Conformational transitions of adenylate kinase: switching by cracking

The folding energy landscape and free energy excitations of cytochrome c

The covalently bound heme cofactor plays a dominant role in the folding of cytochrome c. Because of the complicated inorganic chemistry of the heme, some might consider the folding of cytochrome c to be a special case, following principles different from those used to describe the folding of proteins without cofactors. Recent investigations, however, demonstrate that common models describing folding for many proteins work well for cytochrome c when heme is explicitly introduced, generally providing results that agree with experimental observations. In this Account, we first discuss results from simple native structure-based models. These models include attractive interactions between nonadjacent residues only if they are present in the crystal structure at pH 7. Because attractive nonnative contacts are not included in native structure-based models, their energy landscapes can be described as "perfectly funneled". In other words, native structure-based models are energetically guided towards the native state and contain no energetic traps that would hinder folding. Energetic traps are denoted sources of "frustration", which cause specific transient intermediates to be populated. Native structure-based models do, however, include repulsion between residues due to excluded volume. Nonenergetic traps can therefore exist if the chain, which cannot cross over itself, must partially unfold so that folding can proceed. The ability of native structure-based models to capture this kind of motion is partly responsible for their successful predictions of folding pathways for many types of proteins. Models without frustration describe the sequence of folding events for cytochrome c well (as inferred from hydrogen-exchange experiments), thereby justifying their use as a starting point. At low pH, the experimentally observed folding sequence of cytochrome c deviates from that at pH 7 and from models with perfectly funneled energy landscapes. Here, alternate folding pathways are a result of "chemical frustration". This frustration arises because some regions of the protein are destabilized more than others due to the heterogeneous distribution of titratable residues that are protonated at low pH. Beginning with native structure-based terms, we construct more complex models by adding chemical frustration. These more complex models only modestly perturb the energy landscape, which remains, overall, well funneled. These perturbed models can accurately describe how alternative folding pathways are used at low pH. At alkaline pH, cytochrome c populates distinctly different structural ensembles. For instance, lysine residues are deprotonated and compete for the heme ligation site. The same models that can describe folding at low pH also predict well the structures and relative stabilities of intermediates populated at alkaline pH. The success of models based on funneled energy landscapes suggest that cytochrome c folding is driven primarily by native contacts. The presence of heme appears to add chemical complexity to the folding process, but it does not require fundamental modification of the general principles used to describe folding. Moreover, its added complexity provides a valuable means of probing the folding energy landscape in greater detail than is possible with simpler systems.

Tracing conformational changes in proteins

Background

Many proteins undergo extensive conformational changes as part of their functionality. Tracing these changes is important for understanding the way these proteins function. Traditional biophysics-based conformational search methods require a large number of calculations and are hard to apply to large-scale conformational motions.

Results

In this work we investigate the application of a robotics-inspired method, using backbone and limited side chain representation and a coarse grained energy function to trace large-scale conformational motions. We tested the algorithm on four well known medium to large proteins and we show that even with relatively little information we are able to trace low-energy conformational pathways efficiently. The conformational pathways produced by our methods can be further filtered and refined to produce more useful information on the way proteins function under physiological conditions.

Conclusions

The proposed method effectively captures large-scale conformational changes and produces pathways that are consistent with experimental data and other computational studies. The method represents an important first step towards a larger scale modeling of more complex biological systems.

Many local motions cooperate to produce the adenylate kinase conformational transition

Conformational transitions are functionally important in many proteins. In the enzyme adenylate kinase (AK), two small domains (LID and NMP) close over the larger CORE domain; the reverse (opening) motion limits the rate of catalytic turnover. Here, using double-well Gō simulations of Escherichia coli AK, we elaborate on previous investigations of the AK transition mechanism by characterizing the contributions of rigid-body (Cartesian), backbone dihedral, and contact motions to transition-state (TS) properties. In addition, we compare an apo simulation to a pseudo-ligand-bound simulation to reveal insights into allostery. In Cartesian space, LID closure precedes NMP closure in the bound simulation, consistent with prior coarse-grained models of the AK transition. However, NMP-first closure is preferred in the apo simulation. In backbone dihedral space, we find that, as expected, backbone fluctuations are reduced in the O/C transition in parts of all three domains. Among these "quenching" residues, most in the CORE, especially residues 11-13, are rigidified in the TS of the bound simulation, while residues 42-44 in the NMP are flexible in the TS. In contact space, in both apo and bound simulations, one nucleus of closed-state contacts includes parts of the NMP and CORE; CORE-LID contacts are absent in the TS of the apo simulation but formed in the TS of the bound simulation. From these results, we predict mutations that will perturb the opening and/or closing transition rates by changing the entropy of dihedrals and/or the enthalpy of contacts. Furthermore, regarding allostery, the fully closed structure is populated in the apo simulation, but our contact results imply that ligand binding shifts the preferred O/C transition pathway, thus precluding a simple conformational selection mechanism. Finally, the analytical approach and the insights derived from this work may inform the rational design of flexibility and allostery in proteins.

Computational modeling of phosphotransfer complexes in two-component signaling

Two-component signal transduction systems enable cells in bacteria, fungi, and plants to react to extracellular stimuli. A sensor histidine kinase (SK) detects such stimuli with its sensor domains and transduces the input signals to a response regulator (RR) by trans-phosphorylation. This trans-phosphorylation reaction requires the formation of a complex formed by the two interacting proteins. The complex is stabilized by transient interactions. The nature of the transient interactions makes it challenging for experimental techniques to gain structural information. X-ray crystallography requires stable crystals, which are difficult to grow and stabilize. Similarly, the mere size of these systems proves problematic for NMR. Theoretical methods can, however, complement existing data. The statistical direct coupling analysis presented in the previous chapter reveals the interacting residues at the contact interface of the SK/RR pair. This information can be combined with the structures of the individual proteins in molecular dynamical simulation to generate structural models of the complex. The general approach, referred to as MAGMA, was tested on the sporulation phosphorelay phosphotransfer complex, the Spo0B/Spo0F pair, delivering crystal resolution accuracy. The MAGMA method is described here in a step-by-step explanation. The developed parameters are transferrable to other SK/RR systems.

Crystal structure of a trimeric archaeal adenylate kinase from the mesophile Methanococcus maripaludis with an unusually broad functional range and thermal stability

The structure of the trimeric adenylate kinase from the Archaebacteria Methanococcus mariplaludis (AK(MAR)) has been solved to 2.5-A resolution and the temperature dependent stability and kinetics of the enzyme measured. The K(M) and V(max) of AK(MAR) exhibit only modest temperature dependence from 30 degrees -60 degrees C. Although M. mariplaludis is a mesophile with a maximum growth temperature of 43 degrees C, AK(MAR) has a very broad functional range and stability (T(m) = 74.0 degrees C) that are more consistent with a thermophilic enzyme with high thermostability and exceptional activity over a wide range of temperatures, suggesting that this microbe may have only recently invaded a mesophilic niche and has yet to fully adapt. A comparison of the Local Structural Entropy (LSE) for AK(MAR) to the related adenylate kinases from the mesophile Methanococcus voltae and thermophile Methanococcus thermolithotrophicus show that changes in LSE are able to fully account for the intermediate stability of AK(MAR) and highlights a general mechanism for protein adaptation in this class of enzymes.

Robustness and generalization of structure-based models for protein folding and function

Functional dynamics of native proteins share the energy landscape that guides folding into the native state. Folding simulations of structure-based protein models, using an minimally frustrated energy landscape dominated by native interactions, can describe the geometrical aspects of the folding mechanism. Technical limitations imposed by the fixed shape of conventional contact potentials are a key obstacle toward advanced applications of structure-based models like allostery or ligand binding, which require multiple stable conformations. Generalizations of existing models, commonly using Lennard-Jones-like potentials, lead to inevitable clashes between their repulsive branches. To resolve these challenges, a new contact potential is developed that combines an attractive part based on Gaussians with a separate repulsive term allowing flexibility for adjustments of the potential shape. With this new model multiple minima for studies of functional transitions can be introduced easily and consistently. A sensitivity analysis for five small proteins confirms the robust behavior of structure-based models with our adaptable potential and explores their capacity for quantitative adjustment of the folding thermodynamics. We demonstrate its ability to incorporate alternative contact distances in simulations of structural transitions for the well-studied ROP dimer. Individual contact pairs can switch between distinct states to match the competing syn and anti structures. The flexibility of the new potential facilitates advanced uses of structure-based models. Depending on the application, features can be chosen from physical considerations or to match experiments. Generalized models can be built from multiple structures to study structural transitions or effects of disorder.

Capillarity theory for the fly-casting mechanism

Biomolecular folding and function are often coupled. During molecular recognition events, one of the binding partners may transiently or partially unfold, allowing more rapid access to a binding site. We describe a simple model for this fly-casting mechanism based on the capillarity approximation and polymer chain statistics. The model shows that fly casting is most effective when the protein unfolding barrier is small and the part of the chain which extends toward the target is relatively rigid. These features are often seen in known examples of fly casting in protein-DNA binding. Simulations of protein-DNA binding based on well-funneled native-topology models with electrostatic forces confirm the trends of the analytical theory.

Allosteric Conformational Transition in Adenylate Kinase: Dynamic Correlations and Implication for Allostery

An essential aspect of protein science is to determine the deductive relationship between structure, dynamics, and various sets of functions. The role of dynamics is currently challenging our understanding of protein functions, both experimentally and theoretically. To verify the internal fluctuations and dynamics correlations in an enzyme protein undergoing conformational transitions, we have applied a coarse-grained dynamics algorithm using the elastic network model for adenylate kinase. Normal mode analysis reveals possible dynamical and allosteric pathways for the transition between the open and the closed states of adenylate kinase. As the ligands binding induces significant flexibility changes of the nucleotides monophosphate (NMP) domain and adenosine triphosphate (ATP) domain, the diagonalized correlation between different structural transition states shows that most correlated motions occur between the NMP domain and the helices surrounding the ATP domain. The simultaneous existence of positive and negative correlations indicates that the conformational changes of adenylate kinase take place in an allosteric manner. Analyses of the cumulated normal mode overlap coefficients and long-range correlated motion provide new insights of operating mechanisms and dynamics of adenylate kinase. They also suggest a quantitative dynamics criterion for determining the allosteric cooperativity, which may be applicable to other proteins.

A sequence-compatible amount of native burial information is sufficient for determining the structure of small globular proteins

Protein tertiary structures are known to be encoded in amino acid sequences, but the problem of structure prediction from sequence continues to be a challenge. With this question in mind, recent simulations have shown that atomic burials, as expressed by atom distances to the molecular geometrical center, are sufficiently informative for determining native conformations of small globular proteins. Here we use a simple computational experiment to estimate the amount of this required burial information and find it to be surprisingly small, actually comparable with the stringent limit imposed by sequence statistics. Atomic burials appear to satisfy, therefore, minimal requirements for a putative dominating property in the folding code because they provide an amount of information sufficiently large for structural determination but, at the same time, sufficiently small to be encodable in sequences. In a simple analogy with human communication, atomic burials could correspond to the actual "language" encoded in the amino acid "script" from which the complexity of native conformations is recovered during the folding process.

Rational modulation of conformational fluctuations in adenylate kinase reveals a local unfolding mechanism for allostery and functional adaptation in proteins

Elucidating the complex interplay between protein structure and dynamics is a prerequisite to an understanding of both function and adaptation in proteins. Unfortunately, it has been difficult to experimentally decouple these effects because it is challenging to rationally design mutations that will either affect the structure but not the dynamics, or that will affect the dynamics but not the structure. Here we adopt a mutation approach that is based on a thermal adaptation strategy observed in nature, and we use it to study the binding interaction of Escherichia coli adenylate kinase (AK). We rationally design several single-site, surface-exposed glycine mutations to selectively perturb the excited state conformational repertoire, leaving the ground-state X-ray crystallographic structure unaffected. The results not only demonstrate that the conformational ensemble of AK is significantly populated by a locally unfolded state that is depopulated upon binding, but also that the excited-state conformational ensemble can be manipulated through mutation, independent of perturbations of the ground-state structures. The implications of these results are twofold. First, they indicate that it is possible to rationally design dynamic allosteric mutations, which do not propagate through a pathway of structural distortions connecting the mutated and the functional sites. Secondly and equally as important, the results reveal a general strategy for thermal adaptation that allows enzymes to modulate binding affinity by controlling the amount of local unfolding in the native-state ensemble. These findings open new avenues for rational protein design and fundamentally illuminate the role of local unfolding in function and adaptation.

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.

A force field for virtual atom molecular mechanics of proteins

Activities of many biological macromolecules involve large conformational transitions for which crystallography can specify atomic details of alternative end states, but the course of transitions is often beyond the reach of computations based on full-atomic potential functions. We have developed a coarse-grained force field for molecular mechanics calculations based on the virtual interactions of C alpha atoms in protein molecules. This force field is parameterized based on the statistical distribution of the energy terms extracted from crystallographic data, and it is formulated to capture features dependent on secondary structure and on residue-specific contact information. The resulting force field is applied to energy minimization and normal mode analysis of several proteins. We find robust convergence in minimizations to low energies and energy gradients with low degrees of structural distortion, and atomic fluctuations calculated from the normal mode analyses correlate well with the experimental B-factors obtained from high-resolution crystal structures. These findings suggest that the virtual atom force field is a suitable tool for various molecular mechanics applications on large macromolecular systems undergoing large conformational changes.

Computation of conformational transitions in proteins by virtual atom molecular mechanics as validated in application to adenylate kinase

Many proteins function through conformational transitions between structurally disparate states, and there is a need to explore transition pathways between experimentally accessible states by computation. The sizes of systems of interest and the scale of conformational changes are often beyond the scope of full atomic models, but appropriate coarse-grained approaches can capture significant features. We have designed a comprehensive knowledge-based potential function based on a C alpha representation for proteins that we call the virtual atom molecular mechanics (VAMM) force field. Here, we describe an algorithm for using the VAMM potential to describe conformational transitions, and we validate this algorithm in application to a transition between open and closed states of adenylate kinase (ADK). The VAMM algorithm computes normal modes for each state and iteratively moves each structure toward the other through a series of intermediates. The move from each side at each step is taken along that normal mode showing greatest engagement with the other state. The process continues to convergence of terminal intermediates to within a defined limit--here, a root-mean-square deviation of 1 A. Validations show that the VAMM algorithm is highly effective, and the transition pathways examined for ADK are compatible with other structural and biophysical information. We expect that the VAMM algorithm can address many biological systems.

Structure and biochemical characterization of an adenylate kinase originating from the psychrophilic organism Marinibacillus marinus

Adenylate kinases (AKs; EC 2.7.4.3) are essential members of the NMP kinase family that maintain cellular homeostasis by the interconversion of AMP, ADP and ATP. AKs play a critical role in adenylate homeostasis across all domains of life and have been used extensively as prototypes for the study of protein adaptation and the relationship of protein dynamics and stability to function. To date, kinetic studies of psychrophilic AKs have not been performed. In order to broaden understanding of extremophilic adaptation, the kinetic parameters of adenylate kinase from the psychrophile Marinibacillus marinus were examined and the crystal structure of this cold-adapted enzyme was determined at 2.0 A resolution. As expected, the overall structure and topology of the psychrophilic M. marinus AK are similar to those of mesophilic and thermophilic AKs. The thermal denaturation midpoint of M. marinus AK (321.1 K) is much closer to that of the mesophile Bacillus subtilis (320.7 K) than the more closely related psychrophile B. globisporus (316.4 K). In addition, the enzymatic properties of M. marinus AK are quite close to those of the mesophilic AK and suggests that M. marinus experiences temperature ranges in which excellent enzyme function over a broad temperature range (293-313 K) has been retained for the success of the organism. Even transient loss of AK function is lethal and as a consequence AK must be robust and be well adapted to the environment of the host organism.

Noncooperative folding of subdomains in adenylate kinase

Conformational change is regulating the biological activity of a large number of proteins and enzymes. Efforts in structural biology have provided molecular descriptions of the interactions that stabilize the stable ground states on the reaction trajectories during conformational change. Less is known about equilibrium thermodynamic stabilities of the polypeptide segments that participate in structural changes and whether the stabilities are relevant for the reaction pathway. Adenylate kinase (Adk) is composed of three subdomains: CORE, ATPlid, and AMPbd. ATPlid and AMPbd are flexible nucleotide binding subdomains where large-scale conformational changes are directly coupled to catalytic activity. In this report, the equilibrium thermodynamic stabilities of Adk from both mesophilic and hyperthermophilic bacteria were investigated using solution state NMR spectroscopy together with protein engineering experiments. Equilibrium hydrogen to deuterium exchange experiments indicate that the flexible subdomains are of significantly lower thermodynamic stability compared to the CORE subdomain. Using site-directed mutagenesis, parts of ATPlid and AMPbd could be selectively unfolded as a result of perturbation of hydrophobic clusters located in these respective subdomains. Analysis of the perturbed Adk variants using NMR spin relaxation and C(alpha) chemical shifts shows that the CORE subdomain can fold independently of ATPlid and AMPbd; consequently, folding of the two flexible subdomains occurs independently of each other. Based on the experimental results it is apparent that the flexible subdomains fold into their native structure in a noncooperative manner with respect to the CORE subdomain. These results are discussed in light of the catalytically relevant conformational change of ATPlid and AMPbd.

Segmented transition pathway of the signaling protein nitrogen regulatory protein C

Recent advances in experimental methods provide increasing evidence that proteins sample the conformational substates that are important for function in the absence of their ligands. An example is the receiver domain of nitrogen regulatory protein C, a member of the phosphorylation-mediated signaling family of "two-component systems." The receiver domain of nitrogen regulatory protein C samples both inactive conformation and the active conformation before phosphorylation. Here we determine a possible pathway of interconversion between the active state and the inactive state by targeted molecular dynamics simulations and quasi-harmonic analysis; these methods are used because the experimental conversion rate is in the high microsecond range, longer than those that are easily accessible to atomistic molecular dynamics simulations. The calculated pathway is found to be composed of four consecutive stages described by different progress variables. The lowest quasi-harmonic principal components from unbiased molecular dynamics simulations on the active state correspond to the first stage, but not to the subsequent stages of the transition. The targeted molecular dynamics pathway suggests that several transient nonnative hydrogen bonds may facilitate the transition.

An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Protein dynamics take place on many time and length scales. Coarse-grained structure-based (Go) models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a C(alpha) structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a C(alpha) model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.

Large Protein Dynamics Described by Hierarchical-Component Mode Synthesis

Protein dynamics has played a pivotal role in understanding the biological function of protein. For investigation of such dynamics, normal-mode analysis (NMA) has been broadly employed with atomistic model and/or coarse-grained models such as elastic network model (ENM). For large protein complexes, NMA with even ENM encounters the expensive computational process such as diagonalization of Hessian (stiffness) matrix. Here, we suggest the hierarchical-component mode synthesis (hCMS), which allows the fast computation of low-frequency normal modes related to conformational change. Specifically, a large protein structure is regarded as a combination of several structural units, for which the eigen-value problem is utilized for obtaining the frequencies and their normal modes for each structural unit, and consequently, such frequencies and normal modes are assembled with geometrical constraint for interface between structural units in order to find the low-frequency normal modes of a large protein complex. It is shown that hCMS is able to provide the normal modes with accuracy, quantitatively comparable to those of original NMA. This implies that hCMS may enable the computationally efficient analysis of large protein dynamics.

Allosteric transitions of supramolecular systems explored by network models: application to chaperonin GroEL

Identification of pathways involved in the structural transitions of biomolecular systems is often complicated by the transient nature of the conformations visited across energy barriers and the multiplicity of paths accessible in the multidimensional energy landscape. This task becomes even more challenging in exploring molecular systems on the order of megadaltons. Coarse-grained models that lend themselves to analytical solutions appear to be the only possible means of approaching such cases. Motivated by the utility of elastic network models for describing the collective dynamics of biomolecular systems and by the growing theoretical and experimental evidence in support of the intrinsic accessibility of functional substates, we introduce a new method, adaptive anisotropic network model (aANM), for exploring functional transitions. Application to bacterial chaperonin GroEL and comparisons with experimental data, results from action minimization algorithm, and previous simulations support the utility of aANM as a computationally efficient, yet physically plausible, tool for unraveling potential transition pathways sampled by large complexes/assemblies. An important outcome is the assessment of the critical inter-residue interactions formed/broken near the transition state(s), most of which involve conserved residues.

Most proteins are biomolecular machines. They perform their function by undergoing changes between different structures. Understanding the mechanism of transition between these structures is of major importance to design methods for controlling such transitions, and thereby modulating protein function. Although there are many computational methods for exploring the transitions of small proteins, the task of exploring the transition pathways becomes prohibitively expensive in the case of supramolecular systems. The bacterial chaperonin GroEL is such a supramolecular machine. It plays an important role in assisting protein folding. During its function, GroEL undergoes structural transitions between multiple forms. Here, we are introducing a new methodology, based on elastic network models, for elucidating the transition mechanisms in such supramolecular systems. Application to GroEL provides us with biologically significant information on critical interactions and sequence of events occurring during the chaperonin machinery and key contacts that make and break at the transition. The method can be readily applied to other supramolecular machines.

Protein conformational transitions: the closure mechanism of a kinase explored by atomistic simulations

Kinase large-scale conformational rearrangement is an issue of enormous biological and pharmacological relevance. Atomistic simulations able to capture the dynamics and the energetics of kinase large-scale motions are still in their infancy. Here, we present a computational study in which the atomistic dynamics of the "open-to-closed" movement of the cyclin-dependent kinase 5 (CDK5) have been simulated. Simulations were carried out using a new sampling method that is able to find the lowest free-energy channel between an initial state and a final state. This large-scale movement has a two-step mechanism: first, the alphaC-helix rotates by approximately 45 degrees , allowing the interaction between Glu51 and Arg149; then the CDK5 activation loop refolds to assume the closed conformation. We have also estimated the free-energy profile associated with the global motion and identified a CDK5 intermediate, which could be exploited for drug-design purposes. Our new sampling method turned out to be well-suited for investigating at an atomistic level the energetics and dynamics of kinase large-scale conformational motions.

Insights from coarse-grained Gō models for protein folding and dynamics

Exploring the landscape of large scale conformational changes such as protein folding at atomistic detail poses a considerable computational challenge. Coarse-grained representations of the peptide chain have therefore been developed and over the last decade have proved extremely valuable. These include topology-based Gō models, which constitute a smooth and funnel-like approximation to the folding landscape. We review the many variations of the Gō model that have been employed to yield insight into folding mechanisms. Their success has been interpreted as a consequence of the dominant role of the native topology in folding. The role of local contact density in determining protein dynamics is also discussed and is used to explain the ability of Gō-like models to capture sequence effects in folding and elucidate conformational transitions.

Allosteric communication occurs via networks of tertiary and quaternary motions in proteins

Allosteric proteins bind an effector molecule at one site resulting in a functional change at a second site. We hypothesize that allosteric communication in proteins relies upon networks of quaternary (collective, rigid-body) and tertiary (residue-residue contact) motions. We argue that cyclic topology of these networks is necessary for allosteric communication. An automated algorithm identifies rigid bodies from the displacement between the inactive and the active structures and constructs "quaternary networks" from these rigid bodies and the substrate and effector ligands. We then integrate quaternary networks with a coarse-grained representation of contact rearrangements to form "global communication networks" (GCNs). The GCN reveals allosteric communication among all substrate and effector sites in 15 of 18 multidomain and multimeric proteins, while tertiary and quaternary networks exhibit such communication in only 4 and 3 of these proteins, respectively. Furthermore, in 7 of the 15 proteins connected by the GCN, 50% or more of the substrate-effector paths via the GCN are "interdependent" paths that do not exist via either the tertiary or the quaternary network. Substrate-effector "pathways" typically are not linear but rather consist of polycyclic networks of rigid bodies and clusters of rearranging residue contacts. These results argue for broad applicability of allosteric communication based on structural changes and demonstrate the utility of the GCN. Global communication networks may inform a variety of experiments on allosteric proteins as well as the design of allostery into non-allosteric proteins.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure-function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster-NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of beta1,4-galactosyltransferase-T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed.

Ligand-induced global transitions in the catalytic domain of protein kinase A

Conformational transitions play a central role in the phosphorylation mechanisms of protein kinase. To understand the nature of these transitions, we investigated the dynamics of nucleotide binding to the catalytic domain of PKA, a prototype for the protein kinase enzyme family. The open-to-closed transition in PKA was constructed as a function of ATP association by using available X-ray data and Brownian dynamics. Analyzing the multiple kinetic trajectories at the residue level, we find that the spatial rearrangement of the residues around the nucleotide-binding pocket, along with suppressed local fluctuations, controls the compaction of the entire molecule. In addition, to accommodate the stresses induced by ATP binding at the early transition stage, partial unfoldings (cracking) and reformations of several native contacts occur at the interfaces between the secondary structure motifs enveloping the binding pocket. This suggests that the enzyme experiences local structural deformations while reaching its functional, ATP-bound state. Our dynamical view of the ligand-induced transitions in PKA suggests that the kinetic hierarchy of local and global dynamics, the variable fluctuation of residues and the necessity of partial local unfolding may be fundamental components in other large scale allosteric transitions.

Inherent flexibility determines the transition mechanisms of the EF-hands of calmodulin

We explore how inherent flexibility of a protein molecule influences the mechanism controlling allosteric transitions by using a variational model inspired from work in protein folding. The striking differences in the predicted transition mechanism for the opening of the two domains of calmodulin (CaM) emphasize that inherent flexibility is key to understanding the complex conformational changes that occur in proteins. In particular, the C-terminal domain of CaM (cCaM), which is inherently less flexible than its N-terminal domain (nCaM), reveals "cracking" or local partial unfolding during the open/closed transition. This result is in harmony with the picture that cracking relieves local stresses caused by conformational deformations of a sufficiently rigid protein. We also compare the conformational transition in a recently studied even-odd paired fragment of CaM. Our results rationalize the different relative binding affinities of the EF-hands in the engineered fragment compared with the intact odd-even paired EF-hands (nCaM and cCaM) in terms of changes in flexibility along the transition route. Aside from elucidating general theoretical ideas about the cracking mechanism, these studies also emphasize how the remarkable intrinsic plasticity of CaM underlies conformational dynamics essential for its diverse functions.

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.

Dynamic energy landscape view of coupled binding and protein conformational change: induced-fit versus population-shift mechanisms

Allostery, the coupling between ligand binding and protein conformational change, is the heart of biological network and it has often been explained by two representative models, the induced-fit and the population-shift models. Here, we clarified for what systems one model fits better than the other by performing molecular simulations of coupled binding and conformational change. Based on the dynamic energy landscape view, we developed an implicit ligand-binding model combined with the double-basin Hamiltonian that describes conformational change. From model simulations performed for a broad range of parameters, we uncovered that each of the two models has its own range of applicability, stronger and longer-ranged interaction between ligand and protein favors the induced-fit model, and weaker and shorter-ranged interaction leads to the population-shift model. We further postulate that the protein binding to small ligand tends to proceed via the population-shift model, whereas the protein docking to macromolecules such as DNA tends to fit the induced-fit model.

Conformational transition pathways explored by Monte Carlo simulation integrated with collective modes

Conformational transitions between open/closed or free/bound states in proteins possess functional importance. We propose a technique in which the collective modes obtained from an anisotropic network model (ANM) are used in conjunction with a Monte Carlo (MC) simulation approach, to investigate conformational transition pathways and pathway intermediates. The ANM-MC technique is applied to adenylate kinase (AK) and hemoglobin. The iterative method, in which normal modes are continuously updated during the simulation, proves successful in accomplishing the transition between open-closed conformations of AK and tense-relaxed forms of hemoglobin (C(alpha)-root mean square deviations between two end structures of 7.13 A and 3.55 A, respectively). Target conformations are reached by root mean-square deviations of 2.27 A and 1.90 A for AK and hemoglobin, respectively. The intermediate conformations overlap with crystal structures from the AK family within a 3.0-A root mean-square deviation. In the case of hemoglobin, the transition of tense-to-relaxed passes through the relaxed state. In both cases, the lowest-frequency modes are effective during transitions. The targeted Monte Carlo approach is used without the application of collective modes. Both the ANM-MC and targeted Monte Carlo techniques can explore sequences of events in transition pathways with an efficient yet realistic conformational search.

Src kinase conformational activation: thermodynamics, pathways, and mechanisms

Tyrosine kinases of the Src-family are large allosteric enzymes that play a key role in cellular signaling. Conversion of the kinase from an inactive to an active state is accompanied by substantial structural changes. Here, we construct a coarse-grained model of the catalytic domain incorporating experimental structures for the two stable states, and simulate the dynamics of conformational transitions in kinase activation. We explore the transition energy landscapes by constructing a structural network among clusters of conformations from the simulations. From the structural network, two major ensembles of pathways for the activation are identified. In the first transition pathway, we find a coordinated switching mechanism of interactions among the alphaC helix, the activation-loop, and the beta strands in the N-lobe of the catalytic domain. In a second pathway, the conformational change is coupled to a partial unfolding of the N-lobe region of the catalytic domain. We also characterize the switching mechanism for the alphaC helix and the activation-loop in detail. Finally, we test the performance of a Markov model and its ability to account for the structural kinetics in the context of Src conformational changes. Taken together, these results provide a broad framework for understanding the main features of the conformational transition taking place upon Src activation.

Energy landscape along an enzymatic reaction trajectory: hinges or cracks?

Are the most dynamically flexible regions around the equilibrium structure of an enzyme the same regions involved in the transition state for rate limiting processes involved in the enzymatic reaction? Kern and-coworkers (Wolf-Watzet al., 2004; Henzler-Wildman et al., 2007a, 2007b) have shown that insights about functionally relevant motions that determine the overall enzyme turnover rate can be obtained by investigating conformational dynamics around the equilibrium basin of the enzyme adenylate kinase. An allosteric change in protein structure turns out to be the controlling process. In this commentary we compare results of this study with earlier predictions of the route by which the enzyme undergoes its conformational change. These predictions are based on the idea that the energy surface for the protein is determined by the end structures of the conformational change. A key issue is whether the protein moves by specific hinges or whether it "cracks" and accesses partially unfolded states during its structural change.

Single molecule conformational dynamics of adenylate kinase: energy landscape, structural correlations, and transition state ensembles

We developed a coarse grained two-well model to study the single molecule protein conformational dynamics in microscopic detail at the residue level, overcoming the often encountered computational bottleneck. In particular, we explored the underlying conformational energy landscape of adenylate kinase, a crucial protein for signal transduction in the cell, and identified two major kinetic pathways for the conformational switch between open and closed states through either the intermediate state or the transient state. Based on the parameters fitted to the room-temperature experimental data, we predicted open and closed kinetic rates at the whole temperature ranges from 10 to 50 degrees C, which agree well with the experimental turnover numbers. After uncovering the underlying mechanism for conformational dynamics and exploring the structural correlations, we found the crucial dynamical interplay between the nucleoside monophosphate binding domain (NMP) and the ATP-binding domain (LID) in controlling the conformational switch. The key residues and contacts responsible for the conformational transitions are identified by following the time evolution of the two-dimensional spatial contact maps and characterizing the transition state as well as intermediate structure ensembles through phi value analysis. Our model provides a general framework to study the conformational dynamics of biomolecules and can be applied to many other systems.

Geometrical features of the protein folding mechanism are a robust property of the energy landscape: a detailed investigation of several reduced models

The concept of a funneled energy landscape and the principle of minimal frustration are the theoretical foundation justifying the applicability of structure-based models. In simulations, a protein is commonly reduced to a C(alpha)-bead representation. These simulations are sufficient to predict the geometrical features of the folding mechanism observed experimentally utilizing a concise formulation of the Hamiltonian with low computational costs. Toward a better understanding of the interplay between energetic and geometrical features in folding, the side chain is now explicitly included in the simulations. The simplest choice is the addition of C(beta)-beads at the center-of-mass position of the side chains. While one varies the energetic parameters of the model, the geometric aspects of the folding mechanism remain robust for a broad range of parameters. Energetic properties like folding barriers and protein stability are sensitive to the details of simulations. This robustness to geometry and sensitivity to energetic properties provide flexibility in choosing different parameters to represent changes in sequences, environments, stability or folding rate effects. Therefore, minimal frustration and the funnel concept guarantee that the geometrical features are robust properties of the folding landscape, while mutations and/or changes in the environment easily influence energy-dependent properties like folding rates or stability.

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.

Mutations as trapdoors to two competing native conformations of the Rop-dimer

Conformational transitions play a central role in regulating protein function. Structure-based models with multiple basins have been used to understand the mechanisms governing these transitions. A model able to accommodate multiple folding basins is proposed to explore the mutational effects in the folding of the Rop-dimer (Rop). In experiments, Rop mutants show unusually strong increases in folding rates with marginal effects on stability. We investigate the possibility of two competing conformations representing a parallel (P) and the wild-type antiparallel (AP) arrangement of the monomers as possible native conformations. We observe occupation of both distinct states and characterize the transition pathways. An interesting observation from the simulations is that, for equivalent energetic bias, the transition to the P basin (non-wild-type basin) shows a lower free-energy barrier. Thus, the rapid kinetics observed in experiments appear to be the result of two competing states with different kinetic behavior, triggered upon mutation by the opening of a trapdoor arising from Rop's symmetric structure. The general concept of having competing conformations for the native state goes beyond explaining Rop's mutational behaviors and can be applied to other systems. A switch between competing native structures might be triggered by external factors to allow, for example, allosteric control or signaling.

Efficient and verified simulation of a path ensemble for conformational change in a united-residue model of calmodulin

The computational sampling of rare, large-scale, conformational transitions in proteins is a well appreciated challenge-for which a number of potentially efficient path-sampling methodologies have been proposed. Here, we study a large-scale transition in a united-residue model of calmodulin using the "weighted ensemble" (WE) approach of Huber and Kim. Because of the model's relative simplicity, we are able to compare our results with brute-force simulations. The comparison indicates that the WE approach quantitatively reproduces the brute-force results, as assessed by considering (i) the reaction rate, (ii) the distribution of event durations, and (iii) structural distributions describing the heterogeneity of the paths. Importantly, the WE method is readily applied to more chemically accurate models, and by studying a series of lower temperatures, our results suggest that the WE method can increase efficiency by orders of magnitude in more challenging systems.