Dynamic prestress in a globular protein

Small Molecule Assembly Agonist Alters the Dynamics of Hepatitis B Virus Core Protein Dimer and Capsid

Chronic hepatitis B virus (HBV) poses a significant public health burden worldwide, encouraging the search for curative antivirals. One approach is capsid assembly modulators (CAMs), which are assembly agonists. CAMs lead to empty and defective capsids, inhibiting the formation of new viruses, and can also lead to defects in the release of the viral genome, inhibiting new infections. In this study, we employed hydrogen-deuterium exchange mass spectrometry (HDX-MS) to assess the impact of one such CAM, HAP18, on HBV dimers, capsids composed of 120 (or 90) capsid protein dimers, and cross-linked capsids (xl-capsids). HDX analysis revealed hydrogen bonding networks within and between the dimers. HAP18 disrupted the hydrogen bonding network of dimers, demonstrating a previously unappreciated impact on the dimer structure. Conversely, HAP18 stabilized both unmodified and cross-linked capsids. Intriguingly, cross-linking the capsid, which was accomplished by forming disulfides between an engineered C-terminal cysteine, increased the overall rate of HDX. Moreover, HAP18 binding induced conformational changes beyond the binding sites. Our findings provide evidence for allosteric communication within and between capsid protein dimers. These results show that CAMs are capable of harnessing this allosteric network to modulate the dimer and capsid dynamics.

Decomposition of Forces in Protein: Methodology and General Properties

In contrast to the central role played by the structure of biomolecules, the complementary force-based view has received little attention in past studies. Here, we proposed a simple method for the force decomposition of multibody interactions and provided some techniques to analyze and visualize the general behavior of forces in proteins. It was shown that atomic forces fluctuate at a magnitude of about 3000 pN, which is huge in the context of cell biology. Remarkably, the average scalar product between atomic force and displacement universally approximates -3kBT. This is smaller by an order of magnitude than the simple product of their fluctuation magnitudes due to the unexpectedly weak correlation between the directions of force and displacement. The pairwise forces are highly anisotropic, with elongated fluctuation ellipsoids. Residue-residue forces can be attractive or repulsive (despite being more likely to be attractive), forming some kind of tensegrity structure stabilized by a complicated network of forces. Being able to understand and predict the interaction network provides a basis for rational drug design and uncovering molecular recognition mechanisms.

Mechanical design principles in frustrated thin elastic sheets

Using a geometric formalism of elasticity theory we develop a systematic theoretical framework for shaping and manipulating the energy landscape of slender solids, and consequently their mechanical response to external perturbations. We formally express global mechanical properties associated with non-Euclidean thin sheets in terms of their local rest lengths and rest curvatures, and we interpret the expressions as both forward and inverse problems for designing the desired mechanical properties. We show that by wisely designing geometric frustration, anomalous mechanical properties can be encoded into a material using accessible experimental techniques. To test the methodology we derive a family of ribbon-springs with extreme mechanical behavior such as tunable, anharmonic, and even vanishing rigidities. The presented formalism can be discretized, offering a new methodology for designing mechanical properties and thus opens a new pathway for the design of both continuum and discrete solids and structures.

From tensegrity to human organs-on-chips: implications for mechanobiology and mechanotherapeutics

The field of mechanobiology, which focuses on the key role that physical forces play in control of biological systems, has grown enormously over the past few decades. Here, I provide a brief personal perspective on the development of the tensegrity theory that contributed to the emergence of the mechanobiology field, the key role that crossing disciplines has played in its development, and how it has matured over time. I also describe how pursuing questions relating to mechanochemical transduction and mechanoregulation can lead to the creation of novel technologies and open paths for development of new therapeutic strategies for a broad range of diseases and disorders.

Intramolecular covalent bonds in Gram-positive bacterial surface proteins

Gram-positive bacteria experience considerable mechanical perturbation when adhering to host surfaces during colonization and infection. They have evolved various adhesion proteins that are mechanically robust to ensure strong surface adhesion. Recently, it was discovered that these adhesion proteins contain rare, extra intramolecular covalent bonds that stabilize protein structures and participate in surface bonding. These intramolecular covalent bonds include isopeptides, thioesters, and ester bonds, which often form spontaneously without the need for additional enzymes. With the development of single-molecule force spectroscopy techniques, the detailed mechanical roles of these intramolecular covalent bonds have been revealed. In this review, we summarize the recent advances in this area of research, focusing on the link between the mechanical stability and function of these covalent bonds in Gram-positive bacterial surface proteins. We also highlight the potential impact of these discoveries on the development of novel antibiotics and chemical biology tools.

How Similar Are Proteins and Origami?

Protein folding and structural biology are highly active disciplines that combine basic research in various fields, including biology, chemistry, physics, and computer science, with practical applications in biomedicine and nanotechnology. However, there are still gaps in the understanding of the detailed mechanisms of protein folding, and protein structure-function relations. In an effort to bridge these gaps, this paper studies the equivalence of proteins and origami. Research on proteins and origami provides strong evidence to support the use of origami folding principles and mechanical models to explain aspects of proteins formation and function. Although not identical, the equivalence of origami and proteins emerges in: (i) the folding processes, (ii) the shape and structure of proteins and origami models, and (iii) the intrinsic mechanical properties of the folded structures/models, which allows them to synchronically fold/unfold and effectively distribute forces to the whole structure. As a result, origami can contribute to the understanding of various key protein-related mechanisms and support the design of de novo proteins and nanomaterials.

Spontaneous Rupture and Entanglement of Human Neuronal Tau Protein Induced by Piconewton Compressive Force

Mechanical force vector fluctuations in living cells can have a significant impact on protein behavior and functions. Here we report that a human tau protein tertiary structure can abruptly and spontaneously rupture, like a balloon, under biologically available piconewton compressive force, using a home-modified atomic force microscopy single-molecule manipulation. The rupture behavior is dependent on the physiological level of presence of ions, such as K⁺ and Mg²⁺. We observed rupture events in the presence of K⁺ but not in the presence of Mg²⁺ ions. We have also explored the entangled protein state formed following the events of the multiple and simultaneous protein ruptures under crowding. Crowded proteins simultaneously rupture and then spontaneously refold to an entangled folding state, different from either folded and unfolded states of the tau protein, which can be a plausible pathway for the tau protein aggregation that is related to a number of neurodegenerative diseases.

Professor Lev Beloussov and the birth of morphomechanics

The first explanations of the mechanisms of development of living organisms were proposed in antiquity. At that time two competing ideas existed, about the strict determination of embryonic structures (we call it the "Hippocrates line") and about the possible formation of structures from the unstructured condition ("Aristotle line"). We can trace the opposition between the "Hippocrates line" and "Aristotle line" from antiquity till the present time. At the end of the XIX century, experimental investigation of the mechanisms of integrity of development had started. In the XX century, the "Aristotle line" finds its expression in the Morphogenetic Field Theory of A.G. Gurwitsch, according to which cells of the organism are integrated in an organic whole. Since the 1970s, mechanical forces and tensions have been considered as integral factors of ontogenesis. One of the most productive scientific teams which worked in this area was the laboratory of Professor L.V. Beloussov from the Lomonossov Moscow State University, Russia. In the 1970s, Lev Beloussov and his colleagues discovered the presence of "passive" and "active" (i.e. metabolically-dependent) mechanical stresses in the tissues of developing organisms, their organization and stage-specific patterns. In 1980-1990 s, a lot of experimental data about the role of the patterns of mechanical stresses in morphogenesis and cell differentiation was accumulated. Based on the experimental data, Professor Beloussov and his colleagues developed a theory of the regulation of the development of living organisms on the basis of the interaction of passive and active mechanical stresses (Belousov-Mittenthal Theory), which forms the basis of a new science - morphomechanics.

Art Advancing Science: Filmmaking Leads to Molecular Insights at the Nanoscale

Many have recognized the potential value of facilitating activities that span the art-science interface for the benefit of society; however, there are few examples that demonstrate how pursuit of an artistic agenda can lead to scientific insights. Here, we describe how we set out to produce an entertaining short film depicting the fertilization of the egg by sperm as a parody of a preview for another Star Wars movie to excite the public about science, but ended up developing a simulation tool for multiscale modeling. To produce an aesthetic that communicates mechanical continuity across spatial scales, we developed custom strategies that integrate physics-based animation software from the entertainment industry with molecular dynamics simulation tools, using experimental data from research publications. Using this approach, we were able to depict biological physicality across multiple spatial scales, from how sperm tails move to collective molecular behavior within the axoneme to how the molecular motor, dynein, produces force at the nanometer scale. The dynein simulations, which were validated by replicating results of past simulations and cryo-electron microscopic studies, also predicted a potential mechanism for how ATP hydrolysis drives dynein motion along the microtubule as well as how dynein changes its conformation when it goes through the power stroke. Thus, pursuit of an artistic work led to insights into biology at the nanoscale as well as the development of a highly generalizable modeling and simulation technology that has utility for nanoscience and any other area of scientific investigation that involves analysis of complex multiscale systems.

Designing allostery-inspired response in mechanical networks

Recent advances in designing metamaterials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally efficient approach, we extend this idea to tune more general properties of networks. With nearly complete success, we are able to produce a strain between any two target nodes in a network in response to an applied source strain on any other pair of nodes by removing only ∼1% of the bonds. We are also able to control multiple pairs of target nodes, each with a different individual response, from a single source, and to tune multiple independent source/target responses simultaneously into a network. We have fabricated physical networks in macroscopic 2D and 3D systems that exhibit these responses. This work is inspired by the long-range coupled conformational changes that constitute allosteric function in proteins. The fact that allostery is a common means for regulation in biological molecules suggests that it is a relatively easy property to develop through evolution. In analogy, our results show that long-range coupled mechanical responses are similarly easy to achieve in disordered networks.

One-Way Allosteric Communication between the Two Disulfide Bonds in Tissue Factor

Tissue factor (TF) is a transmembrane glycoprotein that plays distinct roles in the initiation of extrinsic coagulation cascade and thrombosis. TF contains two disulfide bonds, one each in the N-terminal and C-terminal extracellular domains. The C-domain disulfide, Cys186-Cys209, has a -RHStaple configuration in crystal structures, suggesting that this disulfide carries high pre-stress. The redox state of this disulfide has been proposed to regulate TF encryption/decryption. Ablating the N-domain Cys49-Cys57 disulfide bond was found to increase the redox potential of the Cys186-Cys209 bond, implying an allosteric communication between the domains. Using molecular dynamics simulations, we observed that the Cys186-Cys209 disulfide bond retained the -RHStaple configuration, whereas the Cys49-Cys57 disulfide bond fluctuated widely. The Cys186-Cys209 bond featured the typical -RHStaple disulfide properties, such as a longer S-S bond length, larger C-S-S angles, and higher bonded prestress, in comparison to the Cys49-Cys57 bond. Force distribution analysis was used to sense the subtle structural changes upon ablating the disulfide bonds, and allowed us to identify a one-way allosteric communication mechanism from the N-terminal to the C-terminal domain. We propose a force propagation pathway using a shortest-pathway algorithm, which we suggest is a useful method for searching allosteric signal transduction pathways in proteins. As a possible explanation for the pathway being one-way, we identified a pronounced lower degree of conformational fluctuation, or effectively higher stiffness, in the N-terminal domain. Thus, the changes of the rigid domain (N-terminal domain) can induce mechanical force propagation to the soft domain (C-terminal domain), but not vice versa.

Advances in Quantum Mechanochemistry: Electronic Structure Methods and Force Analysis

In quantum mechanochemistry, quantum chemical methods are used to describe molecules under the influence of an external force. The calculation of geometries, energies, transition states, reaction rates, and spectroscopic properties of molecules on the force-modified potential energy surfaces is the key to gain an in-depth understanding of mechanochemical processes at the molecular level. In this review, we present recent advances in the field of quantum mechanochemistry and introduce the quantum chemical methods used to calculate the properties of molecules under an external force. We place special emphasis on quantum chemical force analysis tools, which can be used to identify the mechanochemically relevant degrees of freedom in a deformed molecule, and spotlight selected applications of quantum mechanochemical methods to point out their synergistic relationship with experiments.

Nonuniform elastic properties of macromolecules and effect of prestrain on their continuum nature

Many experimental and theoretical methods have been developed to calculate the coarse-grained continuum elastic properties of macromolecules. However, all of those methods assume uniform elastic properties. Following the continuum mechanics framework, we present a systematic way of calculating the nonuniform effective elastic properties from atomic thermal fluctuations obtained from molecular dynamics simulation at any coarse-grained scale using a potential of the mean-force approach. We present the results for a mutant of Sesbania mosaic virus capsid, where we calculate the elastic moduli at different scales and observe an apparent problem with the chosen reference configuration in some cases. We present a possible explanation using an elastic network model, where inducing random prestrain results in a similar behavior. This phenomenon provides a novel insight into the continuum nature of macromolecules and defines the limits on details that the elasticity theory can capture. Further investigation into prestrains could elucidate important aspects of conformational dynamics of macromolecules.

Identification of allosteric disulfides from prestress analysis

Disulfide bonds serve to form physical cross-links between residues in protein structures, thereby stabilizing the protein fold. Apart from this purely structural role, they can also be chemically active, participating in redox reactions, and they may even potentially act as allosteric switches controlling protein functions. Specific types of disulfide bonds have been identified in static protein structures from their distinctive pattern of dihedral bond angles, and the allosteric function of such bonds is purported to be related to the torsional strain they store. Using all-atom molecular-dynamics simulations for ∼700 disulfide bonded proteins, we analyzed the intramolecular mechanical forces in 20 classes of disulfide bonds. We found that two particular classes, the -RHStaple and the -/+RHHook disulfides, are indeed more stressed than other disulfide bonds, but the stress is carried primarily by stretching of the S-S bond and bending of the neighboring bond angles, rather than by dihedral torsion. This stress corresponds to a tension force of magnitude ∼200 pN, which is balanced by repulsive van der Waals interactions between the cysteine Cα atoms. We confirm stretching of the S-S bond to be a general feature of the -RHStaples and the -/+RHHooks by analyzing ∼20,000 static protein structures. Given that forced stretching of S-S bonds is known to accelerate their cleavage, we propose that prestress of allosteric disulfide bonds has the potential to alter the reactivity of a disulfide, thereby allowing us to readily switch between functional states.

Tensegrity, cellular biophysics, and the mechanics of living systems

The recent convergence between physics and biology has led many physicists to enter the fields of cell and developmental biology. One of the most exciting areas of interest has been the emerging field of mechanobiology that centers on how cells control their mechanical properties, and how physical forces regulate cellular biochemical responses, a process that is known as mechanotransduction. In this article, we review the central role that tensegrity (tensional integrity) architecture, which depends on tensile prestress for its mechanical stability, plays in biology. We describe how tensional prestress is a critical governor of cell mechanics and function, and how use of tensegrity by cells contributes to mechanotransduction. Theoretical tensegrity models are also described that predict both quantitative and qualitative behaviors of living cells, and these theoretical descriptions are placed in context of other physical models of the cell. In addition, we describe how tensegrity is used at multiple size scales in the hierarchy of life—from individual molecules to whole living organisms—to both stabilize three-dimensional form and to channel forces from the macroscale to the nanoscale, thereby facilitating mechanochemical conversion at the molecular level.

Structure and dynamics of molecular networks: a novel paradigm of drug discovery: a comprehensive review

Despite considerable progress in genome- and proteome-based high-throughput screening methods and in rational drug design, the increase in approved drugs in the past decade did not match the increase of drug development costs. Network description and analysis not only give a systems-level understanding of drug action and disease complexity, but can also help to improve the efficiency of drug design. We give a comprehensive assessment of the analytical tools of network topology and dynamics. The state-of-the-art use of chemical similarity, protein structure, protein-protein interaction, signaling, genetic interaction and metabolic networks in the discovery of drug targets is summarized. We propose that network targeting follows two basic strategies. The "central hit strategy" selectively targets central nodes/edges of the flexible networks of infectious agents or cancer cells to kill them. The "network influence strategy" works against other diseases, where an efficient reconfiguration of rigid networks needs to be achieved by targeting the neighbors of central nodes/edges. It is shown how network techniques can help in the identification of single-target, edgetic, multi-target and allo-network drug target candidates. We review the recent boom in network methods helping hit identification, lead selection optimizing drug efficacy, as well as minimizing side-effects and drug toxicity. Successful network-based drug development strategies are shown through the examples of infections, cancer, metabolic diseases, neurodegenerative diseases and aging. Summarizing >1200 references we suggest an optimized protocol of network-aided drug development, and provide a list of systems-level hallmarks of drug quality. Finally, we highlight network-related drug development trends helping to achieve these hallmarks by a cohesive, global approach.

Isopeptide bonds mechanically stabilize spy0128 in bacterial pili

Pili on the surface of Streptococcus pyogenes play a crucial role in adhesion to and colonization in human cells. The major pilin subunit, Spy0128, features intramolecular covalent isopeptide bonds that autocatalytically form between the side chains of lysine and asparagine residues and are regarded as important factors in conveying structural stability. In support of this notion, single-molecule force spectroscopy experiments with Spy0128 recently demonstrated the inextensibility of these bonds under mechanical load. However, the molecular determinants of their apparent absolute durability remain unknown. Here, we studied the impact of the isopeptide bond in the Spy0128 C-terminal domain on the mechanical properties of this subunit using force-probe molecular dynamics simulations and force distribution analysis. Even in the presence of the covalent cross-link, the pili β-sandwich domain undergoes partial unfolding, albeit at ∼50% higher rupture forces and with the ability to rapidly refold on the nanosecond timescale. We find that the isopeptide bond is located right at the point of stress concentration in the protein, leading to relative, yet not absolute, mechanical stabilization by the additional cross-link. Our findings indicate how the isopeptide bond enhances the mechanical stability and refolding capability at the molecular level, ensuring that the domain remains predominantly in a potentially adhesive conformation.

Time-resolved force distribution analysis

Background

Biomolecules or other complex macromolecules undergo conformational transitions upon exposure to an external perturbation such as ligand binding or mechanical force. To follow fluctuations in pairwise forces between atoms or residues during such conformational changes as observed in Molecular Dynamics (MD) simulations, we developed Time-Resolved Force Distribution Analysis (TRFDA).

Results

The implementation focuses on computational efficiency and low-memory usage and, along with the wide range of output options, makes possible time series analysis of pairwise forces variation in long MD simulations and for large molecular systems. It also provides an exact decomposition of pairwise forces resulting from 3- and 4-body potentials and a unified treatment of pairwise forces between atoms or residues. As a proof of concept, we present a stress analysis during unfolding of ubiquitin in a force-clamp MD simulation.

Conclusions

TRFDA can be used, among others, in tracking signal propagation at atomic level, for characterizing dynamical intermolecular interactions (e.g. protein-ligand during flexible docking), in development of force fields and for following stress distribution during conformational changes.

SOD1 exhibits allosteric frustration to facilitate metal binding affinity

Superoxide dismutase-1 (SOD1) is a ubiquitous, Cu and Zn binding, free-radical defense enzyme whose misfolding and aggregation play a potential key role in amyotrophic lateral sclerosis, an invariably fatal neurodegenerative disease. Over 150 mutations in SOD1 have been identified with a familial form of the disease, but it is presently not clear what unifying features, if any, these mutants share to make them pathogenic. Here, we develop several unique computational assays for probing the thermo-mechanical properties of both ALS-associated and rationally designed SOD1 variants. Allosteric interaction-free energies between residues and metals are calculated, and a series of atomic force microscopy experiments are simulated with variable tether positions to quantify mechanical rigidity "fingerprints" for SOD1 variants. Mechanical fingerprinting studies of a series of C-terminally truncated mutants, along with an analysis of equilibrium dynamic fluctuations while varying native constraints, potential energy change upon mutation, frustratometer analysis, and analysis of the coupling between local frustration and metal binding interactions for a glycine scan of 90 residues together, reveal that the apo protein is internally frustrated, that these internal stresses are partially relieved by mutation but at the expense of metal-binding affinity, and that the frustration of a residue is directly related to its role in binding metals. This evidence points to apo SOD1 as a strained intermediate with "self-allostery" for high metal-binding affinity. Thus, the prerequisites for the function of SOD1 as an antioxidant compete with apo state thermo-mechanical stability, increasing the susceptibility of the protein to misfold in the apo state.

RNA under tension: Folding Landscapes, Kinetic partitioning Mechanism, and Molecular Tensegrity

Non-coding RNA sequences play a great role in controlling a number of cellular functions, thus raising the need to understand their complex conformational dynamics in quantitative detail. In this perspective, we first show that single molecule pulling when combined with with theory and simulations can be used to quantitatively explore the folding landscape of nucleic acid hairpins, and riboswitches with tertiary interactions. Applications to riboswitches, which are non-coding RNA elements that control gene expression by undergoing dynamical conformational changes in response to binding of metabolites, lead to an organization principle that assembly of RNA is determined by the stability of isolated helices. We also point out the limitations of single molecule pulling experiments, with molecular extension as the only accessible parameter, in extracting key parameters of the folding landscapes of RNA molecules.