Prebiotic chemical reactivity in solution with quantum accuracy and microsecond sampling using neural network potentials.

While RNA appears as a good candidate for the first autocatalytic systems preceding the emergence of modern life, the synthesis of RNA oligonucleotides without enzymes remains challenging. Because the uncatalyzed reaction is extremely slow, experimental studies bring limited and indirect information on the reaction mechanism, the nature of which remains debated. Here, we develop neural network potentials (NNPs) to study the phosphoester bond formation in water. While NNPs are becoming routinely applied to nonreactive systems or simple reactions, we demonstrate how they can systematically be trained to explore the reaction phase space for complex reactions involving several proton transfers and exchanges of heavy atoms. We then propagate at moderate computational cost hundreds of nanoseconds of a variety of enhanced sampling simulations with quantum accuracy in explicit solvent conditions. The thermodynamically preferred reaction pathway is a concerted, dissociative mechanism, with the transient formation of a metaphosphate transition state and direct participation of water solvent molecules that facilitate the exchange of protons through the nonbridging phosphate oxygens. Associative-dissociative pathways, characterized by a much tighter pentacoordinated phosphate, are higher in free energy. Our simulations also suggest that diprotonated phosphate, whose reactivity is never directly assessed in the experiments, is significantly less reactive than the monoprotonated species, suggesting that it is probably never the reactive species in normal pH conditions. These observations rationalize unexplained experimental results and the temperature dependence of the reaction rate, and they pave the way for the design of more efficient abiotic catalysts and activating groups.

Binding site plasticity regulation of the FimH catch-bond mechanism.

The bacterial fimbrial adhesin FimH is a remarkable and well-studied catch-bond protein found at the tip of E. coli type 1 pili, which allows pathogenic strains involved in urinary tract infections to bind high-mannose glycans exposed on human epithelia. The catch-bond behavior of FimH, where the strength of the interaction increases when a force is applied to separate the two partners, enables the bacteria to resist clearance when they are subjected to shear forces induced by urine flow. Two decades of experimental studies performed at the single-molecule level, as well as x-ray crystallography and modeling studies, have led to a consensus picture whereby force separates the binding domain from an inhibitor domain, effectively triggering an allosteric conformational change in the former. This force-induced allostery is thought to be responsible for an increased binding affinity at the core of the catch-bond mechanism. However, some important questions remain, the most challenging one being that the crystal structures corresponding to these two allosteric states show almost superimposable binding site geometries, which questions the molecular origin for the large difference in affinity. Using molecular dynamics with a combination of enhanced-sampling techniques, we demonstrate that the static picture provided by the crystal structures conceals a variety of binding site conformations that have a key impact on the apparent affinity. Crucially, the respective populations in each of these conformations are very different between the two allosteric states of the binding domain, which can then be related to experimental affinity measurements. We also evidence a previously unappreciated but important effect: in addition to the well-established role of the force as an allosteric regulator via domain separation, application of force tends to directly favor the high-affinity binding site conformations. We hypothesize that this additional "local" catch-bond effect could delay unbinding between the bacteria and the host cell before the "global" allosteric transition occurs, as well as stabilizing the complex even more once in the high-affinity allosteric state.

A Single-Molecule Strategy to Capture Non-native Intramolecular and Intermolecular Protein Disulfide Bridges.

Non-native disulfide bonds are dynamic covalent bridges that form post-translationally between two cysteines within the same protein (intramolecular) or with a neighboring protein (intermolecular), frequently due to changes in the cellular redox potential. The reversible formation of non-native disulfides is intimately linked to alterations in protein function; while they can provide a mechanism to protect against cysteine overoxidation, they are also involved in the early stages of protein multimerization, a hallmark of several protein aggregation diseases. Yet their identification using current protein chemistry technology remains challenging, mainly because of their fleeting reactivity. Here, we use single-molecule spectroscopy AFM and molecular dynamics simulations to capture both intra- and intermolecular disulfide bonds in γD-crystallin, a cysteine-rich, structural human lens protein involved in age-related eye cataracts. Our approach showcases the power of mechanical force as a conformational probe in dynamically evolving proteins and presents a platform to detect non-native disulfide bridges with single-molecule resolution.

Explicit Models of Motion to Understand Protein Side-Chain Dynamics.

Nuclear magnetic relaxation is widely used to probe protein dynamics. For decades, most analyses of relaxation in proteins have relied successfully on the model-free approach, forgoing mechanistic descriptions of motion. Model-free types of correlation functions cannot describe a large carbon-13 relaxation dataset in protein side chains. Here, we use molecular dynamics simulations to design explicit models of motion and solve Fokker-Planck diffusion equations. These models of motion provide better agreement with relaxation data, mechanistic insight, and a direct link to configuration entropy.

Mass effects for thermodiffusion in dilute aqueous solutions.

Thermodiffusion is the phenomenon by which molecules in a mixture present concentration gradients in response to an imposed temperature gradient. Despite decades of investigations, this effect remains poorly understood at a molecular level. A common, phenomenological approach is to individuate the molecular factors that influence the Soret coefficient, the parameter that quantifies the resulting concentration-gradient. Experimental studies, often performed on organic mixtures, as well as simulations of model particle systems have evidenced that the difference in masses between the mixture components has an important effect on the amplitude of the Soret coefficient. Here, we use molecular dynamics simulations of a thermophoretic setting to investigate the mass dependence of the Soret coefficient in dilute aqueous solutions. An advantage of simulation approaches is that they are not limited in the range of explored molecular masses, which is often limited to isotopic substitutions in the experiments. Our simulations reveal that the mass dependence of the Soret coefficient in these solutions is in agreement with previous experimental and simulation work on molecular-size systems. In particular, it is sensitive to the relative mass difference between the solute and the solvent, but not to their absolute mass. Adjusting the mass of the solvent and of the solute can turn a thermophobic solution into a thermophilic one, where solute accumulation is reversed. This demonstrates that the mass effect can indeed compensate for the other contributions to the Soret coefficient. Finally, we find that changing the molecular moments of inertia has a much more limited impact as compared to a change in the total molecular mass.

Structural transitions in the RNA 7SK 5' hairpin and their effect on HEXIM binding.

7SK RNA, as part of the 7SK ribonucleoprotein complex, is crucial to the regulation of transcription by RNA-polymerase II, via its interaction with the positive transcription elongation factor P-TEFb. The interaction is induced by binding of the protein HEXIM to the 5' hairpin (HP1) of 7SK RNA. Four distinct structural models have been obtained experimentally for HP1. Here, we employ computational methods to investigate the relative stability of these structures, transitions between them, and the effects of mutations on the observed structural ensembles. We further analyse the results with respect to mutational binding assays, and hypothesize a mechanism for HEXIM binding. Our results indicate that the dominant structure in the wild type exhibits a triplet involving the unpaired nucleotide U40 and the base pair A43-U66 in the GAUC/GAUC repeat. This conformation leads to an open major groove with enough potential binding sites for peptide recognition. Sequence mutations of the RNA change the relative stability of the different structural ensembles. Binding affinity is consequently lost if these changes alter the dominant structure.

In silico all-atom approach to thermodiffusion in dilute aqueous solutions.

Thermodiffusion (or thermophoresis) is the phenomenon by which the spatial distributions of constituents of liquid or gas phases become inhomogeneous in response to a temperature gradient. It has been evidenced in a variety of systems and has many practical applications as well as implications in the context of the origins of life. A complete molecular picture of thermophoresis is still missing, and phenomenological approaches are often employed to account for the experimental observations. In particular, the amplitude of the resulting concentration-gradients (quantified by the Soret coefficient) depends on many factors that are not straightforwardly rationalized. All-atom molecular dynamics simulations appear as an exquisite tool to shed light on the molecular origins for this phenomenon in molecular systems, but the practical implementation of thermophoretic settings in silico poses significant challenges. Here, we propose a robust approach to tackle thermophoresis in dilute realistic solutions at the molecular level. We rely on a recent enhanced heat-exchange algorithm to generate temperature-gradients. We carefully assess the convergence of thermophoretic simulations in dilute aqueous solutions. We show that simulations typically need to be propagated on long timescales (hundreds of nanoseconds). We find that the magnitude of the temperature gradient and the box sizes have little effect on the measured Soret coefficients. Practical guidelines are derived from such observations. Provided with this reliable setup, we discuss the results of thermophoretic simulations on several examples of molecular, neutral solutes, which we find in very good agreement with experimental measurements regarding the concentration-, mass-, and temperature-dependence of the Soret coefficient.

Conformational entropy of a single peptide controlled under force governs protease recognition and catalysis.

An immense repertoire of protein chemical modifications catalyzed by enzymes is available as proteomics data. Quantifying the impact of the conformational dynamics of the modified peptide remains challenging to understand the decisive kinetics and amino acid sequence specificity of these enzymatic reactions in vivo, because the target peptide must be disordered to accommodate the specific enzyme-binding site. Here, we were able to control the conformation of a single-molecule peptide chain by applying mechanical force to activate and monitor its specific cleavage by a model protease. We found that the conformational entropy impacts the reaction in two distinct ways. First, the flexibility and accessibility of the substrate peptide greatly increase upon mechanical unfolding. Second, the conformational sampling of the disordered peptide drives the specific recognition, revealing force-dependent reaction kinetics. These results support a mechanism of peptide recognition based on conformational selection from an ensemble that we were able to quantify with a torsional free-energy model. Our approach can be used to predict how entropy affects site-specific modifications of proteins and prompts conformational and mechanical selectivity.

Thermal Adaptation of Enzymes: Impacts of Conformational Shifts on Catalytic Activation Energy and Optimum Temperature.

Thermal adaptation of enzymes is essential for both living organism development in extreme conditions and efficient biocatalytic applications. However, the molecular mechanisms leading to a shift in catalytic activity optimum temperatures remain unclear, and there is increasing experimental evidence that thermal adaptation involves complex changes in both structural and reactive properties. Here, a combination of enhanced protein conformational sampling with an explicit chemical reaction description was applied to mesophilic and thermophilic homologues of the dihydrofolate reductase enzyme, and a quantitative description of the stability and catalytic activity shifts between homologues was obtained. The key role played by temperature-induced shifts in protein conformational distributions is revealed. In contrast with pictures focusing on protein flexibility and dynamics, it is shown that while the homologues' reaction free energies are similar, the striking discrepancy between their activation energies is caused by their different conformational changes with temperature. An analytic model is proposed that combines catalytic activity and structural stability, and which quantitatively predicts the shift in homologue optimum temperatures. It is shown that this general model provides a molecular explanation of changes in optimum temperatures for several other enzymes.

Differences in thermal structural changes and melting between mesophilic and thermophilic dihydrofolate reductase enzymes.

A key aspect of life's evolution on Earth is the adaptation of proteins to be stable and work in a very wide range of temperature conditions. A detailed understanding of the associated molecular mechanisms would also help to design enzymes optimized for biotechnological processes. Despite important advances, a comprehensive picture of how thermophilic enzymes succeed in functioning under extreme temperatures remains incomplete. Here, we examine the temperature dependence of stability and of flexibility in the mesophilic monomeric Escherichia coli (Ec) and thermophilic dimeric Thermotoga maritima (Tm) homologs of the paradigm dihydrofolate reductase (DHFR) enzyme. We use all-atom molecular dynamics simulations and a replica-exchange scheme that allows to enhance the conformational sampling while providing at the same time a detailed understanding of the enzymes' behavior at increasing temperatures. We show that this approach reproduces the stability shift between the two homologs, and provides a molecular description of the denaturation mechanism by identifying the sequence of secondary structure elements melting as temperature increases, which is not straightforwardly obtained in the experiments. By repeating our approach on the hypothetical TmDHFR monomer, we further determine the respective effects of sequence and oligomerization in the exceptional stability of TmDFHR. We show that the intuitive expectation that protein flexibility and thermal stability are correlated is not verified. Finally, our simulations reveal that significant conformational fluctuations already take place much below the melting temperature. While the difference between the TmDHFR and EcDHFR catalytic activities is often interpreted via a simplified two-state picture involving the open and closed conformations of the key M20 loop, our simulations suggest that the two homologs' markedly different activity temperature dependences are caused by changes in the ligand-cofactor distance distributions in response to these conformational changes.

Water dynamics at electrified graphene interfaces: a jump model perspective.

The reorientation dynamics of water at electrified graphene interfaces was recently shown [J. Phys. Chem. Lett., 2020, 11, 624-631] to exhibit a surprising and strongly asymmetric behavior: positive electrode potentials slow down interfacial water reorientation, while for increasingly negative potentials water dynamics first accelerates before reaching an extremum and then being retarded for larger potentials. Here we use classical molecular dynamics simulations to determine the molecular mechanisms governing water dynamics at electrified interfaces. We show that changes in water reorientation dynamics with electrode potential arise from the electrified interfaces' impacts on water hydrogen-bond jump exchanges, and can be quantitatively described by the extended jump model. Finally, our simulations indicate that no significant dynamical heterogeneity occurs within the water interfacial layer next to the weakly interacting graphene electrode.

Critical structural fluctuations of proteins upon thermal unfolding challenge the Lindemann criterion.

Internal subnanosecond timescale motions are key for the function of proteins, and are coupled to the surrounding solvent environment. These fast fluctuations guide protein conformational changes, yet their role for protein stability, and for unfolding, remains elusive. Here, in analogy with the Lindemann criterion for the melting of solids, we demonstrate a common scaling of structural fluctuations of lysozyme protein embedded in different environments as the thermal unfolding transition is approached. By combining elastic incoherent neutron scattering and advanced molecular simulations, we show that, although different solvents modify the protein melting temperature, a unique dynamical regime is attained in proximity of thermal unfolding in all solvents that we tested. This solvation shell-independent dynamical regime arises from an equivalent sampling of the energy landscape at the respective melting temperatures. Thus, we propose that a threshold for the conformational entropy provided by structural fluctuations of proteins exists, beyond which thermal unfolding is triggered.

How osmolytes influence hydrophobic polymer conformations: A unified view from experiment and theory.

It is currently the consensus belief that protective osmolytes such as trimethylamine N-oxide (TMAO) favor protein folding by being excluded from the vicinity of a protein, whereas denaturing osmolytes such as urea lead to protein unfolding by strongly binding to the surface. Despite there being consensus on how TMAO and urea affect proteins as a whole, very little is known as to their effects on the individual mechanisms responsible for protein structure formation, especially hydrophobic association. In the present study, we use single-molecule atomic force microscopy and molecular dynamics simulations to investigate the effects of TMAO and urea on the unfolding of the hydrophobic homopolymer polystyrene. Incorporated with interfacial energy measurements, our results show that TMAO and urea act on polystyrene as a protectant and a denaturant, respectively, while complying with Tanford-Wyman preferential binding theory. We provide a molecular explanation suggesting that TMAO molecules have a greater thermodynamic binding affinity with the collapsed conformation of polystyrene than with the extended conformation, while the reverse is true for urea molecules. Results presented here from both experiment and simulation are in line with earlier predictions on a model Lennard-Jones polymer while also demonstrating the distinction in the mechanism of osmolyte action between protein and hydrophobic polymer. This marks, to our knowledge, the first experimental observation of TMAO-induced hydrophobic collapse in a ternary aqueous system.

How force unfolding differs from chemical denaturation.

Single-molecule force spectroscopies are remarkable tools for studying protein folding and unfolding, but force unfolding explores protein configurations that are potentially very different from the ones traditionally explored in chemical or thermal denaturation. Understanding these differences is crucial because such configurations serve as starting points of folding studies, and thus can affect both the folding mechanism and the kinetics. Here we provide a detailed comparison of both chemically induced and force-induced unfolded state ensembles of ubiquitin based on extensive, all-atom simulations of the protein either extended by force or denatured by urea. As expected, the respective unfolded states are very different on a macromolecular scale, being fully extended under force with no contacts and partially extended in urea with many nonnative contacts. The amount of residual secondary structure also differs: A significant population of α-helices is found in chemically denatured configurations but such helices are absent under force, except at the lowest applied force of 30 pN where short helices form transiently. We see that typical-size helices are unstable above this force, and ß-sheets cannot form. More surprisingly, we observe striking differences in the backbone dihedral angle distributions for the protein unfolded under force and the one unfolded by denaturant. A simple model based on the dialanine peptide is shown to not only provide an explanation for these striking differences but also illustrates how the force dependence of the protein dihedral angle distributions give rise to the worm-like chain behavior of the chain upon force.

Orientational Dynamics of Water at an Extended Hydrophobic Interface.

We report on the orientational dynamics of water at an extended hydrophobic interface with an octadecylsilane self-assembled monolayer on fused silica. The interfacial dangling OH stretch mode is excited with a resonant pump, and its evolution followed in time by a surface-specific, vibrationally resonant, infrared-visible sum-frequency probe. High sensitivity pump-probe anisotropy measurements and isotopic dilution clearly reveal that the decay of the dangling OH stretch excitation is almost entirely due to a jump to a hydrogen-bonded configuration that occurs in 1.61 ± 0.10 ps. This is more than twice as fast as the jump time from one hydrogen-bonded configuration to another in bulk H2O but about 50% slower than the reported out-of-plane reorientation at the air/water interface. In contrast, the intrinsic population lifetime of the dangling OH stretch in the absence of such jumps is found to be >10 ps. Molecular dynamics simulations of air/water and hexane/water interfaces reproduce the fast jump dynamics of interfacial dangling OH with calculated jump times of 1.4 and 1.7 ps for the air and hydrophobic interfaces, respectively. The simulations highlight that while the air/water and hydrophobic/water surfaces exhibit great structural similarities, a small stabilization of the OH groups by the hydrophobic interface produces the pronounced difference in the dynamics of dangling bonds.

Elasticity, structure, and relaxation of extended proteins under force.

Force spectroscopies have emerged as a powerful and unprecedented tool to study and manipulate biomolecules directly at a molecular level. Usually, protein and DNA behavior under force is described within the framework of the worm-like chain (WLC) model for polymer elasticity. Although it has been surprisingly successful for the interpretation of experimental data, especially at high forces, the WLC model lacks structural and dynamical molecular details associated with protein relaxation under force that are key to the understanding of how force affects protein flexibility and reactivity. We use molecular dynamics simulations of ubiquitin to provide a deeper understanding of protein relaxation under force. We find that the WLC model successfully describes the simulations of ubiquitin, especially at higher forces, and we show how protein flexibility and persistence length, probed in the force regime of the experiments, are related to how specific classes of backbone dihedral angles respond to applied force. Although the WLC model is an average, backbone model, we show how the protein side chains affect the persistence length. Finally, we find that the diffusion coefficient of the protein's end-to-end distance is on the order of 10(8) nm(2)/s, is position and side-chain dependent, but is independent of the length and independent of the applied force, in contrast with other descriptions.

The elastic free energy of a tandem modular protein under force.

Recent studies have provided a theoretical framework for including entropic elasticity in the free energy landscape of proteins under mechanical force. Accounting for entropic elasticity using polymer physics models has helped explain the hopping behavior seen in single molecule experiments in the low force regime. Here, we expand on the construction of the free energy of a single protein domain under force proposed by Berkovich et al. to provide a free energy landscape for N tandem domains along a continuous polypeptide. Calculation of the free energy of individual domains followed by their concatenation provides a continuous free energy landscape whose curvature is dominated by the worm-like chain at forces below 20 pN. We have validated our free energy model using Brownian dynamics and reproduce key features of protein folding. This free energy model can predict the effects of changes in the elastic properties of a multidomain protein as a consequence of biological modifications such as phosphorylation or the formation of disulfide bonds. This work lays the foundations for the modeling of tissue elasticity, which is largely determined by the properties of tandem polyproteins.

Rate limit of protein elastic response is tether dependent.

The elastic restoring force of tissues must be able to operate over the very wide range of loading rates experienced by living organisms. It is surprising that even the fastest events involving animal muscle tissues do not surpass a few hundred hertz. We propose that this limit is set in part by the elastic dynamics of tethered proteins extending and relaxing under a changing load. Here we study the elastic dynamics of tethered proteins using a fast force spectrometer with sub-millisecond time resolution, combined with Brownian and Molecular Dynamics simulations. We show that the act of tethering a polypeptide to an object, an inseparable part of protein elasticity in vivo and in experimental setups, greatly reduces the attempt frequency with which the protein samples its free energy. Indeed, our data shows that a tethered polypeptide can traverse its free-energy landscape with a surprisingly low effective diffusion coefficient D(eff) ~ 1,200 nm(2)/s. By contrast, our Molecular Dynamics simulations show that diffusion of an isolated protein under force occurs at D(eff) ~ 10(8) nm(2)/s. This discrepancy is attributed to the drag force caused by the tethering object. From the physiological time scales of tissue elasticity, we calculate that tethered elastic proteins equilibrate in vivo with D(eff) ~ 10(4)-10(6) nm(2)/s which is two to four orders magnitude smaller than the values measured for untethered proteins in bulk.

Atomistic simulations of RNA duplex thermal denaturation: Sequence- and forcefield-dependence.

Double-stranded RNA is the end-product of template-based replication, and is also the functional state of some biological RNAs. Similarly to proteins and DNA, they can be denatured by temperature, with important physiological and technological implications. Here, we use an in silico strategy to probe the thermal denaturation of RNA duplexes. Following previous results that were obtained on a few different duplexes, and which nuanced the canonical 2-state picture of nucleic acid denaturation, we here specifically address three different aspects that greatly improve our description of the temperature-induced dsRNA separation. First, we investigate the effect of the spatial distribution of weak and strong base-pairs among the duplex sequence. We show that the deviations from the two-state dehybridization mechanism are more pronounced when a strong core is flanked with weak extremities, while duplexes with a weak core but strong extremities exhibit a two-state behavior, which can be explained by the key role played by base fraying. This was later verified by generating artificial hairpin or circular states containing one or two locked duplex extremities, which results in an important reinforcement of the entire HB structure of the duplex and higher melting temperatures. Finally, we demonstrate that our results are little sensitive to the employed combination of RNA and water forcefields. The trends in thermal stability among the different sequences as well as the observed unfolding mechanisms (and the deviations from a two-state scenario) remain the same regardless of the employed atomistic models. However, our study points to possible limitations of recent reparametrizations of the Amber RNA forcefield, which sometimes results in duplexes that readily denature under ambient conditions, in contradiction with available experimental results.