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.     

In the Multi-domain Protein Adenylate Kinase,Domain Insertion Facilitates Cooperative Folding while Accommodating Function at Domain Interfaces

Having multiple domains in proteins can lead to partial folding and increased aggregation. Folding cooperativity, the all or nothing folding of a protein, can reduce this aggregation propensity. In agreement with bulk experiments, a coarse-grained structure-based model of the three-domain protein, E. coli Adenylate kinase (AKE), folds cooperatively. Domain interfaces have previously been implicated in the cooperative folding of multi-domain proteins. To understand their role in AKE folding, we computationally create mutants with deleted inter-domain interfaces and simulate their folding. We find that inter-domain interfaces play a minor role in the folding cooperativity of AKE. On further analysis, we find that unlike other multi-domain proteins whose folding has been studied, the domains of AKE are not singly-linked. Two of its domains have two linkers to the third one, i.e., they are inserted into the third one. We use circular permutation to modify AKE chain-connectivity and convert inserted-domains into singly-linked domains. We find that domain insertion in AKE achieves the following: (1) It facilitates folding cooperativity even when domains have different stabilities. Insertion constrains the N- and C-termini of inserted domains and stabilizes their folded states. Therefore, domains that perform conformational transitions can be smaller with fewer stabilizing interactions. (2) Inter-domain interactions are not needed to promote folding cooperativity and can be tuned for function. In AKE, these interactions help promote conformational dynamics limited catalysis. Finally, using structural bioinformatics, we suggest that domain insertion may also facilitate the cooperative folding of other multi-domain proteins.     

On the roles of substrate binding and hinge unfolding in conformational changes of adenylate kinase

We characterized the conformational change of adenylate kinase (AK) between open and closed forms by conducting five all-atom molecular-dynamics simulations, each of 100 ns duration. Different initial structures and substrate binding configurations were used to probe the pathways of AK conformational change in explicit solvent, and no bias potential was applied. A complete closed-to-open and a partial open-to-closed transition were observed, demonstrating the direct impact of substrate-mediated interactions on shifting protein conformation. The sampled configurations suggest two possible pathways for connecting the open and closed structures of AK, affirming the prediction made based on available x-ray structures and earlier works of coarse-grained modeling. The trajectories of the all-atom molecular-dynamics simulations revealed the complexity of protein dynamics and the coupling between different domains during conformational change. Calculations of solvent density and density fluctuations surrounding AK did not show prominent variation during the transition between closed and open forms. Finally, we characterized the effects of local unfolding of an important hinge near Pro¹⁷⁷ on the closed-to-open transition of AK and identified a novel mechanism by which hinge unfolding modulates protein conformational change. The local unfolding of Pro¹⁷⁷ hinge induces alternative tertiary contacts that stabilize the closed structure and prevent the opening transition.     

Entropic tension in crowded membranes

Unlike their model membrane counterparts, biological membranes are richly decorated with a heterogeneous assembly of membrane proteins. These proteins are so tightly packed that their excluded area interactions can alter the free energy landscape controlling the conformational transitions suffered by such proteins. For membrane channels, this effect can alter the critical membrane tension at which they undergo a transition from a closed to an open state, and therefore influence protein function in vivo. Despite their obvious importance, crowding phenomena in membranes are much less well studied than in the cytoplasm. Using statistical mechanics results for hard disk liquids, we show that crowding induces an entropic tension in the membrane, which influences transitions that alter the projected area and circumference of a membrane protein. As a specific case study in this effect, we consider the impact of crowding on the gating properties of bacterial mechanosensitive membrane channels, which are thought to confer osmoprotection when these cells are subjected to osmotic shock. We find that crowding can alter the gating energies by more than [Formula: see text] in physiological conditions, a substantial fraction of the total gating energies in some cases. Given the ubiquity of membrane crowding, the nonspecific nature of excluded volume interactions, and the fact that the function of many membrane proteins involve significant conformational changes, this specific case study highlights a general aspect in the function of membrane proteins.     

Molecular dynamics simulations of Factor Xa: insight into conformational transition of its binding subsites

Protein flexibility and conformational diversity is well known to be a key characteristic of the function of many proteins. Human blood coagulation proteins have multiple substrates, and various protein-protein interactions are required for the smooth functioning of the coagulation cascade to maintain blood hemostasis. To address how a protein may cope with multiple interactions with its structurally diverse substrates and the accompanied structural changes that may drive these changes, we studied human Factor X. We employed 20 ns of molecular dynamics (MD) and steered molecular dynamics (SMD) simulations on two different conformational forms of Factor X, open and closed, and observed an interchangeable conformational transition from one to another. This work also demonstrates the roles of various aromatic residues involved in aromatic-aromatic interactions, which make this dynamic transition possible.     

Noninteracting local-structure model of folding and unfolding transition in globular proteins. I. Formulation

A statistical-mechanical model (a noninteracting local structure model) of folding and unfolding transition in globular proteins is described and a formulation is given to calculate the partition function. The process of transition is discussed in this model within the framework of equilibrium statistical mechanics. In order to clarify the range of applicability of such an approach, the characteristics of the folding and unfolding transition in globular proteins are analyzed from the statistical-physical point of view. A theoretical advantage is pointed out in studying folding and unfolding processes taking place as conformational fluctuations in individual protein molecules under macroscopic equilibrium at the melting temperature. In this case, paths of folding and unfolding are shown to be identical in the statistical sense. A key to the noninteracting local structure model lies in the concept of local structures and the assumption of the absence of interactions between local structures. A local structure is defined as a continuous section of the chain which takes the same or similar local conformation as in the native conformation. The assumption of the absence of inter-actions between local structures endows the model with the remarkable character that its partition function can be calculated exactly; thereby the equilibrium population of various conformations along the folding and unfolding paths can be discussed only by a knowledge of the folded native conformation.     

Role of aromatic localization in the gating process of a potassium channel

Position of the transmembrane aromatic residues of the KirBac1.1 potassium channel shifts from an even distribution in the closed state toward the membrane/solute interface in the open state model. This is the first example of an integral membrane protein making use of the observed preference for transmembrane aromatic residues to reside at the interfaces. The process of aromatic localization is proposed as a means of directing and stabilizing structural changes during conformational transitions within the transmembrane region of integral membrane proteins. All-atom molecular dynamics simulations of the open and closed conformers in a membrane environment have been carried out to take account of the interactions between the aromatic residues and the lipids, which may be involved in the conformational change, e.g., the gating of the channel.     

Role of Aromatic Localization in the Gating Process of a Potassium Channel

Position of the transmembrane aromatic residues of the KirBac1.1 potassium channel shifts from an even distribution in the closed state toward the membrane/solute interface in the open state model. This is the first example of an integral membrane protein making use of the observed preference for transmembrane aromatic residues to reside at the interfaces. The process of aromatic localization is proposed as a means of directing and stabilizing structural changes during conformational transitions within the transmembrane region of integral membrane proteins. All-atom molecular dynamics simulations of the open and closed conformers in a membrane environment have been carried out to take account of the interactions between the aromatic residues and the lipids, which may be involved in the conformational change, e.g., the gating of the channel.     

Dynamics of folding and unfolding transition in a globular protein studied by time correlation functions from computer simulation

A method of calculating time correlation functions from records of computer simulated equilibrium conformational fluctuations in a globular protein is discussed. Use of the calculated time correlation function for discussions of dynamics of folding and unfolding transition in the two-dimensional lattice model of proteins. The time correlation functions can be approximated in general by a sum of two simple exponential terms. The relaxation time of the slower mode does not depend on the nature of the physical quantity with respect to which the time correlation function is calculated. This time characterizes the overall folding and unfolding transition. The relaxation time of the faster mode depends on the nature of the physical quantity and characterizes conformational fluctuations within each of the native and denatured states. The mechanism of a previously observed phenomenon of the acceleration of the folding and unfolding transition by short-range interactions is discussed.     

Dual energy landscape: the functional state of the β-barrel outer membrane protein G molds its unfolding energy landscape

We applied dynamic single-molecule force spectroscopy to quantify the parameters (free energy of activation and distance of the transition state from the folded state) characterizing the energy barriers in the unfolding energy landscape of the outer membrane protein G (OmpG) from Escherichia coli. The pH-dependent functional switching of OmpG directs the protein along different regions on the unfolding energy landscape. The two functional states of OmpG take the same unfolding pathway during the sequential unfolding of β-hairpins I-IV. After the initial unfolding events, the unfolding pathways diverge. In the open state, the unfolding of β-hairpin V in one step precedes the unfolding of β-hairpin VI. In the closed state, β-hairpin V and β-strand S11 with a part of extracellular loop L6 unfold cooperatively, and subsequently β-strand S12 unfolds with the remaining loop L6. These two unfolding pathways in the open and closed states join again in the last unfolding step of β-hairpin VII. Also, the conformational change from the open to the closed state witnesses a rigidified extracellular gating loop L6. Thus, a change in the conformational state of OmpG not only bifurcates its unfolding pathways but also tunes its mechanical properties for optimum function.     

The effect of amino acid substitution on protein-folding and -unfolding transition studied by computer simulation

Protein-folding and -unfolding transitions were studied by the method of computer simulation. The protein was modeled as a two-dimensional lattice polymer. Various energy terms were assumed to be operative between units composing the polymer. But hydrophobic interactions were neglected explicitly. Both thermodynamic and kinetic quantities were obtained from the simulation, and from their temperature dependence in the transition zone characteristics of the conformational transition of proteins were discussed. Two amino acid substituted models, differing in the location of substitution, were studied and compared with the original in order to clarify the effect of substitution on conformational transition of proteins. The following conclusions were reached in this study: (1) The relaxation time of the slow mode, which reflects the overall folding and unfolding processes, shows a peak near the transition temperature, while that of the fast mode is almost independent of temperature. The peak of the slow mode occurs at a slightly lower temperature than the transition temperature. (2) The dependence of the logarithm of the rate constants on the inverse of temperature (Arrhenius plot) is linear. Therefore, the plot of the free energy of activation vs temperature is linear. (3) The values of kinetic parameters obtained suggest that in the activated state the intramolecular interactions are half broken, while the state is close to the native state on the entropy axis. (4) The amino acid substitution, which is modeled as having slightly unfavorable short-range interactions, causes the substituted ones to be slightly unstable. Moreover, it causes the folding transition to slow. From the analysis of the way slowing down is observed in the two substituted models, we conclude that a structure, designed to model a β-sheet, is formed before it gets assembled with other structures, which are designed to model α-helices. The process of assembly occurs nearly at the activated state of the folding and unfolding transition. (5) It is suggested from this study that the maximum of folding rate constant in the Arrhenius plot that has been observed experimentally in real proteins is likely due to hydrophobic interactions.     

Conformational stability and thermodynamic characterization of homotetrameric Plasmodium falciparum beta-ketoacyl-ACP reductase

The conformational stability of the homotetrameric Plasmodium falciparum beta-ketoacyl-ACP reductase (FabG) was determined by guanidinium chloride-induced isothermal and thermal denaturation. The reversible unfolding transitions were monitored by intrinsic fluorescence, circular dichroism (CD) spectroscopy and by measuring the enzyme activity of FabG. The denaturation profiles were analyzed to obtain the thermodynamic parameters associated with unfolding of the protein. The data confirm the simple A(4) <--> 4A model of unfolding, based on the corroboration of CD data by fluorescence transition and similar Delta G estimation for denaturation curves obtained at four different concentration of the FabG. Denaturation is well described by the linear extrapolation model for denaturant-protein interactions. In addition, the conformational stability (Delta G(s)) as well as the Delta C(p) for the protein unfolding is quite high, 22.68 kcal/mole and 5.83 kcal/(mole K), respectively, which may be a reflection of the relatively large size of the tetrameric molecule (Mr 120, 000) and a large buried hydrophobic core in the folded protein. This study provides a prototype for determining conformational stability of other members of the short-chain alcohol dehydrogenase/reductase superfamily of proteins to which PfFabG belongs.     

Kinetics of unfolding and folding from amide hydrogen exchange in native ubiquitin

Amide hydrogen (NH) exchange is one of the few experimental techniques with the potential for determining the thermodynamics and kinetics of conformational motions at nearly every residue in native proteins. Quantitative interpretation of NH exchange in terms of molecular motions relies on a simple two-state kinetic model: at any given slowly exchanging NH, a closed or exchange-incompetent conformation is in equilibrium with an open or exchange-competent conformation. Previous studies have demonstrated the accuracy of this model in measuring conformational equilibria by comparing exchange data with the thermodynamics of protein unfolding. We report here a test of the accuracy of the model in determining the kinetics of conformational changes in native proteins. The kinetics of folding and unfolding for ubiquitin have been measured by conventional methods and compared with those derived from a comprehensive analysis of the pH dependence of exchange in native ubiquitin. Rate constants for folding and unfolding from these two very different types of experiments show good agreement. The simple model for NH exchange thus appears to be a robust framework for obtaining quantitative information about molecular motions in native proteins.     

How large are the volume changes accompanying protein transitions and binding?

We present a simple model to describe volume changes accompanying protein folding and binding events. The model enables one to resolve the changes in volume accompanying conformational transitions of proteins as well as association of proteins with other molecules in terms of the intrinsic, thermal and interaction (hydration) contributions. The thermal contribution to protein volume results from thermally activated mutual vibrational motions of contacting solute and solvent molecules. Our calculations suggest that near zero volume changes accompanying protein folding and binding events reflect compensation between significant changes in the intrinsic, thermal and interaction terms. We have quantitatively estimated these terms as a function of the protein's molecular weight and degree of its unfolding. Results described in this work lay foundation for more reliable and physically justified interpretations of volumetric data on protein folding and binding events. We also discuss potential ways of extending applications of our model to analyzing other macromolecular systems and events, including drug-DNA and protein-DNA interactions and helix-to-helix and helix-to-coil transitions of nucleic acids.     

How well can we understand large-scale protein motions using normal modes of elastic network models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.     

Conformational equilibria and free energy profiles for the allosteric transition of the ribose-binding protein

The ribose-binding protein (RBP) is a sugar-binding bacterial periplasmic protein whose function is associated with a large allosteric conformational change from an open to a closed conformation upon binding to ribose. The crystal structures of RBP in open and closed conformations have been solved. It has been hypothesized that the open and closed conformations exist in a dynamic equilibrium in solution, and that sugar binding shifts the population from open conformations to closed conformations. Here, we study by computer simulations the thermodynamic changes that accompany this conformational change, and model the structural changes that accompany the allosteric transition, using umbrella sampling molecular dynamics and the weighted histogram analysis method. The open state is comprised of a diverse ensemble of conformations; the open ribose-free X-ray crystal conformations being representative of this ensemble. The unligated open form of RBP is stabilized by conformational entropy. The simulations predict detectable populations of closed ribose-free conformations in solution. Additional interdomain hydrogen bonds stabilize this state. The predicted shift in equilibrium from the open to the closed state on binding to ribose is in agreement with experiments. This is driven by the energetic stabilization of the closed conformation due to ribose-protein interactions. We also observe a significant population of a hitherto unobserved ribose-bound partially open state. We believe that this state is the one that has been suggested to play a role in the transfer of ribose to the membrane-bound permease complex.     

Mapping the Dynamics Landscape of Conformational Transitions in Enzyme: The Adenylate Kinase Case

Conformational transition describes the essential dynamics and mechanism of enzymes in pursuing their various functions. The fundamental and practical challenge to researchers is to quantitatively describe the roles of large-scale dynamic transitions for regulating the catalytic processes. In this study, we tackled this challenge by exploring the pathways and free energy landscape of conformational changes in adenylate kinase (AdK), a key ubiquitous enzyme for cellular energy homeostasis. Using explicit long-timescale (up to microseconds) molecular dynamics and bias-exchange metadynamics simulations, we determined at the atomistic level the intermediate conformational states and mapped the transition pathways of AdK in the presence and absence of ligands. There is clearly chronological operation of the functional domains of AdK. Specifically in the ligand-free AdK, there is no significant energy barrier in the free energy landscape separating the open and closed states. Instead there are multiple intermediate conformational states, which facilitate the rapid transitions of AdK. In the ligand-bound AdK, the closed conformation is energetically most favored with a large energy barrier to open it up, and the conformational population prefers to shift to the closed form coupled with transitions. The results suggest a perspective for a hybrid of conformational selection and induced fit operations of ligand binding to AdK. These observations, depicted in the most comprehensive and quantitative way to date, to our knowledge, emphasize the underlying intrinsic dynamics of AdK and reveal the sophisticated conformational transitions of AdK in fulfilling its enzymatic functions. The developed methodology can also apply to other proteins and biomolecular systems.     

Molecular mechanisms of activation in CDK2

Cyclin-dependent kinases (CDKs) are enzymes involved in crucial cellular processes. Their biological activity is directly linked to their high conformational variability, which involves large protein conformational rearrangements. We present here the application of an enhancing sampling technique to the study of conformational transitions between the open and closed state of CDKs. The analysis of the conformational intermediates supports the idea that the process is regulated by two important protein regions, which sequentially rearrange in order to allow the protein to reach its final conformation. Furthermore, the two paths involve additional (minor) protein rearrangements which are specific to the paths. Our results show that our procedure can provide reasonable transition pathways between the two protein forms at a very reduced computational cost. The robustness and the simplicity of our approach make it of general application to describe virtually any macromolecular conformational transitions.