Computational Recipe for Efficient Description of Large-Scale Conformational Changes in Biomolecular Systems

Mechanism of proton-powered c-ring rotation in a mitochondrial ATP synthase

Proton-powered c-ring rotation in mitochondrial ATP synthase is crucial to convert the transmembrane protonmotive force into torque to drive the synthesis of adenosine triphosphate (ATP). Capitalizing on recent cryo-EM structures, we aim at a structural and energetic understanding of how functional directional rotation is achieved. We performed multi-microsecond atomistic simulations to determine the free energy profiles along the c-ring rotation angle before and after the arrival of a new proton. Our results reveal that rotation proceeds by dynamic sliding of the ring over the a-subunit surface, during which interactions with conserved polar residues stabilize distinct intermediates. Ordered water chains line up for a Grotthuss-type proton transfer in one of these intermediates. After proton transfer, a high barrier prevents backward rotation and an overall drop in free energy favors forward rotation, ensuring the directionality of c-ring rotation required for the thermodynamically disfavored ATP synthesis. The essential arginine of the a-subunit stabilizes the rotated configuration through a salt bridge with the c-ring. Overall, we describe a complete mechanism for the rotation step of the ATP synthase rotor, thereby illuminating a process critical to all life at atomic resolution.

The Alternating Access Mechanism in Mammalian Multidrug Resistance Transporters and Their Bacterial Homologs

Multidrug resistance (MDR) proteins belonging to the ATP-Binding Cassette (ABC) transporter group play a crucial role in the export of cytotoxic drugs across cell membranes. These proteins are particularly fascinating due to their ability to confer drug resistance, which subsequently leads to the failure of therapeutic interventions and hinders successful treatments. One key mechanism by which multidrug resistance (MDR) proteins carry out their transport function is through alternating access. This mechanism involves intricate conformational changes that enable the binding and transport of substrates across cellular membranes. In this extensive review, we provide an overview of ABC transporters, including their classifications and structural similarities. We focus specifically on well-known mammalian multidrug resistance proteins such as MRP1 and Pgp (MDR1), as well as bacterial counterparts such as Sav1866 and lipid flippase MsbA. By exploring the structural and functional features of these MDR proteins, we shed light on the roles of their nucleotide-binding domains (NBDs) and transmembrane domains (TMDs) in the transport process. Notably, while the structures of NBDs in prokaryotic ABC proteins, such as Sav1866, MsbA, and mammalian Pgp, are identical, MRP1 exhibits distinct characteristics in its NBDs. Our review also emphasizes the importance of two ATP molecules for the formation of an interface between the two binding sites of NBD domains across all these transporters. ATP hydrolysis occurs following substrate transport and is vital for recycling the transporters in subsequent cycles of substrate transportation. Specifically, among the studied transporters, only NBD2 in MRP1 possesses the ability to hydrolyze ATP, while both NBDs of Pgp, Sav1866, and MsbA are capable of carrying out this reaction. Furthermore, we highlight recent advancements in the study of MDR proteins and the alternating access mechanism. We discuss the experimental and computational approaches utilized to investigate the structure and dynamics of MDR proteins, providing valuable insights into their conformational changes and substrate transport. This review not only contributes to an enhanced understanding of multidrug resistance proteins but also holds immense potential for guiding future research and facilitating the development of effective strategies to overcome multidrug resistance, thus improving therapeutic interventions.

Binding affinity estimation from restrained umbrella sampling simulations

The protein-ligand binding affinity quantifies the binding strength between a protein and its ligand. Computer modeling and simulations can be used to estimate the binding affinity or binding free energy using data- or physics-driven methods or a combination thereof. Here we discuss a purely physics-based sampling approach based on biased molecular dynamics simulations. Our proposed method generalizes and simplifies previously suggested stratification strategies that use umbrella sampling or other enhanced sampling simulations with additional collective-variable-based restraints. The approach presented here uses a flexible scheme that can be easily tailored for any system of interest. We estimate the binding affinity of human fibroblast growth factor 1 to heparin hexasaccharide based on the available crystal structure of the complex as the initial model and four different variations of the proposed method to compare against the experimentally determined binding affinity obtained from isothermal titration calorimetry experiments.

Connections between efficient control and spontaneous transitions in an Ising model

A system can be driven between metastable configurations by a time-dependent driving protocol, which uses external control parameters to change the potential energy of the system. Here we investigate the correspondence between driving protocols that are designed to minimize work and the spontaneous transition paths of the system in the absence of driving. We study the spin-inversion reaction in a 2D Ising model, quantifying the timing of each spin flip and heat flow to the system during both a minimum-work protocol and a spontaneous transition. The general order of spin flips during the transition mechanism is preserved between the processes, despite the coarseness of control parameters that are unable to reproduce more detailed features of the spontaneous mechanism. Additionally, external control parameters provide energy to each system component to compensate changes in internal energy, showing how control parameters are tuned during a minimum-work protocol to counteract underlying energetic features. This paper supports a correspondence between minimum-work protocols and spontaneous transition mechanisms.

Enhancing sampling with free-energy calculations

In recent years, considerable progress has been made to enhance sampling and help address biological questions, including, but not limited to conformational transitions in biomolecules and protein-ligand reversible binding, hitherto intractable by brute-force computer simulations. Many of these advances result from the development of a palette of methods aimed at exploring rare events through reliable free-energy calculations. The advent of new, often conceptually related methods has also rendered difficult the choice of the best suited option for a given problem. Here, we focus on geometrical transformations and algorithms designed to enhance sampling along adequately chosen progress variables, tracing their theoretical foundations, and showing how they are connected and can be blended together for improved performance.

Atomic-level characterization of the conformational transition pathways in SARS-CoV-1 and SARS-CoV-2 spike proteins

Severe acute respiratory syndrome (SARS) coronaviruses 1 and 2 (SARS-CoV-1 and SARS-CoV-2) derive transmissibility from spike protein activation in the receptor binding domain (RBD) and binding to the host cell angiotensin converting enzyme 2 (ACE2). However, the mechanistic details that describe the large-scale conformational changes associated with spike protein activation or deactivation are still somewhat unknown. Here, we have employed an extensive set of nonequilibrium all-atom molecular dynamics (MD) simulations, utilizing a novel protocol, for the SARS-CoV-1 (CoV-1) and SARS-CoV-2 (CoV-2) prefusion spike proteins in order to characterize the conformational pathways associated with the active-to-inactive transition. Our results indicate that both CoV-1 and CoV-2 spike proteins undergo conformational transitions along pathways unique to each protein. We have identified a number of key residues that form various inter-domain saltbridges, suggesting a multi-stage conformational change along the pathways. We have also constructed the free energy profiles along the transition pathways for both CoV-1 and CoV-2 spike proteins. The CoV-2 spike protein must overcome larger free energy barriers to undergo conformational changes towards protein activation or deactivation, when compared to CoV-1.

Molecular simulation of lignin-related aromatic compound permeation through gram-negative bacterial outer membranes

Lignin, an abundant aromatic heteropolymer in secondary plant cell walls, is the single largest source of renewable aromatics in the biosphere. Leveraging this resource for renewable bioproducts through targeted microbial action depends on lignin fragment uptake by microbial hosts and subsequent enzymatic action to obtain the desired product. Recent computational work has emphasized that bacterial inner membranes are permeable to many aromatic compounds expected from lignin depolymerization processes. In this study, we expand on these findings through simulations for 42 lignin-related compounds across a gram-negative bacterial outer membrane model. Unbiased simulation trajectories indicate that spontaneous crossing for the full outer membrane is relatively rare at molecular simulation timescales, primarily due to preferential membrane partitioning and slow diffusion within the lipopolysaccharide layer within the outer membrane. Membrane partitioning and permeability coefficients were determined through replica exchange umbrella sampling simulations to overcome sampling limitations. We find that the glycosylated lipopolysaccharides found in the outer membrane increase the permeation barrier to many lignin-related compounds, particularly the most hydrophobic compounds. However, the effect is relatively modest; at industrially relevant concentrations, uncharged lignin-related compounds will readily diffuse across the outer membrane without the need for specific porins. Together, our results provide insight into the permeability of the bacterial outer membrane for assessing lignin fragment uptake and the future production of renewable bioproducts.

Proton-driven alternating access in a spinster lipid transporter

Spinster (Spns) lipid transporters are critical for transporting sphingosine-1-phosphate (S1P) across cellular membranes. In humans, Spns2 functions as the main S1P transporter in endothelial cells, making it a potential drug target for modulating S1P signaling. Here, we employed an integrated approach in lipid membranes to identify unknown conformational states of a bacterial Spns from Hyphomonas neptunium (HnSpns) and to define its proton- and substrate-coupled conformational dynamics. Our systematic study reveals conserved residues critical for protonation steps and their regulation, and how sequential protonation of these proton switches coordinates the conformational transitions in the context of a noncanonical ligand-dependent alternating access. A conserved periplasmic salt bridge (Asp60^TM2:Arg289^TM7) keeps the transporter in a closed conformation, while proton-dependent conformational dynamics are significantly enhanced on the periplasmic side, providing a pathway for ligand exchange.

The Spns lipid transporters use ion gradients to drive substrate transport, including bioactive sphingolipids. Here, Dastvan et al. investigated how binding of protons powers the conformational changes that enable broad transport by a bacterial Spns.

Multidimensional minimum-work control of a 2D Ising model

A system's configurational state can be manipulated using dynamic variation of control parameters, such as temperature, pressure, or magnetic field; for finite-duration driving, excess work is required above the equilibrium free-energy change. Minimum-work protocols in multidimensional control-parameter space have potential to significantly reduce work relative to one-dimensional control. By numerically minimizing a linear-response approximation to the excess work, we design protocols in control-parameter spaces of a 2D Ising model that efficiently drive the system from the all-down to all-up configuration. We find that such designed multidimensional protocols take advantage of more flexible control to avoid control-parameter regions of high system resistance, heterogeneously input and extract work to make use of system relaxation, and flatten the energy landscape, making accessible many configurations that would otherwise have prohibitively high energy and thus decreasing spin correlations. Relative to one-dimensional protocols, this speeds up the rate-limiting spin-inversion reaction, thereby keeping the system significantly closer to equilibrium for a wide range of protocol durations, and significantly reducing resistance and hence work.

Extended-ensemble docking to probe dynamic variation of ligand binding sites during large-scale structural changes of proteins

Proteins can sample a broad landscape as they undergo conformational transition between different functional states. At the same time, as key players in almost all cellular processes, proteins are important drug targets. Considering the different conformational states of a protein is therefore central for a successful drug-design strategy. Here we introduce a novel docking protocol, termed extended-ensemble docking, pertaining to proteins that undergo large-scale (global) conformational changes during their function. In its application to multidrug ABC-transporter P-glycoprotein (Pgp), extensive non-equilibrium molecular dynamics simulations employing system-specific collective variables are first used to describe the transition cycle of the transporter. An extended set of conformations (extended ensemble) representing the full transition cycle between the inward- and the outward-facing states is then used to seed high-throughput docking calculations of known substrates, non-substrates, and modulators of the transporter. Large differences are predicted in the binding affinities to different conformations, with compounds showing stronger binding affinities to intermediate conformations compared to the starting crystal structure. Hierarchical clustering of the binding modes shows all ligands preferably bind to the large central cavity of the protein, formed at the apex of the transmembrane domain (TMD), whereas only small binding populations are observed in the previously described R and H sites present within the individual TMD leaflets. Based on the results, the central cavity is further divided into two major subsites, first preferably binding smaller substrates and high-affinity inhibitors, whereas the second one shows preference for larger substrates and low-affinity modulators. These central subsites along with the low-affinity interaction sites present within the individual TMD leaflets may respectively correspond to the proposed high- and low-affinity binding sites in Pgp. We propose further an optimization strategy for developing more potent inhibitors of Pgp, based on increasing its specificity to the extended ensemble of the protein, instead of using a single protein structure, as well as its selectivity for the high-affinity binding site. In contrast to earlier in silico studies using single static structures of Pgp, our results show better agreement with experimental studies, pointing to the importance of incorporating the global conformational flexibility of proteins in future drug-discovery endeavors.

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

Role of internal loop dynamics in antibiotic permeability of outer membrane porins

Antibiotic resistance in Gram-negative pathogens has been identified as an urgent threat to human health by the World Health Organization. The major challenge with treating infections by these pathogens is developing antibiotics that can traverse the dense bacterial outer membrane (OM) formed by a mesh of lipopolysaccharides. Effective antibiotics permeate through OM porins, which have evolved for nutrient diffusion; however, the conformational states of these porins regulating permeation are still unclear. Here, we used molecular dynamics simulations, free energy calculations, Markov-state modeling, and whole-cell accumulation assays to provide mechanistic insight on how a porin shifts between open and closed states. We provide a mechanism of how Gram-negative bacteria confer resistance to antibiotics.

Gram-negative bacteria pose a serious public health concern due to resistance to many antibiotics, caused by the low permeability of their outer membrane (OM). Effective antibiotics use porins in the OM to reach the interior of the cell; thus, understanding permeation properties of OM porins is instrumental to rationally develop broad-spectrum antibiotics. A functionally important feature of OM porins is undergoing open–closed transitions that modulate their transport properties. To characterize the molecular basis of these transitions, we performed an extensive set of molecular dynamics (MD) simulations of Escherichia coli OM porin OmpF. Markov-state analysis revealed that large-scale motion of an internal loop, L3, underlies the transition between energetically stable open and closed states. The conformation of L3 is controlled by H bonds between highly conserved acidic residues on the loop and basic residues on the OmpF β-barrel. Mutation of key residues important for the loop’s conformation shifts the equilibrium between open and closed states and regulates translocation of permeants (ions and antibiotics), as observed in the simulations and validated by our whole-cell accumulation assay. Notably, one mutant system G119D, which we find to favor the closed state, has been reported in clinically resistant bacterial strains. Overall, our accumulated ∼200 µs of simulation data (the wild type and mutants) along with experimental assays suggest the involvement of internal loop dynamics in permeability of OM porins and antibiotic resistance in Gram-negative bacteria.

Rationalizing the generation of broad spectrum antibiotics with the addition of a positive charge

Antibiotic resistance of Gram-negative bacteria is largely attributed to the low permeability of their outer membrane (OM). Recently, we disclosed the eNTRy rules, a key lesson of which is that the introduction of a primary amine enhances OM permeation in certain contexts. To understand the molecular basis for this finding, we perform an extensive set of molecular dynamics (MD) simulations and free energy calculations comparing the permeation of aminated and amine-free antibiotic derivatives through the most abundant OM porin of E. coli, OmpF. To improve sampling of conformationally flexible drugs in MD simulations, we developed a novel, Monte Carlo and graph theory based algorithm to probe more efficiently the rotational and translational degrees of freedom visited during the permeation of the antibiotic molecule through OmpF. The resulting pathways were then used for free-energy calculations, revealing a lower barrier against the permeation of the aminated compound, substantiating its greater OM permeability. Further analysis revealed that the amine facilitates permeation by enabling the antibiotic to align its dipole to the luminal electric field of the porin and form favorable electrostatic interactions with specific, highly-conserved charged residues. The importance of these interactions in permeation was further validated with experimental mutagenesis and whole cell accumulation assays. Overall, this study provides insights on the importance of the primary amine for antibiotic permeation into Gram-negative pathogens that could help the design of future antibiotics. We also offer a new computational approach for calculating free-energy of processes where relevant molecular conformations cannot be efficiently captured.

Defining the Energetic Basis for a Conformational Switch Mediating Ligand-Independent Activation of Mutant Estrogen Receptors in Breast Cancer

Although most primary estrogen receptor (ER)-positive breast cancers respond well to endocrine therapies, many relapse later as metastatic disease due to endocrine therapy resistance. Over one third of these are associated with mutations in the ligand-binding domain (LBD) that activate the receptor independent of ligand. We have used an array of advanced computational techniques rooted in molecular dynamics simulations, in concert with and validated by experiments, to characterize the molecular mechanisms by which specific acquired somatic point mutations give rise to ER constitutive activation. By comparing structural and energetic features of constitutively active mutants and ligand-bound forms of ER-LBD with unliganded wild-type (WT) ER, we characterize a spring force originating from strain in the Helix 11-12 loop of WT-ER, opposing folding of Helix 12 into the active conformation and keeping WT-ER off and disordered, with the ligand-binding pocket open for rapid ligand binding. We quantify ways in which this spring force is abrogated by activating mutations that latch (Y537S) or relax (D538G) the folded form of the loop, enabling formation of the active conformation without ligand binding. We also identify a new ligand-mediated hydrogen-bonding network that stabilizes the active, ligand-bound conformation of WT-ER LBD, and similarly stabilizes the active conformation of the ER mutants in the hormone-free state. IMPLICATIONS: Our investigations provide deep insight into the energetic basis for the structural mechanisms of receptor activation through mutation, exemplified here with ER in endocrine-resistant metastatic breast cancers, with potential application to other dysregulated receptor signaling due to driver mutations.

Active participation of membrane lipids in inhibition of multidrug transporter P-glycoprotein

P-glycoprotein (Pgp) is a major efflux pump in humans, overexpressed in a variety of cancers and associated with the development of multi-drug resistance. Allosteric modulation by various ligands (e.g., transport substrates, inhibitors, and ATP) has been biochemically shown to directly influence structural dynamics, and thereby, the function of Pgp. However, the molecular details of such effects, particularly with respect to the role and involvement of the surrounding lipids, are not well established. Here, we employ all-atom molecular dynamics (MD) simulations to study the conformational landscape of Pgp in the presence of a high-affinity, third-generation inhibitor, tariquidar, in comparison to the nucleotide-free (APO) and the ATP-bound states, in order to characterize the mechanical effects of the inhibitor that might be of relevance to its blocking mechanism of Pgp. Simulations in a multi-component lipid bilayer show a dynamic equilibrium between open(er) and more closed inward-facing (IF) conformations in the APO state, with binding of ATP shifting the equilibrium towards conformations more prone to ATP hydrolysis and subsequent events in the transport cycle. In the presence of the inhibitor bound to the drug-binding pocket within the transmembrane domain (TMD), Pgp samples more open IF conformations, and the nucleotide binding domains (NBDs) become highly dynamic. Interestingly, and reproduced in multiple independent simulations, the inhibitor is observed to facilitate recruitment of lipid molecules into the Pgp lumen through the two proposed drug-entry portals, where the lipid head groups from the cytoplasmic leaflet penetrate into and, in some cases, translocate inside the TMD, while the lipid tails remain extended into the bulk lipid environment. These "wedge" lipids likely enhance the inhibitor-induced conformational restriction of the TMD leading to the differential modulation of coupling pathways observed with the NBDs downstream. We suggest a novel inhibitory mechanism for tariquidar, and potentially for related third-generation Pgp inhibitors, where lipids are seen to enhance the inhibitory role in the catalytic cycle of membrane transporters.

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.

Confronting pitfalls of AI-augmented molecular dynamics using statistical physics

Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.

Data-guided Multi-Map variables for ensemble refinement of molecular movies

Driving molecular dynamics simulations with data-guided collective variables offer a promising strategy to recover thermodynamic information from structure-centric experiments. Here, the three-dimensional electron density of a protein, as it would be determined by cryo-EM or x-ray crystallography, is used to achieve simultaneously free-energy costs of conformational transitions and refined atomic structures. Unlike previous density-driven molecular dynamics methodologies that determine only the best map-model fits, our work employs the recently developed Multi-Map methodology to monitor concerted movements within equilibrium, non-equilibrium, and enhanced sampling simulations. Construction of all-atom ensembles along the chosen values of the Multi-Map variable enables simultaneous estimation of average properties, as well as real-space refinement of the structures contributing to such averages. Using three proteins of increasing size, we demonstrate that biased simulation along the reaction coordinates derived from electron densities can capture conformational transitions between known intermediates. The simulated pathways appear reversible with minimal hysteresis and require only low-resolution density information to guide the transition. The induced transitions also produce estimates for free energy differences that can be directly compared to experimental observables and population distributions. The refined model quality is superior compared to those found in the Protein Data Bank. We find that the best quantitative agreement with experimental free-energy differences is obtained using medium resolution density information coupled to comparatively large structural transitions. Practical considerations for probing the transitions between multiple intermediate density states are also discussed.

Structural basis for the reaction cycle of DASS dicarboxylate transporters

Citrate, α-ketoglutarate and succinate are TCA cycle intermediates that also play essential roles in metabolic signaling and cellular regulation. These di- and tricarboxylates are imported into the cell by the divalent anion sodium symporter (DASS) family of plasma membrane transporters, which contains both cotransporters and exchangers. While DASS proteins transport substrates via an elevator mechanism, to date structures are only available for a single DASS cotransporter protein in a substrate-bound, inward-facing state. We report multiple cryo-EM and X-ray structures in four different states, including three hitherto unseen states, along with molecular dynamics simulations, of both a cotransporter and an exchanger. Comparison of these outward- and inward-facing structures reveal how the transport domain translates and rotates within the framework of the scaffold domain through the transport cycle. Additionally, we propose that DASS transporters ensure substrate coupling by a charge-compensation mechanism, and by structural changes upon substrate release.

Membrane Interactions of Cy3 and Cy5 Fluorophores and Their Effects on Membrane-Protein Dynamics

Organic fluorophores, such as Cy3 and Cy5, have been widely used as chemical labels to probe the structure and dynamics of membrane proteins. Although a number of previous studies have reported on the possibility of some of the water-soluble fluorophores to interact with lipid bilayers, detailed fluorophore-lipid interactions and, more importantly, the potential effect of such interactions on the natural dynamics of the labeled membrane proteins have not been well studied. We have performed a large set of all-atom molecular dynamics simulations employing the highly mobile membrane mimetic model to describe spontaneous partitioning of the fluorophores into lipid bilayers with different lipid compositions. Spontaneous membrane partitioning of Cy3 and Cy5 fluorophores captured in these simulations proceeds in two steps. Electrostatic interaction between the fluorophores and the lipid headgroups facilitates the initial, fast membrane association of the fluorophores, followed by slow insertion of hydrophobic moieties into the lipid bilayer core. After the conversion of the resulting membrane-bound systems to full-membrane representations, biased-exchange umbrella sampling simulations are performed for free energy calculations, revealing a higher energy barrier for partitioning into negatively charged (phosphatidylserine or phosphatidylcholine) membranes than purely zwitterionic (phosphatidylcholine or phosphatidylethanolamine) ones. Furthermore, the potential effect of fluorophore-lipid interactions on membrane proteins has been examined by covalently linking Cy5 to single- and multipass transmembrane helical proteins. Equilibrium simulations show strong position-dependent effects of Cy5-tagging on the structure and natural dynamics of membrane proteins. Interactions between the tagged protein and Cy5 were also observed. Our results suggest that fluorophore-lipid interactions can affect the structure and dynamics of membrane proteins to various extents, especially in systems with higher structural flexibility.

A Minimal Membrane Metal Transport System: Dynamics and Energetics of mer Proteins

The mer operon in bacteria encodes a set of proteins and enzymes that impart resistance to environmental mercury toxicity by importing Hg2+ and reducing it to volatile Hg(0). Because the reduction occurs in the cytoplasm, mercuric ions must first be transported across the cytoplasmic membrane by one of a few known transporters. MerF is the smallest of these, containing only two transmembrane helices and two pairs of vicinal cysteines that coordinate mercuric ions. In this work, we use molecular dynamics simulations to characterize the dynamics of MerF in its apo and Hg2+ -bound states. We find that the apo state positions one of the cysteine pairs closer to the periplasmic side of the membrane, while in the bound state the same pair approaches the cytoplasmic side. This finding is consistent with the functional requirement of accepting Hg2+ from the periplasmic space, sequestering it on acceptance, and transferring it to the cytoplasm. Conformational changes in the TM helices facilitate the functional interaction of the two cysteine pairs. Free-energy calculations provide a barrier of 16 kcal/mol for the association of the periplasmic Hg2+ -bound protein MerP with MerF and 7 kcal/mol for the subsequent association of MerF's two cysteine pairs. Despite the significant conformational changes required to move the binding site across the membrane, coarse-grained simulations of multiple copies of MerF support the expectation that it functions as a monomer. Our results demonstrate how conformational changes and binding thermodynamics could lead to such a small membrane protein acting as an ion transporter. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.

Locking Two Rigid-body Bundles in an Outward-Facing Conformation: The Ion-coupling Mechanism in a LeuT-fold Transporter

Secondary active transporters use electrochemical gradient of ions to fuel the "uphill" translocation of the substrate following the alternating-access model. The coupling of ions to conformational dynamics of the protein remains one of the least characterized aspects of the transporter function. We employ extended molecular dynamics (MD) simulations to examine the Na+-binding effects on the structure and dynamics of a LeuT-fold, Na+-coupled secondary transporter (Mhp1) in its major conformational states, i.e., the outward-facing (OF) and inward-facing (IF) states, as well as on the OF ↔ IF state transition. Microsecond-long, unbiased MD simulations illustrate that Na+ stabilizes an OF conformation favorable for substrate association, by binding to a highly conserved site at the interface between the two helical bundles and restraining their relative position and motion. Furthermore, a special-protocol biased simulation for state transition suggests that Na+ binding hinders the OF ↔ IF transition. These synergistic Na+-binding effects allosterically couple the ion and substrate binding sites and modify the kinetics of state transition, collectively increasing the lifetime of an OF conformation with high substrate affinity, thereby facilitating substrate recruitment from a low-concentration environment. Based on the similarity between our findings for Mhp1 and experimental reports on LeuT, we propose that this model may represent a general Na+-coupling mechanism among LeuT-fold transporters.

Role of the N-Terminal Transmembrane Helix Contacts in the Activation of FGFR3

Fibroblast growth factor receptor 3 (FGFR3) is a member of receptor tyrosine kinases, which is involved in skeletal cell growth, differentiation, and migration. FGFR3 transduces biochemical signals from the extracellular ligand-binding domain to the intracellular kinase domain through the conformational changes of the transmembrane (TM) helix dimer. Here, we apply generalized replica exchange with solute tempering method to wild type (WT) and G380R mutant (G380R) of FGFR3. The dimer interface in G380R is different from WT and the simulation results are in good agreement with the solid-state nuclear magnetic resonance (NMR) spectroscopy. TM helices in G380R are extended more than WT, and thereby, G375 in G380R contacts near the N-termini of the TM helix dimer. Considering that both G380R and G375C show the constitutive activation, the formation of the N-terminal contacts of the TM helices can be generally important for the activation mechanism. © 2019 Wiley Periodicals, Inc.

Exploring Conformational Transitions and Free-Energy Profiles of Proton-Coupled Oligopeptide Transporters

Proteins involved in peptide uptake and transport belong to the proton-coupled oligopeptide transporter (POT) family. Crystal structures of POT family members reveal a common fold consisting of two domains of six transmembrane α helices that come together to form a "V" shaped transporter with a central substrate binding site. Proton-coupled oligopeptide transporters operate through an alternate access mechanism, where the membrane transporter undergoes global conformational changes, alternating between inward-facing (IF), outward-facing (OF), and occluded (OC) states. Conformational transitions are promoted by proton and ligand binding; however, due to the absence of crystallographic models of the outward-open state, the role of H⁺ and ligands is still not fully understood. To provide a comprehensive picture of the POT conformational equilibrium, conventional and enhanced sampling molecular dynamics simulations of PepT_st in the presence or absence of ligand and protonation were performed. Free-energy profiles of the conformational variability of PepT_st were obtained from microseconds of adaptive biasing force (ABF) simulations. Our results reveal that both proton and ligand significantly change the conformational free-energy landscape. In the absence of ligand and protonation, only transitions involving IF and OC states are allowed. After protonation of the residue Glu300, the wider free-energy well for Glu300 protonated PepT_st indicates a greater conformational variability relative to the apo system, and OF conformations became accessible. For the Glu300 protonated Holo-PepT_st, the presence of a second free-energy minimum suggests that OF conformations are not only accessible, but also stable. The differences in the free-energy profiles demonstrate that transitions toward outward-facing conformation occur only after protonation, which is likely the first step in the mechanism of peptide transport. Our extensive ABF simulations provide a fully atomic description of all states of the transport process, offering a model for the alternating access mechanism and how protonation and ligand control the conformational changes.

Lipid-Dependent Alternating Access Mechanism of a Bacterial Multidrug ABC Exporter

By undergoing conformational changes, active membrane transporters alternate between an inward-facing (IF) and an outward-facing (OF) state to transport their substrates across cellular membrane. The conformational landscape of membrane transporters, however, could be influenced by their environment, and the dependence of the alternating access mechanism on the lipid composition has not been understood at the molecular level. We have performed an extensive set of microsecond-level all-atom molecular dynamics (MD) simulations on bacterial ATP binding cassette (ABC) exporter Sav1866 in six different phosphocholine (PC) and phosphoethanolamine (PE) lipid membrane environments. This study mainly focuses on the energetically downhill OF-to-IF conformational transition of Sav1866 upon the ATP hydrolysis. We observe that the transporter undergoes large-scale conformational changes in the PE environment, particularly in the POPE lipids, resulting in an IF-occluded conformation, a transition that does not occur when the transporter is embedded in any of the PC lipid bilayers. We propose that the PE lipids facilitate the closing of the protein on the periplasmic side due to their highly polar headgroups that mediate the interaction of the two transmembrane (TM) bundles by a network of lipid-lipid and lipid-protein hydrogen bonds. POPE lipids in particular facilitate the closure of periplasmic gate by promoting a hinge formation in TM helices and an interbundle salt bridge formation. This study explains how the alternating access mechanism and the flippase activity in ABC exporters could be lipid-dependent.

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.

Electrostatic lock in the transport cycle of the multidrug resistance transporter EmrE

EmrE is a small, homodimeric membrane transporter that exploits the established electrochemical proton gradient across the Escherichia coli inner membrane to export toxic polyaromatic cations, prototypical of the wider small-multidrug resistance transporter family. While prior studies have established many fundamental aspects of the specificity and rate of substrate transport in EmrE, low resolution of available structures has hampered identification of the transport coupling mechanism. Here we present a complete, refined atomic structure of EmrE optimized against available cryo-electron microscopy (cryo-EM) data to delineate the critical interactions by which EmrE regulates its conformation during the transport process. With the model, we conduct molecular dynamics simulations of the transporter in explicit membranes to probe EmrE dynamics under different substrate loading and conformational states, representing different intermediates in the transport cycle. The refined model is stable under extended simulation. The water dynamics in simulation indicate that the hydrogen-bonding networks around a pair of solvent-exposed glutamate residues (E14) depend on the loading state of EmrE. One specific hydrogen bond from a tyrosine (Y60) on one monomer to a glutamate (E14) on the opposite monomer is especially critical, as it locks the protein conformation when the glutamate is deprotonated. The hydrogen bond provided by Y60 lowers the [Formula: see text] of one glutamate relative to the other, suggesting both glutamates should be protonated for the hydrogen bond to break and a substrate-free transition to take place. These findings establish the molecular mechanism for the coupling between proton transfer reactions and protein conformation in this proton-coupled secondary transporter.

A "cross-stitched" peptide with improved helicity and proteolytic stability

A new computational approach to obtain quantitative energy profiles for helix folding was used in the design of orthogonal hydrocarbon and lactam bicyclic peptides. The proteolytically stable, "cross-stitched" peptide SRC2-BCP1 shows nanomolar affinity for estrogen receptor α and X-ray crystallography confirms a helical binding pose.

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.

Dissecting the Forces that Dominate Dimerization of the Nucleotide Binding Domains of ABCB1

P-glycoprotein, also known as multidrug resistance protein 1 or ABCB1, can export a wide range of chemically unrelated compounds, including chemotherapeutic drugs. ABCB1 consists of two transmembrane domains that form the substrate binding and translocation domain, and of two cytoplasmic nucleotide binding domains (NBDs) that energize substrate transport by ATP binding and hydrolysis. ATP binding triggers dimerization of the NBDs, which switches the transporter from an inward facing to an outward facing transmembrane domain conformation. We performed MD simulations to study the dynamic behavior of the NBD dimer in the presence or absence of nucleotides. In the apo configuration, the NBDs were overall attractive to each other as shown in the potential of mean force profile, but the energy well was shallow and broad. In contrast, a sharp and deep energy minimum (∼-42 kJ/mol) was found in the presence of ATP, leading to a well-defined conformation. Motif interaction network analyses revealed that ATP stabilizes the NBD dimer by serving as the central hub for interdomain connections. Simulations showed that forces promoting dimerization are multilayered, dominated by electrostatic interactions between the nucleotide and conserved amino acids of the signature sequence and the Walker A motif. In addition, direct and water-bridged hydrogen bonds between NBDs provided conformation-defining interactions. Importantly, we characterized a largely unrecognized but essential contribution from hydrophobic interactions between the adenine moiety of the nucleotides and a hydrophobic surface of the X-loop to the stabilization of the nucleotide-bound NBD dimer. These hydrophobic interactions lead to a sharp energy minimum, thereby conformationally restricting the nucleotide-bound state.

Analysis of an ATP-induced conformational transition of ABC transporter MsbA using a coarse-grained model

Upon the binding of ATP molecules to nucleotide binding domains (NBDs), ATP-binding cassette (ABC) exporters undergo a conformational transition from an inward-facing (IF) to an outward-facing (OF) state. This molecular event is a typical example of chemo-mechanical coupling. However, the underlying mechanism remains unclear. In this study, we analyzed the IF→OF transition of a representative ABC exporter, MsbA, by solving the equation of motion under an elastic network model (ENM). ATP was represented as a single node in ENM or replaced by external forces. When two ATP nodes were added to the ENM of the IF state protein, the two NBDs dimerized; subsequently, the two transmembrane domains opened toward the extracellular side, resulting in the formation of the OF structure. Such a conformational transition was also reproduced by applying external forces, which caused the rotational motion of the NBDs instead of the addition of ATP nodes. The process of the conformational transition was analyzed in detail using cross-correlation maps for node-node interactions. More importantly, it was revealed that the ATP binding energy is converted into distortion energy of several transmembrane helices. These results are useful for understanding the chemo-mechanical coupling in ABC transporters.

Membrane Permeability of Fatty Acyl Compounds Studied via Molecular Simulation

Interest in fatty acid-derived products as fuel and chemical precursors has grown substantially. Microbes can be genetically engineered to produce fatty acid-derived products that are able to cross host membranes and can be extracted into an applied organic overlay. This process is thought to be passive, with a rate dependent on the chemistry of the crossing compound. The relationship between the chemical composition and the energetics and kinetics of product accumulation within the overlay is not well understood. Through biased and unbiased molecular simulation, we compute the membrane permeability coefficients from production to extraction for different fatty acyl products, including fatty acids, fatty alcohols, fatty aldehydes, alkanes, and alkenes. These simulations identify specific interactions that accelerate the transit of aldehydes across the membrane bilayer relative to other oxidized products, specifically the lack of hydrogen bonds to the surrounding membrane environment. However, since extraction from the outer membrane leaflet into the organic phase is found to be rate limiting for the entire process, we find that fatty alcohols and fatty aldehydes would both manifest similar fluxes into a dodecane overlay under equivalent conditions, outpacing the accumulation of acids or alkanes into the organic phase. Since aldehydes are known to be highly reactive as well as toxic in high quantities, the findings suggest that indeed fatty alcohols are the optimal long-tail fatty acyl product for extraction.

Comparison of mechanistic transport cycle models of ABC exporters

ABC (ATP binding cassette) transporters, ubiquitous in all kingdoms of life, carry out essential substrate transport reactions across cell membranes. Their transmembrane domains bind and translocate substrates and are connected to a pair of nucleotide binding domains, which bind and hydrolyze ATP to energize import or export of substrates. Over four decades of investigations into ABC transporters have revealed numerous details from atomic-level structural insights to their functional and physiological roles. Despite all these advances, a comprehensive understanding of the mechanistic principles of ABC transporter function remains elusive. The human multidrug resistance transporter ABCB1, also referred to as P-glycoprotein (P-gp), is one of the most intensively studied ABC exporters. Using ABCB1 as the reference point, we aim to compare the dominating mechanistic models of substrate transport and ATP hydrolysis for ABC exporters and to highlight the experimental and computational evidence in their support. In particular, we point out in silico studies that enhance and complement available biochemical data. “This article is part of a Special Issue entitled: Beyond the Structure Function Horizon of Membrane Proteins edited by Ute Hellmich, Rupak Doshi and Benjamin McIlwain.”

Molecular determinants for the thermodynamic and functional divergence of uniporter GLUT1 and proton symporter XylE

GLUT1 facilitates the down-gradient translocation of D-glucose across cell membrane in mammals. XylE, an Escherichia coli homolog of GLUT1, utilizes proton gradient as an energy source to drive uphill D-xylose transport. Previous studies of XylE and GLUT1 suggest that the variation between an acidic residue (Asp27 in XylE) and a neutral one (Asn29 in GLUT1) is a key element for their mechanistic divergence. In this work, we combined computational and biochemical approaches to investigate the mechanism of proton coupling by XylE and the functional divergence between GLUT1 and XylE. Using molecular dynamics simulations, we evaluated the free energy profiles of the transition between inward- and outward-facing conformations for the apo proteins. Our results revealed the correlation between the protonation state and conformational preference in XylE, which is supported by the crystal structures. In addition, our simulations suggested a thermodynamic difference between XylE and GLUT1 that cannot be explained by the single residue variation at the protonation site. To understand the molecular basis, we applied Bayesian network models to analyze the alteration in the architecture of the hydrogen bond networks during conformational transition. The models and subsequent experimental validation suggest that multiple residue substitutions are required to produce the thermodynamic and functional distinction between XylE and GLUT1. Despite the lack of simulation studies with substrates, these computational and biochemical characterizations provide unprecedented insight into the mechanistic difference between proton symporters and uniporters.

We seek to address one intriguing question, the mechanistic distinction between active proton-coupled symporters and passive uniporters that are related in evolution. Proton-coupled symporters harness the transmembrane proton gradient to drive the substrate transport, while uniporters can only facilitate the passive substrate translocation. In this work, we focus on two sugar transporters GLUT1 and XylE, which belong to symporters and uniporters respectively but have high sequence similarity. We first applied molecular dynamics simulations to characterize the thermodynamic behaviors of apo GLUT1 and XylE, which are supposed to provide prominent details of mechanisms. From the identified difference in thermodynamics, we concluded that neutralizing protonation site in XylE is insufficient for its conversion to GLUT1 analog. To pinpoint extra elements contributing to their evolutionary divergence, we developed a novel network modeling scheme based on Bayesian network which shows impressive predictive power on residue mutations. Our models suggested the detailed mechanism of proton coupling in XylE and molecular basis of symporter/uniporter discrepancy. Furthermore, the modeling scheme could help to guide the design of biomolecules for desired functions.

Methodology for the Simulation of Molecular Motors at Different Scales

Millisecond-scale conformational transitions represent a seminal challenge for traditional molecular dynamics simulations, even with the help of high-end supercomputer architectures. Such events are particularly relevant to the study of molecular motors-proteins or abiological constructs that convert chemical energy into mechanical work. Here, we present a hybrid-simulation scheme combining an array of methods including elastic network models, transition path sampling, and advanced free-energy methods, possibly in conjunction with generalized-ensemble schemes to deliver a viable option for capturing the millisecond-scale motor steps of biological motors. The methodology is already implemented in large measure in popular molecular dynamics programs, and it can leverage the massively parallel capabilities of petascale computers. The applicability of the hybrid method is demonstrated with two examples, namely cyclodextrin-based motors and V-type ATPases.

Simulating the Activation of Voltage Sensing Domain for a Voltage-Gated Sodium Channel Using Polarizable Force Field

Voltage-gated sodium (Na_V) channels play vital roles in the signal transduction of excitable cells. Upon activation of a Na_V channel, the change of transmembrane voltage triggers conformational change of the voltage sensing domain, which then elicits opening of the pore domain and thus allows an influx of Na⁺ ions. Description of this process with atomistic details is in urgent demand. In this work, we simulated the partial activation process of the voltage sensing domain of a prokaryotic Na_V channel using a polarizable force field. We not only observed the conformational change of the voltage sensing domain from resting to preactive state, but also rigorously estimated the free energy profile along the identified reaction pathway. Comparison with the control simulation using an additive force field indicates that voltage-gating thermodynamics of Na_V channels may be inaccurately described without considering the electrostatic polarization effect.

Chemomechanical Coupling in Hexameric Protein-Protein Interfaces Harnesses Energy within V-Type ATPases

ATP synthase is the most prominent bioenergetic macromolecular motor in all life forms, utilizing the proton gradient across the cell membrane to fuel the synthesis of ATP. Notwithstanding the wealth of available biochemical and structural information inferred from years of experiments, the precise molecular mechanism whereby vacuolar (V-type) ATP synthase fulfills its biological function remains largely fragmentary. Recently, crystallographers provided the first high-resolution view of ATP activity in Enterococcus hirae V1-ATPase. Employing a combination of transition-path sampling and high-performance free-energy methods, the sequence of conformational transitions involved in a functional cycle accompanying ATP hydrolysis has been investigated in unprecedented detail over an aggregate simulation time of 65 μs. Our simulated pathways reveal that the chemical energy produced by ATP hydrolysis is harnessed via the concerted motion of the protein-protein interfaces in the V1-ring, and is nearly entirely consumed in the rotation of the central stalk. Surprisingly, in an ATPase devoid of a central stalk, the interfaces of this ring are perfectly designed for inducing ATP hydrolysis. However, in a complete V1-ATPase, the mechanical property of the central stalk is a key determinant of the rate of ATP turnover. The simulations further unveil a sequence of events, whereby unbinding of the hydrolysis product (ADP + Pi) is followed by ATP uptake, which, in turn, leads to the torque generation step and rotation of the center stalk. Molecular trajectories also bring to light multiple intermediates, two of which have been isolated in independent crystallography experiments.

What Can and Cannot Be Learned from Molecular Dynamics Simulations of Bacterial Proton-Coupled Oligopeptide Transporter GkPOT?

We have performed an extensive set of all-atom molecular dynamics (MD) simulations of a bacterial proton-coupled oligopeptide transporter (POT) in an explicit membrane environment. We have characterized both the local and global conformational dynamics of the transporter upon the proton and/or substrate binding, within a statistical framework. Our results reveal a clearly distinct behavior for local conformational dynamics in the absence and presence of the proton at the putative proton binding residue E310. Particularly, we find that the substrate binding conformation is drastically different in the two conditions, where the substrate binds to the protein in a lateral/vertical manner, in the presence/absence of the proton. We do not observe any statistically significant distinctive behavior in terms of the global conformational changes in different simulation conditions, within the time scales of our simulations. Our extensive simulations and analyses call into question the implicit assumption of many MD studies that local conformational changes observed in short simulations could provide clues to the global conformational changes that occur on much longer time scales. The linear regression analysis of quantities associated with the global conformational fluctuations, however, provides an indication of a mechanism involving the concerted motion of the transmembrane helices, consistent with the rocker-switch mechanism.

Differential Membrane Binding Mechanics of Synaptotagmin Isoforms Observed in Atomic Detail

Synaptotagmin (Syt) is a membrane-associated protein involved in vesicle fusion through the SNARE complex that is found throughout the human body in 17 different isoforms. These isoforms have two membrane-binding C2 domains, which sense Ca²⁺ and thereby promote anionic membrane binding and lead to vesicle fusion. Through molecular dynamics simulations using the highly mobile membrane mimetic acclerated bilayer model, we have investigated how small protein sequence changes in the Ca²⁺-binding loops of the C2 domains may give rise to the experimentally determined difference in binding kinetics between Syt-1 and Syt-7 isoforms. Syt-7 C2 domains are found to form more close contacts with anionic phospholipid headgroups, particularly in loop 1, where an additional positive charge in Syt-7 draws the loop closer to the membrane and causes the anchoring residue F167 to insert deeper into the bilayer than the corresponding methionine in Syt-1 (M173). By performing additional replica exchange umbrella sampling calculations, we demonstrate that these additional contacts increase the energetic cost of unbinding the Syt-7 C2 domains from the bilayer, causing them to unbind more slowly than their counterparts in Syt-1.

Effective Riemannian Diffusion Model for Conformational Dynamics of Biomolecular Systems

We present a Riemannian formalism for effective diffusion of biomolecules in collective variable spaces that provides a robust framework for conformational free energy calculation methods. Unlike their Euclidean counterparts, the Riemannian potential of mean force (PMF) and minimum free energy path (MFEP) are invariant under coordinate transformations. The presented formalism can be readily employed to modify the collective variable based enhanced sampling techniques, such as umbrella sampling (US) commonly used in biomolecular simulations, to take into account the role of intrinsic geometry of collective variable space. Although our model is mathematically equivalent to a Euclidean diffusion with a position-dependent diffusion tensor, the Riemannian formulation provides a more convenient framework for free energy calculation methods and path-finding algorithms aimed at characterizing the effective conformational dynamics of biomolecules. A simple three-dimensional toy model and a pentapeptide (met-enkephalin) simulated in an explicit solvent environment are used to illustrate the workings of the formalism and its implementation.

Coupling between ATP hydrolysis and protein conformational change in maltose transporter

As the intracellular part of maltose transporter, MalK dimer utilizes the energy of ATP hydrolysis to drive protein conformational change, which then facilitates substrate transport. Free energy evaluation of the complete conformational change before and after ATP hydrolysis is helpful to elucidate the mechanism of chemical-to-mechanical energy conversion in MalK dimer, but is lacking in previous studies. In this work, we used molecular dynamics simulations to investigate the structural transition of MalK dimer among closed, semi-open and open states. We observed spontaneous structural transition from closed to open state in the ADP-bound system and partial closure of MalK dimer from the semi-open state in the ATP-bound system. Subsequently, we calculated the reaction pathways connecting the closed and open states for the ATP- and ADP-bound systems and evaluated the free energy profiles along the paths. Our results suggested that the closed state is stable in the presence of ATP but is markedly destabilized when ATP is hydrolyzed to ADP, which thus explains the coupling between ATP hydrolysis and protein conformational change of MalK dimer in thermodynamics. Proteins 2017; 85:207-220. © 2016 Wiley Periodicals, Inc.

Investigating the dynamic nature of the ABC transporters: ABCB1 and MsbA as examples for the potential synergies of MD theory and EPR applications

ABC transporters are primary active transporters found in all kingdoms of life. Human multidrug resistance transporter ABCB1, or P-glycoprotein, has an extremely broad substrate spectrum and confers resistance against chemotherapy drug treatment in cancer cells. The bacterial ABC transporter MsbA is a lipid A flippase and a homolog to the human ABCB1 transporter, with which it partially shares its substrate spectrum. Crystal structures of MsbA and ABCB1 have been solved in multiple conformations, providing a glimpse into the possible conformational changes the transporter could be going through during the transport cycle. Crystal structures are inherently static, while a dynamic picture of the transporter in motion is needed for a complete understanding of transporter function. Molecular dynamics (MD) simulations and electron paramagnetic resonance (EPR) spectroscopy can provide structural information on ABC transporters, but the strength of these two methods lies in the potential to characterise the dynamic regime of these transporters. Information from the two methods is quite complementary. MD simulations provide an all atom dynamic picture of the time evolution of the molecular system, though with a narrow time window. EPR spectroscopy can probe structural, environmental and dynamic properties of the transporter in several time regimes, but only through the attachment sites of an exogenous spin label. In this review the synergistic effects that can be achieved by combining the two methods are highlighted, and a brief methodological background is also presented.

Microscopic Characterization of Membrane Transporter Function by In Silico Modeling and Simulation

Membrane transporters mediate one of the most fundamental processes in biology. They are the main gatekeepers controlling active traffic of materials in a highly selective and regulated manner between different cellular compartments demarcated by biological membranes. At the heart of the mechanism of membrane transporters lie protein conformational changes of diverse forms and magnitudes, which closely mediate critical aspects of the transport process, most importantly the coordinated motions of remotely located gating elements and their tight coupling to chemical processes such as binding, unbinding and translocation of transported substrate and cotransported ions, ATP binding and hydrolysis, and other molecular events fueling uphill transport of the cargo. An increasing number of functional studies have established the active participation of lipids and other components of biological membranes in the function of transporters and other membrane proteins, often acting as major signaling and regulating elements. Understanding the mechanistic details of these molecular processes require methods that offer high spatial and temporal resolutions. Computational modeling and simulations technologies empowered by advanced sampling and free energy calculations have reached a sufficiently mature state to become an indispensable component of mechanistic studies of membrane transporters in their natural environment of the membrane. In this article, we provide an overview of a number of major computational protocols and techniques commonly used in membrane transporter modeling and simulation studies. The article also includes practical hints on effective use of these methods, critical perspectives on their strengths and weak points, and examples of their successful applications to membrane transporters, selected from the research performed in our own laboratory.

In silico pharmacology: Drug membrane partitioning and crossing

Over the past decade, molecular dynamics (MD) simulations have become particularly powerful to rationalize drug insertion and partitioning in lipid bilayers. MD simulations efficiently support experimental evidences, with a comprehensive understanding of molecular interactions driving insertion and crossing. Prediction of drug partitioning is discussed with respect to drug families (anesthetics; β-blockers; non-steroidal anti-inflammatory drugs; antioxidants; antiviral drugs; antimicrobial peptides). To accurately evaluate passive permeation coefficients turned out to be a complex theoretical challenge; however the recent methodological developments based on biased MD simulations are particularly promising. Particular attention is paid to membrane composition (e.g., presence of cholesterol), which influences drug partitioning and permeation. Recent studies concerning in silico models of membrane proteins involved in drug transport (influx and efflux) are also reported here. These studies have allowed gaining insight in drug efflux by, e.g., ABC transporters at an atomic resolution, explicitly accounting for the mandatory forces induced by the surrounded lipid bilayer. Large-scale conformational changes were thoroughly analyzed.

Enhanced conformational sampling using replica exchange with concurrent solute scaling and hamiltonian biasing realized in one dimension

Replica exchange (REX) is a powerful computational tool for overcoming the quasi-ergodic sampling problem of complex molecular systems. Recently, several multidimensional extensions of this method have been developed to realize exchanges in both temperature and biasing potential space or the use of multiple biasing potentials to improve sampling efficiency. However, increased computational cost due to the multidimensionality of exchanges becomes challenging for use on complex systems under explicit solvent conditions. In this study, we develop a one-dimensional (1D) REX algorithm to concurrently combine the advantages of overall enhanced sampling from Hamiltonian solute scaling and the specific enhancement of collective variables using Hamiltonian biasing potentials. In the present Hamiltonian replica exchange method, termed HREST-BP, Hamiltonian solute scaling is applied to the solute subsystem, and its interactions with the environment to enhance overall conformational transitions and biasing potentials are added along selected collective variables associated with specific conformational transitions, thereby balancing the sampling of different hierarchical degrees of freedom. The two enhanced sampling approaches are implemented concurrently allowing for the use of a small number of replicas (e.g., 6 to 8) in 1D, thus greatly reducing the computational cost in complex system simulations. The present method is applied to conformational sampling of two nitrogen-linked glycans (N-glycans) found on the HIV gp120 envelope protein. Considering the general importance of the conformational sampling problem, HREST-BP represents an efficient procedure for the study of complex saccharides, and, more generally, the method is anticipated to be of general utility for the conformational sampling in a wide range of macromolecular systems.

Dimensionality of Collective Variables for Describing Conformational Changes of a Multi-Domain Protein

Collective variables (CVs) are often used in molecular dynamics simulations based on enhanced sampling algorithms to investigate large conformational changes of a protein. The choice of CVs in these simulations is essential because it affects simulation results and impacts the free-energy profile, the minimum free-energy pathway (MFEP), and the transition-state structure. Here we examine how many CVs are required to capture the correct transition-state structure during the open-to-close motion of adenylate kinase using a coarse-grained model in the mean forces string method to search the MFEP. Various numbers of large amplitude principal components are tested as CVs in the simulations. The incorporation of local coordinates into CVs, which is possible in higher dimensional CV spaces, is important for capturing a reliable MFEP. The Bayesian measure proposed by Best and Hummer is sensitive to the choice of CVs, showing sharp peaks when the transition-state structure is captured. We thus evaluate the required number of CVs needed in enhanced sampling simulations for describing protein conformational changes.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.