Dissociation Rate Calculation via Constant-Force Steered Molecular Dynamics Simulation.

Steered molecular dynamics (SMD) simulations are used to study molecular dissociation events by applying a harmonic force to the molecules and pulling them at a constant velocity. Instead of constant-velocity pulling, we use a constant force: the constant-force SMD (CF-SMD) simulation. The CF-SMD simulation employs a constant force to reduce the activation barrier of molecular dissociation, thereby enhancing the dissociation event. Here, we present the capability of the CF-SMD simulation to estimate the dissociation time at equilibrium. We performed all-atom CF-SMD simulations for NaCl and protein-ligand systems, producing dissociation time at various forces. We extrapolated these values to the dissociation rate without a constant force using Bell's model or the Dudko-Hummer-Szabo model. We demonstrate that the CF-SMD simulations with the models predicted the dissociation time in equilibrium. A CF-SMD simulation is a powerful tool for estimating the dissociation rate in a direct and computationally efficient manner.

Fly casting with ligand sliding and orientational selection supporting complex formation of a GPCR and a middle sized flexible molecule.

A GA-guided multidimensional virtual-system coupled molecular dynamics (GA-mD-VcMD) simulation was conducted to elucidate binding mechanisms of a middle-sized flexible molecule, bosentan, to a GPCR protein, human endothelin receptor type B (hETB). GA-mD-VcMD is a generalized ensemble method that produces a free-energy landscape of the ligand-receptor binding by searching large-scale motions accompanied with stable maintenance of the fragile cell-membrane structure. All molecular components (bosentan, hETB, membrane, and solvent) were represented with an all-atom model. Then sampling was conducted from conformations where bosentan was distant from the binding site in the hETB binding pocket. The deepest basin in the resultant free-energy landscape was assigned to native-like complex conformation. The following binding mechanism was inferred. First, bosentan fluctuating randomly in solution is captured using a tip region of the flexible N-terminal tail of hETB via nonspecific attractive interactions (fly casting). Bosentan then slides occasionally from the tip to the root of the N-terminal tail (ligand-sliding). During this sliding, bosentan passes the gate of the binding pocket from outside to inside of the pocket with an accompanying rapid reduction of the molecular orientational variety of bosentan (orientational selection). Last, in the pocket, ligand-receptor attractive native contacts are formed. Eventually, the native-like complex is completed. The bosentan-captured conformations by the tip-region and root-region of the N-terminal tail correspond to two basins in the free-energy landscape. The ligand-sliding corresponds to overcoming of a free-energy barrier between the basins.

Free energy and kinetic rate calculation via non-equilibrium molecular simulation: application to biomolecules.

Non-equilibrium molecular dynamics (NEMD) simulation has been recognized as a powerful tool for examining biomolecules and provides fruitful insights into not only non-equilibrium but also equilibrium processes. We review recent advances in NEMD simulation and relevant, fundamental results of non-equilibrium statistical mechanics. We first introduce Crooks fluctuation theorem and Jarzynski equality that relate free energy difference to work done on a physical system during a non-equilibrium process. The theorems are beneficial for the analysis of NEMD trajectories. We then describe rate theory, a framework to calculate molecular kinetics from a non-equilibrium process; this theoretical framework enables us to calculate a reaction time-mean-first passage time-from NEMD trajectories. We, in turn, present recent NEMD techniques that apply an external force to a system to enhance molecular dissociation and introduce their application to biomolecules. Lastly, we show the current status of an appropriate selection of reaction coordinates for NEMD simulation.

Asymmetric dynamics of dimeric SARS-CoV-2 and SARS-CoV main proteases in an apo form: Molecular dynamics study on fluctuations of active site, catalytic dyad, and hydration water.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been widely spread around the world. It is necessary to examine the viral proteins that play a notorious role in the invasion of our body. The main protease (3CLpro) facilitates the maturation of the coronavirus. It is thought that the dimerization of 3CLpro leads to its catalytic activity; the detailed mechanism has, however, not been suggested. Furthermore, the structural differences between the predecessor SARS-CoV 3CLpro and SARS-CoV-2 3CLpro have not been fully understood. Here, we show the structural and dynamical differences between the two main proteases, and demonstrate the relationship between the dimerization and the activity via atomistic molecular dynamics simulations. Simulating monomeric and dimeric 3CLpro systems for each protease, we show that (i) global dynamics between the two different proteases are not conserved, (ii) the dimerization stabilizes the catalytic dyad and hydration water molecules behind the dyad, and (iii) the substrate-binding site (active site) and hydration water molecules in each protomer fluctuate asymmetrically. We then speculate the roles of hydration water molecules in their catalytic activity.

Continuum mechanical parameterisation of cytoplasmic dynein from atomistic simulation.

Cytoplasmic dynein is responsible for intra-cellular transport in eukaryotic cells. Using Fluctuating Finite Element Analysis (FFEA), a novel algorithm that represents proteins as continuum viscoelastic solids subject to thermal noise, we are building computational tools to study the mechanics of these molecular machines. Here we present a methodology for obtaining the material parameters required to represent the flexibility of cytoplasmic dynein within FFEA from atomistic molecular dynamics (MD) simulations, and show that this continuum representation is sufficient to capture the principal dynamic properties of the motor.

Structural Fluctuations of Aromatic Residues in an Apo-Form Reveal Cryptic Binding Sites: Implications for Fragment-Based Drug Design.

Cryptic sites are binding pockets that are transiently formed in an apo form or that are induced by ligand binding. The investigation of cryptic sites is crucial for drug discovery, since these sites are ubiquitous in disease-related human proteins, and targeting them expands the number of drug targets greatly. However, although many computational studies have attempted to identify cryptic sites, the detection remains challenging. Here, we aimed to characterize and detect cryptic sites in terms of structural fluctuations in an apo form, investigating proteins each of which possesses a cryptic site. From their X-ray structures, we saw that aromatic residues tended to be found in cryptic sites. To examine structural fluctuations of the apo forms, we performed molecular dynamics (MD) simulations, producing probability distributions of the solvent-accessible surface area per aromatic residue. To detect aromatic residues in cryptic sites, we have proposed a "cryptic-site index" based on the distribution, demonstrating the performance via several measures, such as recall and specificity. Besides, we found that high-ranking aromatic residues were likely to probe concaves in a cryptic site. This implies that such fluctuations provide a profile of scaffolds of compounds with the potential to bind to a particular cryptic site.

Multimodal Structural Distribution of the p53 C-Terminal Domain upon Binding to S100B via a Generalized Ensemble Method: From Disorder to Extradisorder.

Intrinsically disordered regions (IDRs) of a protein employ a flexible binding manner when recognizing a partner molecule. Moreover, it is recognized that binding of IDRs to a partner molecule is accompanied by folding, with a variety of bound conformations often being allowed in formation of the complex. In this study, we investigated a fragment of the disordered p53 C-terminal domain (CTDf) that interacts with one of its partner molecules, S100B, as a representative IDR. Although the 3D structure of CTDf in complex with S100B has been previously reported, the specific interactions remained controversial. To clarify these interactions, we performed generalized ensemble molecular dynamics (MD) simulations (virtual-system coupled multicanonical MD, termed V-McMD), which enable effective conformational sampling beyond that provided by conventional MD. These simulations generated a multimodal structural distribution for our system including CTDf and S100B, indicating that CTDf forms a variety of complex structures upon binding to S100B. We confirmed that our results are consistent with chemical shift perturbations and nuclear Overhauser effects that were observed in previous studies. Furthermore, we calculated the conformational entropy of CTDf in bound and isolated (free) states. Comparison of these CTDf entropies indicated that the disordered CTDf shows further increase in conformational diversity upon binding to S100B. Such entropy gain by binding may comprise an important feature of complex formation for IDRs.

Variation of free-energy landscape of the p53 C-terminal domain induced by acetylation: Enhanced conformational sampling.

The C-terminal domain (CTD) of tumor suppressor protein p53 is an intrinsically disordered region that binds to various partner proteins, where lysine of CTD is acetylated/nonacetylated and histidine neutralized/non-neutralized. Because of the flexibility of the unbound CTD, a free-energy landscape (FEL) is a useful quantity for determining its statistical properties. We conducted enhanced conformational sampling of CTD in the unbound state via virtual system coupled multicanonical molecular dynamics, in which the lysine was acetylated or nonacetylated and histidine was charged or neutralized. The fragments were expressed by an all-atom model and were immersed in an explicit solvent. The acetylation and charge-neutralization varied FEL greatly, which might be convenient to exert a hub property. The acetylation slightly enhanced alpha-helix structures that are more compact than sheet/loop conformations. The charge-neutralization produced hairpins. Additionally, circular dichroism experiments confirmed the computational results. We propose possible binding mechanisms of CTD to partners by investigating FEL. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Enhanced conformational sampling to visualize a free-energy landscape of protein complex formation.

We introduce various, recently developed, generalized ensemble methods, which are useful to sample various molecular configurations emerging in the process of protein-protein or protein-ligand binding. The methods introduced here are those that have been or will be applied to biomolecular binding, where the biomolecules are treated as flexible molecules expressed by an all-atom model in an explicit solvent. Sampling produces an ensemble of conformations (snapshots) that are thermodynamically probable at room temperature. Then, projection of those conformations to an abstract low-dimensional space generates a free-energy landscape. As an example, we show a landscape of homo-dimer formation of an endothelin-1-like molecule computed using a generalized ensemble method. The lowest free-energy cluster at room temperature coincided precisely with the experimentally determined complex structure. Two minor clusters were also found in the landscape, which were largely different from the native complex form. Although those clusters were isolated at room temperature, with rising temperature a pathway emerged linking the lowest and second-lowest free-energy clusters, and a further temperature increment connected all the clusters. This exemplifies that the generalized ensemble method is a powerful tool for computing the free-energy landscape, by which one can discuss the thermodynamic stability of clusters and the temperature dependence of the cluster networks.