of complex lipid membranes is important in many biological processes such as cell signaling and membrane remodeling. Computational studies can aid experiments by identifying physical interactions and structural motifs that determine the binding affinity and specificity. However, previous studies focused on either qualitative behaviors of protein/membrane interactions or the binding affinity of small peptides. Motivated by this observation, we set out to develop computational protocols for bimolecular binding to charged membranes that are applicable to both peptides and large proteins. In this work, we explore a method based on an implicit membrane/solvent model (generalized Born with a simple switching in combination with the Gouy-Chapman-Stern model for a charged interface), which we expect to lead to useful results when the binding does not implicate significant membrane deformation and local demixing of lipids. We show that the binding free energy can be efficiently computed following a thermodynamic cycle similar to protein-ligand binding calculations, especially when a Bennett acceptance ratio based protocol is used to consider both the membrane bound and solution conformational ensembles. Test calculations on a series of peptides show that our computational approach leads to binding affinities in encouraging agreement with experimental data, including for the challenging example of the bringing of flexible MARCKS-ED peptides to membranes. The calculations highlight that for a membrane with a significant fraction of anionic lipids, it is essential to include the effect of ion adsorption using the Stern model, which significantly modifies the effective surface charge. This implicit membrane model based computational protocol helps lay the groundwork for more systematic analysis of protein/peptide binding to membranes of complex shape and composition.

Mapping conformational dynamics of proteins using torsional dynamics simulations

All-atom molecular dynamics simulations are widely used to study the flexibility of protein conformations. However, enhanced sampling techniques are required for simulating protein dynamics that occur on the millisecond timescale. In this work, we show that torsional molecular dynamics simulations enhance protein conformational sampling by performing conformational search in the low-frequency torsional degrees of freedom. In this article, we use our recently developed torsional-dynamics method called Generalized Newton-Euler Inverse Mass Operator (GNEIMO) to study the conformational dynamics of four proteins. We investigate the use of the GNEIMO method in simulations of the conformationally flexible proteins fasciculin and calmodulin, as well as the less flexible crambin and bovine pancreatic trypsin inhibitor. For the latter two proteins, the GNEIMO simulations with an implicit-solvent model reproduced the average protein structural fluctuations and sample conformations similar to those from Cartesian simulations with explicit solvent. The application of GNEIMO with replica exchange to the study of fasciculin conformational dynamics produced sampling of two of this protein's experimentally established conformational substates. Conformational transition of calmodulin from the Ca(2+)-bound to the Ca(2+)-free conformation occurred readily with GNEIMO simulations. Moreover, the GNEIMO method generated an ensemble of conformations that satisfy about half of both short- and long-range interresidue distances obtained from NMR structures of holo to apo transitions in calmodulin. Although unconstrained all-atom Cartesian simulations have failed to sample transitions between the substates of fasciculin and calmodulin, GNEIMO simulations show the transitions in both systems. The relatively short simulation times required to capture these long-timescale conformational dynamics indicate that GNEIMO is a promising molecular-dynamics technique for studying domain motion in proteins.

Molecular dynamics of ribosomal elongation factors G and Tu

Translation on the ribosome is controlled by external factors. During polypeptide lengthening, elongation factors EF-Tu and EF-G consecutively interact with the bacterial ribosome. EF-Tu binds and delivers an aminoacyl-tRNA to the ribosomal A site and EF-G helps translocate the tRNAs between their binding sites after the peptide bond is formed. These processes occur at the expense of GTP. EF-Tu:tRNA and EF-G are of similar shape, share a common binding site, and undergo large conformational changes on interaction with the ribosome. To characterize the internal motion of these two elongation factors, we used 25 ns long all-atom molecular dynamics simulations. We observed enhanced mobility of EF-G domains III, IV, and V and of tRNA in the EF-Tu:tRNA complex. EF-Tu:GDP complex acquired a configuration different from that found in the crystal structure of EF-Tu with a GTP analogue, showing conformational changes in the switch I and II regions. The calculated electrostatic properties of elongation factors showed no global similarity even though matching electrostatic surface patches were found around the domain I that contacts the ribosome, and in the GDP/GTP binding region.

Bounding the electrostatic free energies associated with linear continuum models of molecular solvation

The importance of electrostatic interactions in molecular biology has driven extensive research toward the development of accurate and efficient theoretical and computational models. Linear continuum electrostatic theory has been surprisingly successful, but the computational costs associated with solving the associated partial differential equations (PDEs) preclude the theory's use in most dynamical simulations. Modern generalized-Born models for electrostatics can reproduce PDE-based calculations to within a few percent and are extremely computationally efficient but do not always faithfully reproduce interactions between chemical groups. Recent work has shown that a boundary-integral-equation formulation of the PDE problem leads naturally to a new approach called boundary-integral-based electrostatics estimation (BIBEE) to approximate electrostatic interactions. In the present paper, we prove that the BIBEE method can be used to rigorously bound the actual continuum-theory electrostatic free energy. The bounds are validated using a set of more than 600 proteins. Detailed numerical results are presented for structures of the peptide met-enkephalin taken from a molecular-dynamics simulation. These bounds, in combination with our demonstration that the BIBEE methods accurately reproduce pairwise interactions, suggest a new approach toward building a highly accurate yet computationally tractable electrostatic model.

Calculation of protein heat capacity from replica-exchange molecular dynamics simulations with different implicit solvent models

The heat capacity has played a major role in relating microscopic and macroscopic properties of proteins and their disorder-order phase transition of folding. Its calculation by atomistic simulation methods remains a significant challenge due to the complex and dynamic nature of protein structures, their solvent environment, and configurational averaging. To better understand these factors on calculating a protein heat capacity, we provide a comparative analysis of simulation models that differ in their implicit solvent description and force-field resolution. Our model protein system is the src Homology 3 (SH3) domain of alpha-spectrin, and we report a series of 10 ns replica-exchange molecular dynamics simulations performed at temperatures ranging from 298 to 550 K, starting from the SH3 native structure. We apply the all-atom CHARMM22 force field with different modified analytical generalized Born solvent models (GBSW and GBMV2) and compare these simulation models with the distance-dependent dielectric screening of charge-charge interactions. A further comparison is provided with the united-atom CHARMM19 plus a pairwise GB model. Unfolding-folding transition temperatures of SH3 were estimated from the temperature-dependent profiles of the heat capacity, root-mean-square distance from the native structure, and the fraction of native contacts, each calculated from the density of states by using the weighted histogram analysis method. We observed that, for CHARMM22, the unfolding transition and energy probability density were quite sensitive to the implicit solvent description, in particular, the treatment of the protein-solvent dielectric boundary in GB models and their surface-area-based hydrophobic term. Among the solvent models tested, the calculated melting temperature varied in the range 353-438 K and was higher than the experimental value near 340 K. A reformulated GBMV2 model of employing a smoother molecular-volume dielectric interface was the most accurate in reproducing the native conformation and a two-state folding landscape, although the melting transition temperature did not show the smallest deviation from experiment. For the lower-resolution CHARMM19/GB model, the simulations failed to yield a bimodal energy distribution, yet the melting temperature was observed to be a good estimate of higher-resolution simulation models. We also demonstrate that a careful analysis of a relatively long simulation is necessary to avoid trapping in local minima and to find a true thermodynamic transition temperature.

Interpreting the Coulomb-field approximation for generalized-Born electrostatics using boundary-integral equation theory

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms.

Establishing effective simulation protocols for beta- and alpha/beta-peptides. II. Molecular mechanical (MM) model for a cyclic beta-residue

All-atom molecular mechanical (MM) force field parameters are developed for a cyclic beta-amino acid, amino-cyclo-pentane-carboxylic acid (ACPC), using a multi-objective evolutionary algorithm. The MM model is benchmarked using several short, ACPC-containing alpha/beta-peptides in water and methanol with SCC-DFTB (self consistent charge-density functional tight binding)/MM simulations as the reference. Satisfactory agreements are found between the MM and SCC-DFTB/MM results regarding the distribution of key dihedral angles for the tetra-alpha/beta-peptide in water. For the octa-alpha/beta-peptide in methanol, the MM and SCC-DFTB/MM simulations predict the 11- and 14/15-helical form as the more stable conformation, respectively; however, the two helical forms are very close in energy (2-4 kcal/mol) at both theoretical levels, which is also the conclusion from recent NMR experiments. As the first application, the MM model is applied to an alpha/beta-pentadeca-peptide in water with both explicit and implicit solvent models. The stability of the peptide is sensitive to the starting configuration in the explicit solvent simulations due to their limited length ( approximately 10-40 ns). Multiple ( approximately 20 x 20 ns) implicit solvent simulations consistently show that the 14/15-helix is the predominant conformation of this peptide, although substantially different conformations are also accessible. The calculated nuclear Overhauser effect (NOE) values averaged over different trajectories are consistent with experimental data, which emphasizes the importance of considering conformational heterogeneity in such comparisons for highly dynamical peptides.