Calculating 13 C NMR chemical shifts of large molecules using the eXtended ONIOM method at high accuracy with a low cost.

Fragmentation-based methods for nuclear magnetic resonance (NMR) chemical shift calculations have become more and more popular in first-principles calculations of large molecules. However, there are many options for a fragmentation-based method to select, such as theoretical methods, fragmentation schemes, the number of levels of theory, etc. It is important to study the optimal combination of the options to achieve a good balance between accuracy and efficiency. Here we investigate different combinations of options used by a fragmentation-based method, the eXtended ONIOM (XO) method, for 13 C chemical shift calculations on a set of organic and biological molecules. We found that: (1) introducing Hartree-Fock exchange into density functional theory (DFT) could reduce the calculation error due to fragmentation in contrast to pure DFT functionals, while a hybrid functional, xOPBE, is generally recommended; (2) fragmentation schemes generated from the molecular tailoring approach (MTA) with small level parameter n, for example, n = 2 and the degree-based fragmentation method (DBFM) with n = 1, are sufficient to achieve satisfactory accuracy; (3) the two-level XO (XO2) NMR calculation is superior to the calculation with only one level of theory, as the second level (i.e., low level) of theory provides a way to well describe the long-range effect. These findings are beneficial to practical applications of fragmentation-based methods for NMR chemical shift calculations of large molecules.

Different conformational dynamics of SNARE protein Ykt6 among yeast and mammals.

Ykt6 is one of the most conserved SNARE (N-ethylmaleimide-sensitive factor attachment protein receptor) proteins involved in multiple intracellular membrane trafficking processes. The membrane-anchoring function of Ykt6 has been elucidated to result from its conformational transition from a closed state to an open state. Two ways of regulating the conformational transition were proposed: the C-terminal lipidation and the phosphorylation at the SNARE core. Despite many aspects of common properties, Ykt6 displays differential cellular localizations and functional behaviors in different species, such as yeast, mammals, and worms. The structure-function relationship underlying these differences remains elusive. Here, we combined biochemical characterization, single-molecule FRET measurement, and molecular dynamics simulation to compare the conformational dynamics of yeast and rat Ykt6. Compared to rat Ykt6 (rYkt6), yeast Ykt6 (yYkt6) has more open conformations and could not bind dodecylphosphocholine that inhibits rYkt6 in the closed state. A point mutation T46L/Q57A was shown to be able to convert yYkt6 to a more closed and dodecylphosphocholine-bound state, where Leu46 contributes key hydrophobic interactions for the closed state. We also demonstrated that the phospho-mutation S174D could shift the conformation of rYkt6 to a more open state, but the corresponding mutation S176D in yYkt6 leads to a slightly more closed conformation. These observations shed light on the regulatory mechanism underlying the variations of Ykt6 functions across species.

The importance of the compact disordered state in the fuzzy interactions between intrinsically disordered proteins.

The intrinsically disordered C-terminal domain (CTD) of protein 4.1G is able to specifically bind a 26-residue intrinsically disordered region of NuMA, forming a dynamic fuzzy complex. As one of a few cases of extremely fuzzy interactions between two intrinsically disordered proteins/regions (IDPs/IDRs) without induced folding, the principle of the binding is unknown. Here, we combined experimental and computational methods to explore the detailed mechanism of the interaction between 4.1G-CTD and NuMA. MD simulations suggest that the kinetic hub states in the structure ensemble of 4.1G-CTD are favorable in the fuzzy complex. The feature of these hub states is that the binding 'hot spot' motifs ßA and ßB exhibit ß strand propensities and are well packed to each other. The binding between 4.1G-CTD and NuMA is disrupted at low pH, which changes the intramolecular packing of 4.1G-CTD and weakens the packing between ßA and ßB motifs. Low pH conditions also lead to increased hydrodynamic radius and acceleration of backbone dynamics of 4.1G-CTD. All these results underscore the importance of tertiary structural arrangements and overall compactness of 4.1G-CTD in its binding to NuMA, i.e. the compact disordered state of 4.1G-CTD is crucial for binding. Different from the short linear motifs (SLiMs) that are often found to mediate IDP interactions, 4.1G-CTD functions as an intrinsically disordered domain (IDD), which is a functional and structural unit similar to conventional protein domains. This work sheds light on the molecular recognition mechanism of IDPs/IDRs and expands the conventional structure-function paradigm in protein biochemistry.

Conformational Features of Ras: Key Hydrogen-Bonding Interactions of Gln61 in the Intermediate State during GTP Hydrolysis.

The Ras protein is one of the most important drug targets for battling cancers. To effectively design novel drugs of Ras, we characterize here its conformational ensembles for the hydrolysis intermediate state RasGDP·Pi and the product state RasGDP by extensive replica-exchange molecular dynamics simulations. Several substates for RasGDP·Pi have been identified, while structural analyses have revealed an unrecognized hydrogen-bonding network that stabilizes the hydrolysis intermediate state. More interestingly, Gln61, which is involved in numerous oncogenic mutations, was found to be engaged in this hydrogen-bonding network, adopting a specific conformation that always points to Pi in contrast to that in the RasGTP state. The simulations also reveal that RasGDP has more than one substate, suggesting a conformational selection mechanism for the interaction between Ras and the guanine nucleotide exchange factors (GEFs). These findings offer new opportunities for the drug design of Ras by stabilizing the hydrolysis intermediate or disrupting its interaction with the GEFs.

The Role of Calcium in Regulating the Conformational Dynamics of d-Galactose/d-Glucose-Binding Protein Revealed by Markov State Model Analysis.

The d-glucose/d-galactose-binding protein (GGBP) from Escherichia coli is a substrate-binding protein (SBP) associated with sugar transport and chemotaxis. It is also a calcium-binding protein, which makes it unique in the SBP family. However, the functional importance of Ca2+ binding is not fully understood. Here, the calcium-dependent properties of GGBP were explored by all-atom molecular dynamics simulations and Markov state model (MSM) analysis as well as single-molecule Förster resonance energy transfer (smFRET) measurements. In agreement with previous experimental studies, we observed the structure stabilization effect of Ca2+ binding on the C-terminal domain of GGBP, especially the Ca2+-binding site. Interestingly, the MSMs of calcium-depleted GGBP and calcium-bound GGBP (GGBP/Ca2+) demonstrate that Ca2+ greatly stabilizes the open conformation, and smFRET measurements confirmed this result. Further analysis reveals that Ca2+ binding disturbs the local hydrogen bonding interactions and the conformational dynamics of the hinge region, thereby weakening the long-range interdomain correlations to favor the open conformation. These results suggest an active regulatory role of Ca2+ binding in GGBP, which finely tunes the conformational distribution. The work sheds new light on the study of calcium-binding proteins in prokaryotes.

Revealing Thermodynamics and Kinetics of Lipid Self-Assembly by Markov State Model Analysis.

Self-assembly is ubiquitous in the realm of biology and has become an elegant bottom-up approach to fabricate new materials. Although molecular dynamics (MD) simulations can complement experiments by providing the missing atomic details, it still remains a grand challenge to reveal the thermodynamic and kinetic information on a self-assembly system. In this work, we demonstrate for the first time that the Markov state model analysis can be used to delineate the variation of free energy during the self-assembly process of a typical amphiphilic lipid dipalmitoyl-phosphatidylcholine (DPPC). Free energy profiles against the solvent-accessible surface area and the root-mean-square deviation have been derived from extensive MD results of more than five hundred trajectories, which identified a metastable crossing-cylinder (CC) state and a transition state of the distorted bilayer with a free energy barrier of ∼0.02 kJ mol-1 per DPPC lipid, clarifying a long-standing speculation for 20 years that there exists a free energy barrier during lipid self-assembly. Our simulations also unearth two mesophase structures at the early stage of self-assembly, discovering two assembling pathways to the CC state that have never been reported before. Further thermodynamic analysis derives the contributions from the enthalpy and the entropy terms to the free energy, demonstrating the critical role played by the enthalpy-entropy compensation. Our strategy opens the door to quantitatively understand the self-assembly processes in general and provides new opportunities for identifying common thermodynamic and kinetic patterns in different self-assembly systems and inspiring new ideas for experiments. It may also contribute to the refinement of force field parameters of various self-assembly systems.

The enhanced extended phenomenological kinetics method to deal with timescale disparity problem among different reaction pathways.

Kinetic Monte Carlo method can provide valuable mechanistic insights for catalytic systems. Nonetheless, it suffers from the notorious problem of timescale disparity due to the existence of the complex catalytic network that consists of fast events and slow events. Previously, we have proposed the extended phenomenological kinetics (XPK) method that effectively deals with the timescale disparity problem between diffusion and reaction. However, it remains a great challenge to simulate systems with timescale disparity among different reaction pathways, which is important when selectivity is the major concern. In this study, we implement the enhanced XPK method to address this problem. The new algorithm works by identifying states connected through fast transitions and compressing them into a "superstate" when the chosen states satisfy a local steadystate condition. This state compression algorithm simplifies the reaction network by concealing the fast transitions. The accuracy and efficiency of the algorithm are demonstrated by two model systems: selective catalytic hydrogenation and selective catalytic decomposition. The enhanced XPK method is expected to be beneficial to the kinetic simulations of catalytic systems, especially those with complex reaction networks.

Dynamic multivalent interactions of intrinsically disordered proteins.

Protein-protein interactions involving intrinsically disordered proteins (IDPs) usually display dynamic and multivalent features. Recent experimental data revealed myriad functional roles of the dynamic multivalent interaction (DMI) of IDPs. However, characterization of DMI remains a challenge due to its complex and promiscuous nature. Recent studies start showing that understanding the mechanistic role of DMI relies on combined use of various techniques and construction of microscopic models in elucidating the binding thermodynamics and kinetics.

Glycerol transport through the aquaglyceroporin GlpF: bridging dynamics and kinetics with atomic simulation.

The aquaglyceroporin GlpF is a member of the aquaporin family. It selectively conducts small molecules, such as glycerol, across the cell membrane under a concentration gradient of the substrate. Atomistic molecular dynamics (MD) simulation would provide great insight into the substrate transport mechanism of GlpF and membrane channels alike. Ideally, non-equilibrium simulations under various concentration gradients of glycerol are desired to emulate the transportation in cells, but this kind of simulation is difficult due to a complicated system setup and high computational cost. Here, we present a new strategy to extract non-equilibrium kinetic information from equilibrium MD simulation. We first performed long-time (totally 22.5 µs) multi-copy equilibrium MD simulations of glycerol conduction through GlpF. Tens of times the spontaneous permeation of glycerol through GlpF was observed, allowing us to elucidate the detailed mechanism of the stereoselectivity for glycerol. Then we employed Markov state model (MSM) analysis of the MD trajectories to identify the intermediate states during glycerol transport and calculate the inter-state transition rate constants. Based on the results of MSM analysis, we built the kinetic models of glycerol transport and calculated the glycerol fluxes under various concentration gradients by solving the master equations. The results agree well with the experimental measurement at a certain glycerol concentration, and provide holistic information on the glycerol conduction capacity of GlpF. Our work demonstrates that long-time atomistic MD simulations can now bridge the microscopic dynamics and the kinetic description of substance transport through membrane channels, hopefully facilitating the engineering of new selective channels for various molecules.

An unconventional ligand-binding mechanism of substrate-binding proteins: MD simulation and Markov state model analysis of BtuF.

In conventional "Venus Flytrap" mechanism, substrate-binding proteins (SBPs) interconvert between the open and closed conformations. Upon ligand binding, SBPs form a tightly closed conformation with the ligand bound at the interface of two domains. This mechanism was later challenged by many type III SBPs, such as the vitamin B12 -binding protein BtuF, in which the apo- and holo-state proteins adopt very similar conformations. Here, we combined molecular dynamics simulation and Markov state model analysis to study the conformational dynamics of apo- and B12 -bound BtuF. The results indicate that the crystal structures represent the only stable conformation of BtuF. Meanwhile, both apo- and holo-BtuF undergo large-scale interdomain motions with little energy cost. B12 binding casts little restraints on the interdomain motions, suggesting that ligand binding affinity is enhanced by the remaining conformational entropy of holo-BtuF. These results reveal a new paradigm of ligand recognition mechanism of SBPs. © 2019 Wiley Periodicals, Inc.

Structural Features and Energetics of the Periplasmic Entrance Opening of the Outer Membrane Channel TolC Revealed by Molecular Dynamics Simulation and Markov State Model Analysis.

TolC is a channel protein responsible for substrate translocation across the outer membrane, and it is also a part of the tripartite multidrug efflux pumps in Gram-negative bacteria. The crystal structure of TolC shows that the periplasmic entrance is tightly closed in the resting state, while substrate translocation definitely requires the entrance to open. How the occluded periplasmic entrance opens to allow passage of substrates remains elusive. In this work, we constructed a Markov state model from swarms of all-atom molecular dynamics (MD) simulation trajectories, which delineates the energetics of the conformational changes of TolC. Opening of the periplasmic entrance results in a monotonic increase in free energy and is accompanied by disruption of interprotomer interactions, whereas the intraprotomer interactions remain intact. Multi-ion potential of mean force (PMF) profiles for Na+ and Cl- permeation along the channel have been calculated, and the cation/anion permeability ratio derived from which are in good agreement with electrophysiological experiments. These results not only deepen our understanding of conformational dynamics of isolated TolC but also provide valuable vision of its functioning state in tripartite efflux pumps.

A Residue outside the Binding Site Determines the Gα Binding Specificity of GoLoco Motifs.

GoLoco motif-containing proteins regulate the nucleotide-binding state of Gα proteins in various signaling pathways. As guanine nucleotide dissociation inhibitors (GDIs), they bind Gα·GDP and inhibit GDP to GTP exchange. GoLoco proteins show binding selectivity toward different members of the Gα family. Although the Gαi1·GDP/RGS14 crystal structure explains the specific binding selectivity of the RGS14 GoLoco domain well, the mechanism of selective binding has not been understood for the more general features of short GoLoco domains found in tandem arrays in proteins like GPSM2/LGN/ dPins and GPSM1/AGS3. We explored the mechanism of differential interactions of GoLoco protein LGN with hGαi3 and hGαo. By combining mutagenesis experiments and molecular dynamics simulations, we identified a residue (Asp229 in hGαi3) away from the binding interface that remarkably affects the interaction between LGN and hGαi/o. A negatively charged residue at this position is required for high binding affinity. This affinity regulation mechanism was further verified by the cases of hGαi2 and dGαo, suggesting that this pathway is conserved among members of the Gα family.

A revisit of the conformational dynamics of SNARE protein rYkt6.

N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) proteins are involved in the fusion of vesicles with their target membranes. R-SNARE protein Ykt6 is one of the most conserved SNARE in eukaryotes. The conformational state of Ykt6 is regulated by the lipidations at its C-terminal motif. Previous studies show that the binding of dodecylphosphocholine (DPC) can stabilize a closed conformation of rat Ykt6 (rYkt6) and mimic the farnesylated rYkt6. Despite this model, the detailed conformational dynamics of Ykt6 is still unclear. Here, we combined smFRET and MD simulation to demonstrate that the un-lipidated rYkt6 adopts five major conformational states. DPC binding shifts the conformational distribution toward the more closed states. At the same time, there remain considerable fractions of open and semi-open conformations in the presence of DPC. These newly revealed dynamic features of rYkt6 are consistent with its unique functional diversity in neuronal cells.

The Dynamic Multisite Interactions between Two Intrinsically Disordered Proteins.

Protein interactions involving intrinsically disordered proteins (IDPs) comprise a variety of binding modes, from the well-characterized folding upon binding to dynamic fuzzy complexes. To date, most studies concern the binding of an IDP to a structured protein, while the interaction between two IDPs is poorly understood. In this study, NMR, smFRET, and molecular dynamics (MD) simulation are combined to characterize the interaction between two IDPs, the C-terminal domain (CTD) of protein 4.1G and the nuclear mitotic apparatus (NuMA) protein. It is revealed that CTD and NuMA form a fuzzy complex with remaining structural disorder. Multiple binding sites on both proteins were identified by molecular dynamics and mutagenesis studies. This study provides an atomic scenario in which two IDPs bearing multiple binding sites interact with each other in dynamic equilibrium. The combined approach employed here could be widely applicable for investigating IDPs and their dynamic interactions.

Generalized Switch Functions in the Multilevel Many-Body Expansion Method and Its Application to Water Clusters.

The many-body expansion (MBE) method is the basis of many fragment-based methods and is widely applied to the computation of large molecular systems. To reach linear-scaling computation, a cutoff must be used to discard those subsystems with long interfragment distances. However, this leads to a discontinuous potential energy surface (PES) that would cause various problems in geometry optimizations and molecular dynamics simulations. To solve this problem, we present a generalized-switch-function (GSF) approach to smooth the PES computed by the MBE method with the use of a cutoff distance. The GSFs are naturally normalized and are permutation invariant. This approach can be applied to adaptively computing any order of many-body correction energies with multilevel computational methods and is a dynamic subsystem approach. We have applied the two versions of our method, GSF-MBE(m)/L1 and GSF-MBE(m)/(L1:L2:L3), to water clusters. Thorough tests show that our method can indeed give smooth potential-energy surface and is linear scaling but without losing much accuracy for very large water clusters with appropriately chosen cutoff distances.

Maltose-binding protein effectively stabilizes the partially closed conformation of the ATP-binding cassette transporter MalFGK2.

Maltose transporter MalFGK2 is a type-I importer in the ATP-binding cassette (ABC) transporter superfamily. Upon the binding of its periplasmic binding protein, MalE, the ATPase activity of MalFGK2 can be greatly enhanced. Crystal structures of the MalFGK2-MalE-maltose complex in a so-called "pretranslocation" ("pre-T") state with a partially closed conformation suggest that the formation of this MalE-stabilized intermediate state is a key step leading to the outward-facing catalytic state. On the contrary, crosslinking and fluorescence studies suggest that ATP binding alone is sufficient to promote the outward-facing catalytic state, thereby doubting the role of MalE binding. To clarify the role of MalE binding and to gain deeper understanding of the molecular mechanisms of MalFGK2, we calculated the free energy surfaces (FESs) related to the lateral motion in the presence and absence of MalE using atomistic metadynamics simulations. The results showed that, in the absence of MalE, laterally closing motion was energetically forbidden but, upon MalE binding, more closed conformations similar to the pre-T state become more stable. The significant effect of MalE binding on the free energy landscapes was in agreement with crystallographic studies and confirmed the important role of MalE in stabilizing the pre-T state. Our simulations also revealed that the allosteric effect of MalE stimulation originates from the MalE-binding-promoted vertical motion between MalF and MalG cores, which was further supported by MD simulation of the MalE-independent mutant MalF500.

Difference distance map data of alternative crystal forms of UlaA.

We introduce the value of information obtained by comparing alternative crystal forms of the same sub-state (of outward open UlaA, our example protein), which is found in the same lattice configuration but different space groups. We compare instability estimates obtained using this new method (alternative crystal forms) with temperature factors. Using a transport assay result, we correlate observations for two homologous secondary structure elements, and show that the alternative states method for obtaining instability estimates provide differentiating information about an important and immobilized mid-TMS region. The data presented in this article are related to the article entitled "The V-motifs facilitate the substrate capturing step of the PTS elevator mechanism" (A. Vastermark, A. Driker, J. Weng, X. Li, J. Wang, M.H. Saier Jr., 2016).

Conformational Dynamics and Protein-Substrate Interaction of ABC Transporter BtuCD at the Occluded State Revealed by Molecular Dynamics Simulations.

ATP-binding cassette (ABC) transporters are ubiquitous in all three kingdoms of life and are implicated in many clinically relevant physiological processes. They couple the energy released by ATP hydrolysis to facilitate substrate translocation across cell membranes. The crystal structures of type II ABC importers have revealed their unique transmembrane domain architecture consisting of 10 transmembrane helices and their structurally conserved nucleotide-binding domains among all ABC transporters. However, molecular details of the interactions between the importers and their substrate remain largely elusive. Taking vitamin B12 importer BtuCD as an exemplar of type II importers, we investigated the dynamics of its occluded state and the detailed protein-substrate interactions using molecular dynamics simulation. Our trajectories show that the importer accommodates the substrate through a nonspecific binding mode as the substrate undergoes evident vertical and tilt motions inside the translocation cavity. Extensive hydrogen bond and hydrophobic interactions were observed between the substrate and the importer; however, most of these interactions are weak, with <38% occurrence. The presence of substrate leads to enlargement of the translocation cavity, especially at its cytoplasmic end, which may activate cytoplasmic regions and probably facilitate the transportation. The perturbations caused by periplasmic binding protein and nucleotides were also investigated. The study provides deeper insight into the translocation mechanism of BtuCD.

ATP Hydrolysis Induced Conformational Changes in the Vitamin B12 Transporter BtuCD Revealed by MD Simulations.

ATP binding cassette (ABC) transporters utilize the energy of ATP hydrolysis to uni-directionally transport substrates across cell membrane. ATP hydrolysis occurs at the nucleotide-binding domain (NBD) dimer interface of ABC transporters, whereas substrate translocation takes place at the translocation pathway between the transmembrane domains (TMDs), which is more than 30 angstroms away from the NBD dimer interface. This raises the question of how the hydrolysis energy released at NBDs is "transmitted" to trigger the conformational changes at TMDs. Using molecular dynamics (MD) simulations, we studied the post-hydrolysis state of the vitamin B12 importer BtuCD. Totally 3-µs MD trajectories demonstrate a predominantly asymmetric arrangement of the NBD dimer interface, with the ADP-bound site disrupted and the ATP-bound site preserved in most of the trajectories. TMDs response to ATP hydrolysis by separation of the L-loops and opening of the cytoplasmic gate II, indicating that hydrolysis of one ATP could facilitate substrate translocation by opening the cytoplasmic end of translocation pathway. It was also found that motions of the L-loops and the cytoplasmic gate II are coupled with each other through a contiguous interaction network involving a conserved Asn83 on the extended stretch preceding TM3 helix plus the cytoplasmic end of TM2/6/7 helix bundle. These findings entail a TMD-NBD communication mechanism for type II ABC importers.

The V-motifs facilitate the substrate capturing step of the PTS elevator mechanism.

We propose that the alternative crystal forms of outward open UlaA (which are experimental, not simulated, and contain the substrate in the cavity) can be used to interpret/validate the MD results from MalT (the substrate capture step, which involves the mobile second TMSs of the V-motifs, TMSs 2 and 7). Since the crystal contacts are the same between the two alternative crystal forms of outward open UlaA, the striking biological differences noted, including rearranged hydrogen bonds and salt bridge coordination, are not attributable to crystal packing differences. Using transport assays, we identified G58 and G286 as essential for normal vitamin C transport, but the comparison of alternative crystal forms revealed that these residues to unhinge TMS movements from substrate-binding side chains, rendering the mid-TMS regions of homologous TMSs 2 and 7 relatively immobile. While the TMS that is involved in substrate binding in MalT is part of the homologous bundle that holds the two separate halves of the transport assembly (two proteins) together, an unequal effect of the two knockouts was observed for UlaA where both V-motifs are free from such dimer interface interactions.