Variational implicit-solvent predictions of the dry-wet transition pathways for ligand-receptor binding and unbinding kinetics.

Ligand-receptor binding and unbinding are fundamental biomolecular processes and particularly essential to drug efficacy. Environmental water fluctuations, however, impact the corresponding thermodynamics and kinetics and thereby challenge theoretical descriptions. Here, we devise a holistic, implicit-solvent, multimethod approach to predict the (un)binding kinetics for a generic ligand-pocket model. We use the variational implicit-solvent model (VISM) to calculate the solute-solvent interfacial structures and the corresponding free energies, and combine the VISM with the string method to obtain the minimum energy paths and transition states between the various metastable ("dry" and "wet") hydration states. The resulting dry-wet transition rates are then used in a spatially dependent multistate continuous-time Markov chain Brownian dynamics simulation and the related Fokker-Planck equation calculations of the ligand stochastic motion, providing the mean first-passage times for binding and unbinding. We find the hydration transitions to significantly slow down the binding process, in semiquantitative agreement with existing explicit-water simulations, but significantly accelerate the unbinding process. Moreover, our methods allow the characterization of nonequilibrium hydration states of pocket and ligand during the ligand movement, for which we find substantial memory and hysteresis effects for binding vs. unbinding. Our study thus provides a significant step forward toward efficient, physics-based interpretation and predictions of the complex kinetics in realistic ligand-receptor systems.

The finger loop of the SRA domain in the E3 ligase UHRF1 is a regulator of ubiquitin targeting and is required for the maintenance of DNA methylation.

The Su(var)3-9, enhancer of zeste, and trithorax (SET) and really interesting new gene (RING) finger-associated (SRA) protein domain is conserved across bacteria and eukaryota and coordinates extrahelical or "flipped" DNA bases. A functional SRA domain is required for ubiquitin-like with PHD and RING finger domains 1 (UHRF1) E3 ubiquitin ligase activity toward histone H3, a mechanism for recruiting the DNA methylation maintenance enzyme DNA methyltransferase 1 (DNMT1). The SRA domain supports UHRF1 oncogenic activity in colon cancer cells, highlighting that UHRF1 SRA antagonism could be a cancer therapeutic strategy. Here we used molecular dynamics simulations, DNA binding assays, in vitro ubiquitination reactions, and DNA methylation analysis to identify the SRA finger loop as a regulator of UHRF1 ubiquitin targeting and DNA methylation maintenance. A chimeric UHRF1 (finger swap) with diminished E3 ligase activity toward nucleosomal histones, despite tighter binding to unmodified or asymmetric or symmetrically methylated DNA, uncouples DNA affinity from regulation of E3 ligase activity. Our model suggests that SRA domains sample DNA bases through flipping in the presence or absence of a cytosine modification and that specific interactions of the SRA finger loop with DNA are required for downstream host protein function. Our findings provide insight into allosteric regulation of UHRF1 E3 ligase activity, suggesting that UHRF1's SRA finger loop regulates its conformation and function.

Simulating ion channel activation mechanisms using swarms of trajectories.

Atomic-level studies of protein activity represent a significant challenge as a result of the complexity of conformational changes occurring on wide-ranging timescales, often greatly exceeding that of even the longest simulations. A prime example is the elucidation of protein allosteric mechanisms, where localized perturbations transmit throughout a large macromolecule to generate a response signal. For example, the conversion of chemical to electrical signals during synaptic neurotransmission in the brain is achieved by specialized membrane proteins called pentameric ligand-gated ion channels. Here, the binding of a neurotransmitter results in a global conformational change to open an ion-conducting pore across the nerve cell membrane. X-ray crystallography has produced static structures of the open and closed states of the proton-gated GLIC pentameric ligand-gated ion channel protein, allowing for atomistic simulations that can uncover changes related to activation. We discuss a range of enhanced sampling approaches that could be used to explore activation mechanisms. In particular, we describe recent application of an atomistic string method, based on Roux's "swarms of trajectories" approach, to elucidate the sequence and interdependence of conformational changes during activation. We illustrate how this can be combined with transition analysis and Brownian dynamics to extract thermodynamic and kinetic information, leading to understanding of what controls ion channel function. © 2019 Wiley Periodicals, Inc.

String method solution of the gating pathways for a pentameric ligand-gated ion channel.

Pentameric ligand-gated ion channels control synaptic neurotransmission by converting chemical signals into electrical signals. Agonist binding leads to rapid signal transduction via an allosteric mechanism, where global protein conformational changes open a pore across the nerve cell membrane. We use all-atom molecular dynamics with a swarm-based string method to solve for the minimum free-energy gating pathways of the proton-activated bacterial GLIC channel. We describe stable wetted/open and dewetted/closed states, and uncover conformational changes in the agonist-binding extracellular domain, ion-conducting transmembrane domain, and gating interface that control communication between these domains. Transition analysis is used to compute free-energy surfaces that suggest allosteric pathways; stabilization with pH; and intermediates, including states that facilitate channel closing in the presence of an agonist. We describe a switching mechanism that senses proton binding by marked reorganization of subunit interface, altering the packing of ß-sheets to induce changes that lead to asynchronous pore-lining M2 helix movements. These results provide molecular details of GLIC gating and insight into the allosteric mechanisms for the superfamily of pentameric ligand-gated channels.

Wetting hysteresis induced by nanodefects.

Wetting of actual surfaces involves diverse hysteretic phenomena stemming from ever-present imperfections. Here, we clarify the origin of wetting hysteresis for a liquid front advancing or receding across an isolated defect of nanometric size. Various kinds of chemical and topographical nanodefects, which represent salient features of actual heterogeneous surfaces, are investigated. The most probable wetting path across surface heterogeneities is identified by combining, within an innovative approach, microscopic classical density functional theory and the string method devised for the study of rare events. The computed rugged free-energy landscape demonstrates that hysteresis emerges as a consequence of metastable pinning of the liquid front at the defects; the barriers for thermally activated defect crossing, the pinning force, and hysteresis are quantified and related to the geometry and chemistry of the defects allowing for the occurrence of nanoscopic effects. The main result of our calculations is that even weak nanoscale defects, which are difficult to characterize in generic microfluidic experiments, can be the source of a plethora of hysteretical phenomena, including the pinning of nanobubbles.

Molecular pathways for defect annihilation in directed self-assembly.

Over the last few years, the directed self-assembly of block copolymers by surface patterns has transitioned from academic curiosity to viable contender for commercial fabrication of next-generation nanocircuits by lithography. Recently, it has become apparent that kinetics, and not only thermodynamics, plays a key role for the ability of a polymeric material to self-assemble into a perfect, defect-free ordered state. Perfection, in this context, implies not more than one defect, with characteristic dimensions on the order of 5 nm, over a sample area as large as 100 cm(2). In this work, we identify the key pathways and the corresponding free energy barriers for eliminating defects, and we demonstrate that an extraordinarily large thermodynamic driving force is not necessarily sufficient for their removal. By adopting a concerted computational and experimental approach, we explain the molecular origins of these barriers and how they depend on material characteristics, and we propose strategies designed to overcome them. The validity of our conclusions for industrially relevant patterning processes is established by relying on instruments and assembly lines that are only available at state-of-the-art fabrication facilities, and, through this confluence of fundamental and applied research, we are able to discern the evolution of morphology at the smallest relevant length scales-a handful of nanometers-and present a view of defect annihilation in directed self-assembly at an unprecedented level of detail.

Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques-Searching for Mechanism and Kinetics of Biomolecular Functions.

To understand functions of biomolecules such as proteins, not only structures but their conformational change and kinetics need to be characterized, but its atomistic details are hard to obtain both experimentally and computationally. Here, we review our recent computational studies using novel enhanced sampling techniques for conformational sampling of biomolecules and calculations of their kinetics. For efficiently characterizing the free energy landscape of a biomolecule, we introduce the multiscale enhanced sampling method, which uses a combined system of atomistic and coarse-grained models. Based on the idea of Hamiltonian replica exchange, we can recover the statistical properties of the atomistic model without any biases. We next introduce the string method as a path search method to calculate the minimum free energy pathways along a multidimensional curve in high dimensional space. Finally we introduce novel methods to calculate kinetics of biomolecules based on the ideas of path sampling: one is the Onsager⁻Machlup action method, and the other is the weighted ensemble method. Some applications of the above methods to biomolecular systems are also discussed and illustrated.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method.

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Reliable and efficient reaction path and transition state finding for surface reactions with the growing string method.

The computational challenge of fast and reliable transition state and reaction path optimization requires new methodological strategies to maintain low cost, high accuracy, and systematic searching capabilities. The growing string method using internal coordinates has proven to be highly effective for the study of molecular, gas phase reactions, but difficulties in choosing a suitable coordinate system for periodic systems has prevented its use for surface chemistry. New developments are therefore needed, and presented herein, to handle surface reactions which include atoms with large coordination numbers that cannot be treated using standard internal coordinates. The double-ended and single-ended growing string methods are implemented using a hybrid coordinate system, then benchmarked for a test set of 43 elementary reactions occurring on surfaces. These results show that the growing string method is at least 45% faster than the widely used climbing image-nudged elastic band method, which also fails to converge in several of the test cases. Additionally, the surface growing string method has a unique single-ended search method which can move outward from an initial structure to find the intermediates, transition states, and reaction paths simultaneously. This powerful explorative feature of single ended-growing string method is demonstrated to uncover, for the first time, the mechanism for atomic layer deposition of TiN on Cu(111) surface. This reaction is found to proceed through multiple hydrogen-transfer and ligand-exchange events, while formation of H-bonds stabilizes intermediates of the reaction. Purging gaseous products out of the reaction environment is the driving force for these reactions. © 2017 Wiley Periodicals, Inc.

GENESIS 1.1: A hybrid-parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms.

GENeralized-Ensemble SImulation System (GENESIS) is a software package for molecular dynamics (MD) simulation of biological systems. It is designed to extend limitations in system size and accessible time scale by adopting highly parallelized schemes and enhanced conformational sampling algorithms. In this new version, GENESIS 1.1, new functions and advanced algorithms have been added. The all-atom and coarse-grained potential energy functions used in AMBER and GROMACS packages now become available in addition to CHARMM energy functions. The performance of MD simulations has been greatly improved by further optimization, multiple time-step integration, and hybrid (CPU + GPU) computing. The string method and replica-exchange umbrella sampling with flexible collective variable choice are used for finding the minimum free-energy pathway and obtaining free-energy profiles for conformational changes of a macromolecule. These new features increase the usefulness and power of GENESIS for modeling and simulation in biological research. © 2017 Wiley Periodicals, Inc.

Atomic-resolution dissection of the energetics and mechanism of isomerization of hydrated ATP-Mg(2+) through the SOMA string method.

The atomic mechanisms of isomerization of ATP-Mg(2+) in solution are characterized using the recently developed String Method with Optimal Molecular Alignment (SOMA) and molecular-dynamics simulations. Bias-Exchange Metadynamics simulations are first performed to identify the primary conformers of the ATP-Mg(2+) complex and their connectivity. SOMA is then used to elucidate the minimum free-energy path (MFEP) for each transition, in a 48-dimensional space. Analysis of the per-atom contributions to the global free-energy profiles reveals that the mechanism of these transitions is controlled by the Mg(2+) ion and its coordinating oxygen atoms in the triphosphate moiety, as well as by the ion-hydration shell. Metadynamics simulations in path collective variables based on the MFEP demonstrate these isomerizations proceed across a narrow channel of configurational space, thus validating the premise underlying SOMA. This study provides a roadmap for the examination of conformational changes in biomolecules, based on complementary enhanced-sampling techniques with different strengths. © 2015 Wiley Periodicals, Inc.

Single-ended transition state finding with the growing string method.

Reaction path finding and transition state (TS) searching are important tasks in computational chemistry. Methods that seek to optimize an evenly distributed set of structures to represent a chemical reaction path are known as double-ended string methods. Such methods can be highly reliable because the endpoints of the string are fixed, which effectively lowers the dimensionality of the reaction path search. String methods, however, require that the reactant and product structures are known beforehand, which limits their ability for systematic exploration of reactive steps. In this article, a single-ended growing string method (GSM) is introduced which allows for reaction path searches starting from a single structure. The method works by sequentially adding nodes along coordinates that drive bonds, angles, and/or torsions to a desired reactive outcome. After the string is grown and an approximate reaction path through the TS is found, string optimization commences and the exact TS is located along with the reaction path. Fast convergence of the string is achieved through use of internal coordinates and eigenvector optimization schemes combined with Hessian estimates. Comparison to the double-ended GSM shows that single-ended method can be even more computationally efficient than the already rapid double-ended method. Examples, including transition metal reactivity and a systematic, automated search for unknown reactivity, demonstrate the efficacy of the new method. This automated reaction search is able to find 165 reaction paths from 333 searches for the reaction of NH3 BH3 and (LiH)4 , all without guidance from user intuition.

Phosphorylation at Ser65 modulates ubiquitin conformational dynamics.

Ubiquitin phosphorylation at Ser65 increases the population of a rare C-terminally retracted (CR) conformation. Transition between the Major and CR ubiquitin conformations is critical for promoting mitochondrial degradation. The mechanisms by which the Major and CR conformations of Ser65-phosphorylated (pSer65) ubiquitin interconvert, however, remain unresolved. Here, we perform all-atom molecular dynamics simulations using the string method with swarms of trajectories to calculate the lowest free-energy path between these two conformers. Our analysis reveals the existence of a Bent intermediate in which the C-terminal residues of the ß5 strand shift to resemble the CR conformation, while pSer65 retains contacts resembling the Major conformation. This stable intermediate was reproduced in well-tempered metadynamics calculations but was less stable for a Gln2Ala mutant that disrupts contacts with pSer65. Lastly, dynamical network modeling reveals that the transition from the Major to CR conformations involves a decoupling of residues near pSer65 from the adjacent ß1 strand.

Molecular Dynamics-Based Thermodynamic and Kinetic Characterization of Membrane Protein Conformational Transitions.

Molecular dynamics (MD) simulations are routinely used to study structural dynamics of membrane proteins. However, conventional MD is often unable to sample functionally important conformational transitions of membrane proteins such as those involved in active membrane transport or channel activation process. Here we describe a combination of multiple MD based techniques that allows for a rigorous characterization of energetics and kinetics of large-scale conformational changes in membrane proteins. The methodology is based on biased, nonequilibrium, collective-variable based simulations including nonequilibrium pulling, string method with swarms of trajectories, bias-exchange umbrella sampling, and rate estimation techniques.

Penile strangulation by different objects and its removal by the modified string method: Management of four cases with review of literature.

Penile strangulation is a challenging clinical situation and usually requires prompt treatment. Penile strangulation by a nonmetallic or thin metallic ring is easily overcome by severing/cutting the object; however, a heavy and long metal ring causing penile strangulation is not only difficult to sever but also it may worsen the scenario if removal is tried with inappropriate method. Here, we report four cases of penile strangulation by different objects which were successfully removed by aspiration and string method. We found that instead of using heavy cutting instruments and other surgical methods, string and aspiration technique is much better.

Proton Countertransport and Coupled Gating in the Sarcoplasmic Reticulum Calcium Pump.

The calcium pump of the sarcoplasmic reticulum (SERCA) is an ATP-driven active transporter of Ca2+ ions that functions via an "alternating-access" cycle mechanism. In each cycle, SERCA transports two Ca2+ ions toward the lumen of the sarcoplasmic reticulum and two to three protons to the cytoplasm. How the latter conformational transition is coupled to cytoplasmic release of protons remains poorly understood. The present computational study shows how the mechanism of proton countertransport is coupled to the alternating access gating process in SERCA. Molecular dynamics simulation trajectories are generated starting from a series of configurations taken along the E2 to E1 transition pathway determined by the string method with swarms-of-trajectories. Simulations of different protonation configurations at the binding sites reveal how deprotonation events affect the opening of the cytoplasmic gate. The results show that there is a strong coupling between the chronological order of deprotonation, the entry of water molecules into the TM region, and the opening of the cytoplasmic gate. Deprotonation of E309 and E771 is sequential with E309 being the first to lose the proton. The deprotonation promotes the opening of the cytoplasmic gate but leads to a productive gating transition only if it occurs after the transmembrane domain has reached an intermediate conformation. Deprotonation of E309 and E771 is unproductive when it occurs too early because it causes the re-opening of the luminal gate.

Defect Annihilation Pathways in Directed Assembly of Lamellar Block Copolymer Thin Films.

Defects in highly ordered self-assembled block copolymers represent an important roadblock toward the adoption of these materials in a wide range of applications. This work examines the pathways for annihilation of defects in symmetric diblock copolymers in the context of directed assembly using patterned substrates. Past theoretical and computational studies of such systems have predicted minimum free energy pathways that are characteristic of an activated process. However, they have been limited to adjacent dislocations with opposite Burgers vectors. By relying on a combination of advanced sampling techniques and particle-based simulations, this work considers the long-range interaction between dislocation pairs, both on homogeneous and nanopatterned substrates. As illustrated here, these interactions are central to understanding the defect structures that are most commonly found in applications and in experimental studies of directed self-assembly. More specifically, it is shown that, for dislocation dipoles separated by several lamellae, multiple consecutive free energy barriers lead to effective kinetic barriers that are an order of magnitude larger than those originally reported in the literature for tightly bound dislocation pairs. It is also shown that annihilation pathways depend strongly on both the separation between dislocations and their relative position with respect to the substrate guiding stripes used to direct the assembly.

Energetics and conformational pathways of functional rotation in the multidrug transporter AcrB.

The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive. Here, calculating the minimum free energy pathway of the functional rotation for the complete AcrB trimer, we describe the structural and energetic basis behind the coupling between the functional rotation and the proton translocation at atomic resolution. Free energy calculations show that protonation of Asp408 in the transmembrane portion of the drug-bound protomer drives the functional rotation. The conformational pathway identifies vertical shear motions among several transmembrane helices, which regulate alternate access of water in the transmembrane as well as peristaltic motions that pump drugs in the periplasm.

Conformational Transitions and Alternating-Access Mechanism in the Sarcoplasmic Reticulum Calcium Pump.

Ion pumps are integral membrane proteins responsible for transporting ions against concentration gradients across biological membranes. Sarco/endoplasmic reticulum Ca2+-ATPase (SERCA), a member of the P-type ATPases family, transports two calcium ions per hydrolyzed ATP molecule via an "alternating-access" mechanism. High-resolution crystallographic structures provide invaluable insight on the structural mechanism of the ion pumping process. However, to understand the molecular details of how ATP hydrolysis is coupled to calcium transport, it is necessary to gain knowledge about the conformational transition pathways connecting the crystallographically resolved conformations. Large-scale transitions in SERCA occur at time-scales beyond the current reach of unbiased molecular dynamics simulations. Here, we overcome this challenge by employing the string method, which represents a transition pathway as a chainofstates linking two conformational endpoints. Using a multiscale methodology, we have determined all-atom transition pathways for three main conformational transitions responsible for the alternating-access mechanism. The present pathways provide a clear chronology and ordering of the key events underlying the active transport of calcium ions by SERCA. Important conclusions are that the conformational transition that leads to occlusion with bound ATP and calcium is highly concerted and cooperative, the phosphorylation of Asp351 causes areorganization of the cytoplasmic domains that subsequently drives the opening of the luminal gate, and thereclosing of luminal gate induces a shift in the cytoplasmic domains that subsequently enables the dephosphorylation of Asp351-P. Formation of transient residue-residue contacts along the conformational transitions predicted by the computations provide an experimental route to test the general validity of the computational pathways.

Discontinuous Bubble Nucleation Due to a Metastable Condensation Transition in Polymer-CO2 Mixtures.

We combine a newly developed density-functional theory with the string method to calculate the minimum free energy path of bubble nucleation in compressible polymer-CO2 mixtures. Nucleation is initiated by saturating the polymer liquid with high pressure CO2 and subsequently reducing the pressure to ambient condition. Below a critical temperature, we find that there is a discontinuous drop in the nucleation barrier with increased initial CO2 pressure, as a result of an underlying metastable transition from a CO2-rich-vapor phase to a CO2-rich-liquid phase. This phenomenon is different from previously proposed nucleation mechanisms involving metastable transitions.