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

Perturbative diffraction methods resolve a conformational switch that facilitates a two-step enzymatic mechanism

Enzymes catalyze biochemical reactions through precise positioning of substrates, cofactors, and amino acids to modulate the transition-state free energy. However, the role of conformational dynamics remains poorly understood due to poor experimental access. This shortcoming is evident with Escherichia coli dihydrofolate reductase (DHFR), a model system for the role of protein dynamics in catalysis, for which it is unknown how the enzyme regulates the different active site environments required to facilitate proton and hydride transfer. Here, we describe ligand-, temperature-, and electric-field-based perturbations during X-ray diffraction experiments to map the conformational dynamics of the Michaelis complex of DHFR. We resolve coupled global and local motions and find that these motions are engaged by the protonated substrate to promote efficient catalysis. This result suggests a fundamental design principle for multistep enzymes in which pre-existing dynamics enable intermediates to drive rapid electrostatic reorganization to facilitate subsequent chemical steps.

Physical effects of learning

Interacting many-body physical systems ranging from neural networks in the brain to folding proteins to self-modifying electrical circuits can learn to perform diverse tasks. This learning, both in nature and in engineered systems, can occur through evolutionary selection or through dynamical rules that drive active learning from experience. Here, we show that learning in linear physical networks with weak input signals leaves architectural imprints on the Hessian of a physical system. Compared to a generic organization of the system components, (a) the effective physical dimension of the response to inputs decreases, (b) the response of physical degrees of freedom to random perturbations (or system "susceptibility") increases, and (c) the low-eigenvalue eigenvectors of the Hessian align with the task. Overall, these effects embody the typical scenario for learning processes in physical systems in the weak input regime, suggesting ways of discovering whether a physical network may have been trained.

Molecular analysis of the type III interferon complex and its applications in protein engineering

Type III interferons (IFNλs) are cytokines with critical roles in the immune system and are attractive therapeutic candidates due to their tissue-specific activity. Despite entering several clinical trials, results have demonstrated limited efficacy and potency, partially attributed to low-affinity protein-protein interactions (PPIs) responsible for receptor complex formation. Subsequently, structural studies of the native IFNλ signaling complexes remain inaccessible. While protein engineering can overcome affinity limitations, tools to investigate low-affinity systems like these remain limited. To provide insights into previous efforts to strengthen the PPIs within this complex, we perform a molecular analysis of the extracellular ternary complexes of IFNλ3 using both computational and experimental approaches. We first use molecular simulations and modeling to quantify differences in PPIs and residue strain fluctuations, generate detailed free energy landscapes, and reveal structural differences between an engineered, high-affinity complex, and a model of the wild-type, low-affinity complex. This analysis illuminates distinct behaviors of these ligands, yielding mechanistic insights into IFNλ complex formation. We then apply these computational techniques in protein engineering and design by utilizing simulation data to identify hotspots of interaction to rationally engineer the native cytokine-receptor complex for increased stability. These simulations are then validated by experimental techniques, showing that a single mutation at a computationally predicted site of interaction between the two receptors increases PPIs and improves complex formation for all IFNλs. This study highlights the power of molecular dynamics simulations for protein engineering and design as applied to the IFNλ family but also presents a potential tool for analysis and engineering of other systems with low-affinity PPIs.

Bending forces and nucleotide state jointly regulate F-actin structure

ATP-hydrolysis-coupled actin polymerization is a fundamental mechanism of cellular force generation1-3. In turn, force4,5 and actin filament (F-actin) nucleotide state6 regulate actin dynamics by tuning F-actin's engagement of actin-binding proteins through mechanisms that are unclear. Here we show that the nucleotide state of actin modulates F-actin structural transitions evoked by bending forces. Cryo-electron microscopy structures of ADP-F-actin and ADP-Pi-F-actin with sufficient resolution to visualize bound solvent reveal intersubunit interfaces bridged by water molecules that could mediate filament lattice flexibility. Despite extensive ordered solvent differences in the nucleotide cleft, these structures feature nearly identical lattices and essentially indistinguishable protein backbone conformations that are unlikely to be discriminable by actin-binding proteins. We next introduce a machine-learning-enabled pipeline for reconstructing bent filaments, enabling us to visualize both continuous structural variability and side-chain-level detail. Bent F-actin structures reveal rearrangements at intersubunit interfaces characterized by substantial alterations of helical twist and deformations in individual protomers, transitions that are distinct in ADP-F-actin and ADP-Pi-F-actin. This suggests that phosphate rigidifies actin subunits to alter the bending structural landscape of F-actin. As bending forces evoke nucleotide-state dependent conformational transitions of sufficient magnitude to be detected by actin-binding proteins, we propose that actin nucleotide state can serve as a co-regulator of F-actin mechanical regulation.

Mechanical Allosteric Couplings of Redox-Induced Conformational Changes in Respiratory Complex I

We apply linear response theory to calculate mechanical allosteric couplings in respiratory complex I between the iron sulfur cluster N2, located in the catalytic cavity, and the membrane part of the enzyme, separated from it by more than 50 Å. According to our hypothesis, the redox reaction of ubiquinone in the catalytic cavity of the enzyme generates an unbalanced charge that via repulsion of the charged redox center N2 produces local mechanical stress that transmits into the membrane part of the enzyme where it induces proton pumping. Using coarse-grained simulations of the enzyme, we calculated mechanistic allosteric couplings that reveal the pathways of the mechanical transmission of the stress along the enzyme. The results shed light on the recent experimental studies where a stabilization of the enzyme with an introduced disulfide bridge resulted in the abolishing of proton pumping. Simulation of the disulfide bond action indicates a dramatic change of the mechanistic coupling pathways in line with experimental findings.

Solvent accessibility of E1α and E1β residues with known missense mutations causing pyruvate dehydrogenase complex (PDC) deficiency: Impact on PDC-E1 structure and function

Pyruvate dehydrogenase complex deficiency is a major cause of primary lactic acidemia resulting in high morbidity and mortality, with limited therapeutic options. PDHA1 mutations are responsible for >82% of cases. The E1 component of PDC is a symmetric dimer of heterodimers (αβ/α'β') encoded by PDHA1 and PDHB. We measured solvent accessibility surface area (SASA), utilized nearest-neighbor analysis, incorporated sequence changes using mutagenesis tool in PyMOL, and performed molecular modeling with SWISS-MODEL, to investigate the impact of residues with disease-causing missense variants (DMVs) on E1 structure and function. We reviewed 166 and 13 genetically resolved cases due to PDHA1 and PDHB, respectively, from variant databases. We expanded on 102 E1α and 13 E1β nonduplicate DMVs. DMVs of E1α Arg112-Arg224 stretch (exons 5-7) and of E1α Arg residues constituted 40% and 39% of cases, respectively, with invariant Arg349 accounting for 22% of arginine replacements. SASA analysis showed that 86% and 84% of residues with nonduplicate DMVs of E1α and E1β, respectively, are solvent inaccessible ("buried"). Furthermore, 30% of E1α buried residues with DMVs are deleterious through perturbation of subunit-subunit interface contact (SSIC), with 73% located in the Arg112-Arg224 stretch. E1α Arg349 represented 74% of buried E1α Arg residues involved in SSIC. Structural perturbations resulting from residue replacements in some matched neighboring pairs of amino acids on different subunits involved in SSIC at 2.9-4.0 Å interatomic distance apart, exhibit similar clinical phenotype. Collectively, this work provides insight for future target-based advanced molecular modeling studies, with implications for development of novel therapeutics for specific recurrent DMVs of E1α.

Strain and rupture of HIV-1 capsids during uncoating

SignificanceThe mature capsids of HIV-1 are transiently stable complexes that self-assemble around the viral genome during maturation, and uncoat to release preintegration complexes that archive a double-stranded DNA copy of the virus in the host cell genome. However, a detailed view of how HIV cores rupture remains lacking. Here, we elucidate the physical properties involved in capsid rupture using a combination of large-scale all-atom molecular dynamics simulations and cryo-electron tomography. We find that intrinsic strain on the capsid forms highly correlated patterns along the capsid surface, along which cracks propagate. Capsid rigidity also increases with high strain. Our findings provide fundamental insight into viral capsid uncoating.

Toward wide-spectrum antivirals against coronaviruses: Molecular characterization of SARS-CoV-2 NSP13 helicase inhibitors

To date, effective therapeutic treatments that confer strong attenuation against coronaviruses (CoVs) remain elusive. Among potential drug targets, the helicase of CoVs is attractive due to its sequence conservation and indispensability. We rely on atomistic molecular dynamics simulations to explore the structural coordination and dynamics associated with the SARS-CoV-2 Nsp13 apo enzyme, as well as their complexes with natural ligands. A complex communication network is revealed among the five domains of Nsp13, which is differentially activated because of the presence of the ligands, as shown by shear strain analysis, principal components analysis, dynamical cross-correlation matrix analysis, and water transport analysis. The binding free energy and the corresponding mechanism of action are presented for three small molecules that were shown to be efficient inhibitors of the previous SARS-CoV Nsp13 enzyme. Together, our findings provide critical fresh insights for rational design of broad-spectrum antivirals against CoVs.

GTP Cyclohydrolase I as a Potential Drug Target: New Insights into Its Allosteric Modulation via Normal Mode Analysis

Guanosine triphosphate (GTP) cyclohydrolase I (GCH1) catalyzes the conversion of GTP into dihydroneopterin triphosphate (DHNP). DHNP is the first intermediate of the folate de novo biosynthesis pathway in prokaryotic and lower eukaryotic microorganisms and the tetrahydrobiopterin (BH4) biosynthesis pathway in higher eukaryotes. The de novo folate biosynthesis provides essential cofactors for DNA replication, cell division, and synthesis of key amino acids in rapidly replicating pathogen cells, such as Plasmodium falciparum (P. falciparum), a causative agent of malaria. In eukaryotes, the product of the BH4 biosynthesis pathway is essential for the production of nitric oxide and several neurotransmitter precursors. An increased copy number of the malaria parasite P. falciparum GCH1 gene has been reported to influence antimalarial antifolate drug resistance evolution, whereas mutations in the human GCH1 are associated with neuropathic and inflammatory pain disorders. Thus, GCH1 stands as an important and attractive drug target for developing therapeutics. The GCH1 intrinsic dynamics that modulate its activity remains unclear, and key sites that exert allosteric effects across the structure are yet to be elucidated. This study employed the anisotropic network model to analyze the intrinsic motions of the GCH1 structure alone and in complex with its regulatory partner protein. We showed that the GCH1 tunnel-gating mechanism is regulated by a global shear motion and an outward expansion of the central five-helix bundle. We further identified hotspot residues within sites of structural significance for the GCH1 intrinsic allosteric modulation. The obtained results can provide a solid starting point to design novel antineuropathic treatments for humans and novel antimalarial drugs against the malaria parasite P. falciparum GCH1 enzyme.

Dimensional reduction in complex living systems: Where, why, and how

The unprecedented prowess of measurement techniques provides a detailed, multi-scale look into the depths of living systems. Understanding these avalanches of high-dimensional data-by distilling underlying principles and mechanisms-necessitates dimensional reduction. We propose that living systems achieve exquisite dimensional reduction, originating from their capacity to learn, through evolution and phenotypic plasticity, the relevant aspects of a non-random, smooth physical reality. We explain how geometric insights by mathematicians allow one to identify these genuine hallmarks of life and distinguish them from universal properties of generic data sets. We illustrate these principles in a concrete example of protein evolution, suggesting a simple general recipe that can be applied to understand other biological systems.

Training nonlinear elastic functions: nonmonotonic, sequence dependent and bifurcating

The elastic behavior of materials operating in the linear regime is constrained, by definition, to operations that are linear in the imposed deformation. Although the nonlinear regime holds promise for new functionality, the design in this regime is challenging. In this paper, we demonstrate that a recent approach based on training [Hexner et al., PNAS 2020, 201922847] allows responses that are inherently non-linear. By applying designer strains, a disordered solid evolves through plastic deformations that alter its response. We show examples of elaborate nonlinear training paths that lead to the following functions: (1) frequency conversion, (2) logic gate and (3) expansion or contraction along one axis, depending on the sequence of imposed transverse compressions. We study the convergence rate and find that it depends on the trained function.

Elusive Intermediate State Key in the Conversion of ATP Hydrolysis into Useful Work Driving the Ca2+ Pump SERCA

A key event in the ATP-driven transport cycle of the calcium pump sarco/endoplasmic reticulum Ca²⁺-ATPase (SERCA) occurs when autophosphorylation of the pump with two bound ions Ca²⁺ triggers a large conformational change that opens a gate on the luminal side of the membrane allowing the release of the ions. It is believed that this conformational transition proceeds through a two-step mechanism, with an initial rearrangement of the three cytoplasmic domains of the pump responsible for ATP binding and hydrolysis followed by the opening of the gate toward the luminal side in the transmembrane region. Here, molecular dynamics computation of the free energy landscapes associated with this transition show how, in response to phosphorylation, the cytoplasmic domains are partially reconfigured into an intermediate state on the path toward the E2 state with a closed luminal gate. It is suggested that the free energy associated with this conformational reorganization must subsequently be used to drive the opening of the gate on the luminal side.

Periodic training of creeping solids

We consider disordered solids in which the microscopic elements can deform plastically in response to stresses on them. We show that by driving the system periodically, this plasticity can be exploited to train in desired elastic properties, both in the global moduli and in local "allosteric" interactions. Periodic driving can couple an applied "source" strain to a "target" strain over a path in the energy landscape. This coupling allows control of the system's response, even at large strains well into the nonlinear regime, where it can be difficult to achieve control simply by design.

Molecular characterization of ebselen binding activity to SARS-CoV-2 main protease

There is an urgent need to repurpose drugs against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Recent computational-experimental screenings have identified several existing drugs that could serve as effective inhibitors of the virus' main protease, M^pro, which is involved in gene expression and replication. Among these, ebselen (2-phenyl-1,2-benzoselenazol-3-one) appears to be particularly promising. Here, we examine, at a molecular level, the potential of ebselen to decrease M^pro activity. We find that it exhibits a distinct affinity for the catalytic region. Our results reveal a higher-affinity, previously unknown binding site localized between the II and III domains of the protein. A detailed strain analysis indicates that, on such a site, ebselen exerts a pronounced allosteric effect that regulates catalytic site access through surface-loop interactions, thereby inducing a reconfiguration of water hotspots. Together, these findings highlight the promise of ebselen as a repurposed drug against SARS-CoV-2.

Mycobacterium tuberculosis FasR senses long fatty acyl-CoA through a tunnel and a hydrophobic transmission spine

Mycobacterium tuberculosis is a pathogen with a unique cell envelope including very long fatty acids, implicated in bacterial resistance and host immune modulation. FasR is a TetR-like transcriptional activator that plays a central role in sensing mycobacterial long-chain fatty acids and regulating lipid biosynthesis. Here we disclose crystal structures of M. tuberculosis FasR in complex with acyl effector ligands and with DNA, uncovering its molecular sensory and switching mechanisms. A long tunnel traverses the entire effector-binding domain, enabling long fatty acyl effectors to bind. Only when the tunnel is entirely occupied, the protein dimer adopts a rigid configuration with its DNA-binding domains in an open state, leading to DNA dissociation. The protein-folding hydrophobic core connects the two domains, and is completed into a continuous spine when the effector binds. Such a transmission spine is conserved in a large number of TetR-like regulators, offering insight into effector-triggered allosteric functional control.

FasR is a TetR-like transcriptional activator that plays a central role in sensing mycobacterial long-chain fatty acids and regulating lipid biosynthesis in Mycobacterium tuberculosis. Here authors present crystal structures of M. tuberculosis FasR in complex with acyl effector ligands and with DNA, uncovering its molecular sensory and switching mechanisms.

Direct coupling analysis of epistasis in allosteric materials

In allosteric proteins, the binding of a ligand modifies function at a distant active site. Such allosteric pathways can be used as target for drug design, generating considerable interest in inferring them from sequence alignment data. Currently, different methods lead to conflicting results, in particular on the existence of long-range evolutionary couplings between distant amino-acids mediating allostery. Here we propose a resolution of this conundrum, by studying epistasis and its inference in models where an allosteric material is evolved in silico to perform a mechanical task. We find in our model the four types of epistasis (Synergistic, Sign, Antagonistic, Saturation), which can be both short or long-range and have a simple mechanical interpretation. We perform a Direct Coupling Analysis (DCA) and find that DCA predicts well the cost of point mutations but is a rather poor generative model. Strikingly, it can predict short-range epistasis but fails to capture long-range epistasis, in consistence with empirical findings. We propose that such failure is generic when function requires subparts to work in concert. We illustrate this idea with a simple model, which suggests that other methods may be better suited to capture long-range effects.

Allostery in proteins is the property of highly specific responses to ligand binding at a distant site. To inform protocols of de novo drug design, it is fundamental to understand the impact of mutations on allosteric regulation and whether it can be predicted from evolutionary correlations. In this work we consider allosteric architectures artificially evolved to optimize the cooperativity of binding at allosteric and active site. We first characterize the emergent pattern of epistasis as well as the underlying mechanical phenomena, finding the four types of epistasis (Synergistic, Sign, Antagonistic, Saturation), which can be both short or long-range. The numerical evolution of these allosteric architectures allows us to benchmark Direct Coupling Analysis, a method which relies on co-evolution in sequence data to infer direct evolutionary couplings, in connection to allostery. We show that Direct Coupling Analysis predicts quantitatively point mutation costs but underestimates strong long-range epistasis. We provide an argument, based on a simplified model, illustrating the reasons for this discrepancy. Our analysis suggests neural networks as more promising tool to measure epistasis.

Normal mode analysis and beyond

Normal mode analysis provides a powerful tool in biophysical computations. Particularly, we shed light on its application to protein properties because they directly lead to biological functions. As a result of normal mode analysis, the protein motion is represented as a linear combination of mutually independent normal mode vectors. It has been widely accepted that the large amplitude motions throughout the entire protein molecule can be well described with a few low-frequency normal modes. Furthermore, it is possible to represent the effect of external perturbations, e.g., ligand binding, hydrostatic pressure, as the shifts of normal mode variables. Making use of this advantage, we are able to explore mechanical properties of proteins such as Young's modulus and compressibility. Within thermally fluctuating protein molecules under physiological conditions, tightly packed amino acid residues interact with each other through heat and energy exchanges. Since the structure and dynamics of protein molecules are highly anisotropic, the flow of energy and heat should also be anisotropic. Based on the harmonic approximation of the heat current operator, it is possible to analyze the communication map of a protein molecule. By using this method, the energy transfer pathways of photoactive yellow protein were calculated. It turned out that these pathways are similar to those obtained via the Green-Kubo formalism with equilibrium molecular dynamics simulations, indicating that normal mode analysis captures the intrinsic nature of the transport properties of proteins.

Mechanics of Allostery: Contrasting the Induced Fit and Population Shift Scenarios

In allosteric proteins, binding a ligand can affect function at a distant location, for example, by changing the binding affinity of a substrate at the active site. The induced fit and population shift models, which differ by the assumed number of stable configurations, explain such cooperative binding from a thermodynamic viewpoint. Yet, understanding what mechanical principles constrain these models remains a challenge. Here, we provide an empirical study on 34 proteins supporting the idea that allosteric conformational change generally occurs along a soft elastic mode presenting extended regions of high shear. We argue, based on a detailed analysis of how the energy profile along such a mode depends on binding, that in the induced fit scenario, there is an optimal stiffness ka∗ ∼ 1/N for cooperative binding, where N is the number of residues. We find that the population shift scenario is more robust to mutations affecting stiffness because binding becomes more and more cooperative with stiffness up to the same characteristic value ka∗, beyond which cooperativity saturates instead of decaying. We numerically confirm these findings in a nonlinear mechanical model. Dynamical considerations suggest that a stiffness of order ka∗ is favorable in that scenario as well, supporting that for proper function, proteins must evolve a functional elastic mode that is softer as their size increases. In consistency with this view, we find a fair anticorrelation between the stiffness of the allosteric response and protein size in our data set.

Principles for Optimal Cooperativity in Allosteric Materials

Allosteric proteins transmit a mechanical signal induced by binding a ligand. However, understanding the nature of the information transmitted and the architectures optimizing such transmission remains a challenge. Here we show, using an in silico evolution scheme and theoretical arguments, that architectures optimized to be cooperative, which efficiently propagate energy, qualitatively differ from previously investigated materials optimized to propagate strain. Although we observe a large diversity of functioning cooperative architectures (including shear, hinge, and twist designs), they all obey the same principle of displaying a mechanism, i.e., an extended soft mode. We show that its optimal frequency decreases with the spatial extension L of the system as L^-d/2, where d is the spatial dimension. For these optimal designs, cooperativity decays logarithmically with L for d = 2 and does not decay for d = 3. Overall, our approach leads to a natural explanation for several observations in allosteric proteins and indicates an experimental path to test if allosteric proteins lie close to optimality.

On identifying collective displacements in apo-proteins that reveal eventual binding pathways

Binding of small molecules to proteins often involves large conformational changes in the latter, which open up pathways to the binding site. Observing and pinpointing these rare events in large scale, all-atom, computations of specific protein-ligand complexes, is expensive and to a great extent serendipitous. Further, relevant collective variables which characterise specific binding or un-binding scenarios are still difficult to identify despite the large body of work on the subject. Here, we show that possible primary and secondary binding pathways can be discovered from short simulations of the apo-protein without waiting for an actual binding event to occur. We use a projection formalism, introduced earlier to study deformation in solids, to analyse local atomic displacements into two mutually orthogonal subspaces—those which are “affine” i.e. expressible as a homogeneous deformation of the native structure, and those which are not. The susceptibility to non-affine displacements among the various residues in the apo- protein is then shown to correlate with typical binding pathways and sites crucial for allosteric modifications. We validate our observation with all-atom computations of three proteins, T4-Lysozyme, Src kinase and Cytochrome P450.

Designing drugs which target specific proteins involved in diseases consumes a lot of time and effort in the pharmaceutical industry. In recent times, in silico design of drugs using all-atom molecular modelling has started to provide crucial inputs. Even so, discovery of binding pathways of small molecules both at the primary binding site, as well as sites for allosteric control, is time consuming and often fortuitous. We provide here a framework within which critical conformational changes likely to occur during binding are quantified from statistical analysis of configurations of proteins in their apo, or inactive form, greatly simplifying identification of target residues. We illustrate this idea by analysing ligand binding pathways for three proteins T4- Lysozyme, P450 and Src kinase, which are active respectively in the immune system, metabolism and cancer.

Stochastic protein multimerization, activity, and fitness

Many proteins assemble into homomultimeric structures, with a number of subunits that can vary substantially among phylogenetic lineages. As protein-protein interactions require productive encounters among subunits, such variation might partially be explained by variation in cellular protein abundance. Protein abundance in turn depends on the intrinsic rates of production and decay of mRNA and protein molecules, as well as rates of cell growth and division. Using a stochastic framework for prediction of the multimeric state of a protein as a function of these processes and the free energy associated with interface-interface binding, we demonstrate agreement with a wide class of proteins using E. coli proteome data. As such, this platform, which links protein quaternary structure with biochemical rates governing gene expression, protein association and dissociation, and cell growth and division, can be extended to evolutionary models for the emergence and diversification of multimers. While it is tempting to think of multimerization as adaptive, the diversity of multimeric states raises the question of its functional role and impact on fitness. As a force driving selection, we consider the possible increase in enzymatic activity of proteins arising strictly as a consequence of interface-interface binding-namely, enhanced stability to degradation, substrate binding affinity, or catalytic rate of multimers with respect to monomers without invoking further conformational changes, as in allostery. For fixed cost of protein production, we find a benefit conferred by multimers that is dependent on context and can therefore become different in diverging lineages.

Catalytic enzymes are active matter

Catalysis and mobility of reactants in fluid are normally thought to be decoupled. Violating this classical paradigm, this paper presents the catalyst laws of motion. Comparing experimental data to the theory presented here, we conclude that part of the free energy released by chemical reaction is channeled into driving catalysts to execute wormlike trajectories by piconewton forces performing work of a few k_BT against fluid viscosity, where the rotational diffusion rate dictates the trajectory persistence length. This active motion agitates the fluid medium and produces antichemotaxis, the migration of catalyst down the gradient of the reactant concentration. Alternative explanations of enhanced catalyst mobility are examined critically.

Using a microscopic theory to analyze experiments, we demonstrate that enzymes are active matter. Superresolution fluorescence measurements—performed across four orders of magnitude of substrate concentration, with emphasis on the biologically relevant regime around or below the Michaelis–Menten constant—show that catalysis boosts the motion of enzymes to be superdiffusive for a few microseconds, enhancing their effective diffusivity over longer timescales. Occurring at the catalytic turnover rate, these fast ballistic leaps maintain direction over a duration limited by rotational diffusion, driving enzymes to execute wormlike trajectories by piconewton forces performing work of a few k_BT against viscosity. The boosts are more frequent at high substrate concentrations, biasing the trajectories toward substrate-poor regions, thus exhibiting antichemotaxis, demonstrated here experimentally over a wide range of aqueous concentrations. Alternative noncatalytic, passive mechanisms that predict chemotaxis, cross-diffusion, and phoresis, are critically analyzed. We examine the physical interpretation of our findings, speculate on the underlying mechanism, and discuss the avenues they open with biological and technological implications. These findings violate the classical paradigm that chemical reaction and motility are distinct processes, and suggest reaction–motion coupling as a general principle of catalysis.

The impact of cryosolution thermal contraction on proteins and protein crystals: volumes, conformation and order

Cryocooling of macromolecular crystals is commonly employed to limit radiation damage during X-ray diffraction data collection. However, cooling itself affects macromolecular conformation and often damages crystals via poorly understood processes. Here, the effects of cryosolution thermal contraction on macromolecular conformation and crystal order in crystals ranging from 32 to 67% solvent content are systematically investigated. It is found that the solution thermal contraction affects macromolecule configurations and volumes, unit-cell volumes, crystal packing and crystal order. The effects occur through not only thermal contraction, but also pressure caused by the mismatched contraction of cryosolvent and pores. Higher solvent-content crystals are more affected. In some cases the solvent contraction can be adjusted to reduce mosaicity and increase the strength of diffraction. Ice formation in some crystals is found to cause damage via a reduction in unit-cell volume, which is interpreted through solvent transport out of unit cells during cooling. The results point to more deductive approaches to cryoprotection optimization by adjusting the cryosolution composition to reduce thermal contraction-induced stresses in the crystal with cooling.

Allostery and cooperativity in multimeric proteins: bond-to-bond propensities in ATCase

Aspartate carbamoyltransferase (ATCase) is a large dodecameric enzyme with six active sites that exhibits allostery: its catalytic rate is modulated by the binding of various substrates at distal points from the active sites. A recently developed method, bond-to-bond propensity analysis, has proven capable of predicting allosteric sites in a wide range of proteins using an energy-weighted atomistic graph obtained from the protein structure and given knowledge only of the location of the active site. Bond-to-bond propensity establishes if energy fluctuations at given bonds have significant effects on any other bond in the protein, by considering their propagation through the protein graph. In this work, we use bond-to-bond propensity analysis to study different aspects of ATCase activity using three different protein structures and sources of fluctuations. First, we predict key residues and bonds involved in the transition between inactive (T) and active (R) states of ATCase by analysing allosteric substrate binding as a source of energy perturbations in the protein graph. Our computational results also indicate that the effect of multiple allosteric binding is non linear: a switching effect is observed after a particular number and arrangement of substrates is bound suggesting a form of long range communication between the distantly arranged allosteric sites. Second, cooperativity is explored by considering a bisubstrate analogue as the source of energy fluctuations at the active site, also leading to the identification of highly significant residues to the T ↔ R transition that enhance cooperativity across active sites. Finally, the inactive (T) structure is shown to exhibit a strong, non linear communication between the allosteric sites and the interface between catalytic subunits, rather than the active site. Bond-to-bond propensity thus offers an alternative route to explain allosteric and cooperative effects in terms of detailed atomistic changes to individual bonds within the protein, rather than through phenomenological, global thermodynamic arguments.

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

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

Dissipation at the angstrom scale: Probing the surface and interior of an enzyme

Pursuing a materials science approach to understanding the deformability of enzymes, we introduce measurements of the phase of the mechanical response function within the nanorheology paradigm. Driven conformational motion of the enzyme is dissipative as characterized by the phase measurements. The dissipation originates both from the surface hydration layer and the interior of the molecule, probed by examining the effect of point mutations on the mechanics. We also document changes in the mechanics of the enzyme examined, guanylate kinase, upon binding its four substrates. GMP binding stiffens the molecule, ATP and ADP binding softens it, while there is no clear mechanical signature of GDP binding. A hyperactive two-Gly mutant is found to possibly trade specificity for speed. Global deformations of enzymes are shown to be dependent on both hydration layer and polypeptide chain dynamics.

Elastic strain and twist analysis of protein structural data and allostery of the transmembrane channel KcsA

The abundance of available static protein structural data makes the more effective analysis and interpretation of this data a valuable tool to supplement the experimental study of protein mechanics. Structural displacements can be difficult to analyze and interpret. Previously, we showed that strains provide a more natural and interpretable representation of protein deformations, revealing mechanical coupling between spatially distinct sites of allosteric proteins. Here, we demonstrate that other transformations of displacements yield additional insights. We calculate the divergence and curl of deformations of the transmembrane channel KcsA. Additionally, we introduce quantities analogous to bend, splay, and twist deformation energies of nematic liquid crystals. These transformations enable the decomposition of displacements into different modes of deformation, helping to characterize the type of deformation a protein undergoes. We apply these calculations to study the filter and gating regions of KcsA. We observe a continuous path of rotational deformations physically coupling these two regions, and, we propose, underlying the allosteric interaction between these regions. Bend, splay, and twist distinguish KcsA gate opening, filter opening, and filter-gate coupling, respectively. In general, physically meaningful representations of deformations (like strain, curl, bend, splay, and twist) can make testable predictions and yield insights into protein mechanics, augmenting experimental methods and more fully exploiting available structural data.

Why Ubiquitin Has Not Evolved

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

Printing Non-Euclidean Solids

Geometrically frustrated solids with a non-Euclidean reference metric are ubiquitous in biology and are becoming increasingly relevant in technological applications. Often they acquire a targeted configuration of incompatibility through the surface accretion of mass as in tree growth or dam construction. We use the mechanics of incompatible surface growth to show that geometrical frustration developing during deposition can be fine-tuned to ensure a particular behavior of the system in physiological (or working) conditions. As an illustration, we obtain an explicit 3D printing protocol for arteries, which guarantees stress uniformity under inhomogeneous loading, and for explosive plants, allowing a complete release of residual elastic energy with a single cut. Interestingly, in both cases reaching the physiological target requires the incompatibility to have a topological (global) component.

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.