Self-guided Langevin dynamics study of regulatory interactions in NtrC

Beneficent and Maleficent Effects of Cations on Bufadienolide Binding to Na+,K+-ATPase

Kinetic properties and crystal structures of the Na⁺,K⁺-ATPase in complex with cardiotonic steroids (CTS) revealed significant differences between CTS subfamilies (Laursen et al.). Thus, we found beneficial effects of K⁺ on bufadienolide binding, which strongly contrasted with the well-known antagonism between K⁺ and cardenolides. In order to understand this peculiarity of bufalin interactions, we used docking and molecular dynamics simulations of the complexes involving Na⁺,K⁺-ATPase, bufadienolides (bufalin, cinobufagin), and ions (K⁺, Na⁺, Mg²⁺). The results revealed that bufadienolide binding is affected by (i) electrostatic attraction of the lactone ring by a cation and (ii) the ability of a cation to stabilize and "shape" the site constituted by transmembrane helices of the α-subunit (αM1-6). The latter effect was due to varying coordination patterns involving amino acid residues from helix bundles αM1-4 and αM5-10. Substituents on the steroid core of a bufadienolide add to and modify the cation effects. The above rationale is fully consistent with the ion effects on the kinetics of Na⁺,K⁺-ATPase/bufadienolide interactions.

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.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

Compound Molecular Logic in Accessing the Active Site of Mycobacterium tuberculosis Protein Tyrosine Phosphatase B

Protein tyrosine phosphatase B (PtpB) from Mycobacterium tuberculosis (Mtb) extends the bacteria's survival in hosts and hence is a potential target for Mtb-specific drugs. To study how Mtb-specific sequence insertions in PtpB may regulate access to its active site through large-amplitude conformational changes, we performed free-energy calculations using an all-atom explicit solvent model. Corroborated by biochemical assays, the results show that PtpB's active site is controlled via an "either/or" compound conformational gating mechanism, an unexpected discovery that Mtb has evolved to bestow a single enzyme with such intricate logical operations. In addition to providing unprecedented insights for its active-site surroundings, the findings also suggest new ways of inactivating PtpB.

K+ binding and proton redistribution in the E2P state of the H+, K+-ATPase

The H+, K+-ATPase (HKA) uses ATP to pump protons into the gastric lumen against a million-fold proton concentration gradient while counter-transporting K+ from the lumen. The mechanism of release of a proton into a highly acidic stomach environment, and the subsequent binding of a K+ ion necessitates a network of protonable residues and dynamically changing protonation states in the cation binding pocket dominated by five acidic amino acid residues E343, E795, E820, D824, and D942. We perform molecular dynamics simulations of spontaneous K+ binding to all possible protonation combinations of the acidic amino acids and carry out free energy calculations to determine the optimal protonation state of the luminal-open E2P state of the pump which is ready to bind luminal K+. A dynamic pKa correlation analysis reveals the likelihood of proton transfer events within the cation binding pocket. In agreement with in-vitro measurements, we find that E795 is likely to be protonated, and that E820 is at the center of the proton transfer network in the luminal-open E2P state. The acidic residues D942 and D824 are likely to remain protonated, and the proton redistribution occurs predominantly amongst the glutamate residues exposed to the lumen. The analysis also shows that a lower number of K+ ions bind at lower pH, modeled by a higher number of protons in the cation binding pocket, in agreement with the 'transport stoichiometry variation' hypothesis.

Raf-1 Cysteine-Rich Domain Increases the Affinity of K-Ras/Raf at the Membrane, Promoting MAPK Signaling

K-Ras4B preferentially activates Raf-1. The high-affinity interaction of Ras-binding domain (RBD) of Raf with Ras was solved, but the relative position of Raf's cysteine-rich domain (CRD) in the Ras/Raf complex at the membrane and key question of exactly how it affects Raf signaling are daunting. We show that CRD stably binds anionic membranes inserting a positively charged loop into the amphipathic interface. Importantly, when in complex with Ras/RBD, covalently connected CRD presents the same membrane interaction mechanism, with CRD locating at the space between the RBD and membrane. To date, CRD's role was viewed in terms of stabilizing Raf-membrane interaction. Our observations argue for a key role in reducing Ras/RBD fluctuations at the membrane, thereby increasing Ras/RBD affinity. Even without K-Ras, via CRD, Raf-1 can recruit to the membrane; however, by reducing the Ras/RBD fluctuations and enhancing Ras/RBD affinity at the membrane, CRD promotes Raf's activation and MAPK signaling over other pathways.

The phosphorelay signal transduction system in Candida glabrata: an in silico analysis

Signaling systems allow microorganisms to sense and respond to different stimuli through the modification of gene expression. The phosphorelay signal transduction system in eukaryotes involves three proteins: a sensor protein, an intermediate protein and a response regulator, and requires the transfer of a phosphate group between two histidine-aspartic residues. The SLN1-YPD1-SSK1 system enables yeast to adapt to hyperosmotic stress through the activation of the HOG1-MAPK pathway. The genetic sequences available from Saccharomyces cerevisiae were used to identify orthologous sequences in Candida glabrata, and putative genes were identified and characterized by in silico assays. An interactome analysis was carried out with the complete genome of C. glabrata and the putative proteins of the phosphorelay signal transduction system. Next, we modeled the complex formed between the sensor protein CgSln1p and the intermediate CgYpd1p. Finally, phosphate transfer was examined by a molecular dynamic assay. Our in silico analysis showed that the putative proteins of the C. glabrata phosphorelay signal transduction system present the functional domains of histidine kinase, a downstream response regulator protein, and an intermediate histidine phosphotransfer protein. All the sequences are phylogenetically more related to S. cerevisiae than to C. albicans. The interactome suggests that the C. glabrata phosphorelay signal transduction system interacts with different proteins that regulate cell wall biosynthesis and responds to oxidative and osmotic stress the same way as similar systems in S. cerevisiae and C. albicans. Molecular dynamics simulations showed complex formation between the response regulator domain of histidine kinase CgSln1 and intermediate protein CgYpd1 in the presence of a phosphate group and interactions between the aspartic residue and the histidine residue. Overall, our research showed that C. glabrata harbors a functional SLN1-YPD1-SSK1 phosphorelay system.

Glutamate Water Gates in the Ion Binding Pocket of Na+ Bound Na+, K+-ATPase

The dynamically changing protonation states of the six acidic amino acid residues in the ion binding pocket of the Na+, K+ -ATPase (NKA) during the ion transport cycle are proposed to drive ion binding, release and possibly determine Na+ or K+ selectivity. We use molecular dynamics (MD) and density functional theory (DFT) simulations to determine the protonation scheme of the Na+ bound conformation of NKA. MD simulations of all possible protonation schemes show that the bound Na+ ions are most stably bound when three or four protons reside in the binding sites, and that Glu954 in site III is always protonated. Glutamic acid residues in the three binding sites act as water gates, and their deprotonation triggers water entry to the binding sites. From DFT calculations of Na+ binding energies, we conclude that three protons in the binding site are needed to effectively bind Na+ from water and four are needed to release them in the next step. Protonation of Asp926 in site III will induce Na+ release, and Glu327, Glu954 and Glu779 are all likely to be protonated in the Na+ bound occluded conformation. Our data provides key insights into the role of protons in the Na+ binding and release mechanism of NKA.

Use of restrained molecular dynamics to predict the conformations of phosphorylated receiver domains in two-component signaling systems

Two‐component signaling (TCS) is the primary means by which bacteria, as well as certain plants and fungi, respond to external stimuli. Signal transduction involves stimulus‐dependent autophosphorylation of a sensor histidine kinase and phosphoryl transfer to the receiver domain of a downstream response regulator. Phosphorylation acts as an allosteric switch, inducing structural and functional changes in the pathway's components. Due to their transient nature, phosphorylated receiver domains are challenging to characterize structurally. In this work, we provide a methodology for simulating receiver domain phosphorylation to predict conformations that are nearly identical to experimental structures. Using restrained molecular dynamics, phosphorylated conformations of receiver domains can be reliably sampled on nanosecond timescales. These simulations also provide data on conformational dynamics that can be used to identify regions of functional significance related to phosphorylation. We first validated this approach on several well‐characterized receiver domains and then used it to compare the upstream and downstream components of the fungal Sln1 phosphorelay. Our results demonstrate that this technique provides structural insight, obtained in the absence of crystallographic or NMR information, regarding phosphorylation‐induced conformational changes in receiver domains that regulate the output of their associated signaling pathway. To our knowledge, this is the first time such a protocol has been described that can be broadly applied to TCS proteins for predictive purposes. Proteins 2016; 85:155–176. © 2016 Wiley Periodicals, Inc.

The Structural Basis of Oncogenic Mutations G12, G13 and Q61 in Small GTPase K-Ras4B

Ras mediates cell proliferation, survival and differentiation. Mutations in K-Ras4B are predominant at residues G12, G13 and Q61. Even though all impair GAP-assisted GTP → GDP hydrolysis, the mutation frequencies of K-Ras4B in human cancers vary. Here we aim to figure out their mechanisms and differential oncogenicity. In total, we performed 6.4 μs molecular dynamics simulations on the wild-type K-Ras4B (K-Ras4B(WT)-GTP/GDP) catalytic domain, the K-Ras4B(WT)-GTP-GAP complex, and the mutants (K-Ras4B(G12C/G12D/G12V)-GTP/GDP, K-Ras4B(G13D)-GTP/GDP, K-Ras4B(Q61H)-GTP/GDP) and their complexes with GAP. In addition, we simulated 'exchanged' nucleotide states. These comprehensive simulations reveal that in solution K-Ras4B(WT)-GTP exists in two, active and inactive, conformations. Oncogenic mutations differentially elicit an inactive-to-active conformational transition in K-Ras4B-GTP; in K-Ras4B(G12C/G12D)-GDP they expose the bound nucleotide which facilitates the GDP-to-GTP exchange. These mechanisms may help elucidate the differential mutational statistics in K-Ras4B-driven cancers. Exchanged nucleotide simulations reveal that the conformational transition is more accessible in the GTP-to-GDP than in the GDP-to-GTP exchange. Importantly, GAP not only donates its R789 arginine finger, but stabilizes the catalytically-competent conformation and pre-organizes catalytic residue Q61; mutations disturb the R789/Q61 organization, impairing GAP-mediated GTP hydrolysis. Together, our simulations help provide a mechanistic explanation of key mutational events in one of the most oncogenic proteins in cancer.

Tuning of the Na,K-ATPase by the beta subunit

The vital gradients of Na⁺ and K⁺ across the plasma membrane of animal cells are maintained by the Na,K-ATPase, an αβ enzyme complex, whose α subunit carries out the ion transport and ATP hydrolysis. The specific roles of the β subunit isoforms are less clear, though β2 is essential for motor physiology in mammals. Here, we show that compared to β1 and β3, β2 stabilizes the Na⁺-occluded E1P state relative to the outward-open E2P state, and that the effect is mediated by its transmembrane domain. Molecular dynamics simulations further demonstrate that the tilt angle of the β transmembrane helix correlates with its functional effect, suggesting that the relative orientation of β modulates ion binding at the α subunit. β2 is primarily expressed in granule neurons and glomeruli in the cerebellum, and we propose that its unique functional characteristics are important to respond appropriately to the cerebellar Na⁺ and K⁺ gradients.

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.

Free energy landscape of activation in a signalling protein at atomic resolution

The interconversion between inactive and active protein states, traditionally described by two static structures, is at the heart of signaling. However, how folded states interconvert is largely unknown due to the inability to experimentally observe transition pathways. Here we explore the free energy landscape of the bacterial response regulator NtrC by combining computation and NMR, and discover unexpected features underlying efficient signaling. We find that functional states are defined purely in kinetic and not structural terms. The need of a well-defined conformer, crucial to the active state, is absent in the inactive state, which comprises a heterogeneous collection of conformers. The transition between active and inactive states occurs through multiple pathways, facilitated by a number of nonnative transient hydrogen bonds, thus lowering the transition barrier through both entropic and enthalpic contributions. These findings may represent general features for functional conformational transitions within the folded state.

K+ congeners that do not compromise Na+ activation of the Na+,K+-ATPase: hydration of the ion binding cavity likely controls ion selectivity

The Na(+),K(+)-ATPase is essential for ionic homeostasis in animal cells. The dephosphoenzyme contains Na(+) selective inward facing sites, whereas the phosphoenzyme contains K(+) selective outward facing sites. Under normal physiological conditions, K(+) inhibits cytoplasmic Na(+) activation of the enzyme. Acetamidinium (Acet(+)) and formamidinium (Form(+)) have been shown to permeate the pump through the outward facing sites. Here, we show that these cations, unlike K(+), are unable to enter the inward facing sites in the dephosphorylated enzyme. Consistently, the organic cations exhibited little to no antagonism to cytoplasmic Na(+) activation. Na(+),K(+)-ATPase structures revealed a previously undescribed rotamer transition of the hydroxymethyl side chain of the absolutely conserved Thr(772) of the α-subunit. The side chain contributes its hydroxyl to Na(+) in site I in the E1 form and rotates to contribute its methyl group toward K(+) in the E2 form. Molecular dynamics simulations to the E1·AlF4 (-)·ADP·3Na(+) structure indicated that 1) bound organic cations differentially distorted the ion binding sites, 2) the hydroxymethyl of Thr(772) rotates to stabilize bound Form(+) through water molecules, and 3) the rotamer transition is mediated by water traffic into the ion binding cavity. Accordingly, dehydration induced by osmotic stress enhanced the interaction of the congeners with the outward facing sites and profoundly modified the organization of membrane domains of the α-subunit. These results assign a catalytic role for water in pump function, and shed light on a backbone-independent but a conformation-dependent switch between H-bond and dispersion contact as part of the catalytic mechanism of the Na(+),K(+)-ATPase.

Structure and mechanism of Zn2+-transporting P-type ATPases

Zinc is an essential micronutrient for all living organisms. It is required for signalling and proper functioning of a range of proteins involved in, for example, DNA binding and enzymatic catalysis. In prokaryotes and photosynthetic eukaryotes, Zn(2+)-transporting P-type ATPases of class IB (ZntA) are crucial for cellular redistribution and detoxification of Zn(2+) and related elements. Here we present crystal structures representing the phosphoenzyme ground state (E2P) and a dephosphorylation intermediate (E2·Pi) of ZntA from Shigella sonnei, determined at 3.2 Å and 2.7 Å resolution, respectively. The structures reveal a similar fold to Cu(+)-ATPases, with an amphipathic helix at the membrane interface. A conserved electronegative funnel connects this region to the intramembranous high-affinity ion-binding site and may promote specific uptake of cellular Zn(2+) ions by the transporter. The E2P structure displays a wide extracellular release pathway reaching the invariant residues at the high-affinity site, including C392, C394 and D714. The pathway closes in the E2·Pi state, in which D714 interacts with the conserved residue K693, which possibly stimulates Zn(2+) release as a built-in counter ion, as has been proposed for H(+)-ATPases. Indeed, transport studies in liposomes provide experimental support for ZntA activity without counter transport. These findings suggest a mechanistic link between PIB-type Zn(2+)-ATPases and PIII-type H(+)-ATPases and at the same time show structural features of the extracellular release pathway that resemble PII-type ATPases such as the sarcoplasmic/endoplasmic reticulum Ca(2+)-ATPase (SERCA) and Na(+), K(+)-ATPase. These findings considerably increase our understanding of zinc transport in cells and represent new possibilities for biotechnology and biomedicine.

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.

Simulating rare events using a weighted ensemble-based string method

We introduce an extension to the weighted ensemble (WE) path sampling method to restrict sampling to a one-dimensional path through a high dimensional phase space. Our method, which is based on the finite-temperature string method, permits efficient sampling of both equilibrium and non-equilibrium systems. Sampling obtained from the WE method guides the adaptive refinement of a Voronoi tessellation of order parameter space, whose generating points, upon convergence, coincide with the principle reaction pathway. We demonstrate the application of this method to several simple, two-dimensional models of driven Brownian motion and to the conformational change of the nitrogen regulatory protein C receiver domain using an elastic network model. The simplicity of the two-dimensional models allows us to directly compare the efficiency of the WE method to conventional brute force simulations and other path sampling algorithms, while the example of protein conformational change demonstrates how the method can be used to efficiently study transitions in the space of many collective variables.

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.

Enhanced Sampling in Free Energy Calculations: Combining SGLD with the Bennett's Acceptance Ratio and Enveloping Distribution Sampling Methods

One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.

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.

Toward canonical ensemble distribution from self-guided Langevin dynamics simulation

This work derives a quantitative description of the conformational distribution in self-guided Langevin dynamics (SGLD) simulations. SGLD simulations employ guiding forces calculated from local average momentums to enhance low-frequency motion. This enhancement in low-frequency motion dramatically accelerates conformational search efficiency, but also induces certain perturbations in conformational distribution. Through the local averaging, we separate properties of molecular systems into low-frequency and high-frequency portions. The guiding force effect on the conformational distribution is quantitatively described using these low-frequency and high-frequency properties. This quantitative relation provides a way to convert between a canonical ensemble and a self-guided ensemble. Using example systems, we demonstrated how to utilize the relation to obtain canonical ensemble properties and conformational distributions from SGLD simulations. This development makes SGLD not only an efficient approach for conformational searching, but also an accurate means for conformational sampling.

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

Based on the crystal structure of lactose permease (LacY) open to the cytoplasm, a hybrid molecular simulation approach with self-guided Langevin dynamics is used to describe conformational changes that lead to a periplasmic-open state. This hybrid approach consists of implicit (IM) and explicit (EX) membrane simulations and requires self-guided Langevin dynamics to enhance protein motions during the IM simulations. The pore radius of the lumen increases by 3.5 Å on the periplasmic side and decreases by 2.5 Å on the cytoplasmic side (relative to the crystal structure), suggesting a lumen that is fully open to the periplasm to allow for extracellular sugar transport and closed to the cytoplasm. Based on our simulations, the mechanism that triggers this conformational change to the periplasmic-open state is the protonation of Glu269 and binding of the disaccharide. Then, helix packing is destabilized by breaking of several side chains involved in hydrogen bonding (Asn245, Ser41, Glu374, Lys42, and Gln242). For the periplasmic-open conformations obtained from our simulations, helix-helix distances agree well with experimental measurements using double electron-electron resonance, fluorescence resonance energy transfer, and varying sized cross-linkers. The periplasmic-open conformations are also in compliance with various substrate accessibility/reactivity measurements that indicate an opening of the protein lumen on the periplasmic side on sugar binding. The comparison with these measurements suggests a possible incomplete closure of the cytoplasmic half in our simulations. However, the closure is sufficient to prevent the disaccharide from transporting to the cytoplasm, which is in accordance with the well-established alternating access model. Ser53, Gln60, and Phe354 are determined to be important in sugar transport during the periplasmic-open stage of the sugar transport cycle and the sugar is found to undergo an orientational change in order to escape the protein lumen.

Entropic mechanism of large fluctuation in allosteric transition

A statistical mechanical model of allosteric transitions in proteins is developed by extending the structure-based model of protein folding to cases of multiple native conformations. The partition function is calculated exactly within the model and the free-energy surface reflecting allostery is derived. This approach is applied to an example protein, the receiver domain of the bacterial enhancer-binding protein NtrC. The model predicts the large entropy associated with a combinatorial number of preexisting transition routes. This large entropy lowers the free-energy barrier of the allosteric transition, which explains the large structural fluctuation observed in the NMR data of NtrC. The global allosteric transformation of NtrC is explained by the shift of preexisting distribution of conformations upon phosphorylation, but the local structural adjustment around the phosphorylation site is explained by the complementary induced-fit mechanism. Structural disordering accompanied by fluctuating interactions specific to two allosteric conformations underlies a large number of routes of allosteric transition.

Receiver domain structure and function in response regulator proteins

During signal transduction by two-component regulatory systems, sensor kinases detect and encode input information while response regulators (RRs) control output. Most receiver domains function as phosphorylation-mediated switches within RRs, but some transfer phosphoryl groups in multistep phosphorelays. Conserved features of receiver domain amino acid sequence correlate with structure and hence function. Receiver domains catalyze their own phosphorylation and dephosphorylation in reactions requiring a divalent cation. Molecular dynamics simulations are supplementing structural investigation of the conformational changes that underlie receiver domain switch function. As understanding of features shared by all receiver domains matures, factors conferring differences (e.g. in reaction rate or specificity) are receiving increased attention. Numerous examples of atypical receiver or pseudo-receiver domains that function without phosphorylation have recently been characterized.

Large-scale conformational sampling of proteins using temperature-accelerated molecular dynamics

We show how to apply the method of temperature-accelerated molecular dynamics (TAMD) in collective variables [Maragliano L, Vanden-Eijnden E (2006) Chem Phys Lett 426:168-175] to sample the conformational space of multidomain proteins in all-atom, explicitly solvated molecular dynamics simulations. The method allows the system to hyperthermally explore the free-energy surface in a set of collective variables computed at the physical temperature. As collective variables, we pick Cartesian coordinates of centers of contiguous subdomains. The method is applied to the GroEL subunit, a 55-kDa, three-domain protein, and HIV-1 gp120. For GroEL, the method induces in about 40 ns conformational changes that recapitulate the t --> r('') transition and are not observed in unaccelerated molecular dynamics: The apical domain is displaced by 30 A, with a twist of 90 degrees relative to the equatorial domain, and the root-mean-squared deviation relative to the r('') conformer is reduced from 13 to 5 A, representing fairly high predictive capability. For gp120, the method predicts both counterrotation of inner and outer domains and disruption of the so-called bridging sheet. In particular, TAMD on gp120 initially in the CD4-bound conformation visits conformations that deviate by 3.6 A from the gp120 conformer in complex with antibody F105, again reflecting good predictive capability. TAMD generates plausible all-atom models of the so-far structurally uncharacterized unliganded conformation of HIV-1 gp120, which may prove useful in the development of inhibitors and immunogens. The fictitious temperature employed also gives a rough estimate of 10 kcal/mol for the free-energy barrier between conformers in both cases.