Designing Molecular Dynamics Simulations to Shift Populations of the Conformational States of Calmodulin

We elucidate the mechanisms that lead to population shifts in the conformational states of calcium-loaded calmodulin (Ca²⁺-CaM). We design extensive molecular dynamics simulations to classify the effects that are responsible for adopting occupied conformations available in the ensemble of NMR structures. Electrostatic interactions amongst the different regions of the protein and with its vicinal water are herein mediated by lowering the ionic strength or the pH. Amino acid E31, which is one of the few charged residues whose ionization state is highly sensitive to pH differences in the physiological range, proves to be distinctive in its control of population shifts. E31A mutation at low ionic strength results in a distinct change from an extended to a compact Ca²⁺-CaM conformation within tens of nanoseconds, that otherwise occur on the time scales of microseconds. The kinked linker found in this particular compact form is observed in many of the target-bound forms of Ca²⁺-CaM, increasing the binding affinity. This mutation is unique in controlling C-lobe dynamics by affecting the fluctuations between the EF-hand motif helices. We also monitor the effect of the ionic strength on the conformational multiplicity of Ca²⁺-CaM. By lowering the ionic strength, the tendency of nonspecific anions in water to accumulate near the protein surface increases, especially in the vicinity of the linker. The change in the distribution of ions in the vicinal layer of water allows N- and C- lobes to span a wide variety of relative orientations that are otherwise not observed at physiological ionic strength. E31 protonation restores the conformations associated with physiological environmental conditions even at low ionic strength.     

Molecular insights on CALX-CBD12 interdomain dynamics from MD simulations,RDCs, and SAXS

Na⁺/Ca²⁺ exchangers (NCXs) are secondary active transporters that couple the translocation of Na⁺ with the transport of Ca²⁺ in the opposite direction. The exchanger is an essential Ca²⁺ extrusion mechanism in excitable cells. It consists of a transmembrane domain and a large intracellular loop that contains two Ca²⁺-binding domains, CBD1 and CBD2. The two CBDs are adjacent to each other and form a two-domain Ca²⁺ sensor called CBD12. Binding of intracellular Ca²⁺ to CBD12 activates the NCX but inhibits the NCX of Drosophila, CALX. NMR spectroscopy and SAXS studies showed that CALX and NCX CBD12 constructs display significant interdomain flexibility in the apo state but assume rigid interdomain arrangements in the Ca²⁺-bound state. However, detailed structure information on CBD12 in the apo state is missing. Structural characterization of proteins formed by two or more domains connected by flexible linkers is notoriously challenging and requires the combination of orthogonal information from multiple sources. As an attempt to characterize the conformational ensemble of CALX-CBD12 in the apo state, we applied molecular dynamics (MD) simulations, NMR (¹H-¹⁵N residual dipolar couplings), and small-angle x-ray scattering (SAXS) data in a combined strategy to select an ensemble of conformations in agreement with the experimental data. This joint approach demonstrated that CALX-CBD12 preferentially samples closed conformations, whereas the wide-open interdomain arrangement characteristic of the Ca²⁺-bound state is less frequently sampled. These results are consistent with the view that Ca²⁺ binding shifts the CBD12 conformational ensemble toward extended conformers, which could be a key step in the NCXs’ allosteric regulation mechanism. This strategy, combining MD with NMR and SAXS, provides a powerful approach to select ensembles of conformations that could be applied to other flexible multidomain systems.     

Effects of cyclization on conformational dynamics and binding properties of Lys48-linked di-ubiquitin

In solution, Lys48-linked di-ubiquitin exists in dynamic equilibrium between closed and open conformations. To understand the effect of interdomain motion in polyubiquitin chains on their ability to bind ligands, we cyclized di-ubiquitin by cross-linking the free C terminus of the proximal ubiquitin with the side chain of residue 48 in the distal ubiquitin, using a chemical cross-linker, 1,6-Hexane-bis-vinylsulfone. Our NMR studies confirm that the cyclization affects conformational dynamics in di-ubiquitin by restricting opening of the interface and shifting the conformational equilibrium toward closed conformations. The cyclization, however, did not rigidly lock di-ubiquitin in a single closed conformation: The chain undergoes slow exchange between at least two closed conformations, characterized by interdomain contacts involving the same hydrophobic patch residues (Leu8-Ile44-Val70) as in the uncyclized di-ubiquitin. Lowering the pH changes the relative populations of these conformations, but in contrast with the uncyclized di-ubiquitin, does not lead to opening of the interface. This restriction of domain motions inhibits direct access of protein molecules to the hydrophobic patch residues located at the very center of the interdomain interface in di-ubiquitin, although the residual motions are sufficient to allow access of small molecules to the interface. This renders di-ubiquitin unable to bind protein molecules (e.g., UBA2 domain) in the normal manner, and thus could interfere with Ub(2) recognition by various downstream effectors. These results emphasize the importance of the opening/closing domain motions for the recognition and function of di-ubiquitin and possibly longer polyubiquitin chains.     

Carbon-13 NMR chemical shifts of the common amino acid residues measured in aqueous solutions of the linear tetrapeptides H-Gly-Gly- X-L- Ala-OH

The ¹³C nmr chemical shifts of the common amino acid residues were measured in D₂O solutions of the linear tetrapeptides H-Gly-Gly-X-L -Ala-OH. For Asp, Glu, Lys, Tyr and His, the titration shifts arising from the ionization of te amino acid side chains were also obtained. These data are compared with the corresponding ¹³C chemical shifts in the protected tetrapeptides CF₃CO-Gly-Gly-X-L -Ala-OCH₃, the linear pentapeptides H-Gly-Gly-X-Gly-Gly-OH, and the free amino acids. On this basism the selection of suitable “random coil” ¹³C chemical shifts for conformational studies of polypeptides chain is discussed.     

Conformational State Distributions and Catalytically Relevant Dynamics of?a Hinge-Bending Enzyme Studied by Single-Molecule FRET and a Coarse-Grained Simulation

Over the last few decades, a view has emerged showing that multidomain enzymes are biological machines evolved to harness stochastic kicks of solvent particles into highly directional functional motions. These intrinsic motions are structurally encoded, and Nature makes use of them to catalyze chemical reactions by means of ligand-induced conformational changes and states redistribution. Such mechanisms align reactive groups for efficient chemistry and stabilize conformers most proficient for catalysis. By combining single-molecule Förster resonance energy transfer measurements with normal mode analysis and coarse-grained mesoscopic simulations, we obtained results for a hinge-bending enzyme, namely phosphoglycerate kinase (PGK), which support and extend these ideas. From single-molecule Förster resonance energy transfer, we obtained insight into the distribution of conformational states and the dynamical properties of the domains. The simulations allowed for the characterization of interdomain motions of a compact state of PGK. The data show that PGK is intrinsically a highly dynamic system sampling a wealth of conformations on timescales ranging from nanoseconds to milliseconds and above. Functional motions encoded in the fold are performed by the PGK domains already in its ligand-free form, and substrate binding is not required to enable them. Compared to other multidomain proteins, these motions are rather fast and presumably not rate-limiting in the enzymatic reaction. Ligand binding slightly readjusts the orientation of the domains and feasibly locks the protein motions along a preferential direction. In addition, the functionally relevant compact state is stabilized by the substrates, and acts as a prestate to reach active conformations by means of Brownian motions.     

NMR assignment of the N-terminal region of human La free and in complex with RNA

¹H, ¹⁵N and ¹³C chemical shift assignments are presented for the N-terminal region of human La protein, in the apo and 5′-UUUU RNA-bound state. Secondary structure analysis shows conformational changes in the interdomain linker upon complex formation.     

Conformational State Distributions and Catalytically Relevant Dynamics of a Hinge-Bending Enzyme Studied by Single-Molecule FRET and a Coarse-Grained Simulation

Over the last few decades, a view has emerged showing that multidomain enzymes are biological machines evolved to harness stochastic kicks of solvent particles into highly directional functional motions. These intrinsic motions are structurally encoded, and Nature makes use of them to catalyze chemical reactions by means of ligand-induced conformational changes and states redistribution. Such mechanisms align reactive groups for efficient chemistry and stabilize conformers most proficient for catalysis. By combining single-molecule Förster resonance energy transfer measurements with normal mode analysis and coarse-grained mesoscopic simulations, we obtained results for a hinge-bending enzyme, namely phosphoglycerate kinase (PGK), which support and extend these ideas. From single-molecule Förster resonance energy transfer, we obtained insight into the distribution of conformational states and the dynamical properties of the domains. The simulations allowed for the characterization of interdomain motions of a compact state of PGK. The data show that PGK is intrinsically a highly dynamic system sampling a wealth of conformations on timescales ranging from nanoseconds to milliseconds and above. Functional motions encoded in the fold are performed by the PGK domains already in its ligand-free form, and substrate binding is not required to enable them. Compared to other multidomain proteins, these motions are rather fast and presumably not rate-limiting in the enzymatic reaction. Ligand binding slightly readjusts the orientation of the domains and feasibly locks the protein motions along a preferential direction. In addition, the functionally relevant compact state is stabilized by the substrates, and acts as a prestate to reach active conformations by means of Brownian motions.     

Structural origins of high apparent dielectric constants experienced by ionizable groups in the hydrophobic core of a protein

The side chains of Lys66, Asp66, and Glu66 in staphylococcal nuclease are fully buried and surrounded mainly by hydrophobic matter, except for internal water molecules associated with carboxylic oxygen atoms. These ionizable side chains titrate with pK_a values of 5.7, 8.8, and 8.9, respectively. To reproduce these pK_a values with continuum electrostatics calculations, we treated the protein with high dielectric constants. We have examined the structural origins of these high apparent dielectric constants by using NMR spectroscopy to characterize the structural response to the ionization of these internal side chains. Substitution of Val66 with Lys66 and Asp66 led to increased conformational fluctuations of the microenvironments surrounding these groups, even under pH conditions where Lys66 and Asp66 are neutral. When Lys66, Asp66, and Glu66 are charged, the proteins remain almost fully folded, but resonances for a few backbone amides adjacent to the internal ionizable residues are broadened. This suggests that the ionization of the internal groups promotes a local increase in dynamics on the intermediate timescale, consistent with either partial unfolding or increased backbone fluctuations of helix 1 near residue 66, or, less likely, with increased fluctuations of the charged side chains at position 66. These experiments confirm that the high apparent dielectric constants reported by internal Lys66, Asp66, and Glu66 reflect localized changes in conformational fluctuations without incurring detectable global structural reorganization. To improve structure-based pK_a calculations in proteins, we will need to learn how to treat this coupling between ionization of internal groups and local changes in conformational fluctuations explicitly.     

A new method for modeling large-scale rearrangements of protein domains

A method for modeling large-scale rearrangements of protein domains connected by a single- or a double-stranded linker is proposed. Multidomain proteins may undergo substantial domain displacements, while their intradomain structure remains essentially unchanged. The method allows automatic identification of an interdomain linker and builds an all-atom model of a protein structure in internal coordinates. Torsion angles belonging to the interdomain linkers and side chains potentially able to form domain interfaces are set free while all remaining torsions, bond lengths, and bond angles are fixed. Large-scale sampling of the reduced torsion conformational subspace is effected with the “biased probability Monte Carlo-minimization” method [Abagyan, R.A., Totrov, M.M. (1994): J. Mol. Biol. 235, 983–1002]. Solvation and side-chain entropic contributions are added to the energy function. A special procedure has been developed to generate concerted deformations of a double-stranded interdomain linker in such a way that the polypeptide chain continuity is preserved. The method was tested on Bence-Jones protein with a single-stranded linker and lysine/arginine/ornithine-binding (LAO) protein with a double-stranded linker. For each protein, structurally diverse low-energy conformations with ideal covalent geometry were generated, and an overlap between two sets of conformations generated starting from the crystallographically determined “closed” and “open” forms was found. One of the low-energy conformations generated in a run starting from the LAO “closed” form was only 2.2 Å away from the structure of the “open” form. The method can be useful in predicting the scope of possible domain rearrangements of a multidomain protein. Proteins 27:410–424, 1997. © 1997 Wiley-Liss, Inc.     

Coupled intra- and interdomain dynamics support domain cross-talk in Pin1

The functional mechanisms of multidomain proteins often exploit interdomain interactions, or “cross-talk.” An example is human Pin1, an essential mitotic regulator consisting of a Trp–Trp (WW) domain flexibly tethered to a peptidyl-prolyl isomerase (PPIase) domain, resulting in interdomain interactions important for Pin1 function. Substrate binding to the WW domain alters its transient contacts with the PPIase domain via means that are only partially understood. Accordingly, we have investigated Pin1 interdomain interactions using NMR paramagnetic relaxation enhancement (PRE) and molecular dynamics (MD) simulations. The PREs show that apo-Pin1 samples interdomain contacts beyond the range suggested by previous structural studies. They further show that substrate binding to the WW domain simultaneously alters interdomain separation and the internal conformation of the WW domain. A 4.5-μs all-atom MD simulation of apo-Pin1 suggests that the fluctuations of interdomain distances are correlated with fluctuations of WW domain interresidue contacts involved in substrate binding. Thus, the interdomain/WW domain conformations sampled by apo-Pin1 may already include a range of conformations appropriate for binding Pin1''s numerous substrates. The proposed coupling between intra-/interdomain conformational fluctuations is a consequence of the dynamic modular architecture of Pin1. Such modular architecture is common among cell-cycle proteins; thus, the WW–PPIase domain cross-talk mechanisms of Pin1 may be relevant for their mechanisms as well.     

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.     

Interdomain mobility in di-ubiquitin revealed by NMR

Domain orientation and dynamics can play an essential role in the function of multidomain proteins. Lys48-linked polyubiquitin chains, the principal signal for proteasomal protein degradation, adopt a closed conformation at physiological conditions, in which the functionally important residues Leu8, Ile44, and Val70 are sequestered at the interdomain interface. This interface must open in order for these groups to become available for interactions with various chain-recognition factors. Knowledge of the mechanism of domain motion leading to the opening of the interdomain interface in polyubiqutin is, therefore, essential for the understanding of the processes controlling molecular recognition events in polyubiquitin signaling. Here we use NMR to characterize the interdomain dynamics that open the interface in a di-ubiquitin chain. This process occurs via domain reorientations on a 10-ns time scale and with the amplitudes that are sufficient for making functionally important hydrophobic residues in polyubiquitin available for direct interactions with various ubiquitin-binding factors. The analysis revealed the structures of the interconverting conformational states of di-ubiquitin and the rates and amplitudes of this process at near-physiological and acidic pH. The proposed mechanism of domain reorientation is quite general and could serve as a paradigm of interdomain mobility in other multidomain systems.     

Microscopic mechanisms that govern the titration response and pKa values of buried residues in staphylococcal nuclease mutants

To probe the microscopic mechanisms that govern the titration behavior of buried ionizable groups, microsecond explicit solvent molecular dynamics simulations are carried out for several mutants of Staphylococcal nuclease using both fixed charge and polarizable force fields. While the ionization of Asp 66, Glu 66, and Lys 125 lead to enhanced structural fluctuations and partial unfolding of adjacent α‐helical regions, the ionization of Lys 25 causes local unfolding of adjacent β sheets. Using the sampled conformational ensembles, good agreement with experimental pK_a values is obtained with Poisson–Boltzmann calculations using a protein dielectric constant of 2–4 for V66D/E; slightly larger dielectric constants are needed for Lys mutants especially L25K, suggesting that structural responses beyond microseconds are involved in ionization of Lys 25. Overall, the set of unbiased simulations provides insights into the spatial and temporal scales of protein and solvent motions that dictate the diverse titration behaviors of buried protein residues. Proteins 2017; 85:268–281. © 2016 Wiley Periodicals, Inc.     

Helix Dynamics in LacY: Helices II and IV

Biochemical and biophysical studies based upon crystal structures of both a mutant and wild-type lactose permease from Escherichia coli (LacY) in an inward-facing conformation have led to a model for the symport mechanism in which both sugar and H⁺ binding sites are alternatively accessible to both sides of the membrane. Previous findings indicate that the face of helix II with Asp68 is important for the conformational changes that occur during turnover. As shown here, replacement of Asp68 at the cytoplasmic end of helix II, particularly with Glu, abolishes active transport but the mutants retain the ability to bind galactopyranoside. In the x-ray structure, Asp68 and Lys131 (helix IV) lie within ∼ 4.2 Å of each other. Although a double mutant with Cys replacements at both position 68 and position 131 cross-links efficiently, single replacements for Lys131 exhibit very significant transport activity. Site-directed alkylation studies show that sugar binding by the Asp68 mutants causes closure of the cytoplasmic cavity, similar to wild-type LacY; however, strikingly, the probability of opening the periplasmic pathway upon sugar binding is markedly reduced. Taken together with results from previous mutagenesis and cross-linking studies, these findings lead to a model in which replacement of Asp68 blocks a conformational transition involving helices II and IV that is important for opening the periplasmic cavity. Evidence suggesting that movements of helices II and IV are coupled functionally with movements in the pseudo-symmetrically paired helices VIII and X is also presented.     

Continuous Interdomain Orientation Distributions Reveal Components of Binding Thermodynamics

The flexibility of biological macromolecules is an important structural determinant of function. Unfortunately, the correlations between different motional modes are poorly captured by discrete ensemble representations. Here, we present new ways to both represent and visualize correlated interdomain motions. Interdomain motions are determined directly from residual dipolar couplings, represented as a continuous conformational distribution, and visualized using the disk-on-sphere representation. Using the disk-on-sphere representation, features of interdomain motions, including correlations, are intuitively visualized. The representation works especially well for multidomain systems with broad conformational distributions.This analysis also can be extended to multiple probability density modes, using a Bingham mixture model. We use this new paradigm to study the interdomain motions of staphylococcal protein A, which is a key virulence factor contributing to the pathogenicity of Staphylococcus aureus. We capture the smooth transitions between important states and demonstrate the utility of continuous distribution functions for computing the reorientational components of binding thermodynamics. Such insights allow for the dissection of the dynamic structural components of functionally important intermolecular interactions.     

Prediction of structures of multidomain proteins from structures of the individual domains

We describe the development of a method for assembling structures of multidomain proteins from structures of isolated domains. The method consists of an initial low-resolution search in which the conformational space of the domain linker is explored using the Rosetta de novo structure prediction method, followed by a high-resolution search in which all atoms are treated explicitly and backbone and side chain degrees of freedom are simultaneously optimized. The method recapitulates, often with very high accuracy, the structures of existing multidomain proteins.     

Interaction between residues in the Mg2+-binding site regulates BK channel activation

As a unique member of the voltage-gated potassium channel family, a large conductance, voltage- and Ca²⁺-activated K⁺ (BK) channel has a large cytosolic domain that serves as the Ca²⁺ sensor, in addition to a membrane-spanning domain that contains the voltage-sensing (VSD) and pore-gate domains. The conformational changes of the cytosolic domain induced by Ca²⁺ binding and the conformational changes of the VSD induced by membrane voltage changes trigger the opening of the pore-gate domain. Although some structural information of these individual functional domains is available, how the interactions among these domains, especially the noncovalent interactions, control the dynamic gating process of BK channels is still not clear. Previous studies discovered that intracellular Mg²⁺ binds to an interdomain binding site consisting of D99 and N172 from the membrane-spanning domain and E374 and E399 from the cytosolic domain. The bound Mg²⁺ at this narrow interdomain interface activates the BK channel through an electrostatic interaction with a positively charged residue in the VSD. In this study, we investigated the potential interdomain interactions between the Mg²⁺-coordination residues and their effects on channel gating. By introducing different charges to these residues, we discovered a native interdomain interaction between D99 and E374 that can affect BK channel activation. To understand the underlying mechanism of the interdomain interactions between the Mg²⁺-coordination residues, we introduced artificial electrostatic interactions between residues 172 and 399 from two different domains. We found that the interdomain interactions between these two positions not only alter the local conformations near the Mg²⁺-binding site but also change distant conformations including the pore-gate domain, thereby affecting the voltage- and Ca²⁺-dependent activation of the BK channel. These results illustrate the importance of interdomain interactions to the allosteric gating mechanisms of BK channels.     

NMR insights into the core of GED assembly by H/D exchange coupled with DMSO dissociation and analysis of the denatured state

GTPase effector domain (GED) of dynamin forms megadalton-sized assembly in vitro, rendering its structural characterization highly challenging. To probe the core of the GED assembly, we performed H/D exchange in native state and analyzed the residual amides following dissociation by dimethyl sulfoxide (DMSO). The data indicated a hierarchy in solvent exposure: Ser2-Glu13, Glu23-Phe32, Asp37-Gln43, Val51-Met55, and Lys60-Asp64 followed by the remaining segments. This reflects the chain packing in the core of the assembly. The segment Leu65-Pro138 in the C-terminal half is largely in the interior of the core, while the N-terminal segment Asp37-Asp64 traverses into and out of the core. Next, we characterized the structural and motional behavior of the DMSO-denatured state. The stretches Gly9-Lys18, Asp37-Arg42, Lys68-Met74, and Ser136-Thr137 were seen to display alternate conformations in slow exchange. In the major population, both α and β propensities were seen along the polypeptide chain. Spectral density analysis of ¹⁵N R₁, R₂, and ¹H-¹⁵N nuclear Overhauser effect collected at 600 and 800 MHz suggested the presence of four domains of slow motions, namely, A (Leu40-Tyr91), A′ (Leu124-Ile130); B (Asn97-Gln107), B′ (Tyr117-Leu120), two of which flank the region Arg109-Met116, for which no peaks are seen in the heteronuclear single quantum coherence spectrum. These domains would identify folding and association initiation sites of GED. Interestingly, they also coincide with the helical domain in the native state, suggesting that helix formation leads to self-association of GED.     

pH-dependent random coil 1H, 13C,and 15N chemical shifts of the ionizable amino acids: a guide for protein pK a measurements

The pK _a values and charge states of ionizable residues in polypeptides and proteins are frequently determined via NMR-monitored pH titrations. To aid the interpretation of the resulting titration data, we have measured the pH-dependent chemical shifts of nearly all the ¹H, ¹³C, and ¹⁵N nuclei in the seven common ionizable amino acids (X = Asp, Glu, His, Cys, Tyr, Lys, and Arg) within the context of a blocked tripeptide, acetyl-Gly-X-Gly-amide. Alanine amide and N-acetyl alanine were used as models of the N- and C-termini, respectively. Together, this study provides an essentially complete set of pH-dependent intra-residue and nearest-neighbor reference chemical shifts to help guide protein pK _a measurements. These data should also facilitate pH-dependent corrections in algorithms used to predict the chemical shifts of random coil polypeptides. In parallel, deuterium isotope shifts for the side chain ¹⁵N nuclei of His, Lys, and Arg in their positively-charged and neutral states were also measured. Along with previously published results for Asp, Glu, Cys, and Tyr, these deuterium isotope shifts can provide complementary experimental evidence for defining the ionization states of protein residues.