Probing the periplasmic-open state of lactose permease in response to sugar binding and proton translocation

Reformulation of the self-guided molecular simulation method

Self-guided molecular/Langevin dynamics (SGMD/SGLD) simulation methods were developed to enhance conformational sampling through promoting low frequency motion of molecular systems and have been successfully applied in many simulation studies. Quantitative understanding of conformational distribution in SGLD has been achieved by separating microscopic properties according to frequency. However, a missing link between the guiding factors and conformational distributions makes it highly empirical and system dependent when choosing the values of the guiding parameters. Based on the understanding that molecular interactions are the source of energy barriers and diffusion friction, this work reformulates the equation of the low frequency motion to resemble Langevin dynamics. This reformulation leads to new forms of guiding forces and establishes a relation between the guiding factors and conformational distributions. We call simulations with these new guiding forces the generalized self-guided molecular/Langevin dynamics (SGMDg/SGLDg). In addition, we present a new way to calculate low frequency properties and an efficient algorithm to implement SGMDg/SGLDg that minimizes memory usage and inter-processor communication. Through example simulations with a skewed double well system, an argon fluid, and a cryo-EM map flexible fitting case, we demonstrate the guiding effects on conformational distributions and conformational searching.

Structural and Functional Adaptability of Sucrose and Lactose Permeases from Escherichia coli to the Membrane Lipid Composition

The lipid environment in which membrane proteins are embedded can influence their structure and function. Lipid-protein interactions and lipid-induced conformational changes necessary for protein function remain intractable in vivo using high-resolution techniques. Using Escherichia coli strains in which the normal phospholipid composition can be altered or foreign lipids can be introduced, we established the importance of membrane lipid composition for the proper folding, assembly, and function of E. coli lactose (LacY) and sucrose (CscB) permeases. However, the molecular mechanism underlying the lipid dependence for active transport remains unknown. Herein, we demonstrate that the structure and function of CscB and LacY can be modulated by the composition of the lipid environment. Using a combination of assays (transport activity of the substrate, protein topology, folding, and assembly into the membrane), we found that alterations in the membrane lipid composition lead to lipid-dependent structural changes in CscB and LacY. These changes affect the orientation of residues involved in LacY proton translocation and impact the rates of protonation and deprotonation of E325 by affecting the arrangement of transmembrane domains in the vicinity of the R302-E325 charge pair. Furthermore, the structural changes caused by changes in membrane lipid composition can be altered by a single-point mutation, highlighting the adaptability of these transporters to their environment. Altogether, our results demonstrate that direct interactions between a protein and its lipid environment uniquely contribute to membrane protein organization and function. Because members of the major facilitator superfamily present with well-conserved functional architecture, we anticipate that our findings can be extrapolated to other membrane protein transporters.

Current Advances in Studying Clinically Relevant Transporters of the Solute Carrier (SLC) Family by Connecting Computational Modeling and Data Science

Organic anion and cation transporting proteins (OATs, OATPs, and OCTs), as well as the Multidrug and Toxin Extrusion (MATE) transporters of the Solute Carrier (SLC) family are playing a pivotal role in the discovery and development of new drugs due to their involvement in drug disposition, drug-drug interactions, adverse drug effects and related toxicity. Computational methods to understand and predict clinically relevant transporter interactions can provide useful guidance at early stages in drug discovery and design, especially if they include contemporary data science approaches. In this review, we summarize the current state-of-the-art of computational approaches for exploring ligand interactions and selectivity for these drug (uptake) transporters. The computational methods discussed here by highlighting interesting examples from the current literature are ranging from semiautomatic data mining and integration, to ligand-based methods (such as quantitative structure-activity relationships, and combinatorial pharmacophore modeling), and finally structure-based methods (such as comparative modeling, molecular docking, and molecular dynamics simulations). We are focusing on promising computational techniques such as fold-recognition methods, proteochemometric modeling or techniques for enhanced sampling of protein conformations used in the context of these ADMET-relevant SLC transporters with a special focus on methods useful for studying ligand selectivity.

Uptake dynamics in the Lactose permease (LacY) membrane protein transporter

The sugar transporter Lactose permease (LacY) of Escherichia coli has become a prototype to understand the underlying molecular details of membrane transport. Crystal structures have trapped the protein in sugar-bound states facing the periplasm, but with narrow openings unable to accommodate sugar. Therefore, the molecular details of sugar uptake remain elusive. In this work, we have used extended simulations and metadynamics sampling to explore a putative sugar-uptake pathway and associated free energy landscape. We found an entrance at helix-pair 2 and 11, which involved lipid head groups and residues Gln 241 and Gln 359. Furthermore, the protein displayed high flexibility on the periplasmic side of Phe 27, which is located at the narrowest section of the pathway. Interactions to Phe 27 enabled passage into the binding site, which was associated with a 24 ± 4 kJ/mol binding free energy in excellent agreement with an independent binding free energy calculation and experimental data. Two free energy minima corresponding to the two possible binding poses of the lactose analog β-D-galactopyranosyl-1-thio-β-D-galactopyranoside (TDG) were aligned with the crystal structure-binding pocket. This work outlines the chemical environment of a putative periplasmic sugar pathway and paves way for understanding substrate affinity and specificity in LacY.

Exploration of conformational changes in lactose permease upon sugar binding and proton transfer through coarse-grained simulations

Escherichia coli lactose permease (LacY) actively transports lactose and other galactosides across cell membranes through lactose/H⁺ symport process. Lactose/H⁺ symport is a highly complex process that involves sugar translocation, H⁺ transfer, and large-scale protein conformational changes. The complete picture of lactose/H⁺ symport is largely unclear due to the complexity and multiscale nature of the process. In this work, we develop the force field for sugar molecules compatible with PACE, a hybrid and coarse-grained force field that couples the united-atom protein models with the coarse-grained MARTINI water/lipid. After validation, we implement the new force field to investigate the binding of a β-d-galactopyranosyl-1-thio- β-d-galactopyranoside (TDG) molecule to a wild-type LacY. Results show that the local interactions between TDG and LacY at the binding pocket are consistent with the X-ray experiment. Transitions from inward-facing to outward-facing conformations upon TDG binding and protonation of Glu269 have been achieved from ∼5.5 µs simulations. Both the opening of the periplasmic side and closure of the cytoplasmic side of LacY are consistent with double electron-electron resonance and thiol cross-linking experiments. Our analysis suggests that the conformational changes of LacY are a cumulative consequence of interdomain H-bonds breaking at the periplasmic side, interdomain salt-bridge formation at the cytoplasmic side, and the TDG orientational changes during the transition.

How Tolerant are Membrane Simulations with Mismatch in Area per Lipid between Leaflets?

Difficulties in estimating the correct number of lipids in each leaflet of complex bilayer membrane simulation systems make it inevitable to introduce a mismatch in lipid packing (i.e., area per lipid) and thus alter the lateral pressure of each leaflet. To investigate potential impacts of such mismatch on simulation results, we performed molecular dynamics simulations of saturated and monounsaturated lipid bilayers with and without gramicidin A or WALP23 at various mismatches by adjusting the number of lipids in the lower leaflet from no mismatch to a 25% reduction compared to that in the upper leaflet. All simulations were stable under the constant pressure barostat, but the mismatch induces asymmetric lipid packing between the leaflets, so that the upper leaflet becomes more ordered, and the lower leaflet becomes less ordered. The mismatch impacts on various bilayer properties are mild up to 5–10% mismatch, and bilayers with fully saturated chains appear to be more prone to these impacts than those with unsaturated tails. The nonvanishing leaflet surface tensions and the free energy derivatives with respect to the bilayer curvature indicate that the bilayer would be energetically unstable in the presence of mismatch. We propose a quantitative criterion for allowable mismatch based on the energetics derived from a continuum elastic model, which grows as a square root of the number of the lipids in the system. On the basis of this criterion, we infer that the area per lipid mismatch up to 5% would be tolerable in various membrane simulations of reasonable all-atom system sizes (40–160 lipids per leaflet).

Coarse-grained simulations of proton-dependent conformational changes in lactose permease

During lactose/H(+) symport, the Escherichia coli lactose permease (LacY) undergoes a series of global conformational transitions between inward-facing (open to cytoplasmic side) and outward-facing (open to periplasmic side) states. However, the exact local interactions and molecular mechanisms dictating those large-scale structural changes are not well understood. All-atom molecular dynamics simulations have been performed to investigate the molecular interactions involved in conformational transitions of LacY, but the simulations can only explore early or partial global structural changes because of the computational limits (< 100 ns). In this work, we implement a hybrid force field that couples the united-atom protein models with the coarse-grained MARTINI water/lipid, to investigate the proton-dependent dynamics and conformational changes of LacY. The effects of the protonation states on two key glutamate residues (Glu325 and Glu269) have been studied. Our results on the salt-bridge dynamics agreed with all-atom simulations at early short time period, validating our simulations. From our microsecond simulations, we were able to observe the complete transition from inward-facing to outward-facing conformations of LacY. Our results showed that all helices have participated during the global conformational transitions and helical movements of LacY. The inter-helical distances measured in our simulations were consistent with the double electron-electron resonance experiments at both cytoplasmic and periplasmic sides. Our simulations indicated that the deprotonation of Glu325 induced the opening of the periplasmics side and partial closure of the cytoplasmic side of LacY, while protonation of the Glu269 caused a stable cross-domain salt-bridge (Glu130-Arg344) and completely closed the cytoplasmic side. Proteins 2016; 84:1067-1074. © 2016 Wiley Periodicals, Inc.

CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field

Proper treatment of nonbonded interactions is essential for the accuracy of molecular dynamics (MD) simulations, especially in studies of lipid bilayers. The use of the CHARMM36 force field (C36 FF) in different MD simulation programs can result in disagreements with published simulations performed with CHARMM due to differences in the protocols used to treat the long-range and 1-4 nonbonded interactions. In this study, we systematically test the use of the C36 lipid FF in NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM. A wide range of Lennard-Jones (LJ) cutoff schemes and integrator algorithms were tested to find the optimal simulation protocol to best match bilayer properties of six lipids with varying acyl chain saturation and head groups. MD simulations of a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer were used to obtain the optimal protocol for each program. MD simulations with all programs were found to reasonably match the DPPC bilayer properties (surface area per lipid, chain order parameters, and area compressibility modulus) obtained using the standard protocol used in CHARMM as well as from experiments. The optimal simulation protocol was then applied to the other five lipid simulations and resulted in excellent agreement between results from most simulation programs as well as with experimental data. AMBER compared least favorably with the expected membrane properties, which appears to be due to its use of the hard-truncation in the LJ potential versus a force-based switching function used to smooth the LJ potential as it approaches the cutoff distance. The optimal simulation protocol for each program has been implemented in CHARMM-GUI. This protocol is expected to be applicable to the remainder of the additive C36 FF including the proteins, nucleic acids, carbohydrates, and small molecules.

CHARMM-GUI Input Generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM Simulations Using the CHARMM36 Additive Force Field

Proper treatment of nonbonded interactions is essential for the accuracy of molecular dynamics (MD) simulations, especially in studies of lipid bilayers. The use of the CHARMM36 force field (C36 FF) in different MD simulation programs can result in disagreements with published simulations performed with CHARMM due to differences in the protocols used to treat the long-range and 1-4 nonbonded interactions. In this study, we systematically test the use of the C36 lipid FF in NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM. A wide range of Lennard-Jones (LJ) cutoff schemes and integrator algorithms were tested to find the optimal simulation protocol to best match bilayer properties of six lipids with varying acyl chain saturation and head groups. MD simulations of a 1,2-dipalmitoyl-sn-phosphatidylcholine (DPPC) bilayer were used to obtain the optimal protocol for each program. MD simulations with all programs were found to reasonably match the DPPC bilayer properties (surface area per lipid, chain order parameters, and area compressibility modulus) obtained using the standard protocol used in CHARMM as well as from experiments. The optimal simulation protocol was then applied to the other five lipid simulations and resulted in excellent agreement between results from most simulation programs as well as with experimental data. AMBER compared least favorably with the expected membrane properties, which appears to be due to its use of the hard-truncation in the LJ potential versus a force-based switching function used to smooth the LJ potential as it approaches the cutoff distance. The optimal simulation protocol for each program has been implemented in CHARMM-GUI. This protocol is expected to be applicable to the remainder of the additive C36 FF including the proteins, nucleic acids, carbohydrates, and small molecules.

Probing the importance of lipid diversity in cell membranes via molecular simulation

Lipid membranes in prokaryotes and eukaryotes have a wide array of lipids that are necessary for proper membrane structure and function. In this paper, an introduction to lipid diversity in biology and a mini-review on how molecular simulations have been used to model biological membranes (primarily limited to one to three lipid types in most simulation-based models) is provided, which motivates the use of all-atom molecular dynamics (MD) simulations to study the effect of lipid diversity on properties of realistic membrane models of prokaryotes and eukaryotes. As an example, cytoplasmic membrane models of Escherichia coli were developed at different stages of the colony growth cycle (early-log, mid-log, stationary and overnight). The main difference between lipid compositions at each stage was the concentration of a cyclopropane-containing moiety on the sn-2 lipid acyl chain (cyC17:0). Triplicate MD simulations for each stage were run for 300 ns to study the influence of lipid diversity on the surface area per lipid, area compressibility modulus, deuterium order parameters, and electron density profiles. The overnight stage (also known as the death stage) had the highest average surface area per lipid, highest rigidity, and lowest bilayer thickness compare to other stages of E. coli cytoplasmic membrane. Although bilayer thickness did depend on the growth stage, the changes between these were small suggesting that the hydrophobic core of transmembrane proteins fit well with the membrane in all growth stages. Although it is still common practise in MD simulations of membrane proteins to use simple one- or two-component membranes, it can be important to use diverse lipid model membranes when membrane protein structure and function are influenced by changes in lipid membrane composition.

Self-guided Langevin dynamics via generalized Langevin equation

Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc.

Computational characterization of structural dynamics underlying function in active membrane transporters

Active transport of materials across the cellular membrane is one the most fundamental processes in biology. In order to accomplish this task, membrane transporters rely on a wide range of conformational changes spanning multiple time and size scales. These molecular events govern key functional aspects in membrane transporters, namely, coordinated gating motions underlying the alternating access mode of operation, and coupling of uphill transport of substrate to various sources of energy, for example, transmembrane electrochemical gradients and ATP binding and hydrolysis. Computational techniques such as molecular dynamics simulations and free energy calculations have equipped us with a powerful repertoire of biophysical tools offering unparalleled spatial and temporal resolutions that can effectively complement experimental methodologies, and therefore help fill the gap of knowledge in understanding the molecular basis of function in membrane transporters.

CHARMM-GUI Membrane Builder toward realistic biological membrane simulations

CHARMM-GUI Membrane Builder, http://www.charmm-gui.org/input/membrane, is a web-based user interface designed to interactively build all-atom protein/membrane or membrane-only systems for molecular dynamics simulations through an automated optimized process. In this work, we describe the new features and major improvements in Membrane Builder that allow users to robustly build realistic biological membrane systems, including (1) addition of new lipid types, such as phosphoinositides, cardiolipin (CL), sphingolipids, bacterial lipids, and ergosterol, yielding more than 180 lipid types, (2) enhanced building procedure for lipid packing around protein, (3) reliable algorithm to detect lipid tail penetration to ring structures and protein surface, (4) distance-based algorithm for faster initial ion displacement, (5) CHARMM inputs for P21 image transformation, and (6) NAMD equilibration and production inputs. The robustness of these new features is illustrated by building and simulating a membrane model of the polar and septal regions of E. coli membrane, which contains five lipid types: CL lipids with two types of acyl chains and phosphatidylethanolamine lipids with three types of acyl chains. It is our hope that CHARMM-GUI Membrane Builder becomes a useful tool for simulation studies to better understand the structure and dynamics of proteins and lipids in realistic biological membrane environments.

Flexible gates generate occluded intermediates in the transport cycle of LacY

The major facilitator superfamily (MFS) transporter lactose permease (LacY) alternates between cytoplasmic and periplasmic open conformations to co-transport a sugar molecule together with a proton across the plasma membrane. Indirect experimental evidence suggested the existence of an occluded transition intermediate of LacY, which would prevent leaking of the proton gradient. As no experimental structure is known, the conformational transition is not fully understood in atomic detail. We simulated transition events from a cytoplasmic open conformation to a periplasmic open conformation with the dynamic importance sampling molecular dynamics method and observed occluded intermediates. Analysis of water permeation pathways and the electrostatic free-energy landscape of a solvated proton indicated that the occluded state contains a solvated central cavity inaccessible from either side of the membrane. We propose a pair of geometric order parameters that capture the state of the pathway through the MFS transporters as shown by a survey of available crystal structures and models. We present a model for the occluded state of apo-LacY, which is similar to the occluded crystal structures of the MFS transporters EmrD, PepT_So, NarU, PiPT and XylE. Our simulations are consistent with experimental double electron spin–spin distance measurements that have been interpreted to show occluded conformations. During the simulations, a salt bridge that has been postulated to be involved in driving the conformational transition formed. Our results argue against a simple rigid-body domain motion as implied by a strict “rocker-switch mechanism” and instead hint at an intricate coupling between two flexible gates.

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The transport mechanism of LacY is hypothesized to involve an intermediate “occluded” state.

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Such a state is observed in computer simulations of the conformational transitions.

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Simulation data are validated with experimental double electron–electron spin resonance measurements.

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The structural gating elements of LacY are identified.

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Occluded LacY is similar to known occluded structures of homologous proteins.

Targeted conformational search with map-restrained self-guided Langevin dynamics: application to flexible fitting into electron microscopic density maps

We present a map-restrained self-guided Langevin dynamics (MapSGLD) simulation method for efficient targeted conformational search. The targeted conformational search represents simulations under restraints defined by experimental observations and/or by user specified structural requirements. Through map-restraints, this method provides an efficient way to maintain substructures and to set structure targets during conformational searching. With an enhanced conformational searching ability of self-guided Langevin dynamics, this approach is suitable for simulating large-scale conformational changes, such as the formation of macromolecular assemblies and transitions between different conformational states. Using several examples, we illustrate the application of this method in flexible fitting of atomic structures into density maps derived from cryo-electron microscopy.

Understanding the basis of a class of paradoxical mutations in AraC through simulations

Most mutations at position 15 in the N-terminal arm of the regulatory protein AraC leave the protein incapable of responding to arabinose and inducing the proteins required for arabinose catabolism. Mutations at other positions of the arm do not have this behavior. Simple energetic analysis of the interactions between the arm and bound arabinose do not explain the uninducibility of AraC with mutations at position 15. Extensive molecular dynamics (MD) simulations, carried out largely on the Open Science Grid, were done of the wild-type protein with and without bound arabinose and of all possible mutations at position 15, many of which were constructed and measured for this work. Good correlation was found for deviation of arm position during the simulations and inducibility as measured in vivo of the same mutant proteins. Analysis of the MD trajectories revealed that preservation of the shape of the arm is critical to inducibility. To maintain the correct shape of the arm, the strengths of three interactions observed to be strong in simulations of the wild-type AraC protein need to be preserved. These interactions are between arabinose and residue 15, arabinose and residues 8-9, and residue 13 and residue 15. The latter interaction is notable because residues L9, Y13, F15, W95, and Y97 form a hydrophobic cluster which needs to be preserved for retention of the correct shape.

Use of molecular modelling to probe the mechanism of the nucleoside transporter NupG

Nucleosides play key roles in biology as precursors for salvage pathways of nucleotide synthesis. Prokaryotes import nucleosides across the cytoplasmic membrane by proton- or sodium-driven transporters belonging to the Concentrative Nucleoside Transporter (CNT) family or the Nucleoside:H⁺ Symporter (NHS) family of the Major Facilitator Superfamily. The high resolution structure of a CNT from Vibrio cholerae has recently been determined, but no similar structural information is available for the NHS family. To gain a better understanding of the molecular mechanism of nucleoside transport, in the present study the structures of two conformations of the archetypical NHS transporter NupG from Escherichia coli were modelled on the inward- and outward-facing conformations of the lactose transporter LacY from E. coli, a member of the Oligosaccharide:H⁺ Symporter (OHS) family. Sequence alignment of these distantly related proteins (∼ 10% sequence identity), was facilitated by comparison of the patterns of residue conservation within the NHS and OHS families. Despite the low sequence similarity, the accessibilities of endogenous and introduced cysteine residues to thiol reagents were found to be consistent with the predictions of the models, supporting their validity. For example C358, located within the predicted nucleoside binding site, was shown to be responsible for the sensitivity of NupG to inhibition by p-chloromercuribenzene sulphonate. Functional analysis of mutants in residues predicted by the models to be involved in the translocation mechanism, including Q261, E264 and N228, supported the hypothesis that they play important roles, and suggested that the transport mechanisms of NupG and LacY, while different, share common features.

Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.

Proton-coupled dynamics in lactose permease

Lactose permease of Escherichia coli (LacY) catalyzes symport of a galactopyranoside and an H⁺ via an alternating access mechanism. The transition from an inward- to an outward-facing conformation of LacY involves sugar-release followed by deprotonation. Because the transition depends intimately upon the dynamics of LacY in a bilayer environment, molecular dynamics (MD) simulations may be the only means of following the accompanying structural changes in atomic detail. Here, we describe MD simulations of wild-type apo LacY in phosphatidylethanolamine (POPE) lipids that features two protonation states of the critical Glu325. While the protonated system displays configurational stability, deprotonation of Glu325 causes significant structural rearrangements that bring into proximity side chains important for H⁺ translocation and sugar binding and closes the internal cavity. Moreover, protonated LacY in phosphatidylcholine (DMPC) lipids shows that the observed dynamics are lipid-dependent. Together, the simulations describe early dynamics of the inward-to-outward transition of LacY that agree well with experimental data.

Efficient and Unbiased Sampling of Biomolecular Systems in the Canonical Ensemble: A Review of Self-Guided Langevin Dynamics

This review provides a comprehensive description of the self-guided Langevin dynamics (SGLD) and the self-guided molecular dynamics (SGMD) methods and their applications. Example systems are included to provide guidance on optimal application of these methods in simulation studies. SGMD/SGLD has enhanced ability to overcome energy barriers and accelerate rare events to affordable time scales. It has been demonstrated that with moderate parameters, SGLD can routinely cross energy barriers of 20 kT at a rate that molecular dynamics (MD) or Langevin dynamics (LD) crosses 10 kT barriers. The core of these methods is the use of local averages of forces and momenta in a direct manner that can preserve the canonical ensemble. The use of such local averages results in methods where low frequency motion "borrows" energy from high frequency degrees of freedom when a barrier is approached and then returns that excess energy after a barrier is crossed. This self-guiding effect also results in an accelerated diffusion to enhance conformational sampling efficiency. The resulting ensemble with SGLD deviates in a small way from the canonical ensemble, and that deviation can be corrected with either an on-the-fly or a post processing reweighting procedure that provides an excellent canonical ensemble for systems with a limited number of accelerated degrees of freedom. Since reweighting procedures are generally not size extensive, a newer method, SGLDfp, uses local averages of both momenta and forces to preserve the ensemble without reweighting. The SGLDfp approach is size extensive and can be used to accelerate low frequency motion in large systems, or in systems with explicit solvent where solvent diffusion is also to be enhanced. Since these methods are direct and straightforward, they can be used in conjunction with many other sampling methods or free energy methods by simply replacing the integration of degrees of freedom that are normally sampled by MD or LD.

Force-momentum-based self-guided Langevin dynamics: a rapid sampling method that approaches the canonical ensemble

The self-guided Langevin dynamics (SGLD) is a method to accelerate conformational searching. This method is unique in the way that it selectively enhances and suppresses molecular motions based on their frequency to accelerate conformational searching without modifying energy surfaces or raising temperatures. It has been applied to studies of many long time scale events, such as protein folding. Recent progress in the understanding of the conformational distribution in SGLD simulations makes SGLD also an accurate method for quantitative studies. The SGLD partition function provides a way to convert the SGLD conformational distribution to the canonical ensemble distribution and to calculate ensemble average properties through reweighting. Based on the SGLD partition function, this work presents a force-momentum-based self-guided Langevin dynamics (SGLDfp) simulation method to directly sample the canonical ensemble. This method includes interaction forces in its guiding force to compensate the perturbation caused by the momentum-based guiding force so that it can approximately sample the canonical ensemble. Using several example systems, we demonstrate that SGLDfp simulations can approximately maintain the canonical ensemble distribution and significantly accelerate conformational searching. With optimal parameters, SGLDfp and SGLD simulations can cross energy barriers of more than 15 kT and 20 kT, respectively, at similar rates for LD simulations to cross energy barriers of 10 kT. The SGLDfp method is size extensive and works well for large systems. For studies where preserving accessible conformational space is critical, such as free energy calculations and protein folding studies, SGLDfp is an efficient approach to search and sample the conformational space.

Lactose permease and the alternating access mechanism

Crystal structures of the lactose permease of Escherichia coli (LacY) reveal 12, mostly irregular transmembrane α-helices surrounding a large cavity open to the cytoplasm and a tightly sealed periplasmic side (inward-facing conformation) with the sugar-binding site at the apex of the cavity and inaccessible from the periplasm. However, LacY is highly dynamic, and binding of a galactopyranoside causes closing of the inward-facing cavity with opening of a complementary outward-facing cavity. Therefore, the coupled, electrogenic translocation of a sugar and a proton across the cytoplasmic membrane via LacY very likely involves a global conformational change that allows alternating access of sugar- and H(+)-binding sites to either side of the membrane. Here the various biochemical and biophysical approaches that provide strong support for the alternating access mechanism are reviewed. Evidence is also presented indicating that opening of the periplasmic cavity is probably the limiting step for binding and perhaps transport.