Conformational transitions in adenylate kinase. Allosteric communication reduces misligation

Large conformational changes in the LID and NMP domains of adenylate kinase (AKE) are known to be key to ligand binding and catalysis, yet the order of binding events and domain motion is not well understood. Combining the multiple available structures for AKE with the energy landscape theory for protein folding, a theoretical model was developed for allostery, order of binding events, and efficient catalysis. Coarse-grained models and nonlinear normal mode analysis were used to infer that intrinsic structural fluctuations dominate LID motion, whereas ligand-protein interactions and cracking (local unfolding) are more important during NMP motion. In addition, LID-NMP domain interactions are indispensable for efficient catalysis. LID domain motion precedes NMP domain motion, during both opening and closing. These findings provide a mechanistic explanation for the observed 1:1:1 correspondence between LID domain closure, NMP domain closure, and substrate turnover. This catalytic cycle has likely evolved to reduce misligation, and thus inhibition, of AKE. The separation of allosteric motion into intrinsic structural fluctuations and ligand-induced contributions can be generalized to further our understanding of allosteric transitions in other proteins.     

Binding leverage as a molecular basis for allosteric regulation

Allosteric regulation involves conformational transitions or fluctuations between a few closely related states, caused by the binding of effector molecules. We introduce a quantity called binding leverage that measures the ability of a binding site to couple to the intrinsic motions of a protein. We use Monte Carlo simulations to generate potential binding sites and either normal modes or pairs of crystal structures to describe relevant motions. We analyze single catalytic domains and multimeric allosteric enzymes with complex regulation. For the majority of the analyzed proteins, we find that both catalytic and allosteric sites have high binding leverage. Furthermore, our analysis of the catabolite activator protein, which is allosteric without conformational change, shows that its regulation involves other types of motion than those modulated at sites with high binding leverage. Our results point to the importance of incorporating dynamic information when predicting functional sites. Because it is possible to calculate binding leverage from a single crystal structure it can be used for characterizing proteins of unknown function and predicting latent allosteric sites in any protein, with implications for drug design.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

Comprehensive analysis of motions in molecular dynamics trajectories of the actin capping protein and its inhibitor complexes

The actin capping protein (CP) binds to actin filaments to block further elongation. The capping activity is inhibited by proteins V‐1 and CARMIL interacting with CP via steric and allosteric mechanisms, respectively. The crystal structures of free CP, CP/V‐1, and CP/CARMIL complexes suggest that the binding of CARMIL alters the flexibility of CP rather than the overall structure of CP, and this is an allosteric inhibition mechanism. Here, we performed molecular dynamics (MD) simulations of CP in the free form, and in complex with CARMIL or V‐1. The resulting trajectories were analyzed exhaustively using Motion Tree, which identifies various rigid‐body motions ranging from small local motions to large domain motions. After enumerating all the motions, CP flexibilities with different ligands were characterized by a list of frequencies for 20 dominant rigid‐body motions, some of which were not identified in previous studies. The comparative analysis highlights the influence of the binding of the CARMIL peptide to CP flexibility. In free CP and the CP/V‐1 complex, domain motions around a large crevice between the N‐stalk and the CP‐S domain occur frequently. The CARMIL peptide binds the crevice and suppresses the motions effectively. In addition, the binding of the CARMIL peptide enhances and alters local motions around the pocket that participates in V‐1 binding. These newly identified motions are likely to suppress the binding of V‐1 to CP. The observed changes in CP motion provide insights that describe the mechanism of allosteric regulation by CARMIL through modulating CP flexibility. Proteins 2016; 84:948–956. © 2016 Wiley Periodicals, Inc.     

Nanoscale protein domain motion and long-range allostery in signaling proteins—a view from neutron spin echo spectroscopy

Many cellular proteins are multi-domain proteins. Coupled domain–domain interactions in these multidomain proteins are important for the allosteric relay of signals in the cellular signaling networks. We have initiated the application of neutron spin echo spectroscopy to the study of nanoscale protein domain motions on submicrosecond time scales and on nanometer length scale. Our NSE experiments reveal the activation of protein domain motions over a long distance of over more than 100 Å in a multidomain scaffolding protein NHERF1 upon binding to another protein, Ezrin. Such activation of nanoscale protein domain motions is correlated with the allosteric assembly of multi-protein complexes by NHERF1 and Ezrin. Here, we summarize the theoretical framework that we have developed, which uses simple concepts from nonequilibrium statistical mechanics to interpret the NSE data, and employs a mobility tensor to describe nanoscale protein domain motion. Extracting nanoscale protein domain motion from the NSE does not require elaborate molecular dynamics simulations, nor complex fits to rotational motion, nor elastic network models. The approach is thus more robust than multiparameter techniques that require untestable assumptions. We also demonstrate that an experimental scheme of selective deuteration of a protein subunit in a complex can highlight and amplify specific domain dynamics from the abundant global translational and rotational motions in a protein. We expect NSE to provide a unique tool to determine nanoscale protein dynamics for the understanding of protein functions, such as how signals are propagated in a protein over a long distance to a distal domain.     

Second-chance signal transduction explains cooperative flagellar switching

The reversal of flagellar motion (switching) results from the interaction between a switch complex of the flagellar rotor and a torque-generating stationary unit, or stator (motor unit). To explain the steeply cooperative ligand-induced switching, present models propose allosteric interactions between subunits of the rotor, but do not address the possibility of a reaction that stimulates a bidirectional motor unit to reverse direction of torque. During flagellar motion, the binding of a ligand-bound switch complex at the dwell site could excite a motor unit. The probability that another switch complex of the rotor, moving according to steady-state rotation, will reach the same dwell site before that motor unit returns to ground state will be determined by the independent decay rate of the excited-state motor unit. Here, we derive an analytical expression for the energy coupling between a switch complex and a motor unit of the stator complex of a flagellum, and demonstrate that this model accounts for the cooperative switching response without the need for allosteric interactions. The analytical result can be reproduced by simulation when (1) the motion of the rotor delivers a subsequent ligand-bound switch to the excited motor unit, thereby providing the excited motor unit with a second chance to remain excited, and (2) the outputs from multiple independent motor units are constrained to a single all-or-none event. In this proposed model, a motor unit and switch complex represent the components of a mathematically defined signal transduction mechanism in which energy coupling is driven by steady-state and is regulated by stochastic ligand binding. Mathematical derivation of the model shows the analytical function to be a general form of the Hill equation (Hill AV (1910) The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 40: iv-vii).     

Activation of nanoscale allosteric protein domain motion revealed by neutron spin echo spectroscopy

NHERF1 is a multidomain scaffolding protein that assembles signaling complexes, and regulates the cell surface expression and endocytic recycling of a variety of membrane proteins. The ability of the two PDZ domains in NHERF1 to assemble protein complexes is allosterically modulated by the membrane-cytoskeleton linker protein ezrin, whose binding site is located as far as 110 Ångstroms away from the PDZ domains. Here, using neutron spin echo (NSE) spectroscopy, selective deuterium labeling, and theoretical analyses, we reveal the activation of interdomain motion in NHERF1 on nanometer length-scales and on submicrosecond timescales upon forming a complex with ezrin. We show that a much-simplified coarse-grained model suffices to describe interdomain motion of a multidomain protein or protein complex. We expect that future NSE experiments will benefit by exploiting our approach of selective deuteration to resolve the specific domain motions of interest from a plethora of global translational and rotational motions. Our results demonstrate that the dynamic propagation of allosteric signals to distal sites involves changes in long-range coupled domain motions on submicrosecond timescales, and that these coupled motions can be distinguished and characterized by NSE.     

Allosteric communication in the tryptophan synthase bienzyme complex: roles of the beta-subunit aspartate 305-arginine 141 salt bridge

The allosteric interactions that regulate substrate channeling and catalysis in the tryptophan synthase bienzyme complex from Salmonella typhimurium are triggered by covalent reactions at the beta-site and binding of substrate/product to the alpha-site. The transmission of these allosteric signals between the alpha- and beta-catalytic sites is modulated by an ensemble of weak bonding interactions consisting of salt bridges, hydrogen bonds, and van der Waals contacts that switch the subunits between open and closed conformations. Previous work has identified a scaffolding of salt-bridges extending between the alpha- and beta-sites consisting of alphaAsp 56, betaLys 167, and betaAsp 305. This work investigates the involvement of yet another salt bridging interaction involving the betaAsp 305-betaArg 141 pair via comparison of the spectroscopic, catalytic, and allosteric properties of the betaD305A and betaR141A mutants with the behavior of the wild-type enzyme. These mutations were found to give bienzyme complexes with impaired allosteric communication. The betaD305A mutant also exhibits altered beta-site substrate reaction specificity, while the catalytic activity of the betaR141A mutant exhibits impaired beta-site catalytic activity. The >25-fold activation of the alpha-site by alpha-aminoacrylate Schiff base formation at the beta-site found in the Na(+) form of the wild-type enzyme is abolished in the Na(+) forms of both mutants. Replacing Na(+) by NH(4)(+) or Cs(+) restores the betaD305A to a wild-type-like behavior, whereas only partial restoration is achieved with the betaR141A mutant. These studies establish that the betaD305-betaR141 salt bridge plays a crucial role both in the formation of the closed conformation of the beta-site and in the transmission of allosteric signals between the alpha- and beta-sites that switch the alpha-site on and off.     

Allosteric conversion of Z DNA to an intercalated right-handed conformation by daunomycin

Absorbance and fluorescence methods were used to measure the binding of the anticancer drug daunomycin to poly (dGdC) under ionic conditions that initially favor the left-handed Z conformation of the polymer. Drug binding was cooperative under these conditions and may be fully accounted for by an allosteric model in which the drug binds preferentially (but not exclusively) to the right-handed B conformation and shifts the polymer from the Z to an intercalated right-handed conformation. Quantitative analysis of binding isotherms in terms of the allosteric model allowed for estimation of the equilibrium constants for the conversion of a base pair at a B-Z interface from the Z to the B conformation and for the formation of a base pair in the B conformation within a stretch of helix in the Z conformation. The free energy of the Z to B conversion of a base pair was calculated from this data and ranges from +0.03 to +0.3 kcal/mol over the NaCl range of 2.4-3.5 M. The free energy for the formation of a B-Z junction was nearly constant at +4.0 kcal/mol over the same range of NaCl concentrations. The salt dependence of the free energy of the Z to B transition indicates preferential Na+ binding to the Z form and that there is a net release of Na+ upon conversion of a base pair from the Z to the B conformation. The energetically unfavorable Z to B transition was found by this analysis to be driven by coupling to the energetically favorable interaction of daunomycin with B form DNA. In 3.5 M NaCl, for example, the free energy change for the overall reaction (Z DNA base pairs) + (daunomycin) in equilibrium with (right-handed complex) is -7.0 kcal/mol, nearly all of which is contributed by the binding of drug to B DNA. Analysis using the allosteric model also shows that the number of base pairs converted from the Z to the B conformation per bound drug molecule is salt dependent and provides evidence that drug molecules partition into regions of the polymer in the right-handed conformation.     

Conformational Transitions in Yeast Chorismate Mutase Important for Allosteric Regulation as Identified by Nuclear Magnetic Resonance Spectroscopy

Proteins fluctuate between different conformations in solution, and these conformational fluctuations can be important for protein function and allosteric regulation. The chorismate mutase from Saccharomyces cerevisiae (ScCM), a key enzyme in the biosynthesis of aromatic amino acids, is allosterically activated and inhibited by tryptophan and tyrosine, respectively. It was initially proposed that in the absence of effector, ScCM fluctuates between activated R and inhibited T conformations according to the Monod-Wyman-Changeux (MWC) model, although a more complex regulation pattern was later suggested by mutagenesis and kinetic data. Here we used NMR relaxation dispersion experiments to understand the conformational fluctuations on the microsecond-to-millisecond timescale that occur in ScCM. In the absence of allosteric effectors, ScCM did not exclusively exchange between T and R conformations, suggesting that the two-state MWC model is insufficient to explain conformational dynamics. Addition of tyrosine led to the quenching of much of the motion on this timescale, while new motions were identified in the presence of tryptophan. These new motions are consistent with conformational fluctuations into an alternative conformation that may be important for enzyme activity.     

Collective dynamics of EcoRI-DNA complex by elastic network model and molecular dynamics simulations

Anisotropic network model (ANM) is used to analyze the collective motions of restriction enzyme EcoRI in free form and in complex with DNA. For comparison, three independent molecular dynamics (MD) simulations, each of 1.5 ns duration, are also performed for the EcoRI-DNA complex in explicit water. Although high mobility (equilibrium fluctuations) of inner and outer loops that surround the DNA is consistent in both methods and experiments, MD runs sample different conformational subspaces from which reliable collective dynamics cannot be extracted. However, ANM employed on different conformations from MD simulations indicates very similar collective motions. The stems of the inner loops are quite immobile even in the free enzyme and form a large, almost fixed, pocket for DNA binding. As a result, the residues that make specific and non-specific interactions with the DNA exhibit very low fluctuations in the free enzyme. The vibrational entropy difference between the EcoRI complex and free protein + unkinked DNA is positive (favorable), which may partially counteract the unfavorable enthalpy difference of DNA kink formation. Dynamic domains in EcoRI complex and cross-correlations between residue fluctuations indicate possible means of communication between the distal active sites.     

Thermodynamic dissection of large‐scale domain motions coupled with ligand binding of enzyme I

Domain motions are central to the biological functions of many proteins. The energetics of the motions, however, is often difficult to characterize when motions are coupled with the ligand binding. Here, we determined the thermodynamic parameters of individual domain motions and ligand binding of enzyme I (EI) using strategic domain-deletion mutants that selectively removed particular motions. Upon ligand binding, EI employs two large-scale domain motions, the hinge motion and the swivel motion, to switch between conformational states of distinct domain−domain orientations. Calorimetric analysis of the EI mutants separated the free energy changes of the binding and motions, demonstrating that the unfavorable hinge motion (ΔG = 1.5 kcal mol⁻¹) was driven by the favorable swivel motion (ΔG = −5.2 kcal mol⁻¹). The large free energy differences could be explained by the physicochemical nature of the domain interfaces associated with the motions; the hinge motion employed much narrower interface than the swivel motion without any hydrogen bonds or salt bridges. The small heat capacity further suggested that the packing of the domain interfaces associated with the hinge motion was less compact than that commonly observed in proteins. Lastly, thermodynamic analysis of phosphorylated EI suggests that the domain motions are regulated by the ligand binding and the phosphorylation states. Taken together, the thermodynamic dissection approach illustrates how multiple motions and ligand binding are energetically connected during the functional cycle of EI.     

Nanometer propagation of millisecond motions in V-type allostery

Imidazole glycerol phosphate synthase (IGPS) is a V-type allosteric enzyme, which is catalytically inactive for glutamine hydrolysis until the allosteric effector, N'-[(5'-phosphoribulosyl)formimino]-5-aminoimidazole-4-carboxamide-ribonucleotide (PRFAR) binds 30?? away. In the apo state, NMR relaxation dispersion experiments indicate the absence of millisecond (ms) timescale motions. Binding of the PRFAR to form the active ternary complex is endothermic with a large positive entropy change. In addition, there is a protein wide enhancement of conformational motions in the ternary complex, which connect the two active sites. NMR chemical shift changes and acrylamide quenching experiments suggest that little in the way of structural changes accompany these motions. The data indicate that enzyme activation in the ternary complex is primarily due to an enhancement of ms motions that allows formation of a population of enzymatically active conformers.     

Generalized correlation for biomolecular dynamics

Correlated motions in biomolecules are often essential for their function, e.g., allosteric signal transduction or mechanical/thermodynamic energy transport. Because correlated motions in biomolecules remain difficult to access experimentally, molecular dynamics (MD) simulations are particular useful for their analysis. The established method to quantify correlations from MD simulations via calculation of the covariance matrix, however, is restricted to linear correlations and therefore misses part of the correlations in the atomic fluctuations. Herein, we propose a general statistical mechanics approach to detect and quantify any correlated motion from MD trajectories. This generalized correlation measure is contrasted with correlations obtained from covariance matrices for the B1 domain of protein G and T4 lysozyme. The new method successfully quantifies correlations and provides a valuable global overview over the functionally relevant collective motions of lysozyme. In particular, correlated motions of helix 1 together with the two main lobes of lysozyme are detected, which are not seen by the conventional covariance matrix. Overall, the established method misses more than 50% of the correlation. This failure is attributed to both, an interfering and unnecessary dependence on mutual orientations of the atomic fluctuations and, to a lesser extent, attributed to nonlinear correlations. Our generalized correlation measure overcomes these problems and, moreover, allows for an improved understanding of the conformational dynamics by separating linear and nonlinear contributions of the correlation.     

Mapping backbone dynamics in solution with site-directed spin labeling: GCN4-58 bZip free and bound to DNA

In site-directed spin labeling, a nitroxide-containing side chain is introduced at selected sites in a protein. The EPR spectrum of the labeled protein encodes information about the motion of the nitroxide on the nanosecond time scale, which has contributions from the rotary diffusion of the protein, from internal motions in the side chain, and from backbone fluctuations. In the simplest model for the motion of noninteracting (surface) side chains, the contribution from the internal motion is sequence independent, as is that from protein rotary diffusion. Hence, differences in backbone motions should be revealed by comparing the sequence-dependent motions of nitroxides at structurally homologous sites. To examine this model, nitroxide side chains were introduced, one at a time, along the GCN4-58 bZip sequence, for which NMR (15)N relaxation experiments have identified a striking gradient of backbone mobility along the DNA-binding region [Bracken et al. (1999) J. Mol. Biol. 285, 2133]. Spectral simulation techniques and a simple line width measure were used to extract dynamical parameters from the EPR spectra, and the results reveal a mobility gradient similar to that observed in NMR relaxation, indicating that side chain motions mirror backbone motions. In addition, the sequence-dependent side chain dynamics were analyzed in the DNA/protein complex, which has not been previously investigated by NMR relaxation methods. As anticipated, the backbone motions are damped in the DNA-bound state, although a gradient of motion persists with residues at the DNA-binding site being the most highly ordered, similar to those of helices on globular proteins.     

Proof of principle in a de novo designed protein maquette: an allosterically regulated, charge-activated conformational switch in a tetra-alpha-helix bundle

New understanding of the engineering and allosteric regulation of natural protein conformational switches (such as those that couple chemical and ionic signals, mechanical force, and electro/chemical free energy for biochemical activation, catalysis, and motion) can be derived from simple de novo designed synthetic protein models (maquettes). We demonstrate proof of principle of both reversible switch action and allosteric regulation in a tetra-alpha-helical bundle protein composed of two identical di-helical subunits containing heme coordinated at a specific position close to the disulfide loop region. Individual bundles assume one of two switch states related by large-scale mechanical changes: a syn-topology (helices of the different subunits parallel) or anti-topology (helices antiparallel). Both the spectral properties of a coproporphyrin probe appended to the loop region and the distance-dependent redox interaction between the hemes identify the topologies. Beginning from a syn-topology, introduction of ferric heme in each subunit (either binding or redox change) shifts the topological balance by 25-50-fold (1.9-2.3 kcal/mol) to an anti-dominance. Charge repulsion between the two internal cationic ferric hemes drives the syn- to anti-switch, as demonstrated in two ways. When fixed in the syn-topology, the second ferric heme binding is 25-80-fold (1.9-2.6 kcal/mol) weaker than the first, and adjacent heme redox potentials are split by 80 mV (1.85 kcal/mol), values that energetically match the shift in topological balance. Allosteric and cooperative regulation of the switch by ionic strength exploits the shielded charge interactions between the two hemes and the exposed, cooperative interactions between the coproporphyrin carboxylates.     

Dynamics connect substrate recognition to catalysis in protein kinase A

Atomic resolution studies of protein kinases have traditionally been carried out in the inhibitory state, limiting our current knowledge on the mechanisms of substrate recognition and catalysis. Using NMR, X-ray crystallography and thermodynamic measurements, we analyzed the substrate recognition process of cAMP-dependent protein kinase (PKA), finding that entropy and protein dynamics play a prominent role. The nucleotide acts as a dynamic and allosteric activator by coupling the two lobes of apo PKA, enhancing the enzyme dynamics synchronously and priming it for catalysis. The formation of the ternary complex is entropically driven, and NMR spin relaxation data reveal that both substrate and PKA are dynamic in the closed state. Our results show that the enzyme toggles between open and closed states, which indicates that a conformational selection rather than an induced-fit mechanism governs substrate recognition.     

Mechanical coupling in the nitrogenase complex

The enzyme nitrogenase reduces dinitrogen to ammonia utilizing electrons, protons, and energy obtained from the hydrolysis of ATP. Mo-dependent nitrogenase is a symmetric dimer, with each half comprising an ATP-dependent reductase, termed the Fe Protein, and a catalytic protein, known as the MoFe protein, which hosts the electron transfer P-cluster and the active-site metal cofactor (FeMo-co). A series of synchronized events for the electron transfer have been characterized experimentally, in which electron delivery is coupled to nucleotide hydrolysis and regulated by an intricate allosteric network. We report a graph theory analysis of the mechanical coupling in the nitrogenase complex as a key step to understanding the dynamics of allosteric regulation of nitrogen reduction. This analysis shows that regions near the active sites undergo large-scale, large-amplitude correlated motions that enable communications within each half and between the two halves of the complex. Computational predictions of mechanically regions were validated against an analysis of the solution phase dynamics of the nitrogenase complex via hydrogen-deuterium exchange. These regions include the P-loops and the switch regions in the Fe proteins, the loop containing the residue β-188^Ser adjacent to the P-cluster in the MoFe protein, and the residues near the protein-protein interface. In particular, it is found that: (i) within each Fe protein, the switch regions I and II are coupled to the [4Fe-4S] cluster; (ii) within each half of the complex, the switch regions I and II are coupled to the loop containing β-188^Ser; (iii) between the two halves of the complex, the regions near the nucleotide binding pockets of the two Fe proteins (in particular the P-loops, located over 130 Å apart) are also mechanically coupled. Notably, we found that residues next to the P-cluster (in particular the loop containing β-188^Ser) are important for communication between the two halves.     

Cooperative binding of effectors by an allosteric ribozyme

An allosteric ribozyme that requires two different effectors to induce catalysis was created using modular rational design. This ribozyme construct comprises five conjoined RNA modules that operate in concert as an obligate FMN- and theophylline-dependent molecular switch. When both effectors are present, this 'binary' RNA switch self-cleaves with a rate enhancement of approximately 300-fold over the rate observed in the absence of effectors. Kinetic and structural studies implicate a switching mechanism wherein FMN binding induces formation of the active ribozyme conformation. However, the binding site for FMN is rendered inactive unless theophylline first binds to its corresponding site and reorganizes the RNA structure. This example of cooperative binding between allosteric effectors reveals a level of structural and functional complexity for RNA that is similar to that observed with allosteric proteins.     

Filtering molecular dynamics trajectories to reveal low-frequency collective motions: phospholipase A2

A novel method for analysing molecular dynamics trajectories has been developed, which filters out high frequencies using digital signal processing techniques and facilitates focusing on the low-frequency collective motions of proteins. These motions involve low energy slow motions, which lead to important biological phenomena such as domain closure and allosteric effects in enzymes. The filtering method treats each of the atomic trajectories obtained from the molecular dynamics simulation as a "signal". The trajectories of each of the atoms in the system (or any subset of interest) are Fourier transformed to the frequency domain, a filtering function is applied and then an inverse transformation back to the time domain yields the filtered trajectory. The filtering method has been used to study the dynamics of the enzyme phospholipase A2. In the filtered trajectory, all the high frequency bond and valence angle vibrations were eliminated, leaving only low-frequency motion, mainly fluctuations in torsions and conformational transitions. Analysis of this trajectory revealed interesting motions of the protein, including concerted movements of helices, and changes in shape of the active site cavity. Unlike normal mode analysis, which has been used to study the motion of proteins, this method does not require converged minimizations or diagonalization of a matrix of second derivatives. In addition, anharmonicity, multiple minima and conformational transitions are treated explicitly. Thus, the filtering method avoids most of the approximations implicit in other investigations of the dynamic behaviour of large systems.