Perspective: Mechanochemistry of biological and synthetic molecules

JEDI: A versatile code for strain analysis of molecular and periodic systems under deformation

Stretching or compression can induce significant energetic, geometric, and spectroscopic changes in materials. To fully exploit these effects in the design of mechano- or piezo-chromic materials, self-healing polymers, and other mechanoresponsive devices, a detailed knowledge about the distribution of mechanical strain in the material is essential. Within the past decade, Judgement of Energy DIstribution (JEDI) analysis has emerged as a useful tool for this purpose. Based on the harmonic approximation, the strain energy in each bond length, bond angle, and dihedral angle of the deformed system is calculated using quantum chemical methods. This allows the identification of the force-bearing scaffold of the system, leading to an understanding of mechanochemical processes at the most fundamental level. Here, we present a publicly available code that generalizes the JEDI analysis, which has previously only been available for isolated molecules. Now, the code has been extended to two- and three-dimensional periodic systems, supramolecular clusters, and substructures of chemical systems under various types of deformation. Due to the implementation of JEDI into the Atomic Simulation Environment, the JEDI analysis can be interfaced with a plethora of program packages that allow the calculation of electronic energies for molecular systems and systems with periodic boundary conditions. The automated generation of a color-coded three-dimensional structure via the Visual Molecular Dynamics program allows insightful visual analyses of the force-bearing scaffold of the strained system.

Topology of molecular deformations induces triphasic catch bonding in selectin-ligand bonds

Among the long-standing efforts to elucidate the physical mechanisms of protein-ligand catch bonding, particular attention has been directed at the family of selectin proteins. Selectins exhibit slip, catch-slip, and slip-catch-slip bonding, with minor structural modifications causing major changes in selectins' response to force. How can a single structural mechanism allow interconversion between these various behaviors? We present a unifying theory of selectin-ligand catch bonding, using a structurally motivated free energy landscape to show how the topology of force-induced deformations of the molecular system produces the full range of observed behaviors. We find that the pathway of bond rupture deforms in non-trivial ways, such that unbinding dynamics depend sensitively on force. This implies a severe breakdown of Bell's theory-a paradigmatic theory used widely in catch bond modeling-raising questions about the suitability of Bell's theory in modeling other catch bonds. Our approach can be applied broadly to other protein-ligand systems.

Shear-activation of mechanochemical reactions through molecular deformation

Mechanical stress can directly activate chemical reactions by reducing the reaction energy barrier. A possible mechanism of such mechanochemical activation is structural deformation of the reactant species. However, the effect of deformation on the reaction energetics is unclear, especially, for shear stress-driven reactions. Here, we investigated shear stress-driven oligomerization reactions of cyclohexene on silica using a combination of reactive molecular dynamics simulations and ball-on-flat tribometer experiments. Both simulations and experiments captured an exponential increase in reaction yield with shear stress. Elemental analysis of ball-on-flat reaction products revealed the presence of oxygen in the polymers, a trend corroborated by the simulations, highlighting the critical role of surface oxygen atoms in oligomerization reactions. Structural analysis of the reacting molecules in simulations indicated the reactants were deformed just before a reaction occurred. Quantitative evidence of shear-induced deformation was established by comparing bond lengths in cyclohexene molecules in equilibrium and prior to reactions. Nudged elastic band calculations showed that the deformation had a small effect on the transition state energy but notably increased the reactant state energy, ultimately leading to a reduction in the energy barrier. Finally, a quantitative relationship was developed between molecular deformation and energy barrier reduction by mechanical stress.

Interactions and reactivity in crystalline intermediates of mechanochemical cyclorhodation reactions

There is experimental evidence that solid mixtures of the rhodium dimer [Cp*RhCl2]2 and benzo[h] quinoline (BHQ) produce two different polymorphic molecular cocrystals called 4α and 4β under ball milling conditions. The addition of NaOAc to the mixture leads to the formation of the rhodacycle [Cp*Rh-(BHQ)Cl], where the central Rh atom retains its tetracoordinate character. Isolate 4β reacts with NaOAc leading to the same rhodacycle while isolate 4α does not under the same conditions. We show that the puzzling difference in reactivity between the two cocrystals can be traced back to fundamental aspects of the intermolecular interactions between the BHQ and [Cp*RhCl2]2 fragments in the crystalline environment. To support this view, we report a number of descriptors of the nature and strength of chemical bonds and intermolecular interactions in the extended solids and in a cluster model. We calculate formal quantum mechanical descriptors based on electronic structure, electron density, and binding and interaction energies including an energy decomposition analysis. Without exception, all descriptors point to 4β being a transient structure higher in energy than 4α with larger local and global electrophilic and nucleophilic powers, a more favorable spatial and energetic distribution of the frontier orbitals, and a more fragile crystal structure.

Molecular mechanisms of catch bonds and their implications for platelet hemostasis

Adhesive molecular bonds between blood cells are essential for thrombosis and hemostasis as they provide means for platelet adhesion, aggregation, and signaling in flowing blood. According to the nowadays conventional definition, a "catch" bond is a type of non-covalent bio-molecular bridge, whose dissociation lifetime counter-intuitively increases with applied tensile force. Following recent experimental findings, such receptor-ligand protein bonds are vital to the blood cells involved in the prevention of bleeding (hemostatic response) and infection (immunity). In this review, we examine the up-to-date experimental discoveries and theoretical insights about catch bonds between the blood cells, their biomechanical principles at the molecular level, and their role in platelet thrombosis and hemostasis.

Hypotheses concerning structuring of extruded meat analogs

In this paper, we review the physicochemical phenomena occurring during the structuring processes in the manufacturing of plant-based meat analogs via high-moisture-extrusion (HME). After the initial discussion on the input materials, we discuss the hypotheses behind the physics of the functional tasks that can be defined for HME. For these hypotheses, we have taken a broader view than only the scientific literature on plant-based meat analogs but incorporated also literature from soft matter physics and patent literature. Many of these hypotheses remain to be proven. Hence, we hope that this overview will inspire researchers to fill the still-open knowledge gaps concerning the multiscale structure of meat analogs.

Force Dependent Barriers from Analytic Potentials within Elastic Environments

Bond rupture under the action of external forces is usually induced by temperature fluctuations, where the key quantity is the force dependent barrier that needs to be overcome. Using analytic potentials we find that these barriers are fully determined by the dissociation energy and the maximal force the potential can withstand. The barrier shows a simple dependence on these two quantities that allows for a re-interpretation of the Eyring-Zhurkov-Bell length Δ x ‡ and the expressions in theories going beyond that. It is shown that solely elastic environments do not change this barrier in contrast to the predictions of constraint geometry simulate external force (COGEF) strategies. The findings are confirmed by explicit calculations of bond rupture in a polydimethylsiloxane model.

Cooperative and Geometry-Dependent Mechanochromic Reactivity through Aromatic Fusion of Two Rhodamines in Polymers

The unique topological features of Piezo proteins underlie the lever-like cellular mechanotransduction mechanism. This knowledge inspires us to seek topological/geometric control of mechanochromophores with unprecedentedly amplified, synergistic changes in polymers to serve as ideal stress probes. Here, by judicious placement of two spirolactam rings into aminobenzopyranoxanthene, a series of stereo- and regio-isomeric rhodamine-like mechanophores are developed. With two labile bonds closely coupled into one rigidified scaffold, these π-fused bis-mechanophores enable mechanochromic polymers, featuring cooperative bond scission, low rupture force (lower than rhodamine), and geometry-controlled ring-opening reactivity. Sonication, single-molecule force spectroscopy experiments, and density functional theory calculations provide insight into the force-color relationship and rationalize how the difference in reactivity of the four isomeric mechanophores is affected by their molecular geometry and thermodynamic equilibrium. Our strategy based on the aromatic fusion of bis-mechanophore promises a modular approach to isomeric mechanophores for cooperative bond scission. Also, important insights into internal and external factors governing tandem mechanochemical reactions are gained.

Onsager reciprocal relations and chemo-mechanical coupling for chemically active colloids

Similar to cells, bacteria, and other micro-organisms, synthetic chemically active colloids can harness the energy from their environment through a surface chemical reaction and use the energy to self-propel in fluidic environments. In this paper, we study the chemo-mechanical coupling that leads to the self-propulsion of chemically active colloids. The coupling between chemical reactions and momentum transport is a consequence of Onsager reciprocal relations. They state that the velocity and the surface reaction rate are related to mechanical and chemical affinities through a symmetric matrix. A consequence of Onsager reciprocal relations is that if a chemical reaction drives the motion of the colloid, then an external force generates a reaction rate. Here, we investigate Onsager reciprocal relations for a spherical active colloid that catalyzes a reversible surface chemical reaction between two species. We solve the relevant transport equations using a perturbation expansion and numerical simulations to demonstrate the validity of reciprocal relations around the equilibrium. Our results are consistent with previous studies and highlight the key role of solute advection in preserving the symmetry of the Onsager matrix. Finally, we show that Onsager reciprocal relations break down around a nonequilibrium steady state, which has implications for the thermal fluctuations of the active colloids used in experiments.

Molecular interpretation of single-molecule force spectroscopy experiments with computational approaches

Single molecule force-spectroscopy techniques have granted access to unprecedented molecular-scale details about biochemical and biological mechanisms. However, the interpretation of the experimental data is often challenging. Computational and simulation approaches (all-atom steered MD simulations in particular) are key to provide molecular details about the associated mechanisms, to help test different hypotheses and to predict experimental results. In this review, particular recent efforts directed towards the molecular interpretation of single-molecule force spectroscopy experiments on proteins and protein-related systems (often in close collaboration with experimental groups) will be presented. These results will be discussed in the broader context of the field, highlighting the recent achievements and the ongoing challenges for computational biophysicists and biochemists. In particular, I will focus on the input gained from molecular simulations approaches to rationalize the origin of the unfolded protein elasticity and the protein conformational behavior under force, to understand how force denaturation differs from chemical, thermal or shear unfolding, and to unravel the molecular details of unfolding events for a variety of systems. I will also discuss the use of models based on Langevin dynamics on a 1-D free-energy surface to understand the effect of protein segmentation on the work exerted by a force, or, at the other end of the spectrum of computational techniques, how quantum calculations can help to understand the reactivity of disulfide bridges exposed to force.

Interplay of Affinity and Surface Tethering in Protein Recognition

Surface-tethered ligand-receptor complexes are key components in biological signaling and adhesion. They also find increasing utility in single-molecule assays and biotechnological applications. Here, we study the real-time binding kinetics between various surface-immobilized peptide ligands and their unrestrained receptors. A long peptide tether increases the association of ligand-receptor complexes, experimentally proving the fly casting mechanism where the disorder accelerates protein recognition. On the other hand, a short peptide tether enhances the complex dissociation. Notably, the rate constants measured for the same receptor, but under different spatial constraints, are strongly correlated to one another. Furthermore, this correlation can be used to predict how surface tethering on a ligand-receptor complex alters its binding kinetics. Our results have immediate implications in the broad areas of biomolecular recognition, intrinsically disordered proteins, and biosensor technology.

Assessing models of force-dependent unbinding rates via infrequent metadynamics

Protein–ligand interactions are crucial for a wide range of physiological processes. Many cellular functions result in these non-covalent “bonds” being mechanically strained, and this can be integral to proper cellular function. Broadly, two classes of force dependence have been observed—slip bonds, where the unbinding rate increases, and catch bonds, where the unbinding rate decreases. Despite much theoretical work, we cannot predict for which protein–ligand pairs, pulling coordinates, and forces a particular rate dependence will appear. Here, we assess the ability of MD simulations combined with enhanced sampling techniques to probe the force dependence of unbinding rates. We show that the infrequent metadynamics technique correctly produces both catch and slip bonding kinetics for model potentials. We then apply it to the well-studied case of a buckyball in a hydrophobic cavity, which appears to exhibit an ideal slip bond. Finally, we compute the force-dependent unbinding rate of biotin–streptavidin. Here, the complex nature of the unbinding process causes the infrequent metadynamics method to begin to break down due to the presence of unbinding intermediates, despite the use of a previously optimized sampling coordinate. Allowing for this limitation, a combination of kinetic and free energy computations predicts an overall slip bond for larger forces consistent with prior experimental results although there are substantial deviations at small forces that require further investigation. This work demonstrates the promise of predicting force-dependent unbinding rates using enhanced sampling MD techniques while also revealing the methodological barriers that must be overcome to tackle more complex targets in the future.

Recent Advances and Emerging Challenges in the Molecular Modeling of Mechanobiological Processes

Many biological processes result from the effect of mechanical forces on macromolecular structures and on their interactions. In particular, the cell shape, motion, and differentiation directly depend on mechanical stimuli from the extracellular matrix or from neighboring cells. The development of experimental techniques that can measure and characterize the tiny forces acting at the cellular scale and down to the single-molecule, biomolecular level has enabled access to unprecedented details about the involved mechanisms. However, because the experimental observables often do not provide a direct atomistic picture of the corresponding phenomena, particle-based simulations performed at various scales are instrumental in complementing these experiments and in providing a molecular interpretation. Here, we will review the recent key achievements in the field, and we will highlight and discuss the many technical challenges these simulations are facing, as well as suggest future directions for improvement.

Molecular Paradigms for Biological Mechanosensing

Many proteins in living cells are subject to mechanical forces, which can be generated internally by molecular machines, or externally, e.g., by pressure gradients. In general, these forces fall in the piconewton range, which is similar in magnitude to forces experienced by a molecule due to thermal fluctuations. While we would naively expect such moderate forces to produce only minimal changes, a wide variety of "mechanosensing" proteins have evolved with functions that are responsive to forces in this regime. The goal of this article is to provide a physical chemistry perspective on protein-based molecular mechanosensing paradigms used in living systems, and how these paradigms can be explored using novel computational methods.

Out-of-Equilibrium Biophysical Chemistry: The Case for Multidimensional, Integrated Single-Molecule Approaches

Out-of-equilibrium processes are ubiquitous across living organisms and all structural hierarchies of life. At the molecular scale, out-of-equilibrium processes (for example, enzyme catalysis, gene regulation, and motor protein functions) cause biological macromolecules to sample an ensemble of conformations over a wide range of time scales. Quantifying and conceptualizing the structure–dynamics to function relationship is challenging because continuously evolving multidimensional energy landscapes are necessary to describe nonequilibrium biological processes in biological macromolecules. In this perspective, we explore the challenges associated with state-of-the-art experimental techniques to understanding biological macromolecular function. We argue that it is time to revisit how we probe and model functional out-of-equilibrium biomolecular dynamics. We suggest that developing integrated single-molecule multiparametric force–fluorescence instruments and using advanced molecular dynamics simulations to study out-of-equilibrium biomolecules will provide a path towards understanding the principles of and mechanisms behind the structure–dynamics to function paradigm in biological macromolecules.

Ab initio molecular dynamics modeling of single polyethylene chains: Scission kinetics and influence of radical under mechanical strain

Ab initio molecular dynamics was used to estimate the response to constant imposed strain on a short polyethylene (PE) chain and a radical chain with a removed hydrogen atom. Two independent types of simulations were run. In the first case, the chains were strained by expanding a periodic cell, restraining the length but allowing the internal degrees of freedom to reach equilibrium. From these simulations, the average force on the chain was computed, and the resulting force was integrated to determine the Helmholtz free energy for chain stretching. In the second set of simulations, chains were constrained to various lengths, while a bond was restrained at various bond lengths using umbrella sampling. This provided free energy of bond scission for various chain strains. The sum of the two free energy functions results in an approximation of the free energy of chain scission under various strains and gives a realistic and new picture of the effect of chain strain on bond breaking. Unimolecular scission rates for each chain type were examined as a function of chain strain. The scission rate for the radical chain is several orders of magnitude larger than that of the pristine chain at smaller strains and at equilibrium. This highlights the importance of radical formation in PE rupture and is consistent with experiments. Constant strain results were used to derive a constant-force model for the radical chain that demonstrates a roll over in rate similar to the "catch-bond" behavior observed in protein membrane detachment experiments.

Tribochemistry, Mechanical Alloying, Mechanochemistry: What is in a Name?

Over the decades, the application of mechanical force to influence chemical reactions has been called by various names: mechanochemistry, tribochemistry, mechanical alloying, to name but a few. The evolution of these terms has largely mirrored the understanding of the field. But what is meant by these terms, why have they evolved, and does it really matter how a process is called? Which parameters should be defined to describe unambiguously the experimental conditions such that others can reproduce the results, or to allow a meaningful comparison between processes explored under different conditions? Can the information on the process be encoded in a clear, concise, and self-explanatory way? We address these questions in this Opinion contribution, which we hope will spark timely and constructive discussion across the international mechanochemical community.

Barnes Update Applied in the Gauss-Newton Method: An Improved Algorithm to Locate Bond Breaking Points

A mechanochemical reaction is a reaction induced by mechanical energy. A general accepted model for this type of reaction consists of a first-order perturbation on the associated potential energy surface (PES) of the unperturbed molecular system due to mechanical stress or pulling force. Within this theoretical framework, the so-called optimal barrier breakdown points or optimal bond breaking points (BBPs) are critical points of the unperturbed PES where the Hessian matrix has a zero eigenvector that coincides with the gradient vector. Optimal BBPs are "catastrophe points" that are particularly important because their associated gradient indicates how to optimally harness tensile forces to induce reactions by transforming a chemical reaction into a barrierless process. Building on a previous method based on a nonlinear least-squares minimization to locate BBPs (Bofill et al., J. Chem. Phys. 2017, 147, 152710-10), we propose a new algorithm to locate BBPs of any molecular system based on the Gauss-Newton method combined with the Barnes update for a nonsymmetric Jacobian matrix, which is shown to be more appropriate than the Broyden update. The efficiency of the new method is demonstrated for a multidimensional model PES and two medium size molecular systems of interest in enzymatic catalysis and mechanochemistry.

Soft mechano-chemistry of molecular hubs in mitotic spindle: biomechanics and mechanical proofreading at microtubule ends

A microtubule (MT) is a long stiff tube-shaped filament formed by a hierarchical organization of a large number of tubulin protein molecules. These filaments constitute a major structural component of the scaffold of a multi-component macromolecular machine called mitotic spindle. The plus ends of the MTs are tethered to some specific binding partners by molecular tethers while those of some others are crosslinked by crosslinking molecules. Because of the non-covalent binding involved in the tethering and crosslinking, the attachments formed are intrinsically 'soft'. These attachments are transient because these can get ruptured spontaneously by thermal fluctuations. By implementing in silico the standard protocols of in vitro molecular force spectroscopy, we compute the lifetimes of simple theoretical models of these attachments. The mean lifetime is essentially a mean first-passage time. The stability of cross-linked antiparallel MTs is shown to decrease monotonically with increasing tension, a characteristic of all 'slip-bonds'. This is in sharp contrast to the nonmonotonic variation of the mean lifetime with tension, a mechanical fingerprint of 'catch-bonds', displayed by the MTs tethered to two distinct binding partners. We mention plausible functional implications of these observations in the context of mechanical proofreading.

The generic unfolding of a biomimetic polymer during force spectroscopy

With the help of force spectroscopy, several analytical theories aim at estimating the rate coefficient of folding for various proteins. Nevertheless, a chief bottleneck lies in the fact that there is still no perfect consensus on how does a force generally perturb the crystal-coil transition. Consequently, the goal of our work is in clarifying the generic behavior of most proteins in force spectroscopy; in other words, what general signature does an arbitrary protein exhibit for its rate coefficient as a function of the applied force? By employing a biomimetic polymer in molecular simulations, we focus on evaluating its respective activation energy for unfolding, while pulling on various pairs of its monomers. Above all, we find that in the vicinity of the force-free scenario, this activation energy possesses a negative slope and a negative curvature as a function of the applied force. Our work is in line with the most recent theories for unfolding, which suggest that such a signature is expected for most proteins, and thus, we further reiterate that many of the classical formulae, that estimate the rate coefficient of the crystal-coil transition, are inadequate. Besides, we also present here an analytical expression which experimentalists can use for approximating the activation energy for unfolding; importantly, it is based on measurements for the mean and variance of the distance between the beads which are being pulled. In summary, our work presents an interesting view for protein folding in force spectroscopy.

Non-Markov bond model for dynamic force spectroscopy

Single-molecule force spectroscopy data are conventionally analyzed using a schematic model, wherein a molecular bond is represented as a virtual particle diffusing in a one-dimensional free-energy landscape. However, this simple and efficient approach is unable to account for the "anomalous" bond-breaking kinetics increasingly observed in force spectroscopy experiments and simulations, e.g., in the form of non-exponential distributions of bond lifetimes under constant load. Here, we show that such characteristic traits arise naturally in a rigorous extension of the one-dimensional theory that accounts for the transient dynamics of a generic set of coupled degrees of freedom. These "hidden modes" affect the reaction dynamics in various ways, depending on their relaxation spectrum and the loading protocol, giving rise, in particular, to apparent static and dynamic disorder. In two complementary asymptotic limits, we are able to find exact analytical expressions for pertinent experimental observables, such as the mean rupture force and the rupture-force distribution. Intriguingly, our asymptotic results become unconditionally exact at high loading rates, thus providing us with a microscopically consistent theory of rapid force spectroscopy that avoids the usual Markov assumption.

Measuring and modelling mechanochemical reaction kinetics

Quasi-static quantum calculations of the mechanochemical decomposition rate of methyl thiolate species on Cu(100) accurately reproduce the experimental kinetics measured in ultrahigh vacuum by an atomic force microscopy tip.

Mechanical unfolding of spectrin reveals a super-exponential dependence of unfolding rate on force

We investigated the mechanical unfolding of single spectrin molecules over a broad range of loading rates and thus unfolding forces by combining magnetic tweezers with atomic force microscopy. We find that the mean unfolding force increases logarithmically with loading rate at low loading rates, but the increase slows at loading rates above 1pN/s. This behavior indicates an unfolding rate that increases exponentially with the applied force at low forces, as expected on the basis of one-dimensional models of protein unfolding. At higher forces, however, the increase of the unfolding rate with the force becomes faster than exponential, which may indicate anti-Hammond behavior where the structures of the folded and transition states become more different as their free energies become more similar. Such behavior is rarely observed and can be explained by either a change in the unfolding pathway or as a reflection of a multidimensional energy landscape of proteins under force.

Generalized Langevin Equation as a Model for Barrier Crossing Dynamics in Biomolecular Folding

Conformational memory in single-molecule dynamics has attracted recent attention and, in particular, has been invoked as a possible explanation of some of the intriguing properties of transition paths observed in single-molecule force spectroscopy (SMFS) studies. Here we study one candidate for a non-Markovian model that can account for conformational memory, the generalized Langevin equation with a friction force that depends not only on the instantaneous velocity but also on the velocities in the past. The memory in this model is determined by a time-dependent friction memory kernel. We propose a method for extracting this kernel directly from an experimental signal and illustrate its feasibility by applying it to a generalized Rouse model of a SMFS experiment, where the memory kernel is known exactly. Using the same model, we further study how memory affects various statistical properties of transition paths observed in SMFS experiments and evaluate the performance of recent approximate analytical theories of non-Markovian dynamics of barrier crossing. We argue that the same type of analysis can be applied to recent single-molecule observations of transition paths in protein and DNA folding.

Nanotribological Printing: A Nanoscale Additive Manufacturing Method

Additive manufacturing methods are transforming the way components and devices are fabricated, which in turn is opening up completely new vistas for conceiving and designing products and engineered systems. Small-scale (submicrometer) additive manufacturing methods are largely in their infancy. While a number of methods exist, a particular challenge lies in finding methods that can produce a range of materials while obtaining sufficiently robust mechanical properties. In this paper, we describe a novel nanoscale additive manufacturing technique deemed "Nanotribological Printing" (NTP), which creates structures through tribomechanical and tribochemical surface interactions at the contact between a substrate and an atomic force microscope probe, where material pattern formation is driven by normal and shear contact stresses. The "ink" consists of nanoparticles or molecules dispersed in a carrier fluid surrounding the atomic force microscope (AFM) probe, which are entrained into the contact during sliding. Being stress-driven, patterning only occurs locally within regions which experience contact and sufficiently high stresses. Thus, imaging and measurement to characterize the morphology and properties of the deposited structures can be conducted in situ during the manufacturing process. Moreover, using local mechanical energy as the kinetic driver activating the solidification process, the method is compact and does not require application of a bias voltage or laser exposure and can be performed at ambient temperatures. We demonstrate (1) control of pattern dimensions with sub-100 nm lateral and sub-5 nm thickness control through variations in contact size and applied stress, (2) creation of amorphous, polycrystalline, and nanocomposite structures including sequential multimaterial deposition, and (3) formation of manufactured structures which exhibit mechanical properties approaching those of bulk counterparts. The ability to create nanoscale patterns using standard AFM cantilever probes and operation modes (contact mode scanning in fluid) with commercial AFM instruments, independent of substrate, establishes NTP as a versatile and easily accessible method for nanoscale additive manufacturing.

Substituent Effects and Mechanism in a Mechanochemical Reaction

We report the effect of substituents on the force-induced reactivity of a spiropyran mechanophore. Using single molecule force spectroscopy, force-rate behavior was determined for a series of spiropyran derivatives substituted with H, Br, or NO₂ para to the breaking spirocyclic C-O bond. The force required to achieve the rate constants of ∼10 s^-1 necessary to observe transitions in the force spectroscopy experiments depends on the substituent, with the more electron withdrawing substituent requiring less force. Rate constants at 375 pN were determined for all three derivatives, and the force-coupled rate dependence on substituent identity is well explained by a Hammett linear free energy relationship with a value of ρ = 2.9, consistent with a highly polar transition state with heterolytic, dissociative character. The methodology paves the way for further application of linear free energy relationships and physical organic methodologies to mechanochemical reactions, and the characterization of new force probes should enable additional, quantitative studies of force-coupled molecular behavior in polymeric materials.

The role of mechanical force on the kinetics and dynamics of electrochemical redox reactions on graphene

Electrochemical reactions are a critical class of processes strongly influenced by atomic scale effects, where the relationships between local chemical composition, stress, strain, and reactivity are not well understood. Here we investigate the relationship between applied stress and reaction rates for the oxygen evolution reaction on multi-layered graphene using conductive atomic force microscopy. During the reaction, oxygen groups accumulate on the surface and the oxygenation rate increases with applied load. The results also show that the rate is not uniform across the surface, where local edges and defects are more reactive than the basal plane. The results presented here are interpreted in the context of transition state theory, where applied load over the reaction coordinate linearly modifies the energy landscape. This work motivates the general efficacy of atomic force microscopy as a tool to study relationships between local mechanical surface effects and electrochemical reactivity.

Transition path times reveal memory effects and anomalous diffusion in the dynamics of protein folding

Recent single-molecule experiments probed transition paths of biomolecular folding and, in particular, measured the time biomolecules spend while crossing their free energy barriers. A surprising finding from these studies is that the transition barriers crossed by transition paths, as inferred from experimentally observed transition path times, are often lower than the independently determined free energy barriers. Here we explore memory effects leading to anomalous diffusion as a possible origin of this discrepancy. Our analysis of several molecular dynamics trajectories shows that the dynamics of common reaction coordinates used to describe protein folding is subdiffusive, at least at sufficiently short times. We capture this effect using a one-dimensional fractional Brownian motion (FBM) model, in which the system undergoes a subdiffusive process in the presence of a potential of mean force, and show that this model yields much broader distributions of transition path times with stretched exponential long-time tails. Without any adjustable parameters, these distributions agree well with the transition path times computed directly from protein trajectories. We further discuss how the FBM model can be tested experimentally.

Reconciling transition path time and rate measurements in reactions with large entropic barriers

Recent experiments and simulation studies showed that protein/DNA folding barriers inferred from folding rates or from potentials of mean force are often much higher than the barriers estimated from the distributions of transition path times. Here a toy model is used to explain a possible origin of this effect: It is shown that when the transition in question involves an entropic barrier, the one-dimensional Langevin model commonly used to interpret experimental data, while adequately predicting the transition rate, fails to describe the properties of the subset of the trajectories that form the transition path ensemble; the latter may still be describable in terms of a one-dimensional model, but with a different potential, just as observed experimentally.

Mechanochemical Association Reaction of Interfacial Molecules Driven by Shear

Shear-driven chemical reaction mechanisms are poorly understood because the relevant reactions are often hidden between two solid surfaces moving in relative motion. Here, this phenomenon is explored by characterizing shear-induced polymerization reactions that occur during vapor phase lubrication of α-pinene between sliding hydroxylated and dehydroxylated silica surfaces, complemented by reactive molecular dynamics simulations. The results suggest that oxidative chemisorption of the α-pinene molecules at reactive surface sites, which transfers oxygen atoms from the surface to the adsorbate molecule, is the critical activation step. Such activation takes place more readily on the dehydroxylated surface. During this activation, the most strained part of the α-pinene molecules undergoes a partial distortion from its equilibrium geometry, which appears to be related to the critical activation volume for mechanical activation. Once α-pinene molecules are activated, association reactions occur between the newly attached oxygen and one of the carbon atoms in another molecule, forming ether bonds. These findings have general implications for mechanochemistry because they reveal that shear-driven reactions may occur through reaction pathways very different from their thermally induced counterparts and specifically the critical role of molecular distortion in such reactions.

Mechanochemistry of nucleosides, nucleotides and related materials

The application of mechanical force to induce the formation and cleavage of covalent bonds is a rapidly developing field within organic chemistry which has particular value in reducing or eliminating solvent usage, enhancing reaction rates and also in enabling the preparation of products which are otherwise inaccessible under solution-phase conditions. Mechanochemistry has also found recent attention in materials chemistry and API formulation during which rearrangement of non-covalent interactions give rise to functional products. However, this has been known to nucleic acids science almost since its inception in the late nineteenth century when Miescher exploited grinding to facilitate disaggregation of DNA from tightly bound proteins through selective denaturation of the latter. Despite the wide application of ball milling to amino acid chemistry, there have been limited reports of mechanochemical transformations involving nucleoside or nucleotide substrates on preparative scales. A survey of these reactions is provided, the majority of which have used a mixer ball mill and display an almost universal requirement for liquid to be present within the grinding vessel. Mechanochemistry of charged nucleotide substrates, in particular, provides considerable benefits both in terms of efficiency (reducing total processing times from weeks to hours) and by minimising exposure to aqueous conditions, access to previously elusive materials. In the absence of large quantities of solvent and heating, side-reactions can be reduced or eliminated. The central contribution of mechanochemistry (and specifically, ball milling) to the isolation of biologically active materials derived from nuclei by grinding will also be outlined. Finally non-covalent associative processes involving nucleic acids and related materials using mechanochemistry will be described: specifically, solid solutions, cocrystals, polymorph transitions, carbon nanotube dissolution and inclusion complex formation.

Influence of ligand-receptor interactions on force-extension behavior within the freely jointed chain model

We study the influence of receptor-ligand interactions on the force response of single polymer chains theoretically. The extension of the chain is modeled in terms of freely jointed chain or elastic freely jointed chain (EFJC) models. The situation involving noninteracting bonds is solved exactly, while effects of interactions are treated within a mean-field approximation. The form with shorter bonds governs the low force situation, while the form with longer bonds is relevant in the high force regime. We further discuss the accuracy of approximate relations, which were used to describe the response of the EFJC model.

Size extensivity of elastic properties of alkane fragments

Using MP2, CCSD, and B3LYP methods of computational chemistry, we show length dependence in the intrinsic elastic properties of short alkane fragments. For isolated alkane fragments of finite length in the gas phase and zero temperature, the intrinsic elasticity constants are found to vary with the number of carbon atoms and its parity. From extrapolation of the elasticity constants calculations to infinite chain length, and by comparing with in-situ elasticity constant of single poly(ethylene) molecule obtained with atomic force microscopy, we estimate the softening effect of environment on the extension response of the polymer.

An algorithm to locate optimal bond breaking points on a potential energy surface for applications in mechanochemistry and catalysis

The reaction path of a mechanically induced chemical transformation changes under stress. It is well established that the force-induced structural changes of minima and saddle points, i.e., the movement of the stationary points on the original or stress-free potential energy surface, can be described by a Newton Trajectory (NT). Given a reactive molecular system, a well-fitted pulling direction, and a sufficiently large value of the force, the minimum configuration of the reactant and the saddle point configuration of a transition state collapse at a point on the corresponding NT trajectory. This point is called barrier breakdown point or bond breaking point (BBP). The Hessian matrix at the BBP has a zero eigenvector which coincides with the gradient. It indicates which force (both in magnitude and direction) should be applied to the system to induce the reaction in a barrierless process. Within the manifold of BBPs, there exist optimal BBPs which indicate what is the optimal pulling direction and what is the minimal magnitude of the force to be applied for a given mechanochemical transformation. Since these special points are very important in the context of mechanochemistry and catalysis, it is crucial to develop efficient algorithms for their location. Here, we propose a Gauss-Newton algorithm that is based on the minimization of a positively defined function (the so-called σ-function). The behavior and efficiency of the new algorithm are shown for 2D test functions and for a real chemical example.

First passage, looping, and direct transition in expanding and narrowing tubes: Effects of the entropy potential

We study transitions of diffusing particles between the left and right ends of expanding and narrowing conical tubes. In an expanding tube, such transitions occur faster than in the narrowing tube of the same length and radius variation rate. This happens because the entropy potential pushes the particle towards the wide tube end, thus accelerating the transitions in the expanding tube and slowing them down in the narrowing tube. To gain deeper insight into how the transitions occur, we divide each trajectory into the direct-transit and looping segments. The former is the final part of the trajectory, where the particle starting from the left tube end goes to the right end without returning to the left one. The rest of the trajectory is the looping segment, where the particle, starting from the left tube end, returns to this end again and again until the direct transition happens. Our focus is on the durations of the two segments and their sum, which is the duration of the particle first passage between the left and right ends of the tube. We approach the problem using the one-dimensional description of the particle diffusion along the tube axis in terms of the modified Fick-Jacobs equation. This allows us to derive analytical expressions for the Laplace transforms of the probability densities of the first-passage, direct-transit, and looping times, which we use to find the mean values of these random variables. Our results show that the direct transits are independent of the entropy potential and occur as in free diffusion. However, this "free diffusion" occurs with the effective diffusivity entering the modified Fick-Jacobs equation, which is smaller than the particle diffusivity in a cylindrical tube. This is the only way how the varying tube geometry manifests itself in the direct transits. Since direct-transit times are direction-independent, the difference in the first-passage times in the tubes of the two types is due to the difference in the durations of the looping segments in the expanding and narrowing tubes. Obtained analytical results are supported by three-dimensional Brownian dynamics simulations.

Theoretical simulation of the infrared signature of mechanically stressed polymer solids

Mechanical stress leads to deformation of strands in polymer solids, including elongation of covalent bonds and widening of bond angles, which changes the infrared spectrum. Here, the infrared spectrum of solid polymer samples exposed to mechanical stress is simulated by density functional theory calculations. Mechanical stress is described with the external force explicitly included (EFEI) method. The uneven distribution of the external stress on individual polymer strands is accounted for by a convolution of simulated spectra with a realistic force distribution. N-Propylpropanamide and propyl propanoate are chosen as model molecules for polyamide and polyester, respectively. The effect of a specific force on the polymer backbone is a redshift of vibrational modes involving the C-N and C-O bonds in the backbone, while the free C-O stretching mode perpendicular to the backbone is largely unaffected. The convolution with a realistic force distribution shows that the dominant effect on the strongest infrared bands is not a shift of the peak position, but rather peak broadening and a characteristic change in the relative intensities of the strongest bands, which may serve for the identification and quantification of mechanical stress in polymer solids.

A new insight into diffusional escape from a biased cylindrical trap

Recent experiments with single biological nanopores, as well as single-molecule fluorescence spectroscopy and pulling studies of protein and nucleic acid folding raised a number of questions that stimulated theoretical and computational investigations of barrier crossing dynamics. The present paper addresses a closely related problem focusing on trajectories of Brownian particles that escape from a cylindrical trap in the presence of a force F parallel to the cylinder axis. To gain new insights into the escape dynamics, we analyze the "fine structure" of these trajectories. Specifically, we divide trajectories into two segments: a looping segment, when a particle unsuccessfully tries to escape returning to the trap bottom again and again, and a direct-transit segment, when it finally escapes moving without touching the bottom. Analytical expressions are derived for the Laplace transforms of the probability densities of the durations of the two segments. These expressions are used to find the mean looping and direct-transit times as functions of the biasing force F. It turns out that the force-dependences of the two mean times are qualitatively different. The mean looping time monotonically increases as F decreases, approaching exponential F-dependence at large negative forces pushing the particle towards the trap bottom. In contrast to this intuitively appealing behavior, the mean direct-transit time shows rather counterintuitive behavior: it decreases as the force magnitude, |F|, increases independently of whether the force pushes the particles to the trap bottom or to the exit from the trap, having a maximum at F = 0.

Modeling Mechanochemical Reaction Mechanisms

The mechanochemical reaction between copper and dimethyl disulfide is studied under well-controlled conditions in ultrahigh vacuum (UHV). Reaction is initiated by fast S-S bond scission to form adsorbed methyl thiolate species, and the reaction kinetics are reproduced by two subsequent elementary mechanochemical reaction steps, namely a mechanochemical decomposition of methyl thiolate to deposit sulfur on the surface and evolve small, gas-phase hydrocarbons, and sliding-induced oxidation of the copper by sulfur that regenerates vacant reaction sites. The steady-state reaction kinetics are monitored in situ from the variation in the friction force as the reaction proceeds and modeled using the elementary-step reaction rate constants found for monolayer adsorbates. The analysis yields excellent agreement between the experiment and the kinetic model, as well as correctly predicting the total amount of subsurface sulfur in the film measured using Auger spectroscopy and the sulfur depth distribution measured by angle-resolved X-ray photoelectron spectroscopy.

Mean Direct-Transit and Looping Times as Functions of the Potential Shape

Any trajectory of a diffusing particle making a transition between two end points of an interval can be divided into two segments, which we call direct-transit and looping parts. The former is the final segment of the trajectory, when the particle goes from one end point of the interval to the opposite end point, without retouching the starting point. The rest of the trajectory is the looping part. We study mean durations of the two parts in the presence of a symmetric linear cusp potential which, depending on the parameter values, forms either a barrier or a well between the end points. For the cusp barrier, we find that the mean direct-transit time decreases as the barrier height increases at a fixed interval length. This happens because the increase in the barrier height results in the increase of the magnitude of the force acting on the particle on both sides of the barrier. Interestingly, though the mean looping and direct-transit times are different in the case of the barrier and well potentials with equal height and depth, respectively, the mean first-passage times for the two cases are identical.

Analysis of the Acting Forces in a Theory of Catalysis and Mechanochemistry

The theoretical description of a chemical process resulting from the application of mechanical or catalytical stress to a molecule is performed by the generation of an effective potential energy surface (PES). Changes for minima and saddle points by the stress are described by Newton trajectories (NTs) on the original PES. From the analysis of the acting forces we postulate the existence of pulling corridors built by families of NTs that connect the same stationary points. For different exit saddles of different height we discuss the corresponding pulling corridors; mainly by simple two-dimensional surface models. If there are different exit saddles then there can exist saddles of index two, at least, between. Then the case that a full pulling corridor crosses a saddle of index two is the normal case. It leads to an intrinsic hysteresis of such pullings for the forward or the backward reaction. Assuming such relations we can explain some results in the literature. A new finding is the existence of roundabout corridors that can switch between different saddle points by a reversion of the direction. The findings concern the mechanochemistry of molecular systems under a mechanical load as well as the electrostatic force and can be extended to catalytic and enzymatic accelerated reactions. The basic and ground ansatz includes both kinds of forces in a natural way without an extra modification.