Nonlinear elasticity, proteinquakes, and the energy landscapes of functional transitions in proteins

Structural Insights into Characterizing Binding Sites in Epidermal Growth Factor Receptor Kinase Mutants

Over the last two decades epidermal growth factor receptor (EGFR) kinase has become an important target to treat nonsmall cell lung cancer (NSCLC). Currently, three generations of EGFR kinase-targeted small molecule drugs have been FDA approved. They nominally produce a response at the start of treatment and lead to a substantial survival benefit for patients. However, long-term treatment results in acquired drug resistance and further vulnerability to NSCLC. Therefore, novel EGFR kinase inhibitors that specially overcome acquired mutations are urgently needed. To this end, we carried out a comprehensive study of different EGFR kinase mutants using a structural systems pharmacology strategy. Our analysis shows that both wild-type and mutated structures exhibit multiple conformational states that have not been observed in solved crystal structures. We show that this conformational flexibility accommodates diverse types of ligands with multiple types of binding modes. These results provide insights for designing a new generation of EGFR kinase inhibitor that combats acquired drug-resistant mutations through a multiconformation-based drug design strategy.

2DHybrid Analysis

We have developed an approach termed '2D hybrid analysis' for building three-dimensional (3D) structures from electron microscopy (EM) images of biological molecules. The key advantage is that it is applicable to flexible molecules, which are difficult to analyze by the approach in which 3DEM maps are reconstructed. In the proposed approach, a large number of atomic models with different conformations are first built by computer simulation. Then, simulated EM images are produced from each atomic model. Finally, these images are compared with an experimental EM image to identify the best-fitting atomic model. Two kinds of models are used to simulate the EM images: the negative-stain model and the simple projection model. Although the former is more realistic, the latter permits faster computation. We applied this approach to the averaged EM images of integrin. Although many of these were reproduced well by the best-fitting atomic models, others did not closely resemble any of the simulated EM images. However, the latter group were well reproduced by averaging multiple simulated EM images originating from atomic models with rather different conformations or orientations. This indicated that our approach is capable of detecting mixtures of conformations in the averaged EM images, which should assist in their correct interpretation.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.

Coarse-Grained Protein Dynamics Studies Using Elastic Network Models

Elastic networks have been used as simple models of proteins to study their slow structural dynamics. They consist of point-like particles connected by linear Hookean springs and hence are convenient for linear normal mode analysis around a given reference structure. Furthermore, dynamic simulations using these models can provide new insights. As the computational cost associated with these models is considerably lower compared to that of all-atom models, they are also convenient for comparative studies between multiple protein structures. In this review, we introduce examples of coarse-grained molecular dynamics studies using elastic network models and their derivatives, focusing on the nonlinear phenomena, and discuss their applicability to large-scale macromolecular assemblies.

How the Ligand-Induced Reorganization of Protein Internal Energies Is Coupled to Conformational Events

Here, we introduce a novel computational method to identify the protein substructures most likely to support the functionally oriented structural deformations that occur upon ligand-binding. To this aim, we study the modulation of protein energetics along the trajectory of a molecular dynamics simulation of different proteins in the presence and in the absence of their respective ligands, namely, human FGF, human second PDZ from human PTP1E/PTPL1, and the N terminal domain of human Hsp90. The method is based on the idea that a subset of protein residues (hotspots) may initiate the global response via the disassembly and reassembly of interactions, which is reflected in the modulation of the overall protein energetics. To identify structural hotspots and dynamic states linked to the onset of functionally relevant conformational transitions, we define an energy profile to monitor the protein energetics, based on a previously introduced approach that highlights the essential nonbonded couplings among all residues. The energy profiles are calculated along the trajectory to yield a time-dependent evolution, and their relative population in the presence and absence of the ligand is evaluated by means of a clustering procedure. It is found that interconversion between clusters, as well as their population and the density of specific energy profiles in the vicinity of structural transitions, provides specific information on the impact of the ligand in driving the protein conformational response. This analysis also highlights the hotspot residues that are most responsive to the presence of the ligand. Importantly, identified hotspots are in agreement with experimental evidence in the three considered systems. We propose that this approach can be generally used in the prediction of "allosteric hotspots" and ligand-induced conformational responses, as well as to select conformations more likely to support functional transitions (e.g., in the framework of adaptive sampling approaches).

Building Blocks of the Outer Membrane: Calculating a General Elastic Energy Model for β-Barrel Membrane Proteins

The outer membranes of Gram negative bacteria are the first points of contact these organisms make with their environment. Understanding how composition determines the mechanical properties of this essential barrier is of paramount importance. Therefore, we developed a new computational method to measure the elasticity of transmembrane proteins found in the outer membrane. Using all-atom molecular dynamics simulations of these proteins, we apply a set of external forces to mechanically stress the transmembrane β-barrels. Our results from four representative β-barrels show that outer membrane proteins display elastic properties that are approximately 70 to 190 times stiffer than neat lipid membranes. These findings suggest that outer membrane β-barrels are a significant source of mechanical stability in bacteria. Our all-atom approach further reveals that resistance to radial stress is encoded by a general mechanism that includes stretching of backbone hydrogen bonds and tilting of β-strands with respect to the bilayer normal. This computational framework facilitates an increased theoretical understanding of how varying lipid and protein amounts affect the mechanical properties of the bacterial outer membrane.

Generating conformational transition paths with low potential-energy barriers for proteins

The knowledge of conformational transition paths in proteins can be useful for understanding protein mechanisms. Recently, we have introduced the As-Rigid-As-Possible (ARAP) interpolation method, for generating interpolation paths between two protein conformations. The method was shown to preserve well the rigidity of the initial conformation along the path. However, because the method is totally geometry-based, the generated paths may be inconsistent because the atom interactions are ignored. Therefore, in this article, we would like to introduce a new method to generate conformational transition paths with low potential-energy barriers for proteins. The method is composed of three processing stages. First, ARAP interpolation is used for generating an initial path. Then, the path conformations are enhanced by a clash remover. Finally, Nudged Elastic Band, a path-optimization method, is used to produce a low-energy path. Large energy reductions are found in the paths obtained from the method than in those obtained from the ARAP interpolation method alone. The results also show that ARAP interpolation is a good candidate for generating an initial path because it leads to lower potential-energy paths than two other common methods for path interpolation.

PAGE4 and Conformational Switching: Insights from Molecular Dynamics Simulations and Implications for Prostate Cancer

Prostate-associated gene 4 (PAGE4) is an intrinsically disordered protein implicated in prostate cancer. Thestress-response kinase homeodomain-interacting protein kinase 1 (HIPK1) phosphorylates two residues in PAGE4, serine 9 and threonine 51. Phosphorylation of these two residues facilitates the interaction of PAGE4 with activator protein-1 (AP-1) transcription factor complex to potentiate AP-1's activity. In contrast, hyperphosphorylation of PAGE4 by CDC-like kinase 2 (CLK2) attenuates this interaction with AP-1. Small-angleX-ray scattering and single-molecule fluorescence resonance energy transfer measurements have shown that PAGE4 expands upon hyperphosphorylation and that this expansion is localized to its N-terminal half. To understand the interactions underlying this structural transition, we performed molecular dynamics simulations using Atomistic AWSEM, a multi-scale molecular model that combines atomistic and coarse-grained simulation approaches. Our simulations show that electrostatic interactions drive transient formation of an N-terminal loop, the destabilization of which accounts for the dramatic change in size upon hyperphosphorylation. Phosphorylation also changes the preference of secondary structure formation of the PAGE4 ensemble, which leads to a transition between states that display different degrees of disorder. Finally, we construct a mechanism-based mathematical model that allows us to capture the interactions ofdifferent phosphoforms of PAGE4 with AP-1 and its downstream target, the androgen receptor (AR)-a key therapeutic target in prostate cancer. Our model predicts intracellular oscillatory dynamics of HIPK1-PAGE4, CLK2-PAGE4, and AR activity, indicating phenotypic heterogeneity in an isogenic cell population. Thus, conformational switching of PAGE4 may potentially affect the efficiency of therapeutically targeting AR activity.

Green function of correlated genes in a minimal mechanical model of protein evolution

The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly coupled amino acid network with interactions and motions that are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids and thereby, the transmission of forces. Mutations introduce localized perturbations to the propagator that scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis-the interaction among mutations in the gene-is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution and observe long-range epistasis, which facilitates collective functional modes.

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

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

Tracking the Catalytic Cycle of Adenylate Kinase by Ultraviolet Photodissociation Mass Spectrometry

The complex interplay of dynamic protein plasticity and specific side-chain interactions with substrate molecules that allows enzymes to catalyze reactions has yet to be fully unraveled. Top-down ultraviolet photodissociation (UVPD) mass spectrometry is used to track snapshots of conformational fluctuations in the phosphotransferase adenylate kinase (AK) throughout its active reaction cycle by characterization of complexes containing AK and each of four different adenosine phosphate ligands. Variations in efficiencies of UVPD backbone cleavages were consistently observed for three α-helices and the adenosine binding regions for AK complexes representing different steps of the catalytic cycle, implying that these stretches of the protein sample various structural microstates as the enzyme undergoes global open-to-closed transitions. Focusing on the conformational impact of recruiting or releasing the Mg2+ cofactor highlights two loop regions for which fragmentation increases upon UVPD, signaling an increase in loop flexibility as the metal cation disrupts the loop interactions with the substrate ligands. Additionally, the observation of holo ions and variations in UVPD backbone cleavage efficiency at R138 implicate this conserved active site residue in stabilizing the donor phosphoryl group during catalysis. This study showcases the utility of UVPD-MS to provide insight into conformational fluctuations of single residues for active enzymes.

Hybrid Methods for Macromolecular Modeling by Molecular Mechanics Simulations with Experimental Data

Hybrid approaches for the modeling of macromolecular complexes that combine computational molecular mechanics simulations with experimental data are discussed. Experimental data for biological molecular structures are often low-resolution, and thus, do not contain enough information to determine the atomic positions of molecules. This is especially true when the dynamics of large macromolecules are the focus of the study. However, computational modeling can complement missing information. Significant increase in computational power, as well as the development of new modeling algorithms allow us to model structures of biological macromolecules reliably, using experimental data as references. We review the basics of molecular mechanics approaches, such as atomic model force field, and coarse-grained models, molecular dynamics simulation and normal mode analysis and describe how they could be used for flexible fitting hybrid modeling with experimental data, especially from cryo-EM and SAXS.

Resolving the NFκB Heterodimer Binding Paradox: Strain and Frustration Guide the Binding of Dimeric Transcription Factors

Many eukaryotic transcription factors function after forming oligomers. The choice of protein partners is a nonrandom event that has distinct functional consequences for gene regulation. In the present work we examine three dimers of transcription factors in the NFκB family: p50p50, p50p65, and p65p65. The NFκB dimers bind to a myriad of genomic sites and switch the targeted genes on or off with precision. The p65p50 heterodimer of NFκB is the strongest DNA binder, and its unbinding is controlled kinetically by molecular stripping from the DNA induced by IκB. In contrast, the homodimeric forms of NFκB, p50p50 and p65p65, bind DNA with significantly less affinity, which places the DNA residence of the homodimers under thermodynamic rather than kinetic control. It seems paradoxical that the heterodimer should bind more strongly than either of the symmetric homodimers since DNA is a nearly symmetric target. Using a variety of energy landscape analysis tools, here we uncover the features in the molecular architecture of NFκB dimers that are responsible for these drastically different binding free energies. We show that frustration in the heterodimer interface gives the heterodimer greater conformational plasticity, allowing the heterodimer to better accommodate the DNA. We also show how the elastic energy and mechanical strain in NFκB dimers can be found by extracting the principal components of the fluctuations in Cartesian coordinates as well as fluctuations in the space of physical contacts, which are sampled via simulations with a predictive energy landscape Hamiltonian. These energetic contributions determine the specific detailed mechanisms of binding and stripping for both homo- and heterodimers.

Why Ubiquitin Has Not Evolved

Ubiquitin, discovered less than 50 years ago, tags thousands of diseased proteins for destruction. It is small (only 76 amino acids), and is found unchanged in mammals, birds, fish, and even worms, indicating that ubiquitin is perfect. Key features of its functionality are identified here using critical point thermodynamic scaling theory. These include synchronized pivots and hinges, a stabilizing central pivot, and Fano interference between first- and second-order elements of correlated long-range (allosteric) globular surface shape transitions. Comparison with its closest relative, 76 amino acid Nedd8, shows that the latter lacks all these features. A cracked elastic network model is proposed for the common target shared by many diseased proteins.

Design of Elastic Networks with Evolutionary Optimized Long-Range Communication as Mechanical Models of Allosteric Proteins

Allosteric effects often underlie the activity of proteins, and elucidating generic design aspects and functional principles unique to allosteric phenomena represent a major challenge. Here an approach consisting of the in silico design of synthetic structures, which, as the principal element of allostery, encode dynamical long-range coupling among two sites, is presented. The structures are represented by elastic networks, similar to coarse-grained models of real proteins. A strategy of evolutionary optimization was implemented to iteratively improve allosteric coupling. In the designed structures, allosteric interactions were analyzed in terms of strain propagation, and simple pathways that emerged during evolution were identified as signatures through which long-range communication was established. Moreover, robustness of allosteric performance with respect to mutations was demonstrated. As it turned out, the designed prototype structures reveal dynamical properties resembling those found in real allosteric proteins. Hence, they may serve as toy models of complex allosteric systems, such as proteins. Application of the developed modeling scheme to the allosteric transition in the myosin V molecular motor was also demonstrated.

Protein Assembly and Building Blocks: Beyond the Limits of the LEGO Brick Metaphor

Proteins, like other biomolecules, have a modular and hierarchical structure. Various building blocks are used to construct proteins of high structural complexity and diverse functionality. In multidomain proteins, for example, domains are fused to each other in different combinations to achieve different functions. Although the LEGO brick metaphor is justified as a means of simplifying the complexity of three-dimensional protein structures, several fundamental properties (such as allostery or the induced-fit mechanism) make deviation from it necessary to respect the plasticity, softness, and cross-talk that are essential to protein function. In this work, we illustrate recently reported protein behavior in multidomain proteins that deviates from the LEGO brick analogy. While earlier studies showed that a protein domain is often unaffected by being fused to another domain or becomes more stable following the formation of a new interface between the tethered domains, destabilization due to tethering has been reported for several systems. We illustrate that tethering may sometimes result in a multidomain protein behaving as "less than the sum of its parts". We survey these cases for which structure additivity does not guarantee thermodynamic additivity. Protein destabilization due to fusion to other domains may be linked in some cases to biological function and should be taken into account when designing large assemblies.

Binding mechanism and dynamic conformational change of C subunit of PKA with different pathways

The catalytic subunit of PKA (PKAc) exhibits three major conformational states (open, intermediate, and closed) during the biocatalysis process. Both ATP and substrate/inhibitor can effectively induce the conformational changes of PKAc from open to closed states. Aiming to explore the mechanism of this allosteric regulation, we developed a coarse-grained model and analyzed the dynamics of conformational changes of PKAc during binding by performing molecular dynamics simulations for apo PKAc, binary PKAc (PKAc with ATP, PKAc with PKI), and ternary PKAc (PKAc with ATP and PKI). Our results suggest a mixed binding mechanism of induced fit and conformational selection, with the induced fit dominant. The ligands can drive the movements of Gly-rich loop as well as some regions distal to the active site in PKAc and stabilize them at complex state. In addition, there are two parallel pathways (pathway with PKAc-ATP as an intermediate and pathway PKAc-PKI as an intermediate) during the transition from open to closed states. By molecular dynamics simulations and rate constant analyses, we find that the pathway through PKAc-ATP intermediate is the main binding route from open to closed state because of the fact that the bound PKI will hamper ATP from successful binding and significantly increase the barrier for the second binding subprocess. These findings will provide fundamental insights of the mechanisms of PKAc conformational change upon binding.

Actin Filament Strain Promotes Severing and Cofilin Dissociation

Computational and structural studies have been indispensable in investigating the molecular origins of actin filament mechanical properties and modulation by the regulatory severing protein cofilin. All-atom molecular dynamics simulations of cofilactin filament structures determined by electron cryomicroscopy reveal how cofilin enhances the bending and twisting compliance of actin filaments. Continuum mechanics models suggest that buckled cofilactin filaments localize elastic energy at boundaries between bare and cofilin-decorated segments because of their nonuniform elasticity, thereby accelerating filament severing. Here, we develop mesoscopic length-scale (cofil)actin filament models and evaluate the effects of compressive and twisting loads on strain energy distribution at specific interprotein interfaces. The models reliably capture the filament bending and torsional rigidities and intersubunit torsional flexibility measured experimentally with purified protein components. Buckling is predicted to enhance cofilactin filament severing with minimal effects on cofilin occupancy, whereas filament twisting enhances cofilin dissociation without compromising filament integrity. Preferential severing at actin-cofilactin boundaries of buckled filaments is more prominent than predicted by continuum models because of the enhanced spatial resolution. The models developed here will be valuable for evaluating the effects of filament shape deformations on filament stability and interactions with regulatory proteins, and analysis of single filament manipulation assays.

How Hsp90 and Cdc37 Lubricate Kinase Molecular Switches

The Hsp90/Cdc37 chaperone system interacts with and supports 60% of the human kinome. Not only are Hsp90 and Cdc37 generally required for initial folding, but many kinases rely on the Hsp90/Cdc37 throughout their lifetimes. A large fraction of these 'client' kinases are key oncoproteins, and their interactions with the Hsp90/Cdc37 machinery are crucial for both their normal and malignant activity. Recently, advances in single-particle cryo-electron microscopy (cryoEM) and biochemical strategies have provided the first key molecular insights into kinase-chaperone interactions. The surprising results suggest a re-evaluation of the role of chaperones in the kinase lifecycle, and suggest that such interactions potentially allow kinases to more rapidly respond to key signals while simultaneously protecting unstable kinases from degradation and suppressing unwanted basal activity.

Migration of small ligands in globins: Xe diffusion in truncated hemoglobin N

In heme proteins, the efficient transport of ligands such as NO or O₂ to the binding site is achieved via ligand migration networks. A quantitative assessment of ligand diffusion in these networks is thus essential for a better understanding of the function of these proteins. For this, Xe migration in truncated hemoglobin N (trHbN) of Mycobacterium Tuberculosis was studied using molecular dynamics simulations. Transitions between pockets of the migration network and intra-pocket relaxation occur on similar time scales (10 ps and 20 ps), consistent with low free energy barriers (1-2 kcal/mol). Depending on the pocket from where Xe enters a particular transition, the conformation of the side chains lining the transition region differs which highlights the coupling between ligand and protein degrees of freedom. Furthermore, comparison of transition probabilities shows that Xe migration in trHbN is a non-Markovian process. Memory effects arise due to protein rearrangements and coupled dynamics as Xe moves through it.

Binding and transport of ligands in proteins is essential, in particular in globular proteins which often exhibit internal cavities. In truncated Hemoglobin N (trHbN) these cavities are arranged as a network with particular connectivities. The present work supports the notion that ligand diffusion in trHbN is an active process and coupled to the protein dynamics. Furthermore, transition probabilities between neighboring pockets depend on the location from where the ligand entered the transition, which is typical for non-Markovian processes. Hence, ligand migration in trHbN exhibits memory effects due to dynamical coupling between the protein and ligand motion.

Ultrafast X-Ray Crystallography and Liquidography

Time-resolved X-ray diffraction provides direct information on three-dimensional structures of reacting molecules and thus can be used to elucidate structural dynamics of chemical and biological reactions. In this review, we discuss time-resolved X-ray diffraction on small molecules and proteins with particular emphasis on its application to crystalline (crystallography) and liquid-solution (liquidography) samples. Time-resolved X-ray diffraction has been used to study picosecond and slower dynamics at synchrotrons and can now access even femtosecond dynamics with the recent arrival of X-ray free-electron lasers.

How the Ribosomal A-Site Finger Can Lead to tRNA Species-Dependent Dynamics

Proteins are synthesized by the joint action of the ribosome and tRNA molecules, where the rate of synthesis can be affected by numerous factors, such as the concentration of tRNA, the binding affinity of tRNA for the ribosome, or post-transcriptional modifications. Here, we expand this range of contributors by demonstrating how differences in tRNA structure can give rise to tRNA species-specific dynamics in the ribosome. To show this, we perform simulations of A/P hybrid-state formation for two tRNA species (tRNA^Phe and tRNA^Leu), which differ in the size of their variable loops (VLs). These calculations reveal that steric interactions between the VL and the ribosomal A-site finger (ASF, i.e., H38 of 23S rRNA) can directly modulate the free-energy landscape for each tRNA species. We also find that tRNA and ASF motions are highly correlated, where fluctuations of the ASF are predictive of tRNA transition events. Finally, by introducing perturbations to the model, we demonstrate that ASF flexibility is a determinant of the rate of A/P hybrid-state formation.

2D hybrid analysis: Approach for building three-dimensional atomic model by electron microscopy image matching

In this study, we develop an approach termed “2D hybrid analysis” for building atomic models by image matching from electron microscopy (EM) images of biological molecules. The key advantage is that it is applicable to flexible molecules, which are difficult to analyze by 3DEM approach. In the proposed approach, first, a lot of atomic models with different conformations are built by computer simulation. Then, simulated EM images are built from each atomic model. Finally, they are compared with the experimental EM image. Two kinds of models are used as simulated EM images: the negative stain model and the simple projection model. Although the former is more realistic, the latter is adopted to perform faster computations. The use of the negative stain model enables decomposition of the averaged EM images into multiple projection images, each of which originated from a different conformation or orientation. We apply this approach to the EM images of integrin to obtain the distribution of the conformations, from which the pathway of the conformational change of the protein is deduced.

Minimum action transition paths connecting minima on an energy surface

Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.

Comparing allosteric transitions in the domains of calmodulin through coarse-grained simulations

Calmodulin (CaM) is a ubiquitous Ca(2+)-binding protein consisting of two structurally similar domains with distinct stabilities, binding affinities, and flexibilities. We present coarse grained simulations that suggest that the mechanism for the domain's allosteric transitions between the open and closed conformations depends on subtle differences in the folded state topology of the two domains. Throughout a wide temperature range, the simulated transition mechanism of the N-terminal domain (nCaM) follows a two-state transition mechanism while domain opening in the C-terminal domain (cCaM) involves unfolding and refolding of the tertiary structure. The appearance of the unfolded intermediate occurs at a higher temperature in nCaM than it does in cCaM consistent with nCaM's higher thermal stability. Under approximate physiological conditions, the simulated unfolded state population of cCaM accounts for 10% of the population with nearly all of the sampled transitions (approximately 95%) unfolding and refolding during the conformational change. Transient unfolding significantly slows the domain opening and closing rates of cCaM, which can potentially influence its Ca(2+)-binding mechanism.

Localized structural frustration for evaluating the impact of sequence variants

Population-scale sequencing is increasingly uncovering large numbers of rare single-nucleotide variants (SNVs) in coding regions of the genome. The rarity of these variants makes it challenging to evaluate their deleteriousness with conventional phenotype-genotype associations. Protein structures provide a way of addressing this challenge. Previous efforts have focused on globally quantifying the impact of SNVs on protein stability. However, local perturbations may severely impact protein functionality without strongly disrupting global stability (e.g. in relation to catalysis or allostery). Here, we describe a workflow in which localized frustration, quantifying unfavorable local interactions, is employed as a metric to investigate such effects. Using this workflow on the Protein Databank, we find that frustration produces many immediately intuitive results: for instance, disease-related SNVs create stronger changes in localized frustration than non-disease related variants, and rare SNVs tend to disrupt local interactions to a larger extent than common variants. Less obviously, we observe that somatic SNVs associated with oncogenes and tumor suppressor genes (TSGs) induce very different changes in frustration. In particular, those associated with TSGs change the frustration more in the core than the surface (by introducing loss-of-function events), whereas those associated with oncogenes manifest the opposite pattern, creating gain-of-function events.

Protein dynamics and function from solution state NMR spectroscopy

It is well-established that dynamics are central to protein function; their importance is implicitly acknowledged in the principles of the Monod, Wyman and Changeux model of binding cooperativity, which was originally proposed in 1965. Nowadays the concept of protein dynamics is formulated in terms of the energy landscape theory, which can be used to understand protein folding and conformational changes in proteins. Because protein dynamics are so important, a key to understanding protein function at the molecular level is to design experiments that allow their quantitative analysis. Nuclear magnetic resonance (NMR) spectroscopy is uniquely suited for this purpose because major advances in theory, hardware, and experimental methods have made it possible to characterize protein dynamics at an unprecedented level of detail. Unique features of NMR include the ability to quantify dynamics (i) under equilibrium conditions without external perturbations, (ii) using many probes simultaneously, and (iii) over large time intervals. Here we review NMR techniques for quantifying protein dynamics on fast (ps-ns), slow (μs-ms), and very slow (s-min) time scales. These techniques are discussed with reference to some major discoveries in protein science that have been made possible by NMR spectroscopy.

Strain analysis of protein structures and low dimensionality of mechanical allosteric couplings

In many proteins, especially allosteric proteins that communicate regulatory states from allosteric to active sites, structural deformations are functionally important. To understand these deformations, dynamical experiments are ideal but challenging. Using static structural information, although more limited than dynamical analysis, is much more accessible. Underused for protein analysis, strain is the natural quantity for studying local deformations. We calculate strain tensor fields for proteins deformed by ligands or thermal fluctuations using crystal and NMR structure ensembles. Strains-primarily shears-show deformations around binding sites. These deformations can be induced solely by ligand binding at distant allosteric sites. Shears reveal quasi-2D paths of mechanical coupling between allosteric and active sites that may constitute a widespread mechanism of allostery. We argue that strain-particularly shear-is the most appropriate quantity for analysis of local protein deformations. This analysis can reveal mechanical and biological properties of many proteins.

Role of Proteome Physical Chemistry in Cell Behavior

We review how major cell behaviors, such as bacterial growth laws, are derived from the physical chemistry of the cell’s proteins. On one hand, cell actions depend on the individual biological functionalities of their many genes and proteins. On the other hand, the common physics among proteins can be as important as the unique biology that distinguishes them. For example, bacterial growth rates depend strongly on temperature. This dependence can be explained by the folding stabilities across a cell’s proteome. Such modeling explains how thermophilic and mesophilic organisms differ, and how oxidative damage of highly charged proteins can lead to unfolding and aggregation in aging cells. Cells have characteristic time scales. For example, E. coli can duplicate as fast as 2–3 times per hour. These time scales can be explained by protein dynamics (the rates of synthesis and degradation, folding, and diffusional transport). It rationalizes how bacterial growth is slowed down by added salt. In the same way that the behaviors of inanimate materials can be expressed in terms of the statistical distributions of atoms and molecules, some cell behaviors can be expressed in terms of distributions of protein properties, giving insights into the microscopic basis of growth laws in simple cells.

Transition path theory analysis of c-Src kinase activation

Nonreceptor tyrosine kinases of the Src family are large multidomain allosteric proteins that are crucial to cellular signaling pathways. In a previous study, we generated a Markov state model (MSM) to simulate the activation of c-Src catalytic domain, used as a prototypical tyrosine kinase. The long-time kinetics of transition predicted by the MSM was in agreement with experimental observations. In the present study, we apply the framework of transition path theory (TPT) to the previously constructed MSM to characterize the main features of the activation pathway. The analysis indicates that the activating transition, in which the activation loop first opens up followed by an inward rotation of the αC-helix, takes place via a dense set of intermediate microstates distributed within a fairly broad "transition tube" in a multidimensional conformational subspace connecting the two end-point conformations. Multiple microstates with negligible equilibrium probabilities carry a large transition flux associated with the activating transition, which explains why extensive conformational sampling is necessary to accurately determine the kinetics of activation. Our results suggest that the combination of MSM with TPT provides an effective framework to represent conformational transitions in complex biomolecular systems.

Capturing Transition States for tRNA Hybrid-State Formation in the Ribosome

In order to quantitatively describe the energetics of biomolecular rearrangements, it is necessary to identify reaction coordinates that accurately capture the relevant transition events. Here, we perform simulations of A-site tRNA movement (∼20 Å) during hybrid-state formation in the ribosome and quantify the ability of interatomic distances to capture the transition state ensemble. Numerous coordinates are found to be accurate indicators of the transition state, allowing tRNA rearrangements to be described as diffusion across a one-dimensional free-energy surface. In addition to providing insights into the physical-chemical relationship between biomolecular structure and dynamics, these results can help enable single-molecule techniques to probe the free-energy landscape of the ribosome.

Strain Mediated Adaptation Is Key for Myosin Mechanochemistry: Discovering General Rules for Motor Activity

A structure-based model of myosin motor is built in the same spirit of our early work for kinesin-1 and Ncd towards physical understanding of its mechanochemical cycle. We find a structural adaptation of the motor head domain in post-powerstroke state that signals faster ADP release from it compared to the same from the motor head in the pre-powerstroke state. For dimeric myosin, an additional forward strain on the trailing head, originating from the postponed powerstroke state of the leading head in the waiting state of myosin, further increases the rate of ADP release. This coordination between the two heads is the essence of the processivity of the cycle. Our model provides a structural description of the powerstroke step of the cycle as an allosteric transition of the converter domain in response to the P_i release. Additionally, the variation in structural elements peripheral to catalytic motor domain is the deciding factor behind diverse directionalities of myosin motors (myosin V & VI). Finally, we observe that there are general rules for functional molecular motors across the different families. Allosteric structural adaptation of the catalytic motor head in different nucleotide states is crucial for mechanochemistry. Strain-mediated coordination between motor heads is essential for processivity and the variation of peripheral structural elements is essential for their diverse functionalities.

Molecular motors are perhaps the most important proteins present in the cell. The importance specifically lies with the fact that these proteins use the chemical energy source (such as ATP) of the cell to generate mechanical work and perform a wide range of functionalities. In this article, we generalize the idea of using structure-based models to explore the mechanochemistry of myosin molecular motors in structural terms. We find that a structural adaptation of the motor head domain in post-powerstroke state signals faster ADP release from the trailing head to maintain its processivity while directionality arises from a careful design of peripheral structural elements. These results along with our earlier results on other motors provide a general rule for motor activity.

Model of the Ankyrin and SOCS Box Protein, ASB9, E3 Ligase Reveals a Mechanism for Dynamic Ubiquitin Transfer

Cullin-RING E3 ligases (CRLs) are elongated and bowed protein complexes that transfer ubiquitin over 60 Å to proteins targeted for proteasome degradation. One such CRL contains the ankyrin repeat and SOCS box protein 9 (ASB9), which binds to and partially inhibits creatine kinase (CK). While current models for the ASB9-CK complex contain some known interface residues, the overall structure and precise interface of the ASB9-CK complex remains unknown. Through an integrative modeling approach, we report a third-generation model that reveals precisely the interface interactions and also fits the shape of the ASB9-CK complex as determined by small-angle X-ray scattering. We constructed an atomic model for the entire CK-targeting CRL to uncover dominant modes of motion that could permit ubiquitin transfer. Remarkably, only the correctly docked CK-containing E3 ligase and not incorrectly docked structures permitted close approach of ubiquitin to the CK substrate.

Atomic structure of Hsp90-Cdc37-Cdk4 reveals that Hsp90 traps and stabilizes an unfolded kinase

The Hsp90 molecular chaperone and its Cdc37 cochaperone help stabilize and activate more than half of the human kinome. However, both the mechanism by which these chaperones assist their "client" kinases and the reason why some kinases are addicted to Hsp90 while closely related family members are independent are unknown. Our structural understanding of these interactions is lacking, as no full-length structures of human Hsp90, Cdc37, or either of these proteins with a kinase have been elucidated. Here we report a 3.9 angstrom cryo-electron microscopy structure of the Hsp90-Cdc37-Cdk4 kinase complex. Surprisingly, the two lobes of Cdk4 are completely separated with the β4-β5 sheet unfolded. Cdc37 mimics part of the kinase N lobe, stabilizing an open kinase conformation by wedging itself between the two lobes. Finally, Hsp90 clamps around the unfolded kinase β5 strand and interacts with exposed N- and C-lobe interfaces, protecting the kinase in a trapped unfolded state. On the basis of this structure and an extensive amount of previously collected data, we propose unifying conceptual and mechanistic models of chaperone-kinase interactions.

Theoretical Insights into the Biophysics of Protein Bi-stability and Evolutionary Switches

Deciphering the effects of nonsynonymous mutations on protein structure is central to many areas of biomedical research and is of fundamental importance to the study of molecular evolution. Much of the investigation of protein evolution has focused on mutations that leave a protein’s folded structure essentially unchanged. However, to evolve novel folds of proteins, mutations that lead to large conformational modifications have to be involved. Unraveling the basic biophysics of such mutations is a challenge to theory, especially when only one or two amino acid substitutions cause a large-scale conformational switch. Among the few such mutational switches identified experimentally, the one between the G_A all-α and G_B α+β folds is extensively characterized; but all-atom simulations using fully transferrable potentials have not been able to account for this striking switching behavior. Here we introduce an explicit-chain model that combines structure-based native biases for multiple alternative structures with a general physical atomic force field, and apply this construct to twelve mutants spanning the sequence variation between G_A and G_B. In agreement with experiment, we observe conformational switching from G_A to G_B upon a single L45Y substitution in the GA98 mutant. In line with the latent evolutionary potential concept, our model shows a gradual sequence-dependent change in fold preference in the mutants before this switch. Our analysis also indicates that a sharp G_A/G_B switch may arise from the orientation dependence of aromatic π-interactions. These findings provide physical insights toward rationalizing, predicting and designing evolutionary conformational switches.

The biological functions of globular proteins are intimately related to their folded structures and their associated conformational fluctuations. Evolution of new structures is an important avenue to new functions. Although many mutations do not change the folded state, experiments indicate that a single amino acid substitution can lead to a drastic change in the folded structure. The physics of this switch-like behavior remains to be elucidated. Here we develop a computational model for the relevant physical forces, showing that mutations can lead to new folds by passing through intermediate sequences where the old and new folds occur with varying probabilities. Our approach helps provide a general physical account of conformational switching in evolution and mutational effects on conformational dynamics.

Predicting Allosteric Effects from Orthosteric Binding in Hsp90-Ligand Interactions: Implications for Fragment-Based Drug Design

A key question in mapping dynamics of protein-ligand interactions is to distinguish changes at binding sites from those associated with long range conformational changes upon binding at distal sites. This assumes a greater challenge when considering the interactions of low affinity ligands (dissociation constants, K_D, in the μM range or lower). Amide hydrogen deuterium Exchange mass spectrometry (HDXMS) is a robust method that can provide both structural insights and dynamics information on both high affinity and transient protein-ligand interactions. In this study, an application of HDXMS for probing the dynamics of low affinity ligands to proteins is described using the N-terminal ATPase domain of Hsp90. Comparison of Hsp90 dynamics between high affinity natural inhibitors (K_D ~ nM) and fragment compounds reveal that HDXMS is highly sensitive in mapping the interactions of both high and low affinity ligands. HDXMS reports on changes that reflect both orthosteric effects and allosteric changes accompanying binding. Orthosteric sites can be identified by overlaying HDXMS onto structural information of protein-ligand complexes. Regions distal to orthosteric sites indicate long range conformational changes with implications for allostery. HDXMS, thus finds powerful utility as a high throughput method for compound library screening to identify binding sites and describe allostery with important implications for fragment-based ligand discovery (FBLD).

Ligand interactions with proteins result in broad changes that are propagated throughout the target proteins, across space and time. These changes can be broadly classified into: orthosteric effects at the ligand binding site and allosteric changes at distal sites. These allosteric changes are difficult to localize and distinguish from binding interactions. In this study, we describe the application of amide hydrogen/deuterium exchange mass-spectrometry (HDXMS) to differentiate between changes occurring at the binding site and at distal allosteric sites by combining HDXMS with X-ray crystallography. Every ligand or a fragment mediates distinct contacts and results in changes in deuterium uptake across the protein. By comparing with orthosteric structural information, it is possible to identify long-range changes (action at a distance) due to the ligands. An important application of HDXMS is that it can identify subtle changes in protein dynamics that cannot be picked up by quantitative screens of protein-ligand interactions or crystal structures. This gives us the ability to describe ligand binding based on the response from different regions in the proteins. Thus it provides us with the potential to accurately measure and compare changes in dynamics upon binding different ligands and fragments, which is greatly valuable in fragment-based ligand design.

Statistical mechanics of the Huxley-Simmons model

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

Characterisation of molten globule-like state of sheep serum albumin at physiological pH

Sheep serum albumin (SSA) is a 583 amino acid residues long multidomain monomeric protein which is rich in cysteine and low in tryptophan content. The serum albumins (from human, bovine and sheep) play a vital role among all proteins investigated until now, as they are the most copious circulatory proteins. We have purified SSA from sheep kidneys by a simple and efficient two-step purification procedure. Further, we have studied urea-induced denaturation of SSA by monitoring changes in the difference absorption coefficient at 287nm (Δε287), intrinsic fluorescence emission intensity at 347nm (F347) and mean residue ellipticity at 222nm ([θ]222) at pH 7.4 and 25°C. The coincidence of denaturation curves of these optical properties suggests that urea-induced denaturation is a bi-phasic process (native (N) state↔intermediate (X) state↔denatured (D) state) with a stable intermediate populated around 4.2-4.7M urea. The intermediate (X) state was further characterized by the far-UV and near-UV CD, dynamic light scattering (DLS) and fluorescence using 1-anilinonaphthalene-8-sulfonic acid (ANS) binding method. All denaturation curves were analyzed for Gibbs free energy changes associated with the equilibria, N state↔X state and X state↔D state in the absence of urea.

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.