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

Predicting protein conformational motions using energetic frustration analysis and AlphaFold2

Proteins perform their biological functions through motion. Although high throughput prediction of the three-dimensional static structures of proteins has proved feasible using deep-learning-based methods, predicting the conformational motions remains a challenge. Purely data-driven machine learning methods encounter difficulty for addressing such motions because available laboratory data on conformational motions are still limited. In this work, we develop a method for generating protein allosteric motions by integrating physical energy landscape information into deep-learning-based methods. We show that local energetic frustration, which represents a quantification of the local features of the energy landscape governing protein allosteric dynamics, can be utilized to empower AlphaFold2 (AF2) to predict protein conformational motions. Starting from ground state static structures, this integrative method generates alternative structures as well as pathways of protein conformational motions, using a progressive enhancement of the energetic frustration features in the input multiple sequence alignment sequences. For a model protein adenylate kinase, we show that the generated conformational motions are consistent with available experimental and molecular dynamics simulation data. Applying the method to another two proteins KaiB and ribose-binding protein, which involve large-amplitude conformational changes, can also successfully generate the alternative conformations. We also show how to extract overall features of the AF2 energy landscape topography, which has been considered by many to be black box. Incorporating physical knowledge into deep-learning-based structure prediction algorithms provides a useful strategy to address the challenges of dynamic structure prediction of allosteric proteins.

Integration of a Randomized Sequence Scanning Approach in AlphaFold2 and Local Frustration Profiling of Conformational States Enable Interpretable Atomistic Characterization of Conformational Ensembles and Detection of Hidden Allosteric States in the ABL1 Protein Kinase

Despite the success of AlphaFold methods in predicting single protein structures, these methods showed intrinsic limitations in the characterization of multiple functional conformations of allosteric proteins. The recent NMR-based structural determination of the unbound ABL kinase in the active state and discovery of the inactive low-populated functional conformations that are unique for ABL kinase present an ideal challenge for the AlphaFold2 approaches. In the current study, we employ several adaptations of the AlphaFold2 methodology to predict protein conformational ensembles and allosteric states of the ABL kinase including randomized alanine sequence scanning combined with the multiple sequence alignment subsampling proposed in this study. We show that the proposed new AlphaFold2 adaptation combined with local frustration profiling of conformational states enables accurate prediction of the protein kinase structures and conformational ensembles, also offering a robust approach for interpretable characterization of the AlphaFold2 predictions and detection of hidden allosteric states. We found that the large high frustration residue clusters are uniquely characteristic of the low-populated, fully inactive ABL form and can define energetically frustrated cracking sites of conformational transitions, presenting difficult targets for AlphaFold2. The results of this study uncovered previously unappreciated fundamental connections between local frustration profiles of the functional allosteric states and the ability of AlphaFold2 methods to predict protein structural ensembles of the active and inactive states. This study showed that integration of the randomized sequence scanning adaptation of AlphaFold2 with a robust landscape-based analysis allows for interpretable atomistic predictions and characterization of protein conformational ensembles, providing a physical basis for the successes and limitations of current AlphaFold2 methods in detecting functional allosteric states that play a significant role in protein kinase regulation.

Towards the understanding of molecular motors and its relationship with local unfolding

Molecular motors are machines essential for life since they convert chemical energy into mechanical work. However, the precise mechanism by which nucleotide binding, catalysis, or release of products is coupled to the work performed by the molecular motor is still not entirely clear. This is due, in part, to a lack of understanding of the role of force in the mechanical-structural processes involved in enzyme catalysis. From a mechanical perspective, one promising hypothesis is the Haldane-Pauling hypothesis which considers the idea that part of the enzymatic catalysis is strain-induced. It suggests that enzymes cannot be efficient catalysts if they are fully complementary to the substrates. Instead, they must exert strain on the substrate upon binding, using enzyme-substrate energy interaction (binding energy) to accelerate the reaction rate. A novel idea suggests that during catalysis, significant strain energy is built up, which is then released by a local unfolding/refolding event known as 'cracking'. Recent evidence has also shown that in catalytic reactions involving conformational changes, part of the heat released results in a center-of-mass acceleration of the enzyme, raising the possibility that the heat released by the reaction itself could affect the enzyme's integrity. Thus, it has been suggested that this released heat could promote or be linked to the cracking seen in proteins such as adenylate kinase (AK). We propose that the energy released as a consequence of ligand binding/catalysis is associated with the local unfolding/refolding events (cracking), and that this energy is capable of driving the mechanical work.

Associating protein sequence positions with the modulation of quantitative phenotypes

Although protein sequences encode the information for folding and function, understanding their link is not an easy task. Unluckily, the prediction of how specific amino acids contribute to these features is still considerably impaired. Here, we developed a simple algorithm that finds positions in a protein sequence with potential to modulate the studied quantitative phenotypes. From a few hundred protein sequences, we perform multiple sequence alignments, obtain the per-position pairwise differences for both the sequence and the observed phenotypes, and calculate the correlation between these last two quantities. We tested our methodology with four cases: archaeal Adenylate Kinases and the organisms optimal growth temperatures, microbial rhodopsins and their maximal absorption wavelengths, mammalian myoglobins and their muscular concentration, and inhibition of HIV protease clinical isolates by two different molecules. We found from 3 to 10 positions tightly associated with those phenotypes, depending on the studied case. We showed that these correlations appear using individual positions but an improvement is achieved when the most correlated positions are jointly analyzed. Noteworthy, we performed phenotype predictions using a simple linear model that links per-position divergences and differences in the observed phenotypes. Predictions are comparable to the state-of-art methodologies which, in most of the cases, are far more complex. All of the calculations are obtained at a very low information cost since the only input needed is a multiple sequence alignment of protein sequences with their associated quantitative phenotypes. The diversity of the explored systems makes our work a valuable tool to find sequence determinants of biological activity modulation and to predict various functional features for uncharacterized members of a protein family.

The energy landscape of the ribosome

The ribosome is a prototypical assembly that can be used to establish general principles and techniques for the study of biological molecular machines. Motivated by the fact that the dynamics of every biomolecule is governed by an underlying energy landscape, there has been great interest to understand and quantify ribosome energetics. In the present review, we will focus on theoretical and computational strategies for probing the interactions that shape the energy landscape of the ribosome, with an emphasis on more recent studies of the elongation cycle. These efforts include the application of quantum mechanical methods for describing chemical kinetics, as well as classical descriptions to characterize slower (microsecond to millisecond) large-scale (10-100 Å) rearrangements, where motion is described in terms of diffusion across an energy landscape. Together, these studies provide broad insights into the factors that control a diverse range of dynamical processes in this assembly.

Interpretable Atomistic Prediction and Functional Analysis of Conformational Ensembles and Allosteric States in Protein Kinases Using AlphaFold2 Adaptation with Randomized Sequence Scanning and Local Frustration Profiling

The groundbreaking achievements of AlphaFold2 (AF2) approaches in protein structure modeling marked a transformative era in structural biology. Despite the success of AF2 tools in predicting single protein structures, these methods showed intrinsic limitations in predicting multiple functional conformations of allosteric proteins and fold-switching systems. The recent NMR-based structural determination of the unbound ABL kinase in the active state and two inactive low-populated functional conformations that are unique for ABL kinase presents an ideal challenge for AF2 approaches. In the current study we employ several implementations of AF2 methods to predict protein conformational ensembles and allosteric states of the ABL kinase including (a) multiple sequence alignments (MSA) subsampling approach; (b) SPEACH_AF approach in which alanine scanning is performed on generated MSAs; and (c) introduced in this study randomized full sequence mutational scanning for manipulation of sequence variations combined with the MSA subsampling. We show that the proposed AF2 adaptation combined with local frustration mapping of conformational states enable accurate prediction of the ABL active and intermediate structures and conformational ensembles, also offering a robust approach for interpretable characterization of the AF2 predictions and limitations in detecting hidden allosteric states. We found that the large high frustration residue clusters are uniquely characteristic of the low-populated, fully inactive ABL form and can define energetically frustrated cracking sites of conformational transitions, presenting difficult targets for AF2 methods. This study uncovered previously unappreciated, fundamental connections between distinct patterns of local frustration in functional kinase states and AF2 successes/limitations in detecting low-populated frustrated conformations, providing a better understanding of benefits and limitations of current AF2-based adaptations in modeling of conformational ensembles.

Free Energy Surface and Molecular Mechanism of Slow Structural Transitions in Lipid Bilayers

Lipid membrane remodeling, crucial for many cellular processes, is governed by the coupling of membrane structure and shape fluctuations. Given the importance of the ∼ nm length scale, details of the transition intermediates for conformational change are not fully captured by a continuum-mechanical description. Slow dynamics and the lack of knowledge of reaction coordinates (RCs) for biasing methods pose a challenge for all-atom (AA) simulations. Here, we map system dynamics on Langevin dynamics in a normal mode space determined from an elastic network model representation for the lipid-water Hamiltonian. AA molecular dynamics (MD) simulations are used to determine model parameters, and Langevin dynamics predictions for bilayer structural, mechanical, and dynamic properties are validated against MD simulations and experiments. Transferability to describe the dynamics of a larger lipid bilayer and a heterogeneous membrane-protein system is assessed. A set of generic RCs for pore formation in two tensionless bilayers is obtained by coupling Langevin dynamics to the underlying energy landscape for membrane deformations. Structure evolution is carried out by AA MD, wherein the generic RCs are used in a path metadynamics or an umbrella sampling simulation to determine the thermodynamics of pore formation and its molecular determinants, such as the role of distinct bilayer motions, lipid solvation, and lipid packing.

Energy landscape quantifications of histone H3.3 recognition by chaperone DAXX reveal an uncoupled binding specificity and affinity

Histone variant H3.3 differs from the canonical histone H3.1 by only five amino acids, yet its chaperone death domain-associated protein (DAXX) can specifically recognize H3.3 over H3.1, despite having a large DAXX-interacting surface on the H3.3-H4 heterodimer common to that on the H3.1-H4 complex. This observation gives rise to the question of, from the binding energy point view, how high binding specificity may be achieved with small differences of the overall binding energy for protein-protein interactions in general. Here we investigate the mechanism of coupling of binding specificity and affinity in protein-protein interactions using the DAXX-H3.3-H4 complex as a model. Using a multi-scale method, we found that the hydrophobic interactions between DAXX and the H3.3-specific region contributed to their initial binding process. And the structural flexibility of the interacting partners contributed to the binding affinity after their encounter. By quantifying the free energy landscape, we revealed that the interaction between the specific residues of H3.3 and DAXX decreased the encounter barrier height while the folding of H3.3-H4 and DAXX increased the depth of the free energy basin of the final binding state. The encounter barrier height, which is not coupled to the thermodynamic stability of the final binding state, had a marked effect on the initial binding rate of flexible histones and chaperones. Based on the energy landscape theory, we found that the intrinsic binding energy funnel of this uncoupled recognition process was affected by the structural flexibility and the flexibility modulated the degree of coupling between binding specificity and affinity. Our work offers a biophysical explanation of the specific recognition between the histones and their chaperones, and also extends the use of energy landscape theory for understanding molecular recognitions in general.

Addressing high excitation conditions in time-resolved X-ray diffraction experiments and issues of biological relevance

One of the most important fundamental questions connecting chemistry to biology is how chemistry scales in complexity up to biological systems where there are innumerable possible pathways and competing processes. With the development of ultrabright electron and x-ray sources, it has been possible to literally light up atomic motions to directly observe the reduction in dimensionality in the barrier crossing region to a few key reaction modes. How do these chemical processes further couple to the surrounding protein or macromolecular assembly to drive biological functions? Optical methods to trigger photoactive biological processes are needed to probe this issue on the relevant timescales. However, the excitation conditions have been in the highly nonlinear regime, which questions the biological relevance of the observed structural dynamics.

Structural mechanism of a drug-binding process involving a large conformational change of the protein target

Proteins often undergo large conformational changes when binding small molecules, but atomic-level descriptions of such events have been elusive. Here, we report unguided molecular dynamics simulations of Abl kinase binding to the cancer drug imatinib. In the simulations, imatinib first selectively engages Abl kinase in its autoinhibitory conformation. Consistent with inferences drawn from previous experimental studies, imatinib then induces a large conformational change of the protein to reach a bound complex that closely resembles published crystal structures. Moreover, the simulations reveal a surprising local structural instability in the C-terminal lobe of Abl kinase during binding. The unstable region includes a number of residues that, when mutated, confer imatinib resistance by an unknown mechanism. Based on the simulations, NMR spectra, hydrogen-deuterium exchange measurements, and thermostability measurements and estimates, we suggest that these mutations confer imatinib resistance by exacerbating structural instability in the C-terminal lobe, rendering the imatinib-bound state energetically unfavorable.

Statistical Learning of Protein Elastic Network from Positional Covariance Matrix

Positional fluctuation and covariance during protein dynamics are key observables for understanding the molecular origin of biological functions. A frequently employed potential energy function for describing protein structural variation at the coarse-gained level is elastic network model (ENM). A long-standing issue in biomolecular simulation is thus the parametrization of ENM spring constants from the components of positional covariance matrix (PCM). Based on sensitivity analysis of PCM, the direct-coupling statistics of each spring, which is a specific combination of position fluctuation and covariance, is found to exhibit prominent signal of parameter dependence. This finding provides the basis for devising the objective function and the scheme of running through the effective one-dimensional optimization of every spring by self-consistent iteration. Formal derivation of the positional covariance statistical learning (PCSL) method also motivates the necessary data regularization for stable calculations. Robust convergence of PCSL is achieved in taking an all-atom molecular dynamics trajectory or an ensemble of homologous structures as input data. The PCSL framework can also be generalized with mixed objective functions to capture specific property such as the residue flexibility profile. Such physical chemistry-based statistical learning thus provides a useful platform for integrating the mechanical information encoded in various experimental or computational data.

Locating dynamic contributions to allostery via determining rates of vibrational energy transfer

Determining rates of energy transfer across non-covalent contacts for different states of a protein can provide information about dynamic and associated entropy changes during transitions between states. We investigate the relationship between rates of energy transfer across polar and nonpolar contacts and contact dynamics for the β₂-adrenergic receptor, a rhodopsin-like G-protein coupled receptor, in an antagonist-bound inactive state and agonist-bound active state. From structures sampled during molecular dynamics (MD) simulations, we find the active state to have, on average, a lower packing density, corresponding to generally more flexibility and greater entropy than the inactive state. Energy exchange networks (EENs) are computed for the inactive and active states from the results of the MD simulations. From the EENs, changes in the rates of energy transfer across polar and nonpolar contacts are found for contacts that remain largely intact during activation. Change in dynamics of the contact, and entropy associated with the dynamics, can be estimated from the change in rates of energy transfer across the contacts. Measurement of change in the rates of energy transfer before and after the transition between states thereby provides information about dynamic contributions to activation and allostery.

Protein dynamics: The future is bright and complicated!

Biological life depends on motion, and this manifests itself in proteins that display motion over a formidable range of time scales spanning from femtoseconds vibrations of atoms at enzymatic transition states, all the way to slow domain motions occurring on micro to milliseconds. An outstanding challenge in contemporary biophysics and structural biology is a quantitative understanding of the linkages among protein structure, dynamics, and function. These linkages are becoming increasingly explorable due to conceptual and methodological advances. In this Perspective article, we will point toward future directions of the field of protein dynamics with an emphasis on enzymes. Research questions in the field are becoming increasingly complex such as the mechanistic understanding of high-order interaction networks in allosteric signal propagation through a protein matrix, or the connection between local and collective motions. In analogy to the solution to the "protein folding problem," we argue that the way forward to understanding these and other important questions lies in the successful integration of experiment and computation, while utilizing the present rapid expansion of sequence and structure space. Looking forward, the future is bright, and we are in a period where we are on the doorstep to, at least in part, comprehend the importance of dynamics for biological function.

Frustration and the Kinetic Repartitioning Mechanism of Substrate Inhibition in Enzyme Catalysis

Substrate inhibition, whereby enzymatic activity decreases with excess substrate after reaching a maximum turnover rate, is among the most elusive phenomena in enzymatic catalysis. Here, based on a dynamic energy landscape model, we investigate the underlying mechanism by performing molecular simulations and frustration analysis for a model enzyme adenylate kinase (AdK), which catalyzes the phosphoryl transfer reaction ATP + AMP ⇋ ADP + ADP. Intriguingly, these reveal a kinetic repartitioning mechanism of substrate inhibition, whereby excess substrate AMP suppresses the population of an energetically frustrated, but kinetically activated, catalytic pathway going through a substrate (ATP)-product (ADP) cobound complex with steric incompatibility. Such a frustrated pathway plays a crucial role in facilitating the bottleneck product ADP release, and its suppression by excess substrate AMP leads to a slow down of product release and overall turnover. The simulation results directly demonstrate that substrate inhibition arises from the rate-limiting product-release step, instead of the steps for populating the catalytically competent complex as often suggested in previous works. Furthermore, there is a tight interplay between the enzyme conformational equilibrium and the extent of substrate inhibition. Mutations biasing to more closed conformations tend to enhance substrate inhibition. We also characterized the key features of single-molecule enzyme kinetics with substrate inhibition effect. We propose that the above molecular mechanism of substrate inhibition may be relevant to other multisubstrate enzymes in which product release is the bottleneck step.

Edge weights in a protein elastic network reorganize collective motions and render long-range sensitivity responses

The effects of inter-residue interactions on protein collective motions are analyzed by comparing two elastic network models (ENM)—structural contact ENM (SC-ENM) and molecular dynamics (MD)-ENM—with the edge weights computed from an all-atom MD trajectory by structure-mechanics statistical learning. A theoretical framework is devised to decompose the eigenvalues of ENM Hessian into contributions from individual springs and to compute the sensitivities of positional fluctuations and covariances to spring constant variation. Our linear perturbation approach quantifies the response mechanisms as softness modulation and orientation shift. All contacts of C α positions in SC-ENM have an identical spring constant by fitting the profile of root-of-mean-squared-fluctuation calculated from an all-atom MD simulation, and the same trajectory data are also used to compute the specific spring constant of each contact as an MD-ENM edge weight. We illustrate that the soft-mode reorganization can be understood in terms of gaining weights along the structural contacts of low elastic strengths and loosing magnitude along those of high rigidities. With the diverse mechanical strengths encoded in protein dynamics, MD-ENM is found to have more pronounced long-range couplings and sensitivity responses with orientation shift identified as a key player in driving the specific residues to have high sensitivities. Furthermore, the responses of perturbing the springs of different residues are found to have asymmetry in the action–reaction relationship. In understanding the mutation effects on protein functional properties, such as long-range communications, our results point in the directions of collective motions as a major effector.

Computation of the Protein Conformational Transition Pathway on Ligand Binding by Linear Response-Driven Molecular Dynamics

While extremely important for relating the protein structure to its biological function, determination of the protein conformational transition pathway upon ligand binding is made difficult due to the transient nature of intermediates, a large and rugged conformational space, and coupling between protein dynamics and ligand-protein interactions. Existing methods that rely on prior knowledge of the bound (holo) state structure are restrictive. A second concern relates to the correspondence of intermediates obtained to the metastable states on the apo → holo transition pathway. Here, we have taken the protein apo structure and ligand-binding site as only inputs and combined an elastic network model (ENM) representation of the protein Hamiltonian with linear response theory (LRT) for protein-ligand interactions to identify the set of slow normal modes of protein vibrations that have a high overlap with the direction of the protein conformational change. The structural displacement along the chosen direction was performed using excited normal modes molecular dynamics (MDeNM) simulations rather than by the direct use of LRT. Herein, the MDeNM excitation velocity was optimized on-the-fly on the basis of its coupling to protein dynamics and ligand-protein interactions. Thus, a determined set of structures was validated against crystallographic and simulation data on four protein-ligand systems, namely, adenylate kinase-di(adenosine-5')pentaphosphate, ribose binding protein-β-d-ribopyranose, DNA β-glucosyltransferase-uridine-5'-diphosphate, and G-protein α subunit-guanosine-5'-triphosphate, which present important differences in protein conformational heterogeneity, ligand binding mechanism, viz. induced-fit or conformational selection, extent, and nonlinearity in protein conformational changes upon ligand binding, and presence of allosteric effects. The obtained set of intermediates was used as an input to path metadynamics simulations to obtain the free energy profile for the apo → holo transition.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

The energetics of subunit rotation in the ribosome

Protein synthesis in the cell is controlled by an elaborate sequence of conformational rearrangements in the ribosome. The composition of a ribosome varies by species, though they typically contain ∼ 50-100 RNA and protein molecules. While advances in structural techniques have revolutionized our understanding of long-lived conformational states, a vast range of transiently visited configurations can not be directly observed. In these cases, computational/simulation methods can be used to understand the mechanical properties of the ribosome. Insights from these approaches can then help guide next-generation experimental measurements. In this short review, we discuss theoretical strategies that have been deployed to quantitatively describe the energetics of collective rearrangements in the ribosome. We focus on efforts to probe large-scale subunit rotation events, which involve the coordinated displacement of large numbers of atoms (tens of thousands). These investigations are revealing how the molecular structure of the ribosome encodes the mechanical properties that control large-scale dynamics.

Tracking the ATP-binding response in adenylate kinase in real time

The biological function of proteins is critically dependent on dynamics inherent to the native structure. Such structural dynamics obey a predefined order and temporal timing to execute the specific reaction. Determination of the cooperativity of key structural rearrangements requires monitoring protein reactions in real time. In this work, we used time-resolved x-ray solution scattering (TR-XSS) to visualize structural changes in the Escherichia coli adenylate kinase (AdK) enzyme upon laser-induced activation of a protected ATP substrate. A 4.3-ms transient intermediate showed partial closing of both the ATP- and AMP-binding domains, which indicates a cooperative closing mechanism. The ATP-binding domain also showed local unfolding and breaking of an Arg¹³¹-Asp¹⁴⁶ salt bridge. Nuclear magnetic resonance spectroscopy data identified similar unfolding in an Arg¹³¹Ala AdK mutant, which refolded in a closed, substrate-binding conformation. The observed structural dynamics agree with a “cracking mechanism” proposed to underlie global structural transformation, such as allostery, in proteins.

The dynamics of subunit rotation in a eukaryotic ribosome

Protein synthesis by the ribosome is coordinated by an intricate series of large-scale conformational rearrangements. Structural studies can provide information about long-lived states, however biological kinetics are controlled by the intervening free-energy barriers. While there has been progress describing the energy landscapes of bacterial ribosomes, very little is known about the energetics of large-scale rearrangements in eukaryotic systems. To address this topic, we constructed an all-atom model with simplified energetics and performed simulations of subunit rotation in the yeast ribosome. In these simulations, the small subunit (SSU; ~1MDa) undergoes spontaneous and reversible rotations (~8°). By enabling the simulation of this rearrangement under equilibrium conditions, these calculations provide initial insights into the molecular factors that control dynamics in eukaryotic ribosomes. Through this, we are able to identify specific inter-subunit interactions that have a pronounced influence on the rate-limiting free-energy barrier. We also show that, as a result of changes in molecular flexibility, the thermodynamic balance between the rotated and unrotated states is temperature-dependent. This effect may be interpreted in terms of differential molecular flexibility within the rotated and unrotated states. Together, these calculations provide a foundation, upon which the field may begin to dissect the energetics of these complex molecular machines.

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

A guide to time-resolved structural analysis of light-activated proteins

Dynamical changes in protein structures are essential for protein function and occur over femtoseconds to seconds timescales. X-ray free electron lasers have facilitated investigations of structural dynamics in proteins with unprecedented temporal and spatial resolution. Light-activated proteins are attractive targets for time-resolved structural studies, as the reaction chemistry and associated protein structural changes can be triggered by short laser pulses. Proteins with different light-absorbing centres have evolved to detect light and harness photon energy to bring about downstream chemical and biological output responses. Following light absorption, rapid chemical/small-scale structural changes are typically localised around the chromophore. These localised changes are followed by larger structural changes propagated throughout the photoreceptor/photocatalyst that enables the desired chemical and/or biological output response. Time-resolved serial femtosecond crystallography (SFX) and solution scattering techniques enable direct visualisation of early chemical change in light-activated proteins on timescales previously inaccessible, whereas scattering gives access to slower timescales associated with more global structural change. Here, we review how advances in time-resolved SFX and solution scattering techniques have uncovered mechanisms of photochemistry and its coupling to output responses. We also provide a prospective on how these time-resolved structural approaches might impact on other photoreceptors/photoenzymes that have not yet been studied by these methods.

Folding-controlled assembly of ortho-phenylene-based macrocycles

The self-assembly of foldamers into macrocycles is a simple approach to non-biological higher-order structure. Previous work on the co-assembly of ortho-phenylene foldamers with rod-shaped linkers has shown that folding and self-assembly affect each other; that is, the combination leads to new emergent behavior, such as access to otherwise unfavorable folding states. To this point this relationship has been passive. Here, we demonstrate control of self-assembly by manipulating the foldamers' conformational energy surfaces. A series of o-phenylene decamers and octamers have been assembled into macrocycles using imine condensation. Product distributions were analyzed by gel-permeation chromatography and molecular geometries extracted from a combination of NMR spectroscopy and computational chemistry. The assembly of o-phenylene decamers functionalized with alkoxy groups or hydrogens gives both [2 + 2] and [3 + 3] macrocycles. The mixture results from a subtle balance of entropic and enthalpic effects in these systems: the smaller [2 + 2] macrocycles are entropically favored but require the oligomer to misfold, whereas a perfectly folded decamer fits well within the larger [3 + 3] macrocycle that is entropically disfavored. Changing the substituents to fluoro groups, however, shifts assembly quantitatively to the [3 + 3] macrocycle products, even though the structural changes are well-removed from the functional groups directly participating in bond formation. The electron-withdrawing groups favor folding in these systems by strengthening arene–arene stacking interactions, increasing the enthalpic penalty to misfolding. The architectural changes are substantial even though the chemical perturbation is small: analogous o-phenylene octamers do not fit within macrocycles when perfectly folded, and quantitatively misfold to give small macrocycles regardless of substitution. Taken together, these results represent both a high level of structural control in structurally complex foldamer systems and the demonstration of large-amplitude structural changes as a consequence of a small structural effects.

The folding propensity of ortho-phenylene foldamers dictates the outcome of their self-assembly into macrocycles.

Machine Learning of Allosteric Effects: The Analysis of Ligand-Induced Dynamics to Predict Functional Effects in TRAP1

Allosteric molecules provide a powerful means to modulate protein function. However, the effect of such ligands on distal orthosteric sites cannot be easily described by classical docking methods. Here, we applied machine learning (ML) approaches to expose the links between local dynamic patterns and different degrees of allosteric inhibition of the ATPase function in the molecular chaperone TRAP1. We focused on 11 novel allosteric modulators with similar affinities to the target but with inhibitory efficacy between the 26.3 and 76%. Using a set of experimentally related local descriptors, ML enabled us to connect the molecular dynamics (MD) accessible to ligand-bound (perturbed) and unbound (unperturbed) systems to the degree of ATPase allosteric inhibition. The ML analysis of the comparative perturbed ensembles revealed a redistribution of dynamic states in the inhibitor-bound versus inhibitor-free systems following allosteric binding. Linear regression models were built to quantify the percentage of experimental variance explained by the predicted inhibitor-bound TRAP1 states. Our strategy provides a comparative MD–ML framework to infer allosteric ligand functionality. Alleviating the time scale issues which prevent the routine use of MD, a combination of MD and ML represents a promising strategy to support in silico mechanistic studies and drug design.

Surveying biomolecular frustration at atomic resolution

To function, biomolecules require sufficient specificity of interaction as well as stability to live in the cell while still being able to move. Thermodynamic stability of only a limited number of specific structures is important so as to prevent promiscuous interactions. The individual interactions in proteins, therefore, have evolved collectively to give funneled minimally frustrated landscapes but some strategic parts of biomolecular sequences located at specific sites in the structure have been selected to be frustrated in order to allow both motion and interaction with partners. We describe a framework efficiently to quantify and localize biomolecular frustration at atomic resolution by examining the statistics of the energy changes that occur when the local environment of a site is changed. The location of patches of highly frustrated interactions correlates with key biological locations needed for physiological function. At atomic resolution, it becomes possible to extend frustration analysis to protein-ligand complexes. At this resolution one sees that drug specificity is correlated with there being a minimally frustrated binding pocket leading to a funneled binding landscape. Atomistic frustration analysis provides a route for screening for more specific compounds for drug discovery.

The analysis of biomolecular frustration yielded insights into several aspects of protein behavior. Here the authors describe a framework to efficiently quantify and localize biomolecular frustration within proteins at atomic resolution, and observe that drug specificity is correlated with a minimally frustrated binding pocket leading to a funneled binding landscape.

A Coarse-Grained Methodology Identifies Intrinsic Mechanisms That Dissociate Interacting Protein Pairs

We address the problem of triggering dissociation events between proteins that have formed a complex. We have collected a set of 25 non-redundant, functionally diverse protein complexes having high-resolution three-dimensional structures in both the unbound and bound forms. We unify elastic network models with perturbation response scanning (PRS) methodology as an efficient approach for predicting residues that have the propensity to trigger dissociation of an interacting protein pair, using the three-dimensional structures of the bound and unbound proteins as input. PRS reveals that while for a group of protein pairs, residues involved in the conformational shifts are confined to regions with large motions, there are others where they originate from parts of the protein unaffected structurally by binding. Strikingly, only a few of the complexes have interface residues responsible for dissociation. We find two main modes of response: In one mode, remote control of dissociation in which disruption of the electrostatic potential distribution along protein surfaces play the major role; in the alternative mode, mechanical control of dissociation by remote residues prevail. In the former, dissociation is triggered by changes in the local environment of the protein, e.g., pH or ionic strength, while in the latter, specific perturbations arriving at the controlling residues, e.g., via binding to a third interacting partner is required for decomplexation. We resolve the observations by relying on an electromechanical coupling model which reduces to the usual elastic network result in the limit of the lack of coupling. We validate the approach by illustrating the biological significance of top residues selected by PRS on select cases where we show that the residues whose perturbation leads to the observed conformational changes correspond to either functionally important or highly conserved residues in the complex.

Investigating the trade-off between folding and function in a multidomain Y-family DNA polymerase

The way in which multidomain proteins fold has been a puzzling question for decades. Until now, the mechanisms and functions of domain interactions involved in multidomain protein folding have been obscure. Here, we develop structure-based models to investigate the folding and DNA-binding processes of the multidomain Y-family DNA polymerase IV (DPO4). We uncover shifts in the folding mechanism among ordered domain-wise folding, backtracking folding, and cooperative folding, modulated by interdomain interactions. These lead to ‘U-shaped’ DPO4 folding kinetics. We characterize the effects of interdomain flexibility on the promotion of DPO4–DNA (un)binding, which probably contributes to the ability of DPO4 to bypass DNA lesions, which is a known biological role of Y-family polymerases. We suggest that the native topology of DPO4 leads to a trade-off between fast, stable folding and tight functional DNA binding. Our approach provides an effective way to quantitatively correlate the roles of protein interactions in conformational dynamics at the multidomain level.

ATP-Driven Nonequilibrium Activation of Kinase Clients by the Molecular Chaperone Hsp90

The molecular chaperone 90-kDa heat-shock protein (Hsp90) assists the late-stage folding and activation of diverse types of protein substrates (called clients), including many kinases. Previous studies have established that the Hsp90 homodimer undergoes an ATP-driven cycle through open and closed conformations. Here, I propose a model of client activation by Hsp90 that predicts that this cycle enables Hsp90 to use ATP energy to drive a client out of thermodynamic equilibrium toward its active conformation. My model assumes that an Hsp90-bound client can transition between a deactivating conformation and an activating conformation. It suggests that the cochaperone Cdc37 aids Hsp90 to activate kinase clients by differentiating between these two intermediate conformations. My model makes experimentally testable predictions, including how modulating the stepwise kinetics of the Hsp90 cycle-for example, by various cochaperones-affects the activation of different clients. My model may inform client-specific and cell-type-specific therapeutic intervention of Hsp90-mediated protein activation.

Predicting Protein Functional Motions: an Old Recipe with a New Twist

Large macromolecules, including proteins and their complexes, very often adopt multiple conformations. Some of them can be seen experimentally, for example with x-ray crystallography or cryo-electron microscopy. This structural heterogeneity is not occasional and is frequently linked with specific biological function. Thus, the accurate description of macromolecular conformational transitions is crucial for understanding fundamental mechanisms of life's machinery. We report on a real-time method to predict such transitions by extrapolating from instantaneous eigen motions, computed using the normal mode analysis, to a series of twists. We demonstrate the applicability of our approach to the prediction of a wide range of motions, including large collective opening-closing transitions and conformational changes induced by partner binding. We also highlight particularly difficult cases of very small transitions between crystal and solution structures. Our method guarantees preservation of the protein structure during the transition and allows accessing conformations that are unreachable with classical normal mode analysis. We provide practical solutions to describe localized motions with a few low-frequency modes and to relax some geometrical constraints along the predicted transitions. This work opens the way to the systematic description of protein motions, whatever their degree of collectivity. Our method is freely available as a part of the NOn-Linear rigid Block (NOLB) package.

Allosteric communication in molecular machines via information exchange: what can be learned from dynamical modeling

Allosteric regulation is crucial for the operation of protein machines and molecular motors. A major challenge is to characterize and quantify the information exchange underlying allosteric communication between remote functional sites in a protein, and to identify the involved relevant pathways. We review applications of two topical approaches of dynamical protein modeling, a kinetic-based single-molecule stochastic model, which employs information thermodynamics to quantify allosteric interactions, and structure-based coarse-grained modeling to characterize intra-molecular couplings in terms of conformational motions and propagating mechanical strain. Both descriptions resolve the directionality of allosteric responses within a protein, emphasizing the concept of causality as the principal hallmark of protein allostery. We discuss the application of techniques from information thermodynamics to dynamic protein elastic networks and evolutionary designed model structures, and the ramifications for protein allostery.

Confinement and Crowding Effects on Folding of a Multidomain Y-Family DNA Polymerase

Proteins in vivo endure highly various interactions from the luxuriant surrounding macromolecular cosolutes. Confinement and macromolecular crowding are the two major effects that should be considered while comparing the results of protein dynamics from in vitro to in vivo. However, efforts have been largely focused on single domain protein folding up to now, and the quantifications of the in vivo effects in terms of confinements and crowders on modulating the structure and dynamics as well as the physical understanding of the underlying mechanisms on multidomain protein folding are still challenging. Here we developed a topology-based model to investigate folding of a multidomain Y-family DNA polymerase (DPO4) within spherical confined space and in the presence of repulsive and attractive crowders. We uncovered that the entropic component of the thermodynamic driving force led by confinements and repulsive crowders increases the stability of folded states relative to the folding intermediates and unfolded states, while the enthalpic component of the thermodynamic driving force led by attractive crowders gives rise to the opposite effects with less stability. We found that the shapes of DPO4 conformations influenced by the confinements and the crowders are quite different even when only the entropic component of the thermodynamic driving force is considered. We uncovered that under all in vivo conditions, the folding cooperativity of DPO4 decreases compared to that in bulk. We showed that the loss of folding cooperativity can promote the sequential domain-wise folding, which was widely found in cotranslational multidomain protein folding, and effectively prohibit the backtracking led by topological frustrations during multidomain protein folding processes.

Protein tolerance to random circular permutation correlates with thermostability and local energetics of residue-residue contacts

Adenylate kinase (AK) orthologs with a range of thermostabilities were subjected to random circular permutation, and deep mutational scanning was used to evaluate where new protein termini were nondisruptive to activity. The fraction of circularly permuted variants that retained function in each library correlated with AK thermostability. In addition, analysis of the positional tolerance to new termini, which increase local conformational flexibility, showed that bonds were either functionally sensitive to cleavage across all homologs, differentially sensitive, or uniformly tolerant. The mobile AMP-binding domain, which displays the highest calculated contact energies, presented the greatest tolerance to new termini across all AKs. In contrast, retention of function in the lid and core domains was more dependent upon AK melting temperature. These results show that family permutation profiling identifies primary structure that has been selected by evolution for dynamics that are critical to activity within an enzyme family. These findings also illustrate how deep mutational scanning can be applied to protein homologs in parallel to differentiate how topology, stability, and local energetics govern mutational tolerance.

Gō model revisited

This review discusses Gō models broadly used in biomolecular simulations. I start with a brief description of the original lattice model study by Nobuhiro Gō. Then, the theory of protein folding behind Gō model, free energy approaches, and off-lattice Gō models are reviewed. I also mention a stringent test for the assumption in Gō models given from all-atom molecular dynamics simulations. Subsequently, I move to application of Gō models to protein dynamical functions. Various extension of Gō models is also reviewed. Finally, some publicly available tools to use Gō models are listed.

Detecting and Characterizing the Kinetic Activation of Thermal Networks in Proteins: Thermal Transfer from a Distal, Solvent-Exposed Loop to the Active Site in Soybean Lipoxygenase

The rate-limiting chemical reaction catalyzed by soybean lipoxygenase (SLO) involves quantum mechanical tunneling of a hydrogen atom from substrate to its active site ferric-hydroxide cofactor. SLO has emerged as a prototypical system for linking the thermal activation of a protein scaffold to the efficiency of active site chemistry. Significantly, hydrogen-deuterium exchange-mass spectrometry (HDX-MS) experiments on wild type and mutant forms of SLO have uncovered trends in the enthalpic barriers for HDX within a solvent-exposed loop (positions 317-334) that correlate well with trends in the corresponding enthalpic barriers for kcat. A model for this behavior posits that collisions between water and loop 317-334 initiate thermal activation at the protein surface that is then propagated 15-34 Å inward toward the reactive carbon of substrate in proximity to the iron catalyst. In this study, we have prepared protein samples containing cysteine residues either at the tip of the loop 317-334 (Q322C) or on a control loop, 586-603 (S596C). Chemical modification of cysteines with the fluorophore 6-bromoacetyl-2-dimethylaminonaphthalene (Badan, BD) provides site-specific probes for the measurement of fluorescence relaxation lifetimes and Stokes shift decays as a function of temperature. Computational studies indicate that surface water structure is likely to be largely preserved in each sample. While both loops exhibit temperature-independent fluorescence relaxation lifetimes as do the Stokes shifts for S596C-BD, the activation enthalpy for the nanosecond solvent reorganization at Q322C-BD (Ea(ksolv) = 2.8(0.9) kcal/mol)) approximates the enthalpy of activation for catalytic C-H activation (Ea(kcat) = 2.3(0.4) kcal/mol). This study establishes and validates the methodology for measuring rates of rapid local motions at the protein/solvent interface of SLO. These new findings, when combined with previously published correlations between protein motions and the rate-limiting hydride transfer in a thermophilic alcohol dehydrogenase, provide experimental evidence for thermally induced "protein quakes" as the origin of enthalpic barriers in catalysis.

Critical phenomena in the temperature-pressure-crowding phase diagram of a protein

In the cell, proteins fold and perform complex functions through global structural rearrangements. Function requires a protein to be at the brink of stability to be susceptible to small environmental fluctuations, yet stable enough to maintain structural integrity. These apparently conflicting behaviors are exhibited by systems near a critical point, where distinct phases merge-a concept beyond previous studies indicating proteins have a well-defined folded/unfolded phase boundary in the pressure-temperature plane. Here, by modeling the protein phosphoglycerate kinase (PGK) on the temperature (T), pressure (P), and crowding volume-fraction (ϕ) phase diagram, we demonstrate a critical transition where phases merge, and PGK exhibits large structural fluctuations. Above the critical point, the difference between the intermediate and unfolded phases disappears. When ϕ increases, the critical point moves to lower T _c. We verify the calculations with experiments mapping the T-P-ϕ space, which likewise reveal a critical point at 305 K and 170 MPa that moves to lower T _c as ϕ increases. Crowding places PGK near a critical line in its natural parameter space, where large conformational changes can occur without costly free energy barriers. Specific structures are proposed for each phase based on simulation.

Theory of Nonequilibrium Free Energy Transduction by Molecular Machines

Biomolecular machines are protein complexes that convert between different forms of free energy. They are utilized in nature to accomplish many cellular tasks. As isothermal nonequilibrium stochastic objects at low Reynolds number, they face a distinct set of challenges compared with more familiar human-engineered macroscopic machines. Here we review central questions in their performance as free energy transducers, outline theoretical and modeling approaches to understand these questions, identify both physical limits on their operational characteristics and design principles for improving performance, and discuss emerging areas of research.

Simple mechanics of protein machines

While belonging to the nanoscale, protein machines are so complex that tracing even a small fraction of their cycle requires weeks of calculations on supercomputers. Surprisingly, many aspects of their operation can be however already reproduced by using very simple mechanical models of elastic networks. The analysis suggests that, similar to other self-organized complex systems, functional collective dynamics in such proteins is effectively reduced to a low-dimensional attractive manifold.

Overcoming the Bottleneck of the Enzymatic Cycle by Steric Frustration

The enormous catalytic power of natural enzymes relies on the ability to overcome the bottleneck event in the enzymatic cycle, yet the underlying physical mechanisms are not fully understood. Here, by performing molecular simulations of the whole enzymatic cycle for a model multisubstrate enzyme with a dynamic energy landscape model, we show that multisubstrate enzymes can utilize steric frustration to facilitate the rate-limiting product-release step. During the enzymatic cycles, the bottleneck product is actively squeezed out by the binding of a new substrate at the neighboring site through the population of a substrate-product cobound complex, in which the binding pockets are frustrated due to steric incompatibility. Such steric frustration thereby enables an active mechanism of product release driven by substrate-binding energy, facilitating the enzymatic cycle.

Forging tools for refining predicted protein structures

Refining predicted protein structures with all-atom molecular dynamics simulations is one route to producing, entirely by computational means, structural models of proteins that rival in quality those that are determined by X-ray diffraction experiments. Slow rearrangements within the compact folded state, however, make routine refinement of predicted structures by unrestrained simulations infeasible. In this work, we draw inspiration from the fields of metallurgy and blacksmithing, where practitioners have worked out practical means of controlling equilibration by mechanically deforming their samples. We describe a two-step refinement procedure that involves identifying collective variables for mechanical deformations using a coarse-grained model and then sampling along these deformation modes in all-atom simulations. Identifying those low-frequency collective modes that change the contact map the most proves to be an effective strategy for choosing which deformations to use for sampling. The method is tested on 20 refinement targets from the CASP12 competition and is found to induce large structural rearrangements that drive the structures closer to the experimentally determined structures during relatively short all-atom simulations of 50 ns. By examining the accuracy of side-chain rotamer states in subensembles of structures that have varying degrees of similarity to the experimental structure, we identified the reorientation of aromatic side chains as a step that remains slow even when encouraging global mechanical deformations in the all-atom simulations. Reducing the side-chain rotamer isomerization barriers in the all-atom force field is found to further speed up refinement.

Mechanical properties of BiP protein determined by nano-rheology

Immunoglobulin Binding Protein (BiP) is a chaperone and molecular motor belonging to the Hsp70 family, involved in the regulation of important biological processes such as synthesis, folding and translocation of proteins in the Endoplasmic Reticulum. BiP has two highly conserved domains: the N-terminal Nucleotide-Binding Domain (NBD), and the C-terminal Substrate-Binding Domain (SBD), connected by a hydrophobic linker. ATP binds and it is hydrolyzed to ADP in the NBD, and BiP's extended polypeptide substrates bind in the SBD. Like many molecular motors, BiP function depends on both structural and catalytic properties that may contribute to its performance. One novel approach to study the mechanical properties of BiP considers exploring the changes in the viscoelastic behavior upon ligand binding, using a technique called nano-rheology. This technique is essentially a traditional rheology experiment, in which an oscillatory force is directly applied to the protein under study, and the resulting average deformation is measured. Our results show that the folded state of the protein behaves like a viscoelastic material, getting softer when it binds nucleotides- ATP, ADP, and AMP-PNP-, but stiffer when binding HTFPAVL peptide substrate. Also, we observed that peptide binding dramatically increases the affinity for ADP, decreasing it dissociation constant (K_D ) around 1000 times, demonstrating allosteric coupling between SBD and NBD domains.

Structure, stability and specificity of the binding of ssDNA and ssRNA with proteins

Recognition of single-stranded DNA (ssDNA) or single-stranded RNA (ssRNA) is important for many fundamental cellular functions. A variety of single-stranded DNA-binding proteins (ssDBPs) and single-stranded RNA-binding proteins (ssRBPs) have evolved that bind ssDNA and ssRNA, respectively, with varying degree of affinities and specificities to form complexes. Structural studies of these complexes provide key insights into their recognition mechanism. However, computational modeling of the specific recognition process and to predict the structure of the complex is challenging, primarily due to the heterogeneity of their binding energy landscape and the greater flexibility of ssDNA or ssRNA compared with double-stranded nucleic acids. Consequently, considerably fewer computational studies have explored interactions between proteins and single-stranded nucleic acids compared with protein interactions with double-stranded nucleic acids. Here, we report a newly developed energy-based coarse-grained model to predict the structure of ssDNA–ssDBP and ssRNA–ssRBP complexes and to assess their sequence-specific interactions and stabilities. We tuned two factors that can modulate specific recognition: base–aromatic stacking strength and the flexibility of the single-stranded nucleic acid. The model was successfully applied to predict the binding conformations of 12 distinct ssDBP and ssRBP structures with their cognate ssDNA and ssRNA partners having various sequences. Estimated binding energies agreed well with the corresponding experimental binding affinities. Bound conformations from the simulation showed a funnel-shaped binding energy distribution where the native-like conformations corresponded to the energy minima. The various ssDNA–protein and ssRNA–protein complexes differed in the balance of electrostatic and aromatic energies. The lower affinity of the ssRNA–ssRBP complexes compared with the ssDNA–ssDBP complexes stems from lower flexibility of ssRNA compared to ssDNA, which results in higher rate constants for the dissociation of the complex (k_off) for complexes involving the former.

Quantifying bimolecular self-assembly is pivotal to understanding cellular function. In recent years, a large progress has been made in understanding the structure and biophysics of protein-protein interactions. Particularly, various computational tools are available for predicting these structures and to estimate their stability and the driving forces of their formation. The understating of the interactions between proteins and nucleic acids, however, is still limited, presumably due to the involvement of non-specific interactions as well as the high conformational plasticity that may demand an induced-fit mechanism. In particular, the interactions between proteins and single-stranded nucleic acids (i.e., single-stranded DNA and RNA) is very challenging due to their high flexibility. Furthermore, the interface between proteins and single-stranded nucleic acids is often chemically more heterogeneous than the interface between proteins and double-stranded DNA. In this study, we developed a coarse-grained computational model to predict the structure of complexes between proteins and single-stranded nucleic acids. The model was applied to estimate binding affinities and the estimated binding energies agreed well with the corresponding experimental binding affinities. The kinetics of association as well as the specificity of the complexes between proteins and ssDNA are different than those with ssRNA, mostly due to differences in their conformational flexibility.

Structural and Dynamical Order of a Disordered Protein: Molecular Insights into Conformational Switching of PAGE4 at the Systems Level

Folded proteins show a high degree of structural order and undergo (fairly constrained) collective motions related to their functions. On the other hand, intrinsically disordered proteins (IDPs), while lacking a well-defined three-dimensional structure, do exhibit some structural and dynamical ordering, but are less constrained in their motions than folded proteins. The larger structural plasticity of IDPs emphasizes the importance of entropically driven motions. Many IDPs undergo function-related disorder-to-order transitions driven by their interaction with specific binding partners. As experimental techniques become more sensitive and become better integrated with computational simulations, we are beginning to see how the modest structural ordering and large amplitude collective motions of IDPs endow them with an ability to mediate multiple interactions with different partners in the cell. To illustrate these points, here, we use Prostate-associated gene 4 (PAGE4), an IDP implicated in prostate cancer (PCa) as an example. We first review our previous efforts using molecular dynamics simulations based on atomistic AWSEM to study the conformational dynamics of PAGE4 and how its motions change in its different physiologically relevant phosphorylated forms. Our simulations quantitatively reproduced experimental observations and revealed how structural and dynamical ordering are encoded in the sequence of PAGE4 and can be modulated by different extents of phosphorylation by the kinases HIPK1 and CLK2. This ordering is reflected in changing populations of certain secondary structural elements as well as in the regularity of its collective motions. These ordered features are directly correlated with the functional interactions of WT-PAGE4, HIPK1-PAGE4 and CLK2-PAGE4 with the AP-1 signaling axis. These interactions give rise to repeated transitions between (high HIPK1-PAGE4, low CLK2-PAGE4) and (low HIPK1-PAGE4, high CLK2-PAGE4) cell phenotypes, which possess differing sensitivities to the standard PCa therapies, such as androgen deprivation therapy (ADT). We argue that, although the structural plasticity of an IDP is important in promoting promiscuous interactions, the modulation of the structural ordering is important for sculpting its interactions so as to rewire with agility biomolecular interaction networks with significant functional consequences.

Mechanisms for Benzene Dissociation through the Excited State of T4 Lysozyme L99A Mutant

The atomic-level mechanisms that coordinate ligand release from protein pockets are only known for a handful of proteins. Here, we report results from accelerated molecular dynamics simulations for benzene dissociation from the buried cavity of the T4 lysozyme Leu99Ala mutant (L99A). In these simulations, benzene is released through a previously characterized, sparsely populated room-temperature excited state of the mutant, explaining the coincidence for experimentally measured benzene off rate and apo protein slow-timescale NMR relaxation rates between ground and excited states. The path observed for benzene egress is a multistep ligand migration from the buried cavity to ultimate release through an opening between the F/G-, H-, and I-helices and requires a number of cooperative multiresidue and secondary-structure rearrangements within the C-terminal domain of L99A. These rearrangements are identical to those observed along the ground state to excited state transitions characterized by molecular dynamic simulations run on the Anton supercomputer. Analyses of the molecular properties of the residues lining the egress path suggest that protein surface electrostatic potential may play a role in the release mechanism. Simulations of wild-type T4 lysozyme also reveal that benzene-egress-associated dynamics in the L99A mutant are potentially exaggerations of the substrate-processivity-related dynamics of the wild type.

Electrostatic interactions determine entrance/release order of substrates in the catalytic cycle of adenylate kinase

Adenylate kinase is a monomeric phosphotransferase with important biological function in regulating concentration of adenosine triphosphate (ATP) in cells, by transferring the terminal phosphate group from ATP to adenosine monophosphate (AMP) and forming two adenosine diphosphate (ADP) molecules. During this reaction, the kinase may undergo a large conformational transition, forming different states with its substrates. Although many structures of the protein are available, atomic details of the whole process remain unclear. In this article, we use both conventional molecular dynamics (MD) simulation and an enhanced sampling technique called parallel cascade selection MD simulation to explore different conformational states of the Escherichia coli adenylate kinase. Based on the simulation results, we propose a possible entrance/release order of substrates during the catalytic cycle. The substrate-free protein prefers an open conformation, but changes to a closed state once ATP·Mg enters into its binding pocket first and then AMP does. After the reaction of ATP transferring the terminal phosphate group to AMP, ADP·Mg and ADP are released sequentially, and finally the whole catalyze cycle is completed. Detailed contact and distance analysis reveals that the entrance/release order of substrates may be largely controlled by electrostatic interactions between the protein and the substrates.

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.