Conformational transitions of adenylate kinase: switching by cracking

Backtracking due to residual structure in the unfolded state changes the folding of the third fibronectin type III domain from tenascin-C

Residual structure in the unfolded state of a protein may play a crucial role in folding and stability. In the present study, using an all (heavy)-atom structure based model and replica exchange molecular dynamics simulations, we explored the folding landscape of the third fibronectin type III domain from tenascin-C (TNfn3). Specifically, both the wild type (WT) and a variant with two additional amino acids, Gly-Leu (GL), at the C-terminus (WT(+GL)) were studied. We found that, although both domains of TNfn3 are topologically frustrated, the early formation of the native contacts from the C-terminal end of WT(+GL) causes more "backtracking" than in the WT. As a result, the WT exhibits a two-state folding behavior with a broad transition-state ensemble, whereas the WT(+GL) folds through a metastable intermediate state. Furthermore, our study confirmed that the core of both proteins is conformationally heterogeneous and noncompact, and folds late mainly due to backtracking of the part of the core. Finally, in agreement with the previous experimental studies, our results clearly demonstrated distinct thermodynamic behavior of the two proteins with WT(+GL) being more stable.

Allosteric activation transitions in enzymes and biomolecular motors: insights from atomistic and coarse-grained simulations

The chemical step in enzymes is usually preceded by a kinetically distinct activation step that involves large-scale conformational transitions. In "simple" enzymes this step corresponds to the closure of the active site; in more complex enzymes, such as biomolecular motors, the activation step is more complex and may involve interactions with other biomolecules. These activation transitions are essential to the function of enzymes and perturbations in the scale and/or rate of these transitions are implicated in various serious human diseases; incorporating key flexibilities into engineered enzymes is also considered a major remaining challenge in rational enzyme design. Therefore it is important to understand the underlying mechanism of these transitions. This is a significant challenge to both experimental and computational studies because of the allosteric and multi-scale nature of such transitions. Using our recent studies of two enzyme systems, myosin and adenylate kinase (AK), we discuss how atomistic and coarse-grained simulations can be used to provide insights into the mechanism of activation transitions in realistic systems. Collectively, the results suggest that although many allosteric transitions can be viewed as domain displacements mediated by flexible hinges, there are additional complexities and various deviations. For example, although our studies do not find any evidence for "cracking" in AK, our results do underline the contribution of intra-domain properties (e.g., dihedral flexibility) to the rate of the transition. The study of mechanochemical coupling in myosin highlights that local changes important to chemistry require stabilization from more extensive structural changes; in this sense, more global structural transitions are needed to activate the chemistry in the active site. These discussions further emphasize the importance of better understanding factors that control the degree of co-operativity for allosteric transitions, again hinting at the intimate connection between protein stability and functional flexibility. Finally, a number of topics of considerable future interest are briefly discussed.

Allosteric control in a metalloprotein dramatically alters function

Metalloproteins (MPs) comprise one-third of all known protein structures. This diverse set of proteins contain a plethora of unique inorganic moieties capable of performing chemistry that would otherwise be impossible using only the amino acids found in nature. Most of the well-studied MPs are generally viewed as being very rigid in structure, and it is widely thought that the properties of the metal centers are primarily determined by the small fraction of amino acids that make up the local environment. Here we examine both theoretically and experimentally whether distal regions can influence the metal center in the diabetes drug target mitoNEET. We demonstrate that a loop (L2) 20 Å away from the metal center exerts allosteric control over the cluster binding domain and regulates multiple properties of the metal center. Mutagenesis of L2 results in significant shifts in the redox potential of the [2Fe-2S] cluster and orders of magnitude effects on the rate of [2Fe-2S] cluster transfer to an apo-acceptor protein. These surprising effects occur in the absence of any structural changes. An examination of the native basin dynamics of the protein using all-atom simulations shows that twisting in L2 controls scissoring in the cluster binding domain and results in perturbations to one of the cluster-coordinating histidines. These allosteric effects are in agreement with previous folding simulations that predicted L2 could communicate with residues surrounding the metal center. Our findings suggest that long-range dynamical changes in the protein backbone can have a significant effect on the functional properties of MPs.

The dominant folding route minimizes backbone distortion in SH3

Energetic frustration in protein folding is minimized by evolution to create a smooth and robust energy landscape. As a result the geometry of the native structure provides key constraints that shape protein folding mechanisms. Chain connectivity in particular has been identified as an essential component for realistic behavior of protein folding models. We study the quantitative balance of energetic and geometrical influences on the folding of SH3 in a structure-based model with minimal energetic frustration. A decomposition of the two-dimensional free energy landscape for the folding reaction into relevant energy and entropy contributions reveals that the entropy of the chain is not responsible for the folding mechanism. Instead the preferred folding route through the transition state arises from a cooperative energetic effect. Off-pathway structures are penalized by excess distortion in local backbone configurations and contact pair distances. This energy cost is a new ingredient in the malleable balance of interactions that controls the choice of routes during protein folding.

Exploring the Dynamic Functional Landscape of Adenylate Kinase Modulated by Substrates

Adenylate kinase (ADK) has been explored widely, through both experimental and theoretical studies. However, still less is known about how the functional dynamics of ADK is modulated explicitly by its natural substrates. Here, we report a quantitative study of the dynamic energy landscape for ADK responding to the substrate binding by integrating both experimental investigations and theoretical modeling. We make theoretical predictions which are in remarkable agreement with the single molecule experiments on the substrate-bound complex. With our combined models of ADK in its apo form, in the presence of AMP or ATP, and in complex with both substrates, we specifically address the following key questions: (1) Are there intermediate state(s) during their catalytic cycle and if so how many? (2) How many pathways are there along the open-to-closed transitions and what are their corresponding weights? (3) How do substrates influence the pathway weights and the stability of the intermediates? (4) Which lid's motion is rate-limiting along the turnover cycle, the NMP or the LID domain? Our models predict two major parallel stepwise pathways and two on-pathway intermediates which are denoted as IN (NMP domain open while LID domain closed) and IL (LID domain open and NMP domain closed), respectively. Further investigation of temperature effects suggests that the IN pathway is dominant at room temperature, but the IL pathway is dominant at the optimal temperature. This leads us to propose that the IL pathway is more dominant by entropy and IN pathway by enthalpy. Remarkably, our results show that even with maximum concentrations of natural substrates, ADK still fluctuates between multiple functional states, reflecting an intrinsic capability of large-scale conformational fluctuations which may be essential to its biological function. The results based on the dual-ligands model provide the theoretical validation of random bisubstrate biproducts (Bi-Bi) mechanism for the enzymatic reaction of ADK. Additionally, the pathway flux analysis strongly suggests that the motion of the NMP domain is the rate-determining step for the conformational cycle (opening and closing).

Modulation of folding kinetics of repeat proteins: interplay between intra- and interdomain interactions

Repeat proteins have unique elongated structures that, unlike globular proteins, are quite modular. Despite their simple one-dimensional structure, repeat proteins exhibit intricate folding behavior with a complexity similar to that of globular proteins. Therefore, repeat proteins allow one to quantify fundamental aspects of the biophysics of protein folding. One important feature of repeat proteins is the interfaces between the repeating units. In particular, the distribution of stabilities within and between the repeats was previously suggested to affect their folding characteristics. In this study, we explore how the interface affects folding kinetics and cooperativity by investigating two families of repeat proteins, namely, the Ankyrin and tetratricopeptide repeat proteins, which differ in the number of interfacial contacts that are formed between their units as well as in their folding behavior. By using simple topology-based models, we show that modulating the energetic strength of the interface relative to that of the repeat itself can drastically change the protein stability, folding rate, and cooperativity. By further dissecting the interfacial contacts into several subsets, we isolated the effects of each of these groups on folding kinetics. Our study highlights the importance of interface connectivity in determining the folding behavior.

Cracking phase diagram for the dynamics of an enzyme

We measure the ensemble averaged deformation of an enzyme for an oscillating applied force. From the low frequency divergence of the mechanical susceptibility for the hinge motion of guanylate kinase we obtain a nonequilibrium phase diagram in the frequency-force plane. A phase line separates linear elasticity dynamics from softer (viscoelastic) dynamics. The hinge motion corresponds to crossing this phase line (not to a soft linear elastic mode). The phase line is dramatically shifted in the closed state compared to the open state of the enzyme.

Modulation of a pre-existing conformational equilibrium tunes adenylate kinase activity

Structural plasticity is often required for distinct microscopic steps during enzymatic reaction cycles. Adenylate kinase from Escherichia coli (AK(eco)) populates two major conformations in solution; the open (inactive) and closed (active) state, and the overall turnover rate is inversely proportional to the lifetime of the active conformation. Therefore, structural plasticity is intimately coupled to enzymatic turnover in AK(eco). Here, we probe the open to closed conformational equilibrium in the absence of bound substrate with NMR spectroscopy and molecular dynamics simulations. The conformational equilibrium in absence of substrate and, in turn, the turnover number can be modulated with mutational- and osmolyte-driven perturbations. Removal of one hydrogen bond between the ATP and AMP binding subdomains results in a population shift toward the open conformation and a resulting increase of k(cat). Addition of the osmolyte TMAO to AK(eco) results in population shift toward the closed conformation and a significant reduction of k(cat). The Michaelis constants (K(M)) scale with the change in k(cat), which follows from the influence of the population of the closed conformation for substrate binding affinity. Hence, k(cat) and K(M) are mutually dependent, and in the case of AK(eco), any perturbation that modulates k(cat) is mirrored with a proportional response in K(M). Thus, our results demonstrate that the equilibrium constant of a pre-existing conformational equilibrium directly affects enzymatic catalysis. From an evolutionary perspective, our findings suggest that, for AK(eco), there exists ample flexibility to obtain a specificity constant (k(cat)/K(M)) that commensurate with the exerted cellular selective pressure.

An adaptive weighted ensemble procedure for efficient computation of free energies and first passage rates

We introduce an adaptive weighted-ensemble procedure (aWEP) for efficient and accurate evaluation of first-passage rates between states for two-state systems. The basic idea that distinguishes aWEP from conventional weighted-ensemble (WE) methodology is the division of the configuration space into smaller regions and equilibration of the trajectories within each region upon adaptive partitioning of the regions themselves into small grids. The equilibrated conditional∕transition probabilities between each pair of regions lead to the determination of populations of the regions and the first-passage times between regions, which in turn are combined to evaluate the first passage times for the forward and backward transitions between the two states. The application of the procedure to a non-trivial coarse-grained model of a 70-residue calcium binding domain of calmodulin is shown to efficiently yield information on the equilibrium probabilities of the two states as well as their first passage times. Notably, the new procedure is significantly more efficient than the canonical implementation of the WE procedure, and this improvement becomes even more significant at low temperatures.

Quasi-Continuous Interpolation Scheme for Pathways between Distant Configurations

A quasi-continuous interpolation (QCI) scheme is introduced for characterizing physically realistic initial pathways from which to initiate transition state searches and construct kinetic transition networks. Applications are presented for peptides, proteins, and a morphological transformation in an atomic cluster. The first step in each case involves end point alignment, and we describe the use of a shortest augmenting path algorithm for optimizing permutational isomers. The QCI procedure then employs an interpolating potential, which preserves the covalent bonding framework for the biomolecules and includes repulsive terms between unconstrained atoms. This potential is used to identify an interpolating path by minimizing contributions from a connected set of images, including terms corresponding to minima in the interatomic distances between them. This procedure detects unphysical geometries in the line segments between images. The most difficult cases, where linear interpolation would involve chain crossings, are treated by growing the structure an atom at a time using the interpolating potential. To test the QCI procedure, we carry through a series of benchmark calculations where the initial interpolation is coupled to explicit transition state searches to produce complete pathways between specified local minima.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Minimum free energy path of ligand-induced transition in adenylate kinase

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

Structural basis of histidine kinase autophosphorylation deduced by integrating genomics, molecular dynamics, and mutagenesis

Signal transduction proteins such as bacterial sensor histidine kinases, designed to transition between multiple conformations, are often ruled by unstable transient interactions making structural characterization of all functional states difficult. This study explored the inactive and signal-activated conformational states of the two catalytic domains of sensor histidine kinases, HisKA and HATPase. Direct coupling analyses, a global statistical inference approach, was applied to >13,000 such domains from protein databases to identify residue contacts between the two domains. These contacts guided structural assembly of the domains using MAGMA, an advanced molecular dynamics docking method. The active conformation structure generated by MAGMA simultaneously accommodated the sequence derived residue contacts and the ATP-catalytic histidine contact. The validity of this structure was confirmed biologically by mutation of contact positions in the Bacillus subtilis sensor histidine kinase KinA and by restoration of activity in an inactive KinA(HisKA):KinD(HATPase) hybrid protein. These data indicate that signals binding to sensor domains activate sensor histidine kinases by causing localized strain and unwinding at the end of the C-terminal helix of the HisKA domain. This destabilizes the contact positions of the inactive conformation of the two domains, identified by previous crystal structure analyses and by the sequence analysis described here, inducing the formation of the active conformation. This study reveals that structures of unstable transient complexes of interacting proteins and of protein domains are accessible by applying this combination of cross-validating technologies.

Mirror images as naturally competing conformations in protein folding

Evolution has selected a protein's sequence to be consistent with the native state geometry, as this configuration must be both thermodynamically stable and kinetically accessible to prevent misfolding and loss of function. In simple protein geometries, such as coiled-coil helical bundles, symmetry produces a competing, globally different, near mirror image with identical secondary structure and similar native contact interactions. Experimental techniques such as circular dichroism, which rely on probing secondary structure content, cannot readily distinguish these folds. Here, we want to clarify whether the native fold and mirror image are energetically competitive by investigating the free energy landscape of three-helix bundles. To prevent a bias from a specific computational approach, the present study employs the structure prediction forcefield PFF01/02, explicit solvent replica exchange molecular dynamics (REMD) with the Amber94 forcefield, and structure-based simulations based on energy landscape theory. We observe that the native fold and its mirror image have a similar enthalpic stability and are thermodynamically competitive. There is evidence that the mirror fold has faster folding kinetics and could function as a kinetic trap. All together, our simulations suggest that mirror images might not just be a computational annoyance but are competing folds that might switch depending on environmental conditions or functional considerations.

Configuration-dependent diffusion dynamics of downhill and two-state protein folding

Configuration-dependent diffusion (CDD) is important for protein folding kinetics with small thermodynamic barriers. CDD can be even more crucial in downhill folding without thermodynamic barriers. We explored the CDD of a downhill protein (BBL), and a two-state protein (CI2). The hidden kinetic barriers due to CDD were revealed. The increased ~1 k(B)T kinetic barrier is in line with experimental value based on other fast folding proteins. Compared to that of CI2, the effective free-energy profile of BBL is found to be significantly influenced by CDD, and the kinetics are totally determined by diffusion. These findings are consistent with both earlier bulk and single-molecule fluorescence measurements. In addition, we found the temperature dependence of CDD. We also found that the ratio of folding transition temperature against optimal kinetic folding temperature can provide both a quantitative measure for the underlying landscape topography and an indicator for the possible appearance of downhill folding. Our study can help for a better understanding of the role of diffusion in protein folding dynamics.

Exploration of multi-state conformational dynamics and underlying global functional landscape of maltose binding protein

An increasing number of biological machines have been revealed to have more than two macroscopic states. Quantifying the underlying multiple-basin functional landscape is essential for understanding their functions. However, the present models seem to be insufficient to describe such multiple-state systems. To meet this challenge, we have developed a coarse grained triple-basin structure-based model with implicit ligand. Based on our model, the constructed functional landscape is sufficiently sampled by the brute-force molecular dynamics simulation. We explored maltose-binding protein (MBP) which undergoes large-scale domain motion between open, apo-closed (partially closed) and holo-closed (fully closed) states responding to ligand binding. We revealed an underlying mechanism whereby major induced fit and minor population shift pathways co-exist by quantitative flux analysis. We found that the hinge regions play an important role in the functional dynamics as well as that increases in its flexibility promote population shifts. This finding provides a theoretical explanation of the mechanistic discrepancies in PBP protein family. We also found a functional “backtracking” behavior that favors conformational change. We further explored the underlying folding landscape in response to ligand binding. Consistent with earlier experimental findings, the presence of ligand increases the cooperativity and stability of MBP. This work provides the first study to explore the folding dynamics and functional dynamics under the same theoretical framework using our triple-basin functional model.

A central goal of biology is to understand the function of the organism and its constituent parts at each of its scales of complexity. Function at the molecular level is often realized by changes in conformation. Unfortunately, experimental explorations of global motions critical for functional conformational changes are still challenging. In the present work, we developed a coarse grained triple-well structure-based model to explore the underlying functional landscape of maltose-binding protein (MBP). By quantitative flux analysis, we uncover the underlying mechanism by which the major induced fit and minor population shift pathways co-exist. Though we have previously lent credence to the assertion that dynamical equilibrium between open and minor closed conformations exist for all the free PBPs, the generality of this rule is still a matter of open debate. We found that the hinge flexibility is favorable to population shift mechanism. This finding provides a theoretical explanation of the mechanism discrepancies in PBP protein family. We also simulated the folding dynamics using this functional multi-basin model which successfully reproduced earlier protein melting experiment. This represents an exciting opportunity to characterize the interplay between folding and function, which is a long-standing question in the community. The theoretical approach employed in this study is general and can be applied to other systems.

Large-scale motions in the adenylate kinase solution ensemble: coarse-grained simulations and comparison with solution X-ray scattering

While coarse-grained (CG) simulations provide an efficient approach to identify small- and large-scale motions important to protein conformational transitions, coupling with appropriate experimental validation is essential. Here, by comparing small-angle X-ray scattering (SAXS) predictions from CG simulation ensembles of adenylate kinase (AK) with a range of energetic parameters, we demonstrate that AK is flexible in solution in the absence of ligand and that a small population of the closed form exists without ligand. In addition, by analyzing variation of scattering patterns within CG simulation ensembles, we reveal that rigid-body motion of the LID domain corresponds to a dominant scattering feature. Thus, we have developed a novel approach for three-dimensional structural interpretation of SAXS data. Finally, we demonstrate that the agreement between predicted and experimental SAXS can be improved by increasing the simulation temperature or by computationally mutating selected residues to glycine, both of which perturb LID rigid-body flexibility.

Strand swapping regulates the iron-sulfur cluster in the diabetes drug target mitoNEET

MitoNEET is a recently identified diabetes drug target that coordinates a transferable 2Fe-2S cluster, and additionally contains an unusual strand swap. In this manuscript, we use a dual basin structure-based model to predict and characterize the folding and functionality of strand swapping in mitoNEET. We demonstrate that a strand unswapped conformation is kinetically accessible and that multiple levels of control are employed to regulate the conformational dynamics of the system. Environmental factors such as temperature can shift route preference toward the unswapped pathway. Additionally we see that a region recently identified as contributing to frustration in folding acts as a regulatory hinge loop that modulates conformational balance. Interestingly, strand unswapping transfers strain specifically to cluster-coordinating residues, opening the cluster-coordinating pocket. Strengthening contacts within the cluster-coordinating pocket opens a new pathway between the swapped and unswapped conformation that utilizes cracking to bypass the unfolded basin. These results suggest that local control within distinct regions affect motions important in regulating mitoNEET's 2Fe-2S clusters.

Conformational flexibility and the mechanisms of allosteric transitions in topologically similar proteins

Conformational flexibility plays a central role in allosteric transition of proteins. In this paper, we extend the analysis of our previous study [S. Tripathi and J. J. Portman, Proc. Natl. Acad. Sci. U.S.A. 106, 2104 (2009)] to investigate how relatively minor structural changes of the meta-stable states can significantly influence the conformational flexibility and allosteric transition mechanism. We use the allosteric transitions of the domains of calmodulin as an example system to highlight the relationship between the transition mechanism and the inter-residue contacts present in the meta-stable states. In particular, we focus on the origin of transient local unfolding (cracking), a mechanism that can lower free energy barriers of allosteric transitions, in terms of the inter-residue contacts of the meta-stable states and the pattern of local strain that develops during the transition. We find that the magnitude of the local strain in the protein is not the sole factor determining whether a region will ultimately crack during the transition. These results emphasize that the residue interactions found exclusively in one of the two meta-stable states is the key in understanding the mechanism of allosteric conformational change.

Link between allosteric signal transduction and functional dynamics in a multisubunit enzyme: S-adenosylhomocysteine hydrolase

S-adenosylhomocysteine hydrolase (SAHH), a cellular enzyme that plays a key role in methylation reactions including those required for maturation of viral mRNA, is an important drug target in the discovery of antiviral agents. While targeting the active site is a straightforward strategy of enzyme inhibition, evidence of allosteric modulation of active site in many enzymes underscores the molecular origin of signal transduction. Information of co-evolving sequences in SAHH family and the key residues for functional dynamics that can be identified using native topology of the enzyme provide glimpses into how the allosteric signaling network, dispersed over the molecular structure, coordinates intra- and intersubunit conformational dynamics. To study the link between the allosteric communication and functional dynamics of SAHHs, we performed Brownian dynamics simulations by building a coarse-grained model based on the holo and ligand-bound structures. The simulations of ligand-induced transition revealed that the signal of intrasubunit closure dynamics is transmitted to form intersubunit contacts, which in turn invoke a precise alignment of active site, followed by the dimer-dimer rotation that compacts the whole tetrameric structure. Further analyses of SAHH dynamics associated with ligand binding provided evidence of both induced fit and population shift mechanisms and also showed that the transition-state ensemble is akin to the ligand-bound state. Besides the formation of enzyme-ligand contacts at the active site, the allosteric couplings from the residues distal to the active site are vital to the enzymatic function.

Excited states of ribosome translocation revealed through integrative molecular modeling

The dynamic nature of biomolecules leads to significant challenges when characterizing the structural properties associated with function. While X-ray crystallography and imaging techniques (such as cryo-electron microscopy) can reveal the structural details of stable molecular complexes, strategies must be developed to characterize configurations that exhibit only marginal stability (such as intermediates) or configurations that do not correspond to minima on the energy landscape (such as transition-state ensembles). Here, we present a methodology (MDfit) that utilizes molecular dynamics simulations to generate configurations of excited states that are consistent with available biophysical and biochemical measurements. To demonstrate the approach, we present a sequence of configurations that are suggested to be associated with transfer RNA (tRNA) movement through the ribosome (translocation). The models were constructed by combining information from X-ray crystallography, cryo-electron microscopy, and biochemical data. These models provide a structural framework for translocation that may be further investigated experimentally and theoretically to determine the precise energetic character of each configuration and the transition dynamics between them.

The energy landscape analysis of cancer mutations in protein kinases

The growing interest in quantifying the molecular basis of protein kinase activation and allosteric regulation by cancer mutations has fueled computational studies of allosteric signaling in protein kinases. In the present study, we combined computer simulations and the energy landscape analysis of protein kinases to characterize the interplay between oncogenic mutations and locally frustrated sites as important catalysts of allostetric kinase activation. While structurally rigid kinase core constitutes a minimally frustrated hub of the catalytic domain, locally frustrated residue clusters, whose interaction networks are not energetically optimized, are prone to dynamic modulation and could enable allosteric conformational transitions. The results of this study have shown that the energy landscape effect of oncogenic mutations may be allosteric eliciting global changes in the spatial distribution of highly frustrated residues. We have found that mutation-induced allosteric signaling may involve a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. The presented study has demonstrated that activation cancer mutations may affect the thermodynamic equilibrium between kinase states by allosterically altering the distribution of locally frustrated sites and increasing the local frustration in the inactive form, while eliminating locally frustrated sites and restoring structural rigidity of the active form. The energy landsape analysis of protein kinases and the proposed role of locally frustrated sites in activation mechanisms may have useful implications for bioinformatics-based screening and detection of functional sites critical for allosteric regulation in complex biomolecular systems.

Interconversion of functional motions between mesophilic and thermophilic adenylate kinases

Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), for which the open/closed transition limits the rate of catalytic turnover. Here, we compare our previously published coarse-grained (double-well Gō) simulation of mesophilic AK from E. coli (AKmeso) to simulations of thermophilic AK from Aquifex aeolicus (AKthermo). In AKthermo, as with AKmeso, the LID domain prefers to close before the NMP domain in the presence of ligand, but LID rigid-body flexibility in the open (O) ensemble decreases significantly. Backbone foldedness in O and/or transition state (TS) ensembles increases significantly relative to AKmeso in some interdomain backbone hinges and within LID. In contact space, the TS of AKthermo has fewer contacts at the CORE-LID interface but a stronger contact network surrounding the CORE-NMP interface than the TS of AKmeso. A “heated” simulation of AKthermo at 375K slightly increases LID rigid-body flexibility in accordance with the “corresponding states” hypothesis. Furthermore, while computational mutation of 7 prolines in AKthermo to their AKmeso counterparts produces similar small perturbations, mutation of these sites, especially positions 8 and 155, to glycine is required to achieve LID rigid-body flexibility and hinge flexibilities comparable to AKmeso. Mutating the 7 sites to proline in AKmeso reduces some hinges' flexibilities, especially hinge 2, but does not reduce LID rigid-body flexibility, suggesting that these two types of motion are decoupled in AKmeso. In conclusion, our results suggest that hinge flexibility and global functional motions alike are correlated with but not exclusively determined by the hinge residues. This mutational framework can inform the rational design of functionally important flexibility and allostery in other proteins toward engineering novel biochemical pathways.

Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), which undergoes chemically rate-limiting domain motions coupled to substrate binding. Since mesophiles and thermophiles often differ in functionally important motions, we compare coarse-grained simulations of AKmeso and AKthermo as well as several proline and glycine mutational variants designed to interconvert the dynamics. As might be expected, both domain motions and local unfolding motions are reduced in AKthermo relative to AKmeso. In AKthermo, both of these types of motions can be partially shifted toward more flexible AKmeso by heating or by mutating hinge prolines. However, only mutation to highly flexible glycine produces motions like those of AKmeso. Thus, the rate-limiting global transition likely depends on a combination of hinge flexibility and stability within the LID and NMP domains. Finally, this mutagenic framework can inform the rational design of flexibility and allostery in other proteins toward engineering novel biological control systems.

Beyond microscopic reversibility: Are observable non-equilibrium processes precisely reversible?

Although the principle of microscopic reversibility has been studied for many decades, there remain ambiguities in its application to non-equilibrium processes of importance to chemistry, physics and biology. Examples include whether protein unfolding should follow the same pathways and in the same proportions as folding, and whether unbinding should likewise mirror binding. Using continuum-space calculations which extend previous kinetic analyses, we demonstrate formally that the precise symmetry of forward and reverse processes is expected only under certain special conditions. Approximate symmetry will be exhibited under a separate set of conditions. Exact, approximate, and broken symmetry scenarios are verified in several ways: using numerical calculations on toy and molecular systems; using exact calculations on kinetic models of induced fit in protein-ligand binding; and based on reported experimental results. The analysis highlights intrinsic challenges and ambiguities in the design and analysis of both experiments and simulations.

Thermal motions of the E. coli glucose-galactose binding protein studied using well-sampled, semi-atomistic simulations

The E. coli glucose-galactose chemosensory receptor is a 309 residue, 32 kDa protein consisting of two distinct structural domains. We used two computational methods to examine the protein's thermal fluctuations, including both the large-scale interdomain movements that contribute to the receptor's mechanism of action, as well as smaller-scale motions. We primarily employ extremely fast, "semi-atomistic" Library-Based Monte Carlo (LBMC) simulations, which include all backbone atoms but "implicit" side chains. Our results were compared with previous experiments and all-atom molecular dynamics (MD) simulation. Both LBMC and MD simulations were performed using both the apo and glucose-bound form of the protein, with LBMC exhibiting significantly larger fluctuations. The LBMC simulations are in general agreement with the disulfide trapping experiments of Careaga & Falke (J. Mol. Biol., 1992, Vol. 226, 1219-35), which indicate that distant residues in the crystal structure (i.e. beta carbons separated by 10 to 20 angstroms) form spontaneous transient contacts in solution. Our simulations illustrate several possible "mechanisms" (configurational pathways) for these fluctuations. We also observe several discrepancies between our calculations and experimental rate constants. Nevertheless, we believe that our semi-atomistic approach could be used to study fluctuations in other proteins, perhaps for ensemble docking or other analyses of protein flexibility in virtual screening studies.

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations.

Interdomain communication revealed in the diabetes drug target mitoNEET

MitoNEET is a recently identified drug target for a commonly prescribed diabetes drug, Pioglitazone. It belongs to a previously uncharacterized ancient family of proteins for which the hallmark is the presence of a unique 39 amino acid CDGSH domain. In order to characterize the folding landscape of this novel fold, we performed thermodynamic simulations on MitoNEET using a structure-based model. Additionally, we implement a method of contact map clustering to partition out alternate pathways in folding. This cluster analysis reveals a detour late in folding and enables us to carefully examine the folding mechanism of each pathway rather than the macroscopic average. We observe that tightness in a region distal to the iron-sulfur cluster creates a constraint in folding and additionally appears to mediate communication in folding between the two domains of the protein. We demonstrate that by making changes at this site we are able to tweak the order of folding events in the cluster binding domain as well as decrease the barrier to folding.

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 Pro(177) 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 Pro(177) hinge induces alternative tertiary contacts that stabilize the closed structure and prevent the opening transition.

Identification of functional motions in the adenylate kinase (ADK) protein family by computational hybrid approaches

Based on integrative computational hybrid approaches that combined statistical coupling analysis (SCA), molecular dynamics (MD), and normal mode analysis (NMA), evolutionarily coupled residues involved in functionally relevant motion in the adenylate kinase protein family were identified. The hybrids identified four top-ranking site pairs that belong to a conserved hydrogen bond network that is involved in the enzyme's flexibility. A second group of top-ranking site pairs was identified in critical regions for functional dynamics, such as those related to enzymatic turnover. The high consistency of the results obtained by SCA with NMA (SCA.NMA) and by SCA.MD hybrid analyses suggests that suitable replacement of the matrix of cross-correlation analysis of atomic fluctuations (derived by using NMA) with those based on MD contributes to the identification of such sites by means of a fast computational calculation. The analysis presented here strongly supports the hypothesis that evolutionary forces, such as coevolution at the sequence level, have promoted functional dynamic properties of the adenylate kinase protein family. Finally, these hybrid approaches can be used to identify, at the residue level, protein motion coordination patterns not previously observed, such as in hinge regions.

Frustration, specific sequence dependence, and nonlinearity in large-amplitude fluctuations of allosteric proteins

Proteins have often evolved sequences so as to acquire the ability for regulation via allosteric conformational change. Here we investigate how allosteric dynamics is designed through sequences with nonlinear interaction features. First, for 71 allosteric proteins of which two, open and closed, structures are available, a statistical survey of interactions using an all-atom model with effective solvation shows that those residue contact interactions specific to one of the two states are significantly weaker than are the contact interactions shared by the two states. This interaction feature indicates there is underlying sequence design to facilitate conformational change. Second, based on the energy landscape theory, we implement these interaction features into a new atomic-interaction-based coarse-grained model via a multiscale simulation protocol (AICG). The AICG model outperforms standard coarse-grained models for predictions of the native-state mean fluctuations and of the conformational change direction. Third, using the new model for adenylate kinase, we show that intrinsic fluctuations in one state contain rare and large-amplitude motions nearly reaching the other state. Such large-amplitude motions are realized partly by sequence specificity and partly by the nonlinear nature of contact interactions, leading to cracking. Both features enhance conformational transition rates.

Allostery in the ferredoxin protein motif does not involve a conformational switch

Regulation of protein function via cracking, or local unfolding and refolding of substructures, is becoming a widely recognized mechanism of functional control. Oftentimes, cracking events are localized to secondary and tertiary structure interactions between domains that control the optimal position for catalysis and/or the formation of protein complexes. Small changes in free energy associated with ligand binding, phosphorylation, etc., can tip the balance and provide a regulatory functional switch. However, understanding the factors controlling function in single-domain proteins is still a significant challenge to structural biologists. We investigated the functional landscape of a single-domain plant-type ferredoxin protein and the effect of a distal loop on the electron-transfer center. We find the global stability and structure are minimally perturbed with mutation, whereas the functional properties are altered. Specifically, truncating the L1,2 loop does not lead to large-scale changes in the structure, determined via X-ray crystallography. Further, the overall thermal stability of the protein is only marginally perturbed by the mutation. However, even though the mutation is distal to the iron-sulfur cluster (∼20 Å), it leads to a significant change in the redox potential of the iron-sulfur cluster (57 mV). Structure-based all-atom simulations indicate correlated dynamical changes between the surface-exposed loop and the iron-sulfur cluster-binding region. Our results suggest intrinsic communication channels within the ferredoxin fold, composed of many short-range interactions, lead to the propagation of long-range signals. Accordingly, protein interface interactions that involve L1,2 could potentially signal functional changes in distal regions, similar to what is observed in other allosteric systems.

On the role of frustration in the energy landscapes of allosteric proteins

Natural protein domains must be sufficiently stable to fold but often need to be locally unstable to function. Overall, strong energetic conflicts are minimized in native states satisfying the principle of minimal frustration. Local violations of this principle open up possibilities to form the complex multifunnel energy landscapes needed for large-scale conformational changes. We survey the local frustration patterns of allosteric domains and show that the regions that reconfigure are often enriched in patches of highly frustrated interactions, consistent both with the idea that these locally frustrated regions may act as specific hinges or that proteins may "crack" in these locations. On the other hand, the symmetry of multimeric protein assemblies allows near degeneracy by reconfiguring while maintaining minimally frustrated interactions. We also anecdotally examine some specific examples of complex conformational changes and speculate on the role of frustration in the kinetics of allosteric change.

Mesophilic and hyperthermophilic adenylate kinases differ in their tolerance to random fragmentation

The extent to which thermostability influences the location of protein fragmentation sites that allow retention of function is not known. To evaluate this, we used a novel transposase-based approach to create libraries of vectors that express structurally-related fragments of Bacillus subtilis adenylate kinase (BsAK) and Thermotoga neapolitana adenylate kinase (TnAK) with identical modifications at their termini, and we selected for variants in each library that complement the growth of Escherichia coli with a temperature-sensitive adenylate kinase (AK). Mutants created using the hyperthermophilic TnAK were found to support growth with a higher frequency (44%) than those generated from the mesophilic BsAK (6%), and selected TnAK mutants complemented E. coli growth more strongly than homologous BsAK variants. Sequencing of functional clones from each library also identified a greater dispersion of fragmentation sites within TnAK. Nondisruptive fission sites were observed within the AMP binding and core domains of both AK homologs. However, only TnAK contained sites within the lid domain, which undergoes dynamic fluctuations that are critical for catalysis. These findings implicate the flexible lid domain as having an increased sensitivity to fission events at physiological temperatures. In addition, they provide evidence that comparisons of nondisruptive fission sites in homologous proteins could be useful for finding dynamic regions whose conformational fluctuations are important for function, and they show that the discovery of protein fragments that cooperatively function in mesophiles can be aided by the use of thermophilic enzymes as starting points for protein design.

The origin of nonmonotonic complex behavior and the effects of nonnative interactions on the diffusive properties of protein folding

We present a method for calculating the configurational-dependent diffusion coefficient of a globular protein as a function of the global folding process. Using a coarse-grained structure-based model, we determined the diffusion coefficient, in reaction coordinate space, as a function of the fraction of native contacts formed Q for the cold shock protein (TmCSP). We find nonmonotonic behavior for the diffusion coefficient, with high values for the folded and unfolded ensembles and a lower range of values in the transition state ensemble. We also characterized the folding landscape associated with an energetically frustrated variant of the model. We find that a low-level of frustration can actually stabilize the native ensemble and increase the associated diffusion coefficient. These findings can be understood from a mechanistic standpoint, in that the transition state ensemble has a more homogeneous structural content when frustration is present. Additionally, these findings are consistent with earlier calculations based on lattice models of protein folding and more recent single-molecule fluorescence measurements.

Heterogeneous path ensembles for conformational transitions in semi-atomistic models of adenylate kinase

We performed "weighted ensemble" path-sampling simulations of adenylate kinase, using several semi-atomistic protein models. The models have an all-atom backbone with various levels of residue interactions. The primary result is that full statistically rigorous path sampling required only a few weeks of single-processor computing time with these models, indicating the addition of further chemical detail should be readily feasible. Our semi-atomistic path ensembles are consistent with previous biophysical findings: the presence of two distinct pathways, identification of intermediates, and symmetry of forward and reverse pathways.

Role of water in the enzymatic catalysis: study of ATP + AMP → 2ADP conversion by adenylate kinase

The catalytic conversion ATP + AMP → 2ADP by the enzyme adenylate kinase (ADK) involves the binding of one ATP molecule to the LID domain and one AMP molecule to the NMP domain. The latter is followed by a phosphate transfer and then the release of two ADP molecules. We have computed a novel two-dimensional configurational free energy surface (2DCFES), with one reaction coordinate each for the LID and the NMP domain motions, while considering explicit water interactions. Our computed 2DCFES clearly reveals the existence of a stable half-open half-closed (HOHC) intermediate state of the enzyme. Cycling of the enzyme through the HOHC state reduces the conformational free energy barrier for the reaction by about 20 kJ/mol. We find that the stability of the HOHC state (missed in all earlier studies with implicit solvent model) is largely because of the increase of specific interactions of the polar amino acid side chains with water, particularly with the arginine and the histidine residues. Free energy surface of the LID domain is rather rugged, which can conveniently slow down LID's conformational motion, thus facilitating a new substrate capture after the product release in the catalytic cycle.

Protein functional landscapes, dynamics, allostery: a tortuous path towards a universal theoretical framework

Energy landscape theories have provided a common ground for understanding the protein folding problem, which once seemed to be overwhelmingly complicated. At the same time, the native state was found to be an ensemble of interconverting states with frustration playing a more important role compared to the folding problem. The landscape of the folded protein – the native landscape – is glassier than the folding landscape; hence, a general description analogous to the folding theories is difficult to achieve. On the other hand, the native basin phase volume is much smaller, allowing a protein to fully sample its native energy landscape on the biological timescales. Current computational resources may also be used to perform this sampling for smaller proteins, to build a ‘topographical map’ of the native landscape that can be used for subsequent analysis. Several major approaches to representing this topographical map are highlighted in this review, including the construction of kinetic networks, hierarchical trees and free energy surfaces with subsequent structural and kinetic analyses. In this review, we extensively discuss the important question of choosing proper collective coordinates characterizing functional motions. In many cases, the substates on the native energy landscape, which represent different functional states, can be used to obtain variables that are well suited for building free energy surfaces and analyzing the protein's functional dynamics. Normal mode analysis can provide such variables in cases where functional motions are dictated by the molecule's architecture. Principal component analysis is a more expensive way of inferring the essential variables from the protein's motions, one that requires a long molecular dynamics simulation. Finally, the two popular models for the allosteric switching mechanism, ‘preexisting equilibrium’ and ‘induced fit’, are interpreted within the energy landscape paradigm as extreme points of a continuum of transition mechanisms. Some experimental evidence illustrating each of these two models, as well as intermediate mechanisms, is presented and discussed.

Proteins at work: a combined small angle X-RAY scattering and theoretical determination of the multiple structures involved on the protein kinase functional landscape

C-terminal Src kinase (Csk) phosphorylates and down-regulates the Src family tyrosine kinases (SFKs). Crystallographic studies of Csk found an unusual arrangement of the SH2 and SH3 regulatory domains about the kinase core, forming a compact structure. However, recent structural studies of mutant Csk in the presence of an inhibitor indicate that the enzyme accesses an expanded structure. To investigate whether wt-Csk may also access open conformations we applied small angle x-ray scattering (SAXS). We find wt-Csk frequently occupies an extended conformation where the regulatory domains are removed from the kinase core. In addition, all-atom structure-based simulations indicate Csk occupies two free energy basins. These basins correspond to ensembles of distinct global conformations of Csk: a compact structure and an extended structure. The transitions between these structures are entropically driven and accessible via thermal fluctuations that break local interactions. We further characterized the ensemble by generating theoretical scattering curves for mixed populations of conformations from both basins and compared the predicted scattering curves to the experimental profile. This population-combination analysis is more consistent with the experimental data than any rigid model. It suggests that Csk adopts a broad ensemble of conformations in solution, populating extended conformations not observed in the crystal structure that may play an important role in the regulation of Csk. The methodology developed here is broadly applicable to biological macromolecules and will provide useful information about what ensembles of conformations are consistent with the experimental data as well as the ubiquitous dynamic reversible assembly processes inherent in biology.

Multiscale coarse-graining of the protein energy landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states.

Biological function originates from the dynamical motions of proteins in response to cellular stimuli. Protein dynamics arise from physical interactions that are well-predicted by detailed atomistic simulations. In order to examine large protein complexes on long timescales of biological importance, however, coarse-grained simulation approaches are needed to complement experiment. Previous coarse-grained models have proved successful for investigations involving a given protein's native structure, including protein folding and structure prediction. We construct a model capable of simulating proteins regardless of their sequence or structure. The present coarse-grained model was, however, developed rigorously from the underlying atomistic forces as opposed to knowledge-based or ad hoc parameterizations. Examination of the model predictions on various accessible timescales reveals successes and limitations of the model. While functionally relevant conformational transitions can be studied, the coarse-grained representation has some difficulty with the ab initio folding of the peptide chain into its proper structure. Our observations highlight the complex molecular nature of a protein's underlying energy landscape, offering rigorous insight into the information missing in reduced representations of the peptide chain. With these caveats in mind, the physical interaction–based, coarse-grained model will find application in simulations of a wide variety of proteins and continue to guide future coarse-graining efforts.

SMOG@ctbp: simplified deployment of structure-based models in GROMACS

Molecular dynamics simulations with coarse-grained and/or simplified Hamiltonians are an effective means of capturing the functionally important long-time and large-length scale motions of proteins and RNAs. Structure-based Hamiltonians, simplified models developed from the energy landscape theory of protein folding, have become a standard tool for investigating biomolecular dynamics. SMOG@ctbp is an effort to simplify the use of structure-based models. The purpose of the web server is two fold. First, the web tool simplifies the process of implementing a well-characterized structure-based model on a state-of-the-art, open source, molecular dynamics package, GROMACS. Second, the tutorial-like format helps speed the learning curve of those unfamiliar with molecular dynamics. A web tool user is able to upload any multi-chain biomolecular system consisting of standard RNA, DNA and amino acids in PDB format and receive as output all files necessary to implement the model in GROMACS. Both C_α and all-atom versions of the model are available. SMOG@ctbp resides at http://smog.ucsd.edu.

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.