Hydrogen bond networks determine emergent mechanical and thermodynamic properties across a protein family

Correlation of Solvent Interaction Analysis Signatures with Thermodynamic Properties and In Silico Calculations of the Structural Effects of Point Mutations in Two Proteins

The partition behavior of single and double-point mutants of bacteriophage T4 lysozyme (T4 lysozyme) and staphylococcal nuclease A was examined in different aqueous two-phase systems (ATPSs) and studied by Solvent Interaction Analysis (SIA). Additionally, the solvent accessible surface area (SASA) of modeled mutants of both proteins was calculated. The in silico calculations and the in vitro analyses of the staphylococcal nuclease and T4 lysozyme mutants correlate, indicating that the partition analysis in ATPSs provides a valid descriptor (SIA signature) covering various protein features, such as structure, structural dynamics, and conformational stability.

Number of Hydrogen Bonds per Unit Solvent Accessible Surface Area: A Descriptor of Functional States of Proteins

Proteins function close to native and near-native conformations. These states are evolutionarily selected to ensure the effect of mutations is minimized. The structural organization of a protein is hierarchical and modular, which reduces the dimensionality of the configurational space of the native states. Thus, finding appropriate descriptors that define the native state among all possible states of a protein is a problem of immense interest. The present study explores the correlation between solvent accessible surface areas (SASAs) and different intraprotein as well as protein-water hydrogen bonds of 55 single-chain globular proteins from four different structural classes (all α, all β, α+β, and α/β), 16 multichain proteins, and 4 macromolecular complexes. A systematic analysis of the solvent accessible surface area and intraprotein and protein-water hydrogen bonds suggests a linear relationship between SASAs and hydrogen bonds. The number of protein-water hydrogen bonds per unit SASA ranges from 3 to 4 for all the different structural protein classes. In contrast, the number of intramolecular hydrogen bonds per unit SASA, including the mainchain-mainchain, mainchain-sidechain, and sidechain-sidechain, varies between 0.75 to 2. The solvation free energy of a protein linearly decreases with SASA. Our study also shows that the solvation free energy/SASA varies from -75 to -105 kJ mol^-1 nm^-2 across all the native states studied here. The number conservancy of intraprotein hydrogen bonds per unit SASA possibly imparts structural stability to the native structure. On the other hand, 3-4 protein-water hydrogen bonds per unit SASA are possibly required to maintain a balance between the solubility and functionality of the native states. This study provides a basis for synthetic biologists to design new folds with improved functionality.

Encapsulation of vitexin-rhamnoside based on zein/pectin nanoparticles improved its stability and bioavailability

To improve the solubility, stability, and bioavailability of vitexin-rhamnoside (VR) isolated from hawthorn, it was encapsulated by the zein-pectin nanoparticles system. When the mass ratio of zein to pectin was 1:4, the particle size of nanoparticles was 222.7 nm, and the encapsulation efficiency of VR was 67%. Analysis with the scanning electron microscope (SEM), fourier transform infrared spectroscopy (FTIR) and atomic force microscopy (AFM) revealed that the zein-VR-pectin nanoparticles were spherical and uniformly distributed. The hydrogen bonding and electrostatic interactions were the main forces to assemble the nanoparticles. The nanoparticle had good stability at pH 3-8.5 with particle sizes ranging from 234 to 251 nm, and the nanoparticles were able to resist the relatively lower ionic strength. In vitro simulated digestion and rat in vivo intestinal perfusion experiments showed that the nanoparticles exhibited significant slow-release properties and the highest absorption rate in the duodenal segment of rats, with Ka and Papp of 0.830 ± 0.11 and 17.004 ± 1.09. These results provided a theoretical and technological approach for the construction of flavonoids delivery system with slow-release properties and improved bioavailability.

Protein Function Analysis through Machine Learning

Machine learning (ML) has been an important arsenal in computational biology used to elucidate protein function for decades. With the recent burgeoning of novel ML methods and applications, new ML approaches have been incorporated into many areas of computational biology dealing with protein function. We examine how ML has been integrated into a wide range of computational models to improve prediction accuracy and gain a better understanding of protein function. The applications discussed are protein structure prediction, protein engineering using sequence modifications to achieve stability and druggability characteristics, molecular docking in terms of protein-ligand binding, including allosteric effects, protein-protein interactions and protein-centric drug discovery. To quantify the mechanisms underlying protein function, a holistic approach that takes structure, flexibility, stability, and dynamics into account is required, as these aspects become inseparable through their interdependence. Another key component of protein function is conformational dynamics, which often manifest as protein kinetics. Computational methods that use ML to generate representative conformational ensembles and quantify differences in conformational ensembles important for function are included in this review. Future opportunities are highlighted for each of these topics.

Experimental and theoretical study on converting myoglobin into a stable domain-swapped dimer by utilizing a tight hydrogen bond network at the hinge region

Various factors, such as helical propensity and hydrogen bonds, control protein structures. A frequently used model protein, myoglobin (Mb), can perform 3D domain swapping, in which the loop at the hinge region is converted to a helical structure in the dimer. We have previously succeeded in obtaining monomer–dimer equilibrium in the native state by introducing a high α-helical propensity residue, Ala, to the hinge region. In this study, we focused on another factor that governs the protein structure, hydrogen bonding. X-ray crystal structures and thermodynamic studies showed that the myoglobin dimer was stabilized over the monomer when keeping His82 to interact with Lys79 and Asp141 through water moleclues and mutating Leu137, which was located close to the H-bond network at the dimer hinge region, to a hydrophilic amino acid (Glu or Asp). Molecular dynamics simulation studies confirmed that the number of H-bonds increased and the α-helices at the hinge region became more rigid for mutants with a tighter H-bond network, supporting the hypothesis that the myoglobin dimer is stabilized when the H-bond network at the hinge region is enhanced. This demonstrates the importance and utility of hydrogen bonds for designing a protein dimer from its monomer with 3D domain swapping.

The tight H-bond network enhanced the helices at the hinge region and stabilized the myoglobin dimer, providing a unique example of using H-bonds in the design of a dimeric protein through 3D domain swapping.

Computational study of the intermolecular interactions and their effect on the UV-visible spectra of the ternary liquid mixture of benzene, ethanol and propylene glycol

Quantum chemical calculations are well-equipped to provide answers to the questions regarding the different aspects of intermolecular interactions. We investigate the benzene, ethanol and 1,2 propanediol ternary mixture with theoretical as well as experimental UV-Vis spectroscopy. An extensive theoretical study on the molecular structure and UV-Vis spectral analysis was undertaken using density functional theory (DFT) method. Structural parameter analysis and the HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) energy gap help to describe the possible interaction between molecules in dimer and in combination. Interaction energy has been calculated from topological study. Time-dependent density functional theory (TDDFT) calculations on dimer/cluster in gas phase help to understand the effect of the molecular interaction on the overall spectral shift and related intensity variation. Our results show that in the ternary mixture, the interaction energies of the interactions are π-π interaction: 0.52-2.57 kcal/mol, Hp-π interaction: 1.15 kcal/mol and H-bonding: 2.49 to 4.46 kcal/mol. The π-π interaction and H-bonding cause red shift in absorption spectra while Hp-π interaction causes blue shift. In the ternary mixture, the strength of different kinds of interaction depends on the concentration, and as each interaction has its own effect on spectral shift, the overall experimental spectra get broader and distorted from the Gaussian shape.

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

Elastic network models (ENMs) and constraint-based, topological rigidity analysis are two distinct, coarse-grained approaches to study conformational flexibility of macromolecules. In the two decades since their introduction, both have contributed significantly to insights into protein molecular mechanisms and function. However, despite a shared purpose of these approaches, the topological nature of rigidity analysis, and thereby the absence of motion modes, has impeded a direct comparison. Here, we present an alternative, kinematic approach to rigidity analysis, which circumvents these drawbacks. We introduce a novel protein hydrogen bond network spectral decomposition, which provides an orthonormal basis for collective motions modulated by noncovalent interactions, analogous to the eigenspectrum of normal modes. The zero modes decompose proteins into rigid clusters identical to those from topological rigidity, while nonzero modes rank protein motions by their hydrogen bond collective energy penalty. Our kinematic flexibility analysis bridges topological rigidity theory and ENM, enabling a detailed analysis of motion modes obtained from both approaches. Analysis of a large, structurally diverse data set revealed that collectivity of protein motions, reported by the Shannon entropy, is significantly reduced for rigidity theory compared to normal mode approaches. Strikingly, kinematic flexibility analysis suggests that the hydrogen bonding network encodes a protein-fold specific, spatial hierarchy of motions, which goes nearly undetected in ENM. This hierarchy reveals distinct motion regimes that rationalize experimental and simulated protein stiffness variations. Kinematic motion modes highly correlate with reported crystallographic B factors and molecular dynamics simulations of adenylate kinase. A formal expression for changes in free energy derived from the spectral decomposition indicates that motions across nearly 40% of modes obey enthalpy-entropy compensation. Taken together, our results suggest that hydrogen bond networks have evolved to modulate protein structure and dynamics, which can be efficiently probed by kinematic flexibility analysis.

Rapid Sampling of Hydrogen Bond Networks for Computational Protein Design

Hydrogen bond networks play a critical role in determining the stability and specificity of biomolecular complexes, and the ability to design such networks is important for engineering novel structures, interactions, and enzymes. One key feature of hydrogen bond networks that makes them difficult to rationally engineer is that they are highly cooperative and are not energetically favorable until the hydrogen bonding potential has been satisfied for all buried polar groups in the network. Existing computational methods for protein design are ill-equipped for creating these highly cooperative networks because they rely on energy functions and sampling strategies that are focused on pairwise interactions. To enable the design of complex hydrogen bond networks, we have developed a new sampling protocol in the molecular modeling program Rosetta that explicitly searches for sets of amino acid mutations that can form self-contained hydrogen bond networks. For a given set of designable residues, the protocol often identifies many alternative sets of mutations/networks, and we show that it can readily be applied to large sets of residues at protein-protein interfaces or in the interior of proteins. The protocol builds on a recently developed method in Rosetta for designing hydrogen bond networks that has been experimentally validated for small symmetric systems but was not extensible to many larger protein structures and complexes. The sampling protocol we describe here not only recapitulates previously validated designs with performance improvements but also yields viable hydrogen bond networks for cases where the previous method fails, such as the design of large, asymmetric interfaces relevant to engineering protein-based therapeutics.

Rigidity Emerges during Antibody Evolution in Three Distinct Antibody Systems: Evidence from QSFR Analysis of Fab Fragments

The effects of somatic mutations that transform polyspecific germline (GL) antibodies to affinity mature (AM) antibodies with monospecificity are compared among three GL-AM Fab pairs. In particular, changes in conformational flexibility are assessed using a Distance Constraint Model (DCM). We have previously established that the DCM can be robustly applied across a series of antibody fragments (VL to Fab), and subsequently, the DCM was combined with molecular dynamics (MD) simulations to similarly characterize five thermostabilizing scFv mutants. The DCM is an ensemble based statistical mechanical approach that accounts for enthalpy/entropy compensation due to network rigidity, which has been quite successful in elucidating conformational flexibility and Quantitative Stability/Flexibility Relationships (QSFR) in proteins. Applied to three disparate antibody systems changes in QSFR quantities indicate that the VH domain is typically rigidified, whereas the VL domain and CDR L2 loop become more flexible during affinity maturation. The increase in CDR H3 loop rigidity is consistent with other studies in the literature. The redistribution of conformational flexibility is largely controlled by nonspecific changes in the H-bond network, although certain Arg to Asp salt bridges create highly localized rigidity increases. Taken together, these results reveal an intricate flexibility/rigidity response that accompanies affinity maturation.

Antibodies are protective proteins used by the immune system to recognize and neutralize foreign objects through interactions with a specific part of the target, called an antigen. Antibody structures are Y-shaped, contain multiple protein chains, and include two antigen-binding sites. The binding sites are located at the end of the Fab fragments, which are the upward facing arms of the Y-structure. The Fab fragments maintain binding affinity by themselves, and are thus often used as surrogates to student antibody-antigen interactions. High affinity antibodies are produced during the course of an immune response by successive mutations to germline gene-encoded antibodies. Germline antibodies are more likely to be polyspecific, whereas the affinity maturation process yields monoclonal antibodies that bind specifically to the target antigen. In this work, we use a computational Distance Constraint Model to characterize how mechanical properties change as three disparate germline antibodies are converted to affinity mature. Our results reveal a rich set of mechanical responses throughout the Fab structure. Nevertheless, increased rigidity in the VH domain is consistently observed, which is consistent with the transition from polyspecificity to monospecificity. That is, flexible antibody structures are able to recognize multiple antigens, while increased affinity and specificity is achieved—in part—by structural rigidification.

Flexibility Correlation between Active Site Regions Is Conserved across Four AmpC β-Lactamase Enzymes

β-lactamases are bacterial enzymes that confer resistance to β-lactam antibiotics, such as penicillins and cephalosporins. There are four classes of β-lactamase enzymes, each with characteristic sequence and structure properties. Enzymes from class A are the most common and have been well characterized across the family; however, less is known about how physicochemical properties vary across the C and D families. In this report, we compare the dynamical properties of four AmpC (class C) β-lactamases using our distance constraint model (DCM). The DCM reliably predicts thermodynamic and mechanical properties in an integrated way. As a consequence, quantitative stability/flexibility relationships (QSFR) can be determined and compared across the whole family. The DCM calculates a large number of QSFR metrics. Perhaps the most useful is the flexibility index (FI), which quantifies flexibility along the enzyme backbone. As typically observed in other systems, FI is well conserved across the four AmpC enzymes. Cooperativity correlation (CC), which quantifies intramolecular couplings within structure, is rarely conserved across protein families; however, it is in AmpC. In particular, the bulk of each structure is composed of a large rigid cluster, punctuated by three flexibly correlated regions located at the active site. These regions include several catalytic residues and the Ω-loop. This evolutionary conservation combined with active their site location strongly suggests that these coupled dynamical modes are important for proper functioning of the enzyme.

Redistribution of flexibility in stabilizing antibody fragment mutants follows Le Châtelier's principle

Le Châtelier's principle is the cornerstone of our understanding of chemical equilibria. When a system at equilibrium undergoes a change in concentration or thermodynamic state (i.e., temperature, pressure, etc.), La Châtelier's principle states that an equilibrium shift will occur to offset the perturbation and a new equilibrium is established. We demonstrate that the effects of stabilizing mutations on the rigidity ⇔ flexibility equilibrium within the native state ensemble manifest themselves through enthalpy-entropy compensation as the protein structure adjusts to restore the global balance between the two. Specifically, we characterize the effects of mutation to single chain fragments of the anti-lymphotoxin-β receptor antibody using a computational Distance Constraint Model. Statistically significant changes in the distribution of both rigidity and flexibility within the molecular structure is typically observed, where the local perturbations often lead to distal shifts in flexibility and rigidity profiles. Nevertheless, the net gain or loss in flexibility of individual mutants can be skewed. Despite all mutants being exclusively stabilizing in this dataset, increased flexibility is slightly more common than increased rigidity. Mechanistically the redistribution of flexibility is largely controlled by changes in the H-bond network. For example, a stabilizing mutation can induce an increase in rigidity locally due to the formation of new H-bonds, and simultaneously break H-bonds elsewhere leading to increased flexibility distant from the mutation site via Le Châtelier. Increased flexibility within the VH β4/β5 loop is a noteworthy illustration of this long-range effect.

How cellulose stretches: synergism between covalent and hydrogen bonding

Cellulose is the most familiar and most abundant strong biopolymer, but the reasons for its outstanding mechanical performance are not well understood. Each glucose unit in a cellulose chain is joined to the next by a covalent C-O-C linkage flanked by two hydrogen bonds. This geometry suggests some form of cooperativity between covalent and hydrogen bonding. Using infrared spectroscopy and X-ray diffraction, we show that mechanical tension straightens out the zigzag conformation of the cellulose chain, with each glucose unit pivoting around a fulcrum at either end. Straightening the chain leads to a small increase in its length and is resisted by one of the flanking hydrogen bonds. This constitutes a simple form of molecular leverage with the covalent structure providing the fulcrum and gives the hydrogen bond an unexpectedly amplified effect on the tensile stiffness of the chain. The principle of molecular leverage can be directly applied to certain other carbohydrate polymers, including the animal polysaccharide chitin. Related but more complex effects are possible in some proteins and nucleic acids. The stiffening of cellulose by this mechanism is, however, in complete contrast to the way in which hydrogen bonding provides toughness combined with extensibility in protein materials like spider silk.

Towards comprehensive analysis of protein family quantitative stability-flexibility relationships using homology models

The Distance Constraint Model (DCM) is a computational modeling scheme that uniquely integrates thermodynamic and mechanical descriptions of protein structure. As such, quantitative stability-flexibility relationships (QSFR) that describe the interrelationships of thermodynamics and mechanics can be quickly computed. Using comparative QSFR analyses, we have previously investigated these relationships across a small number of protein orthologs, ranging from two to a dozen [1, 2]. However, our ultimate goal is provide a comprehensive analysis of whole protein families, which requires consideration of many more structures. To that end, we have developed homology modeling and assessment protocols so that we can robustly calculate QSFR properties for proteins without experimentally derived structures. The approach, which is presented here, starts from a large ensemble of potential homology models and uses a clustering algorithm to identify the best models, thus paving the way for a comprehensive QSFR analysis across hundreds of proteins in a protein family.

A case study comparing quantitative stability-flexibility relationships across five metallo-β-lactamases highlighting differences within NDM-1

The Distance Constraint Model (DCM) is an ensemble-based biophysical model that integrates thermodynamic and mechanical viewpoints of protein structure. The DCM outputs a large number of structural characterizations that collectively allow for Quantified Stability-Flexibility Relationships (QSFR) to be identified and compared across protein families. Using five metallo-β-lactamases (MBLs) as a representative set, we demonstrate how QSFR properties are both conserved and varied across protein families. Similar to our characterizations on other protein families, the backbone flexibility of the five MBLs are overall visually conserved, yet there are interesting specific quantitative differences. For example, the plasmid-encoded NDM-1 enzyme, which leads to a fast spreading drug-resistant version of Klebsiella pneumoniae, has several regions of significantly increased rigidity relative to the other four. In addition, the set of intramolecular couplings within NDM-1 are also atypical. While long-range couplings frequently vary significantly across protein families, NDM-1 is distinct because it has limited correlated flexibility, which is isolated within the active site S3/S4 and S11/H6 loops. These loops are flexibly correlated in the other members, suggesting it is important to function, but the others also have significant amounts of correlated flexibility throughout the rest of their structures.

Variations within class-A β-lactamase physiochemical properties reflect evolutionary and environmental patterns, but not antibiotic specificity

The bacterial enzyme β-lactamase hydrolyzes the β-lactam ring of penicillin and chemically related antibiotics, rendering them ineffective. Due to rampant antibiotic overuse, the enzyme is evolving new resistance activities at an alarming rate. Related, the enzyme's global physiochemical properties exhibit various amounts of conservation and variability across the family. To that end, we characterize the extent of property conservation within twelve different class-A β-lactamases, and conclusively establish that the systematic variations therein parallel their evolutionary history. Large and systematic differences within electrostatic potential maps and pairwise residue-to-residue couplings are observed across the protein, which robustly reflect phylogenetic outgroups. Other properties are more conserved (such as residue pKa values, electrostatic networks, and backbone flexibility), yet they also have systematic variations that parallel the phylogeny in a statistically significant way. Similarly, the above properties also parallel the environmental condition of the bacteria they are from in a statistically significant way. However, it is interesting and surprising that the only one of the global properties (protein charge) parallels the functional specificity patterns; meaning antibiotic resistance activities are not significantly constraining the global physiochemical properties. Rather, extended spectrum activities can emerge from the background of nearly any set of electrostatic and dynamic properties.

Non-specificity and synergy at the binding site of the carboplatin-induced DNA adduct via molecular dynamics simulations of the MutSα-DNA recognition complex

MutSα is the most abundant mismatch-binding factor of human DNA mismatch repair (MMR) proteins. MMR maintains genetic stability by recognizing and repairing DNA defects. Failure to accomplish their function may lead to cancer. In addition, MutSα recognizes at least some types of DNA damage making it a target for anticancer agents. Here, complementing scarce experimental data, we report unique hydrogen-bonding motifs associated with the recognition of the carboplatin induced DNA damage by MutSα. These data predict that carboplatin and cisplatin induced damaging DNA adducts are recognized by MutSα in a similar manner. Our simulations also indicate that loss of base pairing at the damage site results in (1) non-specific binding and (2) changes in the atomic flexibility at the lesion site and beyond. To further quantify alterations at MutSα-DNA interface in response to damage recognition, non-bonding interactions and salt bridges were investigated. These data indicate (1) possible different packing and (2) disruption of the salt bridges at the MutSα-DNA interface in the damaged complex. These findings (1) underscore the general observation of disruptions at the MutSα-DNA interface and (2) highlight the nature of the anticancer effect of the carboplatin agent. The analysis was carried out from atomistic simulations.

Protein mechanics: how force regulates molecular function

BACKGROUND

Regulation of proteins is ubiquitous and vital for any organism. Protein activity can be altered chemically, by covalent modifications or non-covalent binding of co-factors. Mechanical forces are emerging as an additional way of regulating proteins, by inducing a conformational change or by partial unfolding.

SCOPE

We review some advances in experimental and theoretical techniques to study protein allostery driven by mechanical forces, as opposed to the more conventional ligand driven allostery. In this respect, we discuss recent single molecule pulling experiments as they have substantially augmented our view on the protein allostery by mechanical signals in recent years. Finally, we present a computational analysis technique, Force Distribution Analysis, that we developed to reveal allosteric pathways in proteins.

MAJOR CONCLUSIONS

Any kind of external perturbation, being it ligand binding or mechanical stretching, can be viewed as an external force acting on the macromolecule, rendering force-based experimental or computational techniques, a very general approach to the mechanics involved in protein allostery.

GENERAL SIGNIFICANCE

This unifying view might aid to decipher how complex allosteric protein machineries are regulated on the single molecular level.

Theoretical study on the polar hydrogen-π (Hp-π) interactions between protein side chains

BACKGROUND

In the study of biomolecular structures and interactions the polar hydrogen-π bonds (Hp-π) are an extensive molecular interaction type. In proteins 11 of 20 natural amino acids and in DNA (or RNA) all four nucleic acids are involved in this type interaction.

RESULTS

The Hp-π in proteins are studied using high level QM method CCSD/6-311 + G(d,p) + H-Bq (ghost hydrogen basis functions) in vacuum and in solutions (water, acetonitrile, and cyclohexane). Three quantum chemical methods (B3LYP, CCSD, and CCSD(T)) and three basis sets (6-311 + G(d,p), TZVP, and cc-pVTZ) are compared. The Hp-π donors include R2NH, RNH2, ROH, and C6H5OH; and the acceptors are aromatic amino acids, peptide bond unit, and small conjugate π-groups. The Hp-π interaction energies of four amino acid pairs (Ser-Phe, Lys-Phe, His-Phe, and Tyr-Phe) are quantitatively calculated.

CONCLUSIONS

Five conclusion points are abstracted from the calculation results. (1) The common DFT method B3LYP fails in describing the Hp-π interactions. On the other hand, CCSD/6-311 + G(d,p) plus ghost atom H-Bq can yield better results, very close to the state-of-the-art method CCSD(T)/cc-pVTZ. (2) The Hp-π interactions are point to π-plane interactions, possessing much more interaction conformations and broader energy range than other interaction types, such as common hydrogen bond and electrostatic interactions. (3) In proteins the Hp-π interaction energies are in the range 10 to 30 kJ/mol, comparable or even larger than common hydrogen bond interactions. (4) The bond length of Hp-π interactions are in the region from 2.30 to 3.00 Å at the perpendicular direction to the π-plane, much longer than the common hydrogen bonds (~1.9 Å). (5) Like common hydrogen bond interactions, the Hp-π interactions are less affected by solvation effects.

Global and local indices for characterizing biomolecular flexibility and rigidity

Understanding flexibility and rigidity characteristics of biomolecules is a prerequisite for understanding biomolecular structural stability and function. Computational methods have been implemented that directly characterize biomolecular flexibility and rigidity by constraint network analysis. For deriving maximal advantage from these analyses, their results need to be linked to biologically relevant characteristics of a structure. Such links are provided by global and local measures ("indices") of biomolecular flexibility and rigidity. To date, more than 14 indices are available with sometimes overlapping or only vague definitions. We present concise definitions of these indices, analyze the relation between, and the scope and limitations of them, and compare their informative value. For this, we probe the structural stability of the calcium binding protein α-lactalbumin as a showcase, both in the "ground state" and after perturbing the system by changing the network topology. In addition, we introduce three indices for the first time that extend the application domain of flexibility and rigidity analyses. The results allow us to provide guidelines for future studies suggesting which of these indices could best be used for analyzing, understanding, and quantifying structural features that are important for biomolecular stability and function. Finally, we make suggestions for proper index notations in future studies to prevent the misinterpretation and to facilitate the comparison of results obtained from flexibility and rigidity analyses.

Targeted In Situ Biosynthetic Transcriptional Activation in Native Surface-Level Human Articular Chondrocytes during Lesion Stabilization

OBJECTIVE

Safe articular cartilage lesion stabilization is an important early surgical intervention advance toward mitigating articular cartilage disease burden. While short-term chondrocyte viability and chondrosupportive matrix modification have been demonstrated within tissue contiguous to targeted removal of damaged articular cartilage, longer term tissue responses require evaluation to further clarify treatment efficacy. The purpose of this study was to examine surface chondrocyte responses within contiguous tissue after lesion stabilization.

METHODS

Nonablation radiofrequency lesion stabilization of human cartilage explants obtained during knee replacement was performed for surface fibrillation. Time-dependent chondrocyte viability, nuclear morphology and cell distribution, and temporal response kinetics of matrix and chaperone gene transcription indicative of differentiated chondrocyte function were evaluated in samples at intervals to 96 hours after treatment.

RESULTS

Subadjacent surface articular cartilage chondrocytes demonstrated continued viability for 96 hours after treatment, a lack of increased nuclear fragmentation or condensation, persistent nucleic acid production during incubation reflecting cellular assembly behavior, and transcriptional up-regulation of matrix and chaperone genes indicative of retained biosynthetic differentiated cell function.

CONCLUSIONS

The results of this study provide further evidence of treatment efficacy and suggest the possibility to manipulate or induce cellular function, thereby recruiting local chondrocytes to aid lesion recovery. Early surgical intervention may be viewed as a tissue rescue, allowing articular cartilage to continue displaying biological responses appropriate to its function rather than converting to a tissue ultimately governed by the degenerative material property responses of matrix failure. Early intervention may positively impact the late changes and reduce disease burden of damaged articular cartilage.

Changes in Lysozyme Flexibility upon Mutation Are Frequent, Large and Long-Ranged

We investigate changes in human c-type lysozyme flexibility upon mutation via a Distance Constraint Model, which gives a statistical mechanical treatment of network rigidity. Specifically, two dynamical metrics are tracked. Changes in flexibility index quantify differences within backbone flexibility, whereas changes in the cooperativity correlation quantify differences within pairwise mechanical couplings. Regardless of metric, the same general conclusions are drawn. That is, small structural perturbations introduced by single point mutations have a frequent and pronounced affect on lysozyme flexibility that can extend over long distances. Specifically, an appreciable change occurs in backbone flexibility for 48% of the residues, and a change in cooperativity occurs in 42% of residue pairs. The average distance from mutation to a site with a change in flexibility is 17–20 Å. Interestingly, the frequency and scale of the changes within single point mutant structures are generally larger than those observed in the hen egg white lysozyme (HEWL) ortholog, which shares 61% sequence identity with human lysozyme. For example, point mutations often lead to substantial flexibility increases within the β-subdomain, which is consistent with experimental results indicating that it is the nucleation site for amyloid formation. However, β-subdomain flexibility within the human and HEWL orthologs is more similar despite the lowered sequence identity. These results suggest compensating mutations in HEWL reestablish desired properties.

The functional importance of protein dynamics is universally accepted, making the study of dynamical similarities and differences among proteins of the same function an intriguing problem. While some metrics are likely to be conserved across family, differences are also very common. In previous works we have used a Distance Constraint Model to quantify flexibility differences across sets of orthologous proteins, which reproduce this diversity. In the same manner, this work investigates changes occurring upon individual point mutations. Somewhat surprisingly, the small structural perturbations caused by mutation lead to changes throughout the protein. These changes can be quite large, actually surpassing the scale for differences between ortholog pairs. Moreover, changes in flexibility frequently occur at sites far from the mutation site. These results underscore the sensitivity of protein dynamics in connection with allostery, and help explain why differences across protein families are so common.

Calculating ensemble averaged descriptions of protein rigidity without sampling

Previous works have demonstrated that protein rigidity is related to thermodynamic stability, especially under conditions that favor formation of native structure. Mechanical network rigidity properties of a single conformation are efficiently calculated using the integer body-bar Pebble Game (PG) algorithm. However, thermodynamic properties require averaging over many samples from the ensemble of accessible conformations to accurately account for fluctuations in network topology. We have developed a mean field Virtual Pebble Game (VPG) that represents the ensemble of networks by a single effective network. That is, all possible number of distance constraints (or bars) that can form between a pair of rigid bodies is replaced by the average number. The resulting effective network is viewed as having weighted edges, where the weight of an edge quantifies its capacity to absorb degrees of freedom. The VPG is interpreted as a flow problem on this effective network, which eliminates the need to sample. Across a nonredundant dataset of 272 protein structures, we apply the VPG to proteins for the first time. Our results show numerically and visually that the rigidity characterizations of the VPG accurately reflect the ensemble averaged properties. This result positions the VPG as an efficient alternative to understand the mechanical role that chemical interactions play in maintaining protein stability.

Ensemble properties of network rigidity reveal allosteric mechanisms

The distance constraint model (DCM) is a unique computational modeling paradigm that integrates mechanical and thermodynamic descriptions of macromolecular structure. That is, network rigidity calculations are used to account for nonadditivity within entropy components, thus restoring the utility of free-energy decomposition. The DCM outputs a large number of structural characterizations that collectively allow for quantified stability-flexibility relationships (QSFR) to be identified. In this review, we describe the theoretical underpinnings of the DCM and introduce several common QSFR metrics. Application of the DCM across protein families highlights the sensitivity within the set of protein structure residue-to-residue couplings. Further, we have developed a perturbation method to identify putative allosteric sites, where large changes in QSFR upon rigidification (mimicking ligand-binding) detect sites likely to invoke allosteric changes.

Characterizing protein motions from structure

To clarify the extent structure plays in determining protein dynamics, a comparative study is made using three models that characterize native state dynamics of single domain proteins starting from known structures taken from four distinct SCOP classifications. A geometrical simulation using the framework rigidity optimized dynamics algorithm (FRODA) based on rigid cluster decomposition is compared to the commonly employed elastic network model (specifically the Anisotropic Network Model ANM) and molecular dynamics (MD) simulation. The essential dynamics are quantified by a mode subspace constructed from ANM and a principal component analysis (PCA) on FRODA and MD trajectories. Aggregate conformational ensembles are constructed to provide a basis for quantitative comparisons between FRODA runs using different parameter settings to critically assess how the predictions of essential dynamics depend on a priori arbitrary user-defined distance constraint rules. We established a range of physicality for these parameters. Surprisingly, FRODA maintains greater intra-consistent results than obtained from MD trajectories, comparable to ANM. Additionally, a mode subspace is constructed from PCA on an exemplar set of myoglobin structures from the Protein Data Bank. Significant overlap across the three model subspaces and the experimentally derived subspace is found. While FRODA provides the most robust sampling and characterization of the native basin, all three models give similar dynamical information of a native state, further demonstrating that structure is the key determinant of dynamics.

Nonadditivity in conformational entropy upon molecular rigidification reveals a universal mechanism affecting folding cooperativity

Previously, we employed a Maxwell counting distance constraint model (McDCM) to describe α-helix formation in polypeptides. Unlike classical helix-coil transition theories, the folding mechanism derives from nonadditivity in conformational entropy caused by rigidification of molecular structure as intramolecular cross-linking interactions form along the backbone. For example, when a hydrogen bond forms within a flexible region, both energy and conformational entropy decrease. However, no conformational entropy is lost when the region is already rigid because atomic motions are not constrained further. Unlike classical zipper models, the same mechanism also describes a coil-to-β-hairpin transition. Special topological features of the helix and hairpin structures allow the McDCM to be solved exactly. Taking full advantage of the fact that Maxwell constraint counting is a mean field approximation applied to the distribution of cross-linking interactions, we present an exact transfer matrix method that does not require any special topological feature. Upon application of the model to proteins, cooperativity within the folding transition is yet again appropriately described. Notwithstanding other contributing factors such as the hydrophobic effect, this simple model identifies a universal mechanism for cooperativity within polypeptide and protein-folding transitions, and it elucidates scaling laws describing hydrogen-bond patterns observed in secondary structure. In particular, the native state should have roughly twice as many constraints as there are degrees of freedom in the coil state to ensure high fidelity in two-state folding cooperativity, which is empirically observed.

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

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

Allosteric response is both conserved and variable across three CheY orthologs

A computational method to identify residues likely to initiate allosteric signals has been developed. The method is based on differences within stability and flexibility profiles between wild-type and perturbed structures as computed by a distance constraint model. Application of the approach to three bacterial chemotaxis protein Y (CheY) orthologs provides a comparison of allosteric response across protein family divergence. Interestingly, we observe a rich mixture of both conservation and variability within the identified allosteric sites. While similarity within the overall response parallels the evolutionary relationships, >50% of the best scoring putative sites are only identified in a single ortholog. These results suggest that detailed descriptions of intraprotein communication are substantially more variable than structure and function, yet do maintain some evolutionary relationships. Finally, structural clusters of large response identify four allosteric hotspots, including the β4/α4 loop known to be critical to relaying the CheY phosphorylation signal.

Ensemble-based methods for describing protein dynamics

Molecular dynamics (MD) simulation is a natural approach for studying protein dynamics, and coupled with the ideas of multiscale modeling, MD proves to be the gold standard in computational biology to investigate mechanistic details related to protein function. In principle, if MD trajectories are long enough, the ensemble of protein conformations generated allows thermodynamic and kinetic properties to be predicted. We know from experiments that proteins exhibit a high degree of fidelity in function, and that empirical kinetic models are successful in describing kinetics, suggesting that the ensemble of conformations cluster into well-defined thermodynamic states, which are frequently metastable. The experimental evidence suggest that more efficient computational models that retain only essential properties of the protein can be constructed to faithfully reproduce the relatively few observed thermodynamic states, and perhaps describe transition states if the model is sufficiently detailed. Indeed, there are many so-called ensemble-based methods that attempt to generate more complete ensembles than MD can provide by focusing on the most important driving forces through simplified representations of how elements within the protein interact. Although coarse-graining is employed in MD and other approaches, such as in elastic network models, the key distinguishing factor of ensemble-based methods is that they are meant to efficiently generate a large ensemble of conformations without solving explicit equations of motion. This review highlights three types of ensemble-based methods, illustrated by 'COREX' and the Wako-Saito-Munoz-Eaton (WSME) model, the Framework Rigidity Optimized Dynamic Algorithm (FRODA) and the distance constraint model (DCM).

Helix/coil nucleation: a local response to global demands

A complete description of protein structure and function must include a proper treatment of mechanisms that lead to cooperativity. The helix/coil transition serves as a simple example of a cooperative folding process, commonly described by a nucleation-propagation mechanism. The prevalent view is that coil structure must first form a short segment of helix in a localized region despite paying a free energy cost (nucleation). Afterward, helical structure propagates outward from the nucleation site. Both processes entail enthalpy-entropy compensation that derives from the loss in conformational entropy on helix formation with concomitant gain in favorable interactions. Nucleation-propagation models inherently assume that cooperativity arises from a sequential series of local events. An alternative distance constraint model asserts there is a direct link between available degrees of freedom and cooperativity through the nonadditivity in conformational entropy. That is, helix nucleation is a concerted manifestation of rigidity propagating through atomic structure. The link between network rigidity and nonadditivity of conformational entropy is shown in this study by solving the distance constraint model using a simple global constraint counting approximation. Cooperativity arises from competition between excess and deficiency in available degrees of freedom in the coil and helix states respectively.

Unifying mechanical and thermodynamic descriptions across the thioredoxin protein family

We compare various predicted mechanical and thermodynamic properties of nine oxidized thioredoxins (TRX) using a Distance Constraint Model (DCM). The DCM is based on a nonadditive free energy decomposition scheme, where entropic contributions are determined from rigidity and flexibility of structure based on distance constraints. We perform averages over an ensemble of constraint topologies to calculate several thermodynamic and mechanical response functions that together yield quantitative stability/flexibility relationships (QSFR). Applied to the TRX protein family, QSFR metrics display a rich variety of similarities and differences. In particular, backbone flexibility is well conserved across the family, whereas cooperativity correlation describing mechanical and thermodynamic couplings between the residue pairs exhibit distinctive features that readily standout. The diversity in predicted QSFR metrics that describe cooperativity correlation between pairs of residues is largely explained by a global flexibility order parameter describing the amount of intrinsic flexibility within the protein. A free energy landscape is calculated as a function of the flexibility order parameter, and key values are determined where the native-state, transition-state, and unfolded-state are located. Another key value identifies a mechanical transition where the global nature of the protein changes from flexible to rigid. The key values of the flexibility order parameter help characterize how mechanical and thermodynamic response is linked. Variation in QSFR metrics and key characteristics of global flexibility are related to the native state X-ray crystal structure primarily through the hydrogen bond network. Furthermore, comparison of three TRX redox pairs reveals differences in thermodynamic response (i.e., relative melting point) and mechanical properties (i.e., backbone flexibility and cooperativity correlation) that are consistent with experimental data on thermal stabilities and NMR dynamical profiles. The results taken together demonstrate that small-scale structural variations are amplified into discernible global differences by propagating mechanical couplings through the H-bond network.

Conformational Entropy of an Ideal Cross-Linking Polymer Chain

We present a novel analytical method to calculate conformational entropy of ideal cross-linking polymers from the configuration integral by employing a Mayer series expansion. Mayer-functions describing chemical bonds within the chain and for cross-links are sharply peaked over the temperature range of interest, and, are well approximated as statistically weighted Dirac delta-functions that enforce distance constraints. All geometrical deformations consistent with a set of distance constraints are integrated over. Exact results for a contiguous series of connected loops are employed to substantiate the validity of a previous phenomenological distance constraint model that describes protein thermodynamics successfully based on network rigidity.