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

Switching Go̅-Martini for Investigating Protein Conformational Transitions and Associated Protein-Lipid Interactions

Proteins are dynamic biomolecules that can transform between different conformational states when exerting physiological functions, which is difficult to simulate using all-atom methods. Coarse-grained (CG) Go̅-like models are widely used to investigate large-scale conformational transitions, which usually adopt implicit solvent models and therefore cannot explicitly capture the interaction between proteins and surrounding molecules, such as water and lipid molecules. Here, we present a new method, named Switching Go̅-Martini, to simulate large-scale protein conformational transitions between different states, based on the switching Go̅ method and the CG Martini 3 force field. The method is straightforward and efficient, as demonstrated by the benchmarking applications for multiple protein systems, including glutamine binding protein (GlnBP), adenylate kinase (AdK), and β2-adrenergic receptor (β2AR). Moreover, by employing the Switching Go̅-Martini method, we can not only unveil the conformational transition from the E2Pi-PL state to E1 state of the type 4 P-type ATPase (P4-ATPase) flippase ATP8A1-CDC50 but also provide insights into the intricate details of lipid transport.

Evolution shapes interaction patterns for epistasis and specific protein binding in a two-component signaling system

The elegant design of protein sequence/structure/function relationships arises from the interaction patterns between amino acid positions. A central question is how evolutionary forces shape the interaction patterns that encode long-range epistasis and binding specificity. Here, we combined family-wide evolutionary analysis of natural homologous sequences and structure-oriented evolution simulation for two-component signaling (TCS) system. The magnitude-frequency relationship of coupling conservation between positions manifests a power-law-like distribution and the positions with highly coupling conservation are sparse but distributed intensely on the binding surfaces and hydrophobic core. The structure-specific interaction pattern involves further optimization of local frustrations at or near the binding surface to adapt the binding partner. The construction of family-wide conserved interaction patterns and structure-specific ones demonstrates that binding specificity is modulated by both direct intermolecular interactions and long-range epistasis across the binding complex. Evolution sculpts the interaction patterns via sequence variations at both family-wide and structure-specific levels for TCS system.

The Statistical Trends of Protein Evolution: A Lesson from AlphaFold Database

The recent development of artificial intelligence provides us with new and powerful tools for studying the mysterious relationship between organism evolution and protein evolution. In this work, based on the AlphaFold Protein Structure Database (AlphaFold DB), we perform comparative analyses of the proteins of different organisms. The statistics of AlphaFold-predicted structures show that, for organisms with higher complexity, their constituent proteins will have larger radii of gyration, higher coil fractions, and slower vibrations, statistically. By conducting normal mode analysis and scaling analyses, we demonstrate that higher organismal complexity correlates with lower fractal dimensions in both the structure and dynamics of the constituent proteins, suggesting that higher functional specialization is associated with higher organismal complexity. We also uncover the topology and sequence bases of these correlations. As the organismal complexity increases, the residue contact networks of the constituent proteins will be more assortative, and these proteins will have a higher degree of hydrophilic-hydrophobic segregation in the sequences. Furthermore, by comparing the statistical structural proximity across the proteomes with the phylogenetic tree of homologous proteins, we show that, statistical structural proximity across the proteomes may indirectly reflect the phylogenetic proximity, indicating a statistical trend of protein evolution in parallel with organism evolution. This study provides new insights into how the diversity in the functionality of proteins increases and how the dimensionality of the manifold of protein dynamics reduces during evolution, contributing to the understanding of the origin and evolution of lives.

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.

Role of water-bridged interactions in metal ion coupled protein allostery

Allosteric communication between distant parts of proteins controls many cellular functions, in which metal ions are widely utilized as effectors to trigger the allosteric cascade. Due to the involvement of strong coordination interactions, the energy landscape dictating the metal ion binding is intrinsically rugged. How metal ions achieve fast binding by overcoming the landscape ruggedness and thereby efficiently mediate protein allostery is elusive. By performing molecular dynamics simulations for the Ca²⁺ binding mediated allostery of the calmodulin (CaM) domains, each containing two Ca²⁺ binding helix-loop-helix motifs (EF-hands), we revealed the key role of water-bridged interactions in Ca²⁺ binding and protein allostery. The bridging water molecules between Ca²⁺ and binding residue reduces the ruggedness of ligand exchange landscape by acting as a lubricant, facilitating the Ca²⁺ coupled protein allostery. Calcium-induced rotation of the helices in the EF-hands, with the hydrophobic core serving as the pivot, leads to exposure of hydrophobic sites for target binding. Intriguingly, despite being structurally similar, the response of the two symmetrically arranged EF-hands upon Ca²⁺ binding is asymmetric. Breakage of symmetry is needed for efficient allosteric communication between the EF-hands. The key roles that water molecules play in driving allosteric transitions are likely to be general in other metal ion mediated protein allostery.

Natural proteins often utilize allostery in executing a variety of functions. Metal ions are typical cofactors to trigger the allosteric cascade. In this work, using the Ca²⁺ sensor protein calmodulin as the model system, we revealed crucial roles of water-bridged interactions in the metal ion coupled protein allostery. The coordination of the Ca²⁺ to the binding site involves an intermediate in which the water molecule bridges the Ca²⁺ and the liganding residue. The bridging water reduces the free energy barrier height of ligand exchange, therefore facilitating the ligand exchange and allosteric coupling by acting as a lubricant. We also showed that the response of the two symmetrically arranged EF-hand motifs of CaM domains upon Ca²⁺ binding is asymmetric, which is directly attributed to the differing dehydration process of the Ca²⁺ ions and is needed for efficient allosteric communication.

Enhanced Conformational Sampling with an Adaptive Coarse-Grained Elastic Network Model Using Short-Time All-Atom Molecular Dynamics

Compared to all-atom molecular dynamics (AA-MD) simulations, coarse-grained (CG) MD simulations can significantly reduce calculation costs. However, existing CG-MD methods are unsuitable for sampling structures that depart significantly from the initial structure without any biased force. In this study, we developed a new adaptive CG elastic network model (ENM), in which the dynamic cross-correlation coefficient based on short-time AA-MD of at most ns order is considered. By applying Bayesian optimization to search for a suitable parameter among the vast parameter space of adaptive CG-ENM, we succeeded in reducing the searching cost to approximately 10% of those for random sampling and exhaustive sampling. To evaluate the performance of adaptive CG-ENM, we applied the new methodology to adenylate kinase (ADK) and glutamine binding protein (GBP) in the apo state. The results showed that the structural ensembles explored by adaptive CG-ENM could be considerably more diverse than those by conventional ENMs with enhanced sampling such as temperature replica exchange MD and long-time AA-MD of 1 μs. In particular, some of the structures sampled by adaptive ENM are relatively close to the holo-type structures of ADK and GBP. Furthermore, as a challenging task, to demonstrate the advantages of the CG model with lower calculation cost, we applied our new methodology to a larger biomolecule, integrin (αV) in the inactive state. Then, we sampled various structural ensembles, including extended structures that are apparently different from inactive ones.

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.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

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.

Enhanced sampling method with coarse graining of conformational space

The sampling of conformations in the molecular simulations for systems with complicated free energy landscapes is always difficult. Here, we report a method for enhanced sampling based on the coarse-graining of conformational space. In this method, the locally converged region of the conformational space is coarse-grained with its population characterized by the related average residence time and visiting number, and at the same time, the direct simulations inside it are eliminated. The detailed balance is satisfied by updating the visiting number and generating outgoing trajectories of this region. This kind of coarse-graining operation can be further carried out by merging all the neighboring regions which are already converged together. The global equilibrium is achieved when the local equilibrated regions cover all the interested areas of the landscape. We tested the method by applying it to two model potentials and one protein system with multiple-basin energy landscapes. The sampling efficiency is found to be enhanced by more than three orders of magnitude compared to conventional molecular simulations, and are comparable with other widely used enhanced sampling methods. In addition, the kinetic information can also be well captured. All these results demonstrate that our method can help to solve the sampling problems efficiently and precisely without applying high temperatures or biasing potentials.

Energy landscape remodeling mechanism of Hsp70-chaperone-accelerated protein folding

Hsp70 chaperone is one of the key protein machines responsible for the quality control of protein production in cells. Facilitating in vivo protein folding by counteracting misfolding and aggregation is the essence of its biological function. Although the allosteric cycle during its functional actions has been well characterized both experimentally and computationally, the mechanism by which Hsp70 assists protein folding is still not fully understood. In this work, we studied the Hsp70-mediated folding of model proteins with rugged energy landscape by using molecular simulations. Different from the canonical scenario of Hsp70 functioning, which assumes that folding of substrate proteins occurs spontaneously after releasing from chaperones, our results showed that the substrate protein remains in contacts with the chaperone during its folding process. The direct chaperone-substrate interactions in the open conformation of Hsp70 tend to shield the substrate sites prone to form non-native contacts, which therefore avoids the frustrated folding pathway, leading to a higher folding rate and less probability of misfolding. Our results suggest that in addition to the unfoldase and holdase functions widely addressed in previous studies, Hsp70 can facilitate the folding of its substrate proteins by remodeling the folding energy landscape and directing the folding processes, demonstrating the foldase scenario. These findings add new, to our knowledge, insights into the general molecular mechanisms of chaperone-mediated protein folding.

Optimizing Gō-MARTINI Coarse-Grained Model for F-BAR Protein on Lipid Membrane

Coarse-grained (CG) molecular dynamics (MD) simulations allow us to access much larger length and time scales than atomistic MD simulations, providing an attractive alternative to the conventional simulations. Based on the well-known MARTINI CG force field, the recently developed Gō-MARTINI model for proteins describes large-amplitude structural dynamics, which has not been possible with the commonly used elastic network model. Using the Gō-MARTINI model, we conduct MD simulations of the F-BAR Pacsin1 protein on lipid membrane. We observe that structural changes of the non-globular protein are largely dependent on the definition of the native contacts in the Gō model. To address this issue, we introduced a simple cutoff scheme and tuned the cutoff distance of the native contacts and the interaction strength of the Lennard-Jones potentials in the Gō-MARTINI model. With the optimized Gō-MARTINI model, we show that it reproduces structural fluctuations of the Pacsin1 dimer from atomistic simulations. We also show that two Pacsin1 dimers properly assemble through lateral interaction on the lipid membrane. Our work presents a first step towards describing membrane remodeling processes in the Gō-MARTINI CG framework by simulating a crucial step of protein assembly on the membrane.

Funneled energy landscape unifies principles of protein binding and evolution

Most proteins have evolved to spontaneously fold into native structure and specifically bind with their partners for the purpose of fulfilling biological functions. According to Darwin, protein sequences evolve through random mutations, and only the fittest survives. The understanding of how the evolutionary selection sculpts the interaction patterns for both biomolecular folding and binding is still challenging. In this study, we incorporated the constraint of functional binding into the selection fitness based on the principle of minimal frustration for the underlying biomolecular interactions. Thermodynamic stability and kinetic accessibility were derived and quantified from a global funneled energy landscape that satisfies the requirements of both the folding into the stable structure and binding with the specific partner. The evolution proceeds via a bowl-like evolution energy landscape in the sequence space with a closed-ring attractor at the bottom. The sequence space is increasingly reduced until this ring attractor is reached. The molecular-interaction patterns responsible for folding and binding are identified from the evolved sequences, respectively. The residual positions participating in the interactions responsible for folding are highly conserved and maintain the hydrophobic core under additional evolutionary constraints of functional binding. The positions responsible for binding constitute a distributed network via coupling conservations that determine the specificity of binding with the partner. This work unifies the principles of protein binding and evolution under minimal frustration and sheds light on the evolutionary design of proteins for functions.

Role of substrate-product frustration on enzyme functional dynamics

Natural enzymes often have enormous catalytic power developed by evolution. Revealing the underlying physical strategy used by enzymes to achieve high catalysis efficiency is one of the central focuses in the field of biological physics. Our recent work demonstrated that multisubstrate enzymes can utilize steric frustration encountered in the substrate-product cobound complex to overcome the bottleneck of the enzymatic cycle [W. Li et al., Phys. Rev. Lett. 122, 238102 (2019)10.1103/PhysRevLett.122.238102]. However, the key atomic-level interactions by which the steric frustration contributes to the enzymatic cycle remain elusive. In this work we study the microscopic mechanism for the role of the substrate-product frustration on the key physical steps in the enzymatic cycle of adenylate kinase (AdK), a multisubstrate enzyme catalyzing the reversible phosphoryl transfer reaction ATP+AMP⇋ADP+ADP. By using atomistic molecular dynamics simulations with enhanced sampling, we showed that the competitive interactions from the phosphate groups of the substrate ATP and product ADP in the ATP-ADP cobound complex of the AdK lead to local frustration in the binding pockets. Such local frustration disrupts the hydrogen bond network around the binding pockets, which causes lowered barrier height for the opening of the enzyme conformations and expedited release of the bottleneck product ADP. Our results directly demonstrated from the atomistic level that the local frustration in the active sites of the enzyme can be utilized to facilitate the key physical steps of the enzymatic cycle, providing numerical evidence to the predictions of the previous theoretical work.

Bottom-Up Meets Top-Down: The Crossroads of Multiscale Chromatin Modeling

Chromatin can be viewed as a hierarchically structured fiber that regulates gene expression. It consists of a complex network of DNA and proteins whose characteristic dynamical modes facilitate compaction and rearrangement in the cell nucleus. These modes stem from chromatin's fundamental unit, the nucleosome, and their effects are propagated across length scales. Understanding the effects of nucleosome dynamics on the chromatin fiber, primarily through post-translational modifications that occur on the histones, is of central importance to epigenetics. Within the last decade, imaging and chromosome conformation capture techniques have revealed a number of structural and statistical features of the packaged chromatin fiber at a hitherto unavailable level of resolution. Such experiments have led to increased efforts to develop polymer models that aim to reproduce, explain, and predict the contact probability scaling and density heterogeneity. At nanometer scales, available models have focused on the role of the nucleosome and epigenetic marks on local chromatin structure. At micrometer scales, existing models have sought to explain scaling laws and density heterogeneity. Less work, however, has been done to reconcile these two approaches: bottom-up and top-down models of chromatin. In this perspective, we highlight the multiscale simulation models that are driving toward an understanding of chromatin structure and function, from the nanometer to the micron scale, and we highlight areas of opportunity and some of the prospects for new frameworks that bridge these two scales. Taken together, experimental and modeling advances over the last few years have established a robust platform for the study of chromatin fiber structure and dynamics, which will be of considerable use to the chromatin community in developing an understanding of the interplay between epigenomic regulation and molecular structure.

Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning

Accompanied with an increase of revealed biomolecular structures owing to advancements in structural biology, the molecular dynamics (MD) approach, especially coarse-grained (CG) MD suitable for macromolecules, is becoming increasingly important for elucidating their dynamics and behavior. In fact, CG-MD simulation has succeeded in qualitatively reproducing numerous biological processes for various biomolecules such as conformational changes and protein folding with reasonable calculation costs. However, CG-MD simulations strongly depend on various parameters, and selecting an appropriate parameter set is necessary to reproduce a particular biological process. Because exhaustive examination of all candidate parameters is inefficient, it is important to identify successful parameters. Furthermore, the successful region, in which the desired process is reproducible, is essential for describing the detailed mechanics of functional processes and environmental sensitivity and robustness. We propose an efficient search method for identifying the successful region by using two machine learning techniques, Bayesian optimization and active learning. We evaluated its performance using F1-ATPase, a biological rotary motor, with CG-MD simulations. We successfully identified the successful region with lower computational costs (12.3% in the best case) without sacrificing accuracy compared to exhaustive search. This method can accelerate not only parameter search but also biological discussion of the detailed mechanics of functional processes and environmental sensitivity based on MD simulation studies.

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.

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

Can Conformational Changes of Proteins Be Represented in Torsion Angle Space? A Study with Rescaled Ridge Regression

Torsion angles are the natural degrees of freedom of protein structures. The ability to determine torsional variations corresponding to observed changes in Cartesian coordinates is highly valuable, notably to investigate the mechanisms of functional conformational changes or to develop computational models of protein dynamics. This issue is far from trivial in practice since the impact of modifying one torsion angle strongly depends on all other angles, and the compounding effects of small variations in bond lengths and valence angles can completely disrupt a protein fold. We demonstrate that naive strategies, such as directly comparing torsion angles between structures without correcting for variations in bond lengths and valence angles or fitting torsional variations without a proper regularization scheme, fail at producing an adequate representation of conformational changes in internal coordinates. In contrast, rescaled ridge regression, a method recently introduced to regularize multidimensional regressions with correlated explanatory variables, is shown to consistently identify a minimal set of torsion angles variations that closely reproduce changes in Cartesian coordinates. This torsional representation of conformational changes is shown to be robust to the choice of experimental structures. It also provides a better agreement with theoretical models of protein dynamics than the Cartesian representation, regarding notably the predominance of low-frequency normal modes in functional motions and the presence, in predicted equilibrium dynamics, of hints of natural selection for specific functional motions. The software is available at https://github.com/ugobas/tnm .

Thermodynamics and folding landscapes of large proteins from a statistical mechanical model

Statistical mechanical models that afford an intermediate resolution between macroscopic chemical models and all-atom simulations have been successful in capturing folding behaviors of many small single-domain proteins. However, the applicability of one such successful approach, the Wako-Saitô-Muñoz-Eaton (WSME) model, is limited by the size of the protein as the number of conformations grows exponentially with protein length. In this work, we surmount this size limitation by introducing a novel approximation that treats stretches of 3 or 4 residues as blocks, thus reducing the phase space by nearly three orders of magnitude. The performance of the 'bWSME' model is validated by comparing the predictions for a globular enzyme (RNase H) and a repeat protein (IκBα), against experimental observables and the model without block approximation. Finally, as a proof of concept, we predict the free-energy surface of the 370-residue, multi-domain maltose binding protein and identify an intermediate in good agreement with single-molecule force-spectroscopy measurements. The bWSME model can thus be employed as a quantitative predictive tool to explore the conformational landscapes of large proteins, extract the structural features of putative intermediates, identify parallel folding paths, and thus aid in the interpretation of both ensemble and single-molecule experiments.

Protein plasticity driven by disorder and collapse governs the heterogeneous binding of CytR to DNA

The amplitude of thermodynamic fluctuations in biological macromolecules determines their conformational behavior, dimensions, nature of phase transitions and effectively their specificity and affinity, thus contributing to fine-tuned molecular recognition. Unique among large-scale conformational changes in proteins are temperature-induced collapse transitions in intrinsically disordered proteins (IDPs). Here, we show that CytR DNA-binding domain, an IDP that folds on binding DNA, undergoes a coil-to-globule transition with temperature in the absence of DNA while exhibiting energetically decoupled local and global structural rearrangements, and maximal thermodynamic fluctuations at the optimal bacterial growth temperature. The collapse is shown to be a continuous transition through a combination of statistical-mechanical modeling and all-atom implicit solvent simulations. Surprisingly, CytR binds single-site cognate DNA with negative cooperativity, described by Hill coefficients less than one, resulting in a graded binding response. We show that heterogeneity arising from varying binding-competent CytR conformations or orientations at the single-molecular level contributes to negative binding cooperativity at the level of bulk measurements due to the conflicting requirements of collapse transition, large fluctuations and folding-upon-binding. Our work reports strong evidence for functionally driven thermodynamic fluctuations in determining the extent of collapse and disorder with implications in protein search efficiency of target DNA sites and regulation.

Consequences of Hydrophobic Nanotube Binding on the Functional Dynamics of Signaling Protein Calmodulin

The wide applications of nanomaterials in industry and our daily life have raised growing concerns on their toxicity to human body. Increasing evidence links the cytotoxicity of nanoparticles to the disruption of cellular signaling pathways. Here, we report a computational study on the mechanisms of the cytotoxicity of carbon nanotubes (CNTs) by investigating the direct impacts of CNTs on the functional motions of calmodulin (CaM), which is one of the most important signaling proteins in a cell, and its signaling function relies on the Ca2+ binding-coupled conformational switching. Computational simulations with a coarse-grained model showed that binding of CNTs modifies the conformational equilibrium of CaM and induces the closed-to-open conformational transition, leading to the loss of its Ca2+-sensing ability. In addition, the binding of CNTs drastically increases the calcium affinity of CaM, which may disrupt the Ca2+ homeostasis in a cell. These results suggest that the binding of hydrophobic nanotubes not only inhibits the signaling function of CaM as a calcium sensor but also renders CaM to toxic species through sequestering Ca2+ from other competing calcium-binding proteins, suggesting a new physical mechanism of the cytotoxicity of nanoparticles.

Binding of Copper Ions with Octapeptide Region in Prion Protein: Simulations with Charge Transfer Model

Copper ions are important cofactors of many metalloproteins. The binding dynamics of proteins to the copper ion is important for biological functions but is less understood at the microscopic level. What are the key factors determining the recognition and the stabilization of the copper ion during the binding? Our work investigates the binding dynamics of the copper ion with a simple system (the N-terminus of PrP) using simulation methods. To precisely characterize the protein?ion interaction, we build up an effective copper?peptide force field based on quantum chemistry calculations. In our model, the effects of charge transfer, protonation/deprotonation, and induced polarization are considered. With this force field, we successfully characterize the local structures and the complex interactions of the octapeptide around the copper ion. Furthermore, using an enhanced sampling method, the binding/unbinding processes of the copper ion with the octapeptide are simulated. Free-energy landscapes are generated in consequence, and multiple binding pathways are characterized. It is observed that various native ligands contribute differently to the binding processes. Some residues are related to the capture of the ion (behaving like ?arm?s), and some others contribute to the stabilization of the coordination structure (acting like ?core?s). These different interactions induce various pathways. Besides, a nonnative binding ligand is determined, and it has essential contributions and modulations to the binding pathways. With all these results, the picture of copper?octapeptide binding is outlined. These features are believed to happen in many ion?peptide interactions, such as the cooperative stabilization between the coordinations with neighboring backbone nitrogens and an auxiliary intermediate coordination with the neighboring oxygen from the N-terminal direction. We believe that our studies are valuable to understand the complicated ion?peptide binding processes.

Tunable order-disorder continuum in protein-DNA interactions

DNA-binding protein domains (DBDs) sample diverse conformations in equilibrium facilitating the search and recognition of specific sites on DNA over millions of energetically degenerate competing sites. We hypothesize that DBDs have co-evolved to sense and exploit the strong electric potential from the array of negatively charged phosphate groups on DNA. We test our hypothesis by employing the intrinsically disordered DBD of cytidine repressor (CytR) as a model system. CytR displays a graded increase in structure, stability and folding rate on increasing the osmolarity of the solution that mimics the non-specific screening by DNA phosphates. Electrostatic calculations and an Ising-like statistical mechanical model predict that CytR exhibits features of an electric potential sensor modulating its dimensions and landscape in a unique distance-dependent manner, while DNA plays the role of a non-specific macromolecular chaperone. Accordingly, CytR binds its natural half-site faster than the diffusion-controlled limit and even random DNA conforming to an electrostatic-steering binding mechanism. Our work unravels for the first time the synergistic features of a natural electrostatic potential sensor, a novel binding mechanism driven by electrostatic frustration and disorder, and the role of DNA in promoting distance-dependent protein structural transitions critical for switching between specific and non-specific DNA-binding modes.

1CPN: A coarse-grained multi-scale model of chromatin

A central question in epigenetics is how histone modifications influence the 3D structure of eukaryotic genomes and, ultimately, how this 3D structure is manifested in gene expression. The wide range of length scales that influence the 3D genome structure presents important challenges; epigenetic modifications to histones occur on scales of angstroms, yet the resulting effects of these modifications on genome structure can span micrometers. There is a scarcity of computational tools capable of providing a mechanistic picture of how molecular information from individual histones is propagated up to large regions of the genome. In this work, a new molecular model of chromatin is presented that provides such a picture. This new model, referred to as 1CPN, is structured around a rigorous multiscale approach, whereby free energies from an established and extensively validated model of the nucleosome are mapped onto a reduced coarse-grained topology. As such, 1CPN incorporates detailed physics from the nucleosome, such as histone modifications and DNA sequence, while maintaining the computational efficiency that is required to permit kilobase-scale simulations of genomic DNA. The 1CPN model reproduces the free energies and dynamics of both single nucleosomes and short chromatin fibers, and it is shown to be compatible with recently developed models of the linker histone. It is applied here to examine the effects of the linker DNA on the free energies of chromatin assembly and to demonstrate that these free energies are strongly dependent on the linker DNA length, pitch, and even DNA sequence. The 1CPN model is implemented in the LAMMPS simulation package and is distributed freely for public use.

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.

A new method for the construction of coarse-grained models of large biomolecules from low-resolution cryo-electron microscopy data

The rapid development of cryo-electron microscopy (cryo-EM) has led to the generation of significant low-resolution electron density data of biomolecules. However, the atomistic details of huge biomolecules usually cannot be obtained because it is very difficult to construct all-atom models for MD simulations. Thus, it is still a challenge to make use of the rich low-resolution cryo-EM data for computer simulation and functional study. In this study, we proposed a new method called Convolutional and K-means Coarse-Graining (CK-CG) for the efficient coarse-graining of large biological systems. Using the CK-CG method, we could directly map the cryo-EM data into coarse-grained (CG) beads. Furthermore, the CG beads were parameterized with an empirical harmonic potential to construct a new CG model. We subjected the CK-CG models of the fibrillar protein assemblies F-actin and collagen to external forces in pulling dynamic simulations to assess their mechanical response. The agreement between the estimated tensile stiffness between CG models and experiments demonstrates the validity of the CK-CG method. Thus, our method provides a practical strategy for the direct construction of a structural model from low-resolution data for biological function studies.

Extracting collective motions underlying nucleosome dynamics via nonlinear manifold learning

The identification of effective collective variables remains a challenge in molecular simulations of complex systems. Here, we use a nonlinear manifold learning technique known as the diffusion map to extract key dynamical motions from a complex biomolecular system known as the nucleosome: a DNA-protein complex consisting of a DNA segment wrapped around a disc-shaped group of eight histone proteins. We show that without any a priori information, diffusion maps can identify and extract meaningful collective variables that characterize the motion of the nucleosome complex. We find excellent agreement between the collective variables identified by the diffusion map and those obtained manually using a free energy-based analysis. Notably, diffusion maps are shown to also identify subtle features of nucleosome dynamics that did not appear in those manually specified collective variables. For example, diffusion maps identify the importance of looped conformations in which DNA bulges away from the histone complex that are important for the motion of DNA around the nucleosome. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and for identifying their characteristic slow modes.

The Free Energy Landscape of Internucleosome Interactions and Its Relation to Chromatin Fiber Structure

The supramolecular chromatin fiber is governed by molecular scale energetics and interactions. Such energetics originate from the fiber's building block, the nucleosome core particle (NCP). In recent years, the chromatin fiber has been examined through perturbative methods in attempts to extract the energetics of nucleosome association in the fiber. This body of work has led to different results from experiments and simulations concerning the nucleosome-nucleosome energetics. Here, we expand on previous experiments and use coarse-grained simulations to evaluate the energetics inherent to nucleosomes across a variety of parameters in configurational and environmental space. Through this effort, we are able to uncover molecular processes that are critical to understanding the 30 nm chromatin fiber structure. In particular, we describe the NCP-NCP interactions by relying on an anisotropic energetic landscape, rather than a single potential energy value. The attractions in that landscape arise predominantly from the highly anisotropic interactions provided by the NCP histone N-terminal domain (NTD) tails. Our results are found to be in good agreement with recent nucleosome interaction experiments that suggest a maximum interaction energy of 2.69k _B T. Furthermore, we examine the influence of crucial epigenetic modifications, such as acetylation of the H4 tail, and how they modify the underlying landscape. Our results for acetylated NCP interactions are also in agreement with experiment. We additionally find an induced chirality in NCP-NCP interactions upon acetylation that reduces interactions which would correspond to a left-handed superhelical chromatin fiber.

Local frustration around enzyme active sites

Conflicting biological goals often meet in the specification of protein sequences for structure and function. Overall, strong energetic conflicts are minimized in folded native states according to the principle of minimal frustration, so that a sequence can spontaneously fold, but local violations of this principle open up the possibility to encode the complex energy landscapes that are required for active biological functions. We survey the local energetic frustration patterns of all protein enzymes with known structures and experimentally annotated catalytic residues. In agreement with previous hypotheses, the catalytic sites themselves are often highly frustrated regardless of the protein oligomeric state, overall topology, and enzymatic class. At the same time a secondary shell of more weakly frustrated interactions surrounds the catalytic site itself. We evaluate the conservation of these energetic signatures in various family members of major enzyme classes, showing that local frustration is evolutionarily more conserved than the primary structure itself.

Rotational Mechanism Model of the Bacterial V1 Motor Based on Structural and Computational Analyses

V₁-ATPase exemplifies the ubiquitous rotary motor, in which a central shaft DF complex rotates inside a hexagonally arranged catalytic A₃B₃ complex, powered by the energy from ATP hydrolysis. We have recently reported a number of crystal structures of the Enterococcus hirae A₃B₃DF (V₁) complex corresponding to its nucleotide-bound intermediate states, namely the forms waiting for ATP hydrolysis (denoted as catalytic dwell), ATP binding (ATP-binding dwell), and ADP release (ADP-release dwell) along the rotatory catalytic cycle of ATPase. Furthermore, we have performed microsecond-scale molecular dynamics simulations and free-energy calculations to investigate the conformational transitions between these intermediate states and to probe the long-time dynamics of the molecular motor. In this article, the molecular structure and dynamics of the V₁-ATPase are reviewed to bring forth a unified model of the motor’s remarkable rotational mechanism.

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.

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.

Elucidation of the structural stability and dynamics of heterogeneous intermediate ensembles in unfolding pathway of the N-terminal domain of TDP-43

The N-terminal domain of the RNA binding protein TDP-43 (NTD) is essential to both physiology and proteinopathy; however, elucidation of its folding/unfolding still remains a major quest. In this study, we have investigated the biophysical behavior of intermediate ensembles employing all-atom molecular dynamics simulations in 8 M urea accelerated with high temperatures to achieve unfolded states in a confined computation time. The cumulative results of the 2.75 μs simulations show that unfolding of the NTD at 350 K evolves through different stable and meta-stable intermediate states. The free-energy landscape reveals two meta-stable intermediates (IN and IU) stabilized by non-native interactions, which are largely hydrophilic and highly energetically frustrated. A single buried tryptophan residue, W80, undergoes solvent exposure to different extents during unfolding; this suggests a structurally heterogeneous population of intermediate ensembles. Furthermore, the structure properties of the IN state show a resemblance to the molten globule (MG) state with most of the secondary structures intact. The unfolding of the NTD is initiated by the loss of β-strands, and the unfolded (U) states exhibit a population of non-native α-helices. These non-native unfolded intermediate ensembles may mediate protein oligomerization, leading to the formation of pathological, irreversible aggregates, characteristics of disease pathogenesis.

Interactions of HP1 Bound to H3K9me3 Dinucleosome by Molecular Simulations and Biochemical Assays

Heterochromatin protein 1 (HP1), associated with heterochromatin formation, recognizes an epigenetically repressive marker, trimethylated lysine 9 in histone H3 (H3K9me3), and generally contributes to long-term silencing. How HP1 induces heterochromatin is not fully understood. Recent experiments suggested that not one, but two nucleosomes provide a platform for this recognition. Integrating previous and new biochemical assays with computational modeling, we provide near-atomic structural models for HP1 binding to the dinucleosomes. We found that the dimeric HP1α tends to bind two H3K9me3s that are in adjacent nucleosomes, thus bridging two nucleosomes. We identified, to our knowledge, a novel DNA binding motif in the hinge region that is specific to HP1α and is essential for recognizing the H3K9me3 sites of two nucleosomes. An HP1 isoform, HP1γ, does not easily bridge two nucleosomes in extended conformations because of the absence of the above binding motif and its shorter hinge region. We propose a molecular mechanism for chromatin structural changes caused by HP1.

Metal cofactor modulated folding and target recognition of HIV-1 NCp7

The HIV-1 nucleocapsid 7 (NCp7) plays crucial roles in multiple stages of HIV-1 life cycle, and its biological functions rely on the binding of zinc ions. Understanding the molecular mechanism of how the zinc ions modulate the conformational dynamics and functions of the NCp7 is essential for the drug development and HIV-1 treatment. In this work, using a structure-based coarse-grained model, we studied the effects of zinc cofactors on the folding and target RNA(SL3) recognition of the NCp7 by molecular dynamics simulations. After reproducing some key properties of the zinc binding and folding of the NCp7 observed in previous experiments, our simulations revealed several interesting features in the metal ion modulated folding and target recognition. Firstly, we showed that the zinc binding makes the folding transition states of the two zinc fingers less structured, which is in line with the Hammond effect observed typically in mutation, temperature or denaturant induced perturbations to protein structure and stability. Secondly, We showed that there exists mutual interplay between the zinc ion binding and NCp7-target recognition. Binding of zinc ions enhances the affinity between the NCp7 and the target RNA, whereas the formation of the NCp7-RNA complex reshapes the intrinsic energy landscape of the NCp7 and increases the stability and zinc affinity of the two zinc fingers. Thirdly, by characterizing the effects of salt concentrations on the target RNA recognition, we showed that the NCp7 achieves optimal balance between the affinity and binding kinetics near the physiologically relevant salt concentrations. In addition, the effects of zinc binding on the inter-domain conformational flexibility and folding cooperativity of the NCp7 were also discussed.

Exploration of Multistate Conformational Dynamics upon Ligand Binding of a Monomeric Enzyme Involved in Pyrophosphoryl Transfer

HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) is a monomeric protein with 158 residues, which undergoes large-scale conformational changes between apo, open, and holo states responding to ligand binding for its function. It has been explored widely as an excellent target for potential antibacterial drug development. However, little is known about how conformational dynamics between the native states influences the substrate recognition and the functionality of enzymatic catalysis. Here, we report a coarse-grained triple-basin structure-based model upon ligand binding to describe such multiple-state system by the molecular dynamics simulation. With our model, we have made theoretical predictions that are in good agreement with the experimental measurements. Our results revealed the intrinsic conformational fluctuations between apo and open states without ligand binding. We found that HPPK can switch to the activated holo state upon the ordered binding of the two ligands (ATP and HP). We uncovered the underlying mechanism by which major induced fit and minor population shift pathways coexist upon ligand binding by quantitative flux analysis. Additionally, we pointed out the structural origin for the conformational changes and identified the key residues as well as contact interactions. We further explored the temperature effect on the conformational distributions and pathway weights. It gave strong support that higher temperatures promote population shift, while the induced fit pathway is always the predominant activation route of the HPPK system. These findings will provide significant insights of the mechanisms of the multistate conformational dynamics of HPPK upon ligand binding.

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.

Multiscale molecular dynamics simulations of rotary motor proteins

Protein functions require specific structures frequently coupled with conformational changes. The scale of the structural dynamics of proteins spans from the atomic to the molecular level. Theoretically, all-atom molecular dynamics (MD) simulation is a powerful tool to investigate protein dynamics because the MD simulation is capable of capturing conformational changes obeying the intrinsically structural features. However, to study long-timescale dynamics, efficient sampling techniques and coarse-grained (CG) approaches coupled with all-atom MD simulations, termed multiscale MD simulations, are required to overcome the timescale limitation in all-atom MD simulations. Here, we review two examples of rotary motor proteins examined using free energy landscape (FEL) analysis and CG-MD simulations. In the FEL analysis, FEL is calculated as a function of reaction coordinates, and the long-timescale dynamics corresponding to conformational changes is described as transitions on the FEL surface. Another approach is the utilization of the CG model, in which the CG parameters are tuned using the fluctuation matching methodology with all-atom MD simulations. The long-timespan dynamics is then elucidated straightforwardly by using CG-MD simulations.

Frustration, function and folding

Natural protein molecules are exceptional polymers. Encoded in apparently random strings of amino-acids, these objects perform clear physical tasks that are rare to find by simple chance. Accurate folding, specific binding, powerful catalysis, are examples of basic chemical activities that the great majority of polypeptides do not display, and are thought to be the outcome of the natural history of proteins. Function, a concept genuine to Biology, is at the core of evolution and often conflicts with the physical constraints. Locating the frustration between discrepant goals in a recurrent system leads to fundamental insights about the chances and necessities that shape the encoding of biological information.

In silico evidence for sequence-dependent nucleosome sliding

Nucleosomes represent the basic building block of chromatin and provide an important mechanism by which cellular processes are controlled. The locations of nucleosomes across the genome are not random but instead depend on both the underlying DNA sequence and the dynamic action of other proteins within the nucleus. These processes are central to cellular function, and the molecular details of the interplay between DNA sequence and nucleosome dynamics remain poorly understood. In this work, we investigate this interplay in detail by relying on a molecular model, which permits development of a comprehensive picture of the underlying free energy surfaces and the corresponding dynamics of nucleosome repositioning. The mechanism of nucleosome repositioning is shown to be strongly linked to DNA sequence and directly related to the binding energy of a given DNA sequence to the histone core. It is also demonstrated that chromatin remodelers can override DNA-sequence preferences by exerting torque, and the histone H4 tail is then identified as a key component by which DNA-sequence, histone modifications, and chromatin remodelers could in fact be coupled.

Rotation Mechanism of Molecular Motor V1-ATPase Studied by Multiscale Molecular Dynamics Simulation

Enterococcus hirae V₁-ATPase is a molecular motor composed of the A₃B₃ hexamer ring and the central stalk. In association with ATP hydrolysis, three catalytic AB pairs in the A₃B₃ ring undergo conformational changes, which lead to a 120° rotation of the central stalk. To understand how the conformational changes of three catalytic pairs induce the 120° rotation of the central stalk, we performed multiscale molecular dynamics (MD) simulations in which coarse-grained and all-atom MD simulations were combined using a fluctuation matching methodology. During the rotation, a catalytic AB pair spontaneously adopted an intermediate conformation, which was not included in the initial inputs of the simulations and was essentially close to the “bindable-like” structure observed in a recently solved crystal structure. Furthermore, the creation of a space between the bindable-like and tight pairs was required for the central stalk to rotate without steric hindrance. These cooperative rearrangements of the three catalytic pairs are crucial for the rotation of the central stalk.

Piecing Together the Allosteric Patterns of Chaperonin GroEL

Despite considerable efforts, elucidating the allostery of large macromolecular assemblies at a molecular level in solution remains technically challenging due to its structural complexity. Here we have employed an approach combining amide backbone hydrogen/deuterium exchange coupled with mass spectrometry, fluorescence spectroscopy, and molecular simulations to characterize allosteric patterns of chaperonin GroEL, an ∼800 kDa tetradecamer from E. coli. Using available crystal structures of GroEL, we quantitatively map out GroEL allosteric changes in solution by resolving exchange behaviors of 133 overlapping proteolytic peptides with more than 95% sequence coverage. This comprehensive analysis gives a refined resolution down to five residues to pilot the GroEL allosteric determinants, of which the localized dynamics is monitored by tryptophan-mutated GroEL. Furthermore, the GroEL conformational transition is evaluated by molecular dynamics simulations with an atomic-interaction-based coarse-grained model. Collectively, we provide a practical methodology to analyze GroEL allostery in solution.

Knowledge-based entropies improve the identification of native protein structures

Evaluating protein structures requires reliable free energies with good estimates of both potential energies and entropies. Although there are many demonstrated successes from using knowledge-based potential energies, computing entropies of proteins has lagged far behind. Here we take an entirely different approach and evaluate knowledge-based conformational entropies of proteins based on the observed frequencies of contact changes between amino acids in a set of 167 diverse proteins, each of which has two alternative structures. The results show that charged and polar interactions break more often than hydrophobic pairs. This pattern correlates strongly with the average solvent exposure of amino acids in globular proteins, as well as with polarity indices and the sizes of the amino acids. Knowledge-based entropies are derived by using the inverse Boltzmann relationship, in a manner analogous to the way that knowledge-based potentials have been extracted. Including these new knowledge-based entropies almost doubles the performance of knowledge-based potentials in selecting the native protein structures from decoy sets. Beyond the overall energy-entropy compensation, a similar compensation is seen for individual pairs of interacting amino acids. The entropies in this report have immediate applications for 3D structure prediction, protein model assessment, and protein engineering and design.

Packing energetics determine the folding routes of the RNase-H proteins

The RNase-H proteins show a diverse range of folding routes with structurally distinct folding nuclei.