A directed essential dynamics simulation of peptide folding

Is the Triggering of PD-L1 Dimerization a Potential Mechanism for Food-Derived Small Molecules in Cancer Immunotherapy? A Study by Molecular Dynamics

Using small molecules to inhibit the PD-1/PD-L1 pathway is an important approach in cancer immunotherapy. Natural compounds such as capsaicin, zucapsaicin, 6-gingerol and curcumin have been proposed to have anticancer immunologic functions by downregulating the PD-L1 expression. PD-L1 dimerization promoted by small molecules was recently reported to be a potential mechanism to inhibit the PD-1/PD-L1 pathway. To clarify the molecular mechanism of such compounds on PD-L1 dimerization, molecular docking and molecular dynamics simulations were performed. The results evidenced that these compounds could inhibit PD-1/PD-L1 interactions by directly targeting PD-L1 dimerization. Binding free energy calculations showed that capsaicin, zucapsaicin, 6-gingerol and curcumin have strong binding ability with the PD-L1 dimer, where the affinities of them follow the trend of zucapsaicin > capsaicin > 6-gingerol ≈ curcumin. Analysis by residue energy decomposition, contact numbers and nonbonded interactions revealed that these compounds have a tight interaction with the C-sheet, F-sheet and G-sheet fragments of the PD-L1 dimer, which were also involved in the interactions with PD-1. Moreover, non-polar interactions between these compounds and the key residues Ile54, Tyr56, Met115 and Ala121 play a key role in stabilizing the protein−ligand complexes in solution, in which the 4′-hydroxy-3′-methoxyphenyl group and the carbonyl group of zucapsaicin, capsaicin, 6-ginger and curcumin were significant for the complexation of small molecules with the PD-L1 dimer. The conformational variations of these complexes were further analyzed by free energy landscape (FEL) and principal component analysis (PCA) and showed that these small molecules could make the structure of dimers more stable. This work provides a mechanism insight for food-derived small molecules blocking the PD-1/PD-L1 pathway via directly targeting the PD-L1 dimerization and offers theoretical guidance to discover more effective small molecular drugs in cancer immunotherapy.

Equilibrium Ensembles for Insulin Folding from Bias-Exchange Metadynamics

Earliest events in the aggregation process, such as single molecule reconfiguration, are extremely important and the most difficult to characterize in experiments. To this end, we have used well-tempered bias exchange metadynamics simulations to determine the equilibrium ensembles of an insulin molecule under amyloidogenic conditions of low pH and high temperature. A bin-based clustering method that uses statistics accumulated in bias exchange metadynamics trajectories was employed to construct a detailed thermodynamic and kinetic model of insulin folding. The highest lifetime, lowest free-energy ensemble identified consisted of native conformations adopted by a folded insulin monomer in solution, namely, the R-, the R^f-, and the T-states of insulin. The lowest free-energy structure had a root mean square deviation of only 0.15 nm from native x-ray structure. The second longest-lived metastable state was an unfolded, compact monomer with little similarity to the native structure. We have identified three additional long-lived, metastable states from the bin-based model. We then carried out an exhaustive structural characterization of metastable states on the basis of tertiary contact maps and per-residue accessible surface areas. We have also determined the lowest free-energy path between two longest-lived metastable states and confirm earlier findings of non-two-state folding for insulin through a folding intermediate. The ensemble containing the monomeric intermediate retained 58% of native hydrophobic contacts, however, accompanied by a complete loss of native secondary structure. We have discussed the relative importance of nativelike versus nonnative tertiary contacts for the folding transition. We also provide a simple measure to determine the importance of an individual residue for folding transition. Finally, we have compared and contrasted this intermediate with experimental data obtained in spectroscopic, crystallographic, and calorimetric measurements during early stages of insulin aggregation. We have also determined stability of monomeric insulin by incubation at a very low concentration to isolate protein-protein interaction effects.

Improving the replica-exchange molecular-dynamics method for efficient sampling in the temperature space

Replica-exchange molecular dynamics (REMD) is a popular sampling method in the molecular simulation. By frequently exchanging the replicas at different temperatures, the molecule can jump out of the minima and sample efficiently in the conformational space. Although REMD has been shown to be practical in a lot of applications, it does have a critical limitation. All the replicas at all the temperatures must be simulated for a period between the replica-exchange steps. This may be problematic for the reaction with high free energy barriers. In that case, too many replicas are required in the simulation. To reduce the calculation quantity and improve its performance, in this paper we propose a modified REMD method. During the simulation, each replica at each temperature can stay in either the active or inactive state and only switch between the states at the exchange step. In the active state, the replica moves freely in the canonical ensemble by the normal molecular dynamics, and in the inactive state, the replica is frozen temporarily until the next exchange step. The number of the replicas in the active states (active replicas) depends on the number of CPUs in the computer. Using the additional inactive replicas, one can perform an REMD simulation in a wider temperature space. The practical applications show that the modified REMD method is reliable. With the same number of active replicas, this REMD method can produce a more reasonable free energy surface around the free energy minima than the standard REMD method.

Predicting the impact of single-nucleotide polymorphisms in CDK2-flavopiridol complex by molecular dynamics analysis

Cyclic-dependent kinase 2 (CDK2) is one of the primary protein kinases involved in the regulation of cell cycle progression. Flavopiridol is a flavonoid derived from an indigenous plant act as a potent antitumor drug showing increased inhibitory activity toward CDK2. The presence of deleterious variations in CDK2 may produce different effects in drug-binding adaptability. Studies on nsSNPs of CDK2 gene will provide information on the most likely variants associated with the disease. Furthermore, investigating the relationship between deleterious variants and its ripple effect in the inhibitory action with drug will provide fundamental information for the development of personalized therapies. In this study, we predicted four variants Y15S, V18L, P45L, and V69A of CDK2 as highly deleterious. Occurrence of these variations seriously affected the normal binding capacity of flavopiridol with CDK2. Analysis of 10-ns molecular dynamics (MD) simulation trajectories indicated that the predicted deleterious variants altered the CDK2 stability, flexibility, and surface area. Notably, we noticed the decrease in number of hydrogen bonds between CDK2 and flavopiridol mutant complexes in the whole dynamic period. Overall, this study explores the possible relationship between the CDK2 deleterious variants and the drug-binding ability with the help of molecular docking and MD approaches.

Free-energy calculations along a high-dimensional fragmented path with constrained dynamics

Free-energy calculations for high-dimensional systems, such as peptides or proteins, always suffer from a serious sampling problem in a huge conformational space. For such systems, path-based free-energy methods, such as thermodynamic integration or free-energy perturbation, are good choices. However, both of them need sufficient sampling along a predefined transition path, which can only be controlled using restrained or constrained dynamics. Constrained simulations produce more reasonable free-energy profiles than restrained simulations. But calculations of standard constrained dynamics require an explicit expression of reaction coordinates as a function of Cartesian coordinates of all related atoms, which may be difficult to find for the complex transition of biomolecules. In this paper, we propose a practical solution: (1) We use restrained dynamics to define an optimized transition path, divide it into small fragments, and define a virtual reaction coordinate to denote a position along the path. (2) We use constrained dynamics to perform a formal free-energy calculation for each fragment and collect the values together to provide the entire free-energy profile. This method avoids the requirement to explicitly define reaction coordinates in Cartesian coordinates and provides a novel strategy to perform free-energy calculations for biomolecules along any complex transition path.

Enhanced sampling of molecular dynamics simulation of peptides and proteins by double coupling to thermal bath

Low sampling efficiency in conformational space is the well-known problem for conventional molecular dynamics. It greatly increases the difficulty for molecules to find the transition path to native state, and costs amount of CPU time. To accelerate the sampling, in this paper, we re-couple the critical degrees of freedom in the molecule to environment temperature, like dihedrals in generalized coordinates or nonhydrogen atoms in Cartesian coordinate. After applying to ALA dipeptide model, we find that this modified molecular dynamics greatly enhances the sampling behavior in the conformational space and provides more information about the state-to-state transition, while conventional molecular dynamics fails to do so. Moreover, from the results of 16 independent 100 ns simulations by the new method, it shows that trpzip2 has one-half chances to reach the naive state in all the trajectories, which is greatly higher than conventional molecular dynamics. Such an improvement would provide a potential way for searching the conformational space or predicting the most stable states of peptides and proteins.

Role of ligand binding in structural organization of add A-riboswitch aptamer: a molecular dynamics simulation

The specific binding of ligands is the first step of gene expression or translation regulation by riboswitches. However, understanding the mechanism of the specific binding is still difficult because the tertiary structures of the riboswitch aptamers are available almost only for ligand-bound state at present. In this paper we hope to give some insights into this problem through the studies of the role of ligand-aptamer interaction in the structural organization of add A-riboswitch aptamer, based on the crystal structure of the ligand-bound aptamer. We use all-atom molecular dynamics to simulate the behaviors of the aptamer in ligand-bound, free and mutated states by Amber force field. The results show that the correct paring of the ligand adenine with the nucleotide U74 in the binding pocket is crucial to stabilizing the conformations of the ligand-bound aptamer, especially the helix P1 connecting the expression platform. Our results also suggest that both the nucleotide U74 and U51 may be the key sites of the ligand recognition but the former has much higher probability as the initial docking site. This is in agreement with previous experimental results.

Order parameters for macromolecules: application to multiscale simulation

Order parameters (OPs) characterizing the nanoscale features of macromolecules are presented. They are generated in a general fashion so that they do not need to be redesigned with each new application. They evolve on time scales much longer than 10(-14) s typical for individual atomic collisions/vibrations. The list of OPs can be automatically increased, and completeness can be determined via a correlation analysis. They serve as the basis of a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Smoluchowski/Langevin equations of stochastic OP dynamics. Such OPs and the multiscale analysis imply computational algorithms that we demonstrate in an application to ribonucleic acid structural dynamics for 50 ns.

Molecular dynamics simulations of hemoglobin A in different states and bound to DPG: effector-linked perturbation of tertiary conformations and HbA concerted dynamics

Recent functional studies reported on human adult hemoglobin (HbA) show that heterotropic effector-linked tertiary structural changes are primarily responsible for modulating the oxygen affinity of hemoglobin. We present the results of 6-ns molecular dynamics simulations performed to gain insights into the dynamical and structural details of these effector-linked tertiary changes. All-atom simulations were carried out on a series of models generated for T- and R-state HbA, and for 2,3-diphosphoglycerate-bound models. Cross-correlation analyses identify both intra- and intersubunit correlated motions that are perturbed by the presence of the effector. Principal components analysis was used to decompose the covariance matrix extracted from the simulations and reconstruct the trajectories along the principal coordinates representative of functionally important collective motions. It is found that HbA in both quaternary states exists as ensembles of tertiary conformations that introduce dynamic heterogeneity in the protein. 2,3-Diphosphoglycerate induces significant perturbations in the fluctuations of both HbA states that translate into the protein visiting different tertiary conformations within each quaternary state. The analysis reveals that the presence of the effector affects the most important components of HbA motions and that heterotropic effectors modify the overall dynamics of the quaternary equilibrium via tertiary changes occurring in regions where conserved functionally significant residues are located, namely in the loop regions between helices C and E, E and F, and F and G, and in concerted helix motions. The changes are not apparent when comparing the available x-ray crystal structures in the presence and absence of effector, but are striking when comparing the respective dynamic tertiary conformations of the R and T tetramers.

Functional flexibility of human cyclin-dependent kinase-2 and its evolutionary conservation

Cyclin-dependent kinase 2 (CDK2) is the most thoroughly studied of the cyclin-dependent kinases that regulate essential cellular processes, including the cell cycle, and it has become a model for studies of regulatory mechanisms at the molecular level. This contribution identifies flexible and rigid regions of CDK2 based on temperature B-factors acquired from both X-ray data and molecular dynamics simulations. In addition, the biological relevance of the identified flexible regions and their motions is explored using information from the essential dynamics analysis related to conformational changes of CDK2 and knowledge of its biological function(s). The conserved regions of CMGC protein kinases' primary sequences are located in the most rigid regions identified in our analyses, with the sole exception of the absolutely conserved G13 in the tip of the glycine-rich loop. The conserved rigid regions are important for nucleotide binding, catalysis, and substrate recognition. In contrast, the most flexible regions correlate with those where large conformational changes occur during CDK2 regulation processes. The rigid regions flank and form a rigid skeleton for the flexible regions, which appear to provide the plasticity required for CDK2 regulation. Unlike the rigid regions (which as mentioned are highly conserved) no evidence of evolutionary conservation was found for the flexible regions.

Two-center-multipole expansion method: application to macromolecular systems

We propose a theoretical method for the calculation of the interaction energy between macromolecular systems at large distances. The method provides a linear scaling of the computing time with the system size and is considered as an alternative to the well-known fast multipole method. Its efficiency, accuracy, and applicability to macromolecular systems is analyzed and discussed in detail.

Improved sampling methods for molecular simulation

Molecular simulation has broad application in the biological sciences. One of the greatest challenges in molecular simulation is the limited conformational sampling due to slow barrier crossing on the rugged energy landscape of complex biomolecules and to the relatively short simulation time. Many enhanced sampling techniques have been developed over the years to alleviate this problem. Significant progress has been made in the past couple of years, with emerging methods targeting specific aspects of the potential energy surface and new variants of the replica exchange method.

Metadynamics in Essential Coordinates: Free Energy Simulation of Conformational Changes

We propose an approach that combines an extraction of collective motions of a molecular system with a sampling of its free energy surface. A recently introduced method of metadynamics allows exploration of the free energy surface of a molecular system by means of coarse-grained dynamics with flooding of free energy minima. This free energy surface is defined as a function of a set of collective variables (e.g., interatomic distances, angles, torsions, and others). In this study, essential coordinates determined by essential dynamics (principle component analysis) were used as collective variables in metadynamics. First, dynamics of the model system (explicitly solvated alanine dipeptide, Ace-Ala-Nme) was simulated by a classical molecular dynamics simulation. The trajectory (1 ns) was then analyzed by essential dynamics to obtain essential coordinates. The free energy surface as a function of the first and second essential coordinates was then explored by metadynamics. The resulting free energy surface is in agreement with other studies of this system. We propose that a combination of these two methods (metadynamics and essential dynamics) has great potential in studies of conformational changes in peptides and proteins.

Bayesian model based clustering analysis: application to a molecular dynamics trajectory of the HIV-1 integrase catalytic core

This work describes the application of a Bayesian method for clustering protein conformations sampled during a molecular dynamics simulation of the HIV-1 integrase catalytic core. A clustering analysis is carried out under the assumption of normal distribution without fixing the number of clusters in advance. Some performance measures, such as posterior probability and class cross entropy, are used to determine the most probable set of clusters. The Bayesian clustering method results in meaningful groups identifying transitions between conformational ensembles. The dihedral angles involved in such transitions are also examined in detail. The conformations in high dimensional space are projected into 3D space employing a multidimensional scaling technique to provide a visual inspection.

Molecular dynamics simulations of folding processes of a β-hairpin in an implicit solvent

Computer simulations of beta-hairpin folding are relatively difficult, especially those based on the explicit water model. This greatly limits the complete analysis and understanding of their folding mechanisms. In this paper, we use the generalized Born/solvent accessible implicit solvent model to simulate the folding processes of a nine-residue beta-hairpin. We find that the beta-hairpin can fold into its native structure very easily, even using the traditional molecular dynamics method. This allows us to extract 21 complete folding events and investigate the folding process sufficiently. Our results show that there exist four most stable states on the free energy landscape of the short peptide, one native state and three intermediates. We find that two of the non-native stable states have almost the same potential energy as the native state but with lower entropy. This suggests that the native state can be stabilized entropically. Furthermore, we find that the folding processes of this peptide have common features: to fold into its native state, the peptide undergoes a continuous collapsing-extending-recollapsing process to adjust the positions of the side chains in order to form the native middle inter-strand hydrogen bonds. The formations of these bonds are the key step of the folding process. Once these bonds are formed, the peptide can fold into the native state quickly.

Role of disulfide bonds in modulating internal motions of proteins to tune their function: molecular dynamics simulation of scorpion toxin Lqh III

A series of 1-ns MD simulations were performed on the scorpion toxin Lqh III in native and disulfide bond broken states. The removal of disulfide bonds has caused hydrogen bond network alteration in the five-residue turn, the long loop, the alpha-helix, the loop connecting strands II and III, and the C-terminal region. In addition and more importantly, it has influenced the amplitude of the fluctuations of five-residue turn, loops, and C-terminal region with a minor effect on the fluctuations of the cysteines in the broken bond sites. These findings suggest that disulfide bonds are not the most important factors in rigidifying their own locations, while they have more important effects at a global scale. Furthermore, our results reveal that disulfide bonds have considerable influence on the functionally important essential modes of motions and the correlations between the motions of the binding site residues. Therefore, we can conclude that disulfide bonds have a crucial role in modulating the function via adjusting the dynamics of scorpion toxin molecules. Although this conclusion cannot be generalized to all peptides and proteins, it demonstrates the importance of more investigations on this aspect of disulfide bond efficacy.