Activation Energy of Catalysis-Related Domain Motion in E. coli Adenylate Kinase

NH125 Sensitizes Staphylococcus aureus to Cell Wall-Targeting Antibiotics through the Inhibition of the VraS Sensor Histidine Kinase

Staphylococcus aureus utilizes the two-component regulatory system VraSR to receive and relay environmental stress signals, and it is implicated in the development of bacterial resistance to several antibiotics through the upregulation of cell wall synthesis. VraS inhibition was shown to extend or restore the efficacy of several clinically used antibiotics. In this work, we study the enzymatic activity of the VraS intracellular domain (GST-VraS) to determine the kinetic parameters of the ATPase reaction and characterize the inhibition of NH125 under in vitro and microbiological settings. The rate of the autophosphorylation reaction was determined at different GST-VraS concentrations (0.95 to 9.49 μM) and temperatures (22 to 40°C) as well as in the presence of different divalent cations. The activity and inhibition by NH125, which is a known kinase inhibitor, were assessed in the presence and absence of the binding partner, VraR. The effects of inhibition on the bacterial growth kinetics and gene expression levels were determined. The GST-VraS rate of autophosphorylation increases with temperature and with the addition of VraR, with magnesium being the preferred divalent cation for the metal-ATP substrate complex. The mechanism of inhibition of NH125 was noncompetitive in nature and was attenuated in the presence of VraR. The addition of NH125 in the presence of sublethal doses of the cell wall-targeting antibiotics carbenicillin and vancomycin led to the complete abrogation of Staphylococcus aureus Newman strain growth and significantly decreased the gene expression levels of pbpB, blaZ, and vraSR in the presence of the antibiotics. IMPORTANCE This work characterizes the activity and inhibition of VraS, which is a key histidine kinase in a bacterial two-component system that is involved in Staphylococcus aureus antibiotic resistance. The results show the effect of temperature, divalent ions, and VraR on the activity and the kinetic parameters of ATP binding. The value of the KM of ATP is vital in designing screening assays to discover potent and effective VraS inhibitors with high translational potential. We report the ability of NH125 to inhibit VraS in vitro in a noncompetitive manner and investigate its effect on gene expression and bacterial growth kinetics in the presence and absence of cell wall-targeting antibiotics. NH125 effectively potentiated the effects of the antibiotics on bacterial growth and altered the expression of the genes that are regulated by VraS and are involved in mounting a resistance to antibiotics.

ADP-Induced Conformational Transition of Human Adenylate Kinase 1 Is Triggered by Suppressing Internal Motion of α3α4 and α7α8 Fragments on the ps-ns Timescale

Human adenylate kinase 1 (hAK1) plays a vital role in the energetic and metabolic regulation of cell life, and impaired functions of hAK1 are closely associated with many diseases. In the presence of Mg²⁺ ions, hAK1 in vivo can catalyze two ADP molecules into one ATP and one AMP molecule, activating the downstream AMP signaling. The ADP-binding also initiates AK1 transition from an open conformation to a closed conformation. However, how substrate binding triggers the conformational transition of hAK1 is still unclear, and the underlying molecular mechanisms remain elusive. Herein, we determined the solution structure of apo-hAK1 and its key residues for catalyzing ADP, and characterized backbone dynamics characteristics of apo-hAK1 and hAK1-Mg²⁺-ADP complex (holo-hAK1) using NMR relaxation experiments. We found that ADP was primarily bound to a cavity surrounded by the LID, NMP, and CORE domains of hAK1, and identified several critical residues for hAK1 catalyzing ADP including G16, G18, G20, G22, T39, G40, R44, V67, D93, G94, D140, and D141. Furthermore, we found that apo-hAK1 adopts an open conformation with significant ps-ns internal mobility, and Mg²⁺-ADP binding triggered conformational transition of hAK1 by suppressing the ps-ns internal motions of α₃α₄ in the NMP domain and α₇α₈ in the LID domain. Both α₃α₄ and α₇α₈ fragments became more rigid so as to fix the substrate, while the catalyzing center of hAK1 experiences promoted µs-ms conformational exchange, potentially facilitating catalysis reaction and conformational transition. Our results provide the structural basis of hAK1 catalyzing ADP into ATP and AMP, and disclose the driving force that triggers the conformational transition of hAK1, which will deepen understanding of the molecular mechanisms of hAK1 functions.

Correlating the Local and Global Dynamics of an Enzyme in the Crowded Milieu

Enzymes are dynamic biological macromolecules, with their catalytic function(s) being largely influenced by the changes in local fluctuations of amino acid side chains as well as global structural modulations that the enzyme undergoes. Such local and global motions can be highly affected inside the crowded physiological interior of the cell. Here, we have addressed the role of dynamic structural flexibility in affecting the activation energy barrier of a flexible multidomain enzyme adenylate kinase (AK3L1, UniProtKB: Q9UIJ7). Activation energy profiles of both local (at three different sites along the polypeptide backbone) and global dynamics of the enzyme have been monitored using solvation studies on the subnanosecond time scale and tryptophan quenching studies over the temperature range of 278-323 K, respectively, under crowded conditions (Ficoll 70, Dextran 40, Dextran 70, and PEG 8). This study not only provides the site-specific mapping of dynamics but reveals that the activation energies associated with these local motions undergo a significant decrease in the presence of macromolecular crowders, providing new insights into how crowding affects internal protein dynamics. The crowded scenario also aids in enhancing the coupling between the local and global motions of the enzyme. Moreover, select portions/regions of the enzyme when taken together can well mirror the overall dynamics of the biomolecule, showing possible energy hotspots along the polypeptide backbone.

Impacts of mutations on dynamic allostery of adenylate kinase

Escherichia coli adenylate kinase (AK) is composed of CORE domain and two branch domains: LID and AMP-binding domain (AMPbd). AK exhibits considerable allostery in a reversible phosphoryl transfer reaction, which is largely attributed to the relative motion of LID and AMPbd with respect to CORE. Such an allosteric conformational change is also evident in the absence of ligands. Recent studies showed that the mutations in branch domains can adjust dynamic allostery and alter the substrate affinity and enzyme activity. In this work, we use all-atom molecular dynamics simulation to study the impacts of mutations in branch domains on AK's dynamic allostery by comparing two double mutants, i.e., LID mutant (Val135Gly, Val142Gly) and AMPbd mutant (Ala37Gly, Ala55Gly), with wild-type. Two mutants undergo considerable conformational fluctuation and exhibit deviation from the initially extended apo state to more compact structures. The LID domain in the LID mutant adjusts its relative position and firmly adheres to CORE. More strikingly, AMPbd mutations affect the relative positions of both the AMPbd domain and remote LID domain. Both domains undergo considerable movement, especially the inherent hinge swing motion of the flexible LID domain. In both mutants, the mutations can enhance the inter-domain interaction. The results about the conformation change of AK in both mutants are in line with the experiment of AK's affinity and activity. As revealed by our findings, the flexibility of branch domains and their inherent motions, especially LID domain, is highly relevant to dynamic allostery in the AK system.

Understanding enzyme behavior in a crowded scenario through modulation in activity, conformation and dynamics

Macromolecular crowding, inside the physiological interior, modulates the energy landscape of biological macromolecules in multiple ways. Amongst these, enzymes occupy a special place and hence understanding the function of the same in the crowded interior is of utmost importance. In this study, we have investigated the manner in which the multidomain enzyme, AK3L1 (PDB ID: 1ZD8), an isoform of adenylate kinase, has its features affected in presence of commonly used crowders (PEG 8, Dextran 40, Dextran 70, and Ficoll 70). Michaelis Menten plots reveal that the crowders in general enhance the activity of the enzyme, with the K_m and V_max values showing significant variations. Ficoll 70, induced the maximum activity for AK3L1 at 100 g/L, beyond which the activity reduced. Ensemble FRET studies were performed to provide insights into the relative domain (LID and CORE) displacements in presence of the crowders. Solvation studies reveal that the protein matrix surrounding the probe CPM (7-diethylamino-3-(4-maleimido-phenyl)-4-methylcoumarin) gets restricted in presence of the crowders, with Ficoll 70 providing the maximum rigidity, the same being linked to the decrease in the activity of the enzyme. Through our multipronged approach, we have observed a distinct correlation between domain displacement, enzyme activity and associated dynamics. Thus, keeping in mind the complex nature of enzyme activity and the surrounding bath of dense soup that the biological entity remains immersed in, indeed more such approaches need to be undertaken to have a better grasp of the "enzymes in the crowd".

The crystal structures of Thermus thermophilus CMP kinase complexed with a phosphoryl group acceptor and donor

Nucleoside monophosphate kinases play crucial roles in biosynthesis and regeneration of nucleotides. These are bi-substrate enzymes that catalyze reversible transfers of a phosphoryl group between ATP and nucleoside monophosphate. These enzymes are comprised of the CORE domain, the NMP-binding domain, and the LID domain. Large conformational rearrangement of the three domains occurs during the catalytic cycle. Although many structures of CMP kinase have been determined, only limited structural information has been available on the conformational changes along the reaction pathway. We determined five crystal structures of CMP kinase of Thermus thermophilus HB8 in ligand-free form and the CMP "open", CMP "closed", ADP-CDP-Gd3+-, and CDP-bound forms at resolutions of 1.7, 2.2, 1.5, 1.6, and 1.7 Å, respectively. The ligand-free form was in an open conformation, whereas the structures of the CMP "closed", ADP-CDP-Gd3+-, and CDP-bound forms were in a closed conformation, in which the shift of the NMP-binding domain and LID domain caused closure of the substrate-binding cleft. Interestingly, the CMP "open" form was in an open conformation even with CMP bound, implying intrinsic conformational fluctuation. The structure of the ADP-CDP complex is the first structure of CMP kinase with a phosphoryl group donor and an acceptor. Upon simultaneous binding of ADP and CDP, the side chains of several residues in the LID domain moved toward the nucleotides without global open-closed conformational changes compared to those in the CMP "closed" and CDP complexes. These global and local conformational changes may be crucial for the substrate recognition and catalysis. The terminal phosphate groups of ADP and CDP had similar geometry to those of two ADP in AMP kinase, suggesting common catalytic mechanisms to other nucleoside monophosphate kinases. Our findings are expected to contribute to detailed understanding of the reaction mechanism of CMP kinase.

Multiple Pathways and Time Scales for Conformational Transitions in apo-Adenylate Kinase

The open/close transition in adenylate kinase (AK) is regarded as a representative example for large-scale conformational transition in proteins, yet its mechanism remains unclear despite numerous experimental and computational studies. Using extensive (∼50 μs) explicit solvent atomistic simulations and Markov state analysis, we shed new lights on the mechanism of this transition in the apo form of AK. The closed basin of apo AK features an open NMP domain while the LID domain closes and rotates toward it. Therefore, although the computed structural properties of the closed ensemble are consistent with previously reported FRET and PRE measurements, our simulations suggest that NMP closure is likely to follow AMP binding, in contrast to the previous interpretation of FRET and PRE data that the apo state was able to sample the fully closed conformation for "ligand selection". The closed state ensemble is found to be kinetically heterogeneous; multiple pathways and time scales are associated with the open/close transition, providing new clues to the disparate time scales observed in different experiments. Besides interdomain interactions, a novel mutual information analysis identifies specific intradomain interactions that correlate strongly to transition kinetics, supporting observations from previous chimera experiments. While our results underscore the role of internal domain properties in determining the kinetics of open/close transition in apo AK, no evidence is observed for any significant degree of local unfolding during the transition. These observations about AK have general implications to our view of conformational states, transition pathways, and time scales of conformational changes in proteins. The key features and time scales of observed transition pathways are robust and similar from simulations using two popular fixed charge force fields.

Hybrid All-Atom/Coarse-Grained Simulations of Proteins by Direct Coupling of CHARMM and PRIMO Force Fields

Hybrid all-atom/coarse-grained (AA/CG) simulations of proteins offer a computationally efficient compromise where atomistic details are only applied to biologically relevant regions while benefiting from the speedup of treating the remaining parts of a given system at the CG level. The recently developed CG model, PRIMO, allows a direct coupling with an atomistic force field with no additional modifications or coupling terms and the ability to carry out dynamic simulations without any restraints on secondary or tertiary structures. A hybrid AA/CG scheme based on combining all-atom CHARMM and coarse-grained PRIMO representations was validated via molecular dynamics and replica exchange simulations of soluble and membrane proteins. The AA/CG scheme was also tested in the calculation of the free energy profile for the transition from the closed to the open state of adenylate kinase via umbrella sampling molecular dynamics method. The overall finding is that the AA/CG scheme generates dynamics and energetics that are qualitatively and quantitatively comparable to AA simulations while offering the computational advantages of coarse-graining. This model opens the door to challenging applications where high accuracy is required only in parts of large biomolecular complexes.

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA was applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.

Many proteins are nanomachines that perform mechanical or chemical work by changing their three-dimensional shape and cycle between multiple conformational states. Computer simulations of such conformational transitions provide mechanistic insights into protein function but such simulations have been challenging. In particular, it is not clear how to quantitatively compare current simulation methods or to assess their accuracy. To that end, we present a general and flexible computational framework for quantifying transition paths—by measuring mutual geometric similarity—that, compared with existing approaches, requires minimal a-priori assumptions and can take advantage of full atomic detail alongside heuristic information derived from intuition. Using our Path Similarity Analysis (PSA) framework in parallel with several existing quantitative approaches, we examine transitions generated for a toy model of a transition and two biological systems, the enzyme adenylate kinase and diphtheria toxin. Our results show that PSA enables the quantitative comparison of different path sampling methods and aids the identification of potentially important atomistic motions by exploiting geometric information in transition paths. The method has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing macromolecular conformational transitions.

Global transitions of proteins explored by a multiscale hybrid methodology: application to adenylate kinase

Efficient and accurate mapping of transition pathways is a challenging problem in allosteric proteins. We propose here a to our knowledge new methodology called collective molecular dynamics (coMD). coMD takes advantage of the collective modes of motions encoded by the fold, simultaneously evaluating the interactions and energetics via a full-atomic MD simulation protocol. The basic approach is to deform the structure collectively along the modes predicted by the anisotropic network model, upon selecting them via a Monte Carlo/Metropolis algorithm from among the complete pool of all accessible modes. Application to adenylate kinase, an allosteric enzyme composed of three domains, CORE, LID, and NMP, shows that both open-to-closed and closed-to-open transitions are readily sampled by coMD, with large-scale motions of the LID dominating. An energy-barrier crossing occurs during the NMP movements. The energy barrier originates from a switch between the salt bridges K136-D118 at the LID-CORE interface and K57-E170 and D33-R156 at the CORE-NMP and LID-NMP interfaces, respectively. Despite its simplicity and computing efficiency, coMD yields ensembles of transition pathways in close accord with detailed full atomic simulations, lending support to its utility as a multiscale hybrid method for efficiently exploring the allosteric transitions of multidomain or multimeric proteins.

Conformational dynamics of a ligand-free adenylate kinase

Adenylate kinase (AdK) is a phosphoryl-transfer enzyme with important physiological functions. Based on a ligand-free open structure and a ligand-bound closed structure solved by crystallography, here we use molecular dynamics simulations to examine the stability and dynamics of AdK conformations in the absence of ligands. We first perform multiple simulations starting from the open or the closed structure, and observe their free evolutions during a simulation time of 100 or 200 nanoseconds. In all seven simulations starting from the open structure, AdK remained stable near the initial conformation. The eight simulations initiated from the closed structure, in contrast, exhibited large variation in the subsequent evolutions, with most (seven) undergoing large-scale spontaneous conformational changes and approaching or reaching the open state. To characterize the thermodynamics of the transition, we propose and apply a new sampling method that employs a series of restrained simulations to calculate a one-dimensional free energy along a curved pathway in the high-dimensional conformational space. Our calculated free energy profile features a single minimum at the open conformation, and indicates that the closed state, with a high (∼13 kcal/mol) free energy, is not metastable, consistent with the observed behaviors of the unrestrained simulations. Collectively, our simulations suggest that it is energetically unfavorable for the ligand-free AdK to access the closed conformation, and imply that ligand binding may precede the closure of the enzyme.

Molecular dynamics studies on the conformational transitions of adenylate kinase: a computational evidence for the conformational selection mechanism

Escherichia coli adenylate kinase (ADK) is a monomeric phosphotransferase enzyme that catalyzes reversible transfer of phosphoryl group from ATP to AMP with a large-scale domain motion. The detailed mechanism for this conformational transition remains unknown. In the current study, we performed long time-scale molecular dynamics simulations on both open and closed states of ADK. Based on the structural analyses of the simulation trajectories, we detected over 20 times conformational transitions between the open and closed states of ADK and identified two novel conformations as intermediate states in the catalytic processes. With these findings, we proposed a possible mechanism for the large-scale domain motion of Escherichia coli ADK and its catalytic process: (1) the substrate free ADK adopted an open conformation; (2) ATP bound with LID domain closure; (3) AMP bound with NMP domain closure; (4) phosphoryl transfer occurred with ATP, and AMP converted into two ADPs, and no conformational transition was detected in the enzyme; (5) LID domain opened with one ADP released; (6) another ADP released with NMP domain open. As both open and closed states sampled a wide range of conformation transitions, our simulation strongly supported the conformational selection mechanism for Escherichia coli ADK.

SRLS analysis of 15N relaxation from bacteriophage T4 lysozyme: a tensorial perspective that features domain motion

Bacteriophage T4L lysozyme (T4L) comprises two domains connected by a helical linker. Several methods detected ns domain motion associated with the binding of the peptidoglycan substrate. An ESR study of nitroxide-labeled T4L, based on the slowly relaxing local structure (SRLS) approach, detected ns local motion involving the nitroxide and the helix housing it. (15)N−H spin relaxation data from T4L acquired at magnetic fields of 11.7 and 18.8 T, and 298 K, were analyzed previously with the model-free (MF) method. The results did not detect domain motion. SRLS is the generalization of MF. Here, we apply it to the same data analyzed previously with MF. The restricted local N−H motion is described in terms of tilted axial local ordering (S) and local diffusion (D(2)) tensors; dynamical coupling to the global tumbling is accounted for. We find that D(2,⊥) is 1.62 × 10(7) (1.56 × 10(7)) s(−1) for the N-terminal (C-terminal) domain. This dynamic mode represents domain motion. For the linker D(2,⊥) is the same as the rate of global tumbling, given by (1.46 ± 0.04) × 10(7) s(−1). D(2,∥) is 1.3 × 10(9), 1.8 × 10(9) and 5.3 × 10(9) s(−1) for the N-terminal domain, the C-terminal domain, and the linker, respectively. This dynamic mode represents N−H bond vector fluctuations. The principal axis of D(2) is virtually parallel to the N−H bond. The order parameter, S(0)(2), is 0.910 ± 0.046 for most N−H bonds. The principal axis of S is tilted from the C(i−1)(α) −C(i)(α) axis by −2° to 6° for the N-, and C-terminal domains, and by 2.5° for the linker. The tensorial-perspective-based and mode-coupling-based SRLS picture provides new insights into the structural dynamics of bacteriophage T4 lysozyme.

SRLS analysis of 15N spin relaxation from E. coli ribonuclease HI: the tensorial perspective

15N–H relaxation parameters from ribonuclease HI (RNase H), acquired in previous work at magnetic fields of 14.1 and 18.8 T, and at 300 K, are analyzed with the mode-coupling slowly relaxing local structure (SRLS) approach. In accordance with standard theoretical treatments of restricted motions, SRLS approaches N-H bond dynamics from a tensorial perspective. As shown previously, a physically adequate description of this phenomenon has to account for the asymmetry of the local spatial restrictions. So far, we used rhombic local ordering tensors; this is straightforward but computationally demanding. Here, we propose substantiating the asymmetry of the local spatial restrictions in terms of tilted axial local ordering (S) and local diffusion (D2) tensors. Although less straightforward, this description provides physically sound structural and dynamic information and is efficient computationally. We find that the local order parameter, S(0)2, is on average 0.89 (0.84, and may be as small as 0.6) for the secondary structure elements (loops). The main local ordering axis deviates from the C(i-1)α-C(i)α axis by less than 6°. At 300 K, D(2,perpendicular) is virtually the same as the global diffusion rate, D1 = 1.8 × 10(7) s(-1). The correlation time 1/6D(2,parallel) ranges from 3-125 (208-344) ps for the secondary structure elements (loops) and is on average 125 ps for the C-terminal segment. The main local diffusion axis deviates from the N-H bond by less than 2° (10°) for the secondary structure elements (loops). An effective data-fitting protocol, which leads in most cases to unambiguous results with limited uncertainty, has been devised. A physically sound and computationally effective methodology for analyzing 15N relaxation in proteins, that provides a new picture of N–H bond structural dynamics in proteins, has been set forth.

Backbone dynamics of deoxy and carbonmonoxy hemoglobin by NMR/SRLS

The slowly relaxing local structure (SRLS) approach, developed for NMR spin relaxation analysis in proteins, is applied herein to amide ¹⁵N relaxation in deoxy and carbonmonoxy hemoglobin. Experimental data including ¹⁵N T₁, T₂ and ¹⁵N-{¹H} NOE, acquired at 11.7 and 14.1 T, and 29 and 34 °C, are analyzed. The restricted local motion of the N-H bond is described in terms of the principal value (S(0)(2)) and orientation (β(D)) of an axial local ordering tensor, S, and the principal values (R(||)(L) and R(⊥)(L)) and orientation (β(O)) of an axial local diffusion tensor, R(L). The parameters c₀² (the potential coefficient in terms of which S(0)(2) is defined), R(||)(L), β(D), and β(O) are determined by data fitting; R(⊥)(L) is set equal to the global motional rate, R(C), found previously to be (5.2-5.8) × 10⁶ 1/s in the temperature range investigated. The principal axis of S is (nearly) parallel to the C(i-1)(α)-C(i)(α) axis; when the two axes are parallel, β(D) = -101.3° (in the frame used). The principal axis of R(L) is (nearly) parallel to the N-H bond; when the two axes are parallel, β(O) = -101.3°. For "rigid" N-H bonds located in secondary structure elements the best-fit parameters are S(0)(2) = 0.88-0.95 (corresponding to local potentials of 8.6-19.9 k(B)T), R(||)(L) = 10⁹-10¹⁰ 1/s, β(D) = -101.3° ± 2.0°, and β(O) = -101.3° ± 4°. For flexible N-H bonds located in loops the best-fit values are S(0)(2) = 0.75-0.80 (corresponding to local potentials of 4.5-5.5 k(B)T), R(||)(L) = (1.0-6.3) × 10⁸ 1/s, β(D) = -101.3° ± 4.0°, and β(O) = -101.3° ± 10°. These results are important in view of their physical clarity, inherent potential for further interpretation, consistency, and new qualitative insights provided (vide infra).

General theoretical/computational tool for interpreting NMR spin relaxation in proteins

We developed in recent years the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS is a two-body coupled rotator model which accounts rigorously for mode-coupling between the global motion of the protein and the local motion of the spin-bearing probe and allows for general properties of the second rank tensors involved. We showed that a general tool of data analysis requires both capabilities. Several important functionalities were missing in our previous implementations of SRLS in data fitting schemes, and in some important cases, the calculations were tedious. Here we present a general implementation which allows for asymmetric local and global diffusion tensors, distinct local ordering and local diffusion frames, and features a rhombic local potential which includes Wigner matrix element terms of ranks 2 and 4. A recently developed hydrodynamics-based approach for calculating global diffusion tensors has been incorporated into the data-fitting scheme. The computational efficiency of the latter has been increased significantly through object-oriented programming within the scope of the C++ programming language, and code parallelization. A convenient graphical user interface is provided. Currently autocorrelated (15)N spin relaxation data can be analyzed effectively. Adaptation to any autocorrelated and cross-correlated relaxation analysis is straightforward. New physical insight is gleaned on largely preserved local structure in solution, even in chain segments which experience slow local motion. Prospects associated with improved dynamic models, and new applications made possible by the current implementation of SRLS, are delineated.

Zipping and unzipping of adenylate kinase: atomistic insights into the ensemble of open<-->closed transitions

Adenylate kinase (AdK), a phosphotransferase enzyme, plays an important role in cellular energy homeostasis. It undergoes a large conformational change between an open and a closed state, even in the absence of substrate. We investigate the apo-AdK transition at the atomic level both with free-energy calculations and with our new dynamic importance sampling (DIMS) molecular dynamics method. DIMS is shown to sample biologically relevant conformations as verified by comparing an ensemble of hundreds of DIMS transitions to AdK crystal structure intermediates. The simulations reveal in atomic detail how hinge regions partially and intermittently unfold during the transition. Conserved salt bridges are seen to have important structural and dynamic roles; in particular, four ionic bonds that open in a sequential, zipper-like fashion and, thus, dominate the free-energy landscape of the transition are identified. Transitions between the closed and open conformations only have to overcome moderate free-energy barriers. Unexpectedly, the closed state and the open state encompass broad free-energy basins that contain conformations differing in domain hinge motions by up to 40 degrees . The significance of these extended states is discussed in relation to recent experimental Förster resonance energy transfer measurements. Taken together, these results demonstrate how a small number of cooperative key interactions can shape the overall dynamics of an enzyme and suggest an "all-or-nothing" mechanism for the opening and closing of AdK. Our efficient DIMS molecular dynamics computer simulation approach can provide a detailed picture of a functionally important macromolecular transition and thus help to interpret and suggest experiments to probe the conformational landscape of dynamic proteins such as AdK.

Evidence for domain motion in proteins affecting global diffusion properties: a nuclear magnetic resonance study

The rotational diffusion of proteins is an important hydrodynamic property. Compact protein structures were found previously to exhibit hydration layer viscosity, etaloc, higher than the viscosity of bulk water, eta. This implies an apparent activation energy for rotational diffusion higher than the activation energy of water viscosity, Eeta=15.4+/-0.3 kJ/mol. In this study we examine etaloc of internally mobile proteins using 15N spin relaxation methods. We also examine the activation enthalpy, DeltaH#, and activation entropy, DeltaS#, for rotational diffusion. Of particular relevance are internally mobile ligand-free forms and compact ligand-bound forms of multidomain proteins. Adenylate kinase (AKeco) and Ca2+-calmodulin (Ca2+-CaM) are typical examples. For AKeco (Ca2+-CaM) we find that DeltaH# is 14.5+/-0.5 (15.7+/-0.4) kJ/mol. For the complex of AKeco with the inhibitor AP5A (the complex of Ca2+-CaM with the peptide smMLCKp), we find that DeltaH# is 18.1+/-0.7 (18.2+/-0.5) kJ/mol. The internally mobile outer surface protein A has DeltaH#=12.6+/-0.8 kJ/mol, and the compact protein Staphylococcal nuclease has DeltaH#=18.8+/-0.6 kJ/mol. For the internally mobile and compact proteins studied, <|DeltaS(|> equals 62+/-7 J/(mol K) and 44+/-5 J/(mol K), respectively. The fact is that etaloc>eta (DeltaH#>Eeta) for compact proteins was ascribed previously to electrostatic interactions between surface sites and water rigidifying the hydration layer. We find herein that obliteration of these interactions by domain motion leads to etaloc approximately eta, DeltaH# approximately Eeta, and large activation entropy for internally mobile protein structures.

Small- and large-scale conformational changes of adenylate kinase: a molecular dynamics study of the subdomain motion and mechanics

Adenylate kinase, an enzyme that catalyzes the phosphoryl transfer between ATP and AMP, can interconvert between the open and catalytically potent (closed) forms even without binding ligands. Several aspects of the enzyme elasticity and internal dynamics are analyzed here by atomistic molecular dynamics simulations covering a total time span of 100 ns. This duration is sufficiently long to reveal a partial conversion of the enzyme that proceeds through jumps between structurally different substates. The intra- and intersubstates contributions to the enzyme's structural fluctuations are analyzed and compared both in magnitude and directionality. It is found that, despite the structural heterogeneity of the visited conformers, the generalized directions accounting for conformational fluctuations within and across the substates are mutually consistent and can be described by a limited set of collective modes. The functional-oriented nature of the consensus modes is suggested by their good overlap with the deformation vector bridging the open and closed crystal structures. The consistency of adenylate kinase's internal dynamics over timescales wide enough to capture intra- and intersubstates fluctuations adds elements in favor of the recent proposal that the free (apo) enzyme possesses an innate ability to sustain the open/close conformational changes.

Large-scale allosteric conformational transitions of adenylate kinase appear to involve a population-shift mechanism

Large-scale conformational changes in proteins are often associated with the binding of a substrate. Because conformational changes may be related to the function of an enzyme, understanding the kinetics and energetics of these motions is very important. We have delineated the atomically detailed conformational transition pathway of the phosphotransferase enzyme adenylate kinase (AdK) in the absence and presence of an inhibitor. The computed free energy profiles associated with conformational transitions offer detailed mechanistic insights into, as well as kinetic information on, the ligand binding mechanism. Specifically, potential of mean force calculations reveal that in the ligand-free state, there is no significant barrier separating the open and closed conformations of AdK. The enzyme samples near closed conformations, even in the absence of its substrate. The ligand binding event occurs late, toward the closed state, and transforms the free energy landscape. In the ligand-bound state, the closed conformation is energetically most favored with a large barrier to opening. These results emphasize the underlying dynamic nature of the enzyme and indicate that the conformational transitions in AdK are more intricate than a mere two-state jump between the crystal-bound and -unbound states. Based on the existence of the multiple conformations of the enzyme in the open and closed states, a different viewpoint of ligand binding is presented. Our estimated activation energy barrier for the conformational transition is also in reasonable accord with the experimental findings.

An improved picture of methyl dynamics in proteins from slowly relaxing local structure analysis of 2H spin relaxation

Protein dynamics is intimately related to biological function. Core dynamics is usually studied with 2H spin relaxation of the 13CDH2 group, analyzed traditionally with the model-free (MF) approach. We showed recently that MF is oversimplified in several respects. This includes the assumption that the local motion of the dynamic probe and the global motion of the protein are decoupled, the local geometry is simple, and the local ordering is axially symmetric. Because of these simplifications MF has yielded a puzzling picture where the methyl rotation axis is moving rapidly with amplitudes ranging from nearly complete disorder to nearly complete order in tightly packed protein cores. Our conclusions emerged from applying to methyl dynamics in proteins the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Polimeno, A.; Freed, J. H. J. Phys. Chem. 1995, 99, 10995-11006.), which can be considered the generalization of MF, with all the simplifications mentioned above removed. The SRLS picture derived here for the B1 immunoglobulin binding domain of peptostreptococcal protein L, studied over the temperature range of 15-45 degrees C, is fundamentally different from the MF picture. Thus, methyl dynamics is characterized structurally by rhombic local potentials with varying symmetries and dynamically by tenfold slower rates of local motion. On average, potential rhombicity decreases, mode-coupling increases, and the rate of local motion increases with increasing temperature. The average activation energy for local motion is 2.0 +/- 0.2 kcal/mol. Mode-coupling affects the analysis even at 15 degrees C. The accuracy of the results is improved by including in the experimental data set relaxation rates associated with rank 2 coherences.