Molecular Paradigms for Biological Mechanosensing

Non-linear stress-softening of the bacterial cell wall confers cell shape homeostasis

The bacillus - or rod - is a pervasive cellular morphology among bacteria. Rod-shaped cells elongate without widening by reinforcing their cell wall anisotropically to prevent turgor pressure from inflating cell width. Here, we demonstrate that a constrictive force is also essential for avoiding pressure-driven widening in Gram-positive bacteria. Specifically, super-resolution measurements of the nonlinear mechanical properties of the cell wall revealed that across a range of turgor pressure cell elongation directly causes width constriction, similar to a "finger trap" toy. As predicted by theory, this property depends on cell-wall anisotropy and is precisely correlated with the cell's ability to maintain a rod shape. Furthermore, the acute non-linearities in the dependence between cell length and width deformation result in a negative-feedback mechanism that confers cell-width homeostasis. That is, the Gram-positive cell wall is a "smart material" whose exotic mechanical properties are exquisitely adapted to execute cellular morphogenesis.

Molecular simulation approaches to probing the effects of mechanical forces in the actin cytoskeleton

In this article we give our perspective on the successes and promise of various molecular and coarse-grained simulation approaches to probing the effect of mechanical forces in the actin cytoskeleton.

Good Rates From Bad Coordinates: The Exponential Average Time-dependent Rate Approach

Our ability to calculate rate constants of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barrier heights. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables (CVs). This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the "CV biasing efficiency" γ. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect CV, where γ = 1. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different CVs to bias, but which is sufficiently simple that we are able to compute the unbiased rate directly. For this system, we demonstrate that predictions from our new Exponential Average Time-Dependent Rate (EATR) estimator converge to the true rate constant more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the γ parameter can serve as a good metric for assessing the quality of the biasing coordinate. We demonstrate that these results hold when applying the methods to an atomistic protein folding example. Finally, we demonstrate that our approach works when combining multiple less-than-optimal bias coordinates, and adapt our method to the related "OPES flooding" approach. Overall, our time-dependent rate approach offers a powerful framework for predicting rate constants from biased simulations.

Improved Prediction of Molecular Response to Pulling by Combining Force Tempering with Replica Exchange Methods

Small mechanical forces play important functional roles in many crucial cellular processes, including in the dynamic behavior of the cytoskeleton and in the regulation of osmotic pressure through membrane-bound proteins. Molecular simulations offer the promise of being able to design the behavior of proteins that sense and respond to these forces. However, it is difficult to predict and identify the effect of the relevant piconewton (pN) scale forces due to their small magnitude. Previously, we introduced the Infinite Switch Simulated Tempering in Force (FISST) method, which allows one to estimate the effect of a range of applied forces from a single molecular dynamics simulation, and also demonstrated that FISST additionally accelerates sampling of a molecule's conformational landscape. For some problems, we find that this acceleration is not sufficient to capture all relevant conformational fluctuations, and hence, here we demonstrate that FISST can be combined with either temperature replica exchange or solute tempering approaches to produce a hybrid method that enables more robust prediction of the effect of small forces on molecular systems.

Asymmetric framework motion of TCRαβ controls load-dependent peptide discrimination

Mechanical force is critical for the interaction between an αβ T cell receptor (TCR) and a peptide-bound major histocompatibility complex (pMHC) molecule to initiate productive T-cell activation. However, the underlying mechanism remains unclear. We use all-atom molecular dynamics simulations to examine the A6 TCR bound to HLA-A*02:01 presenting agonist or antagonist peptides under different extensions to simulate the effects of applied load on the complex, elucidating their divergent biological responses. We found that TCR α and β chains move asymmetrically, which impacts the interface with pMHC, in particular the peptide-sensing CDR3 loops. For the wild-type agonist, the complex stabilizes in a load-dependent manner while antagonists destabilize it. Simulations of the Cβ FG-loop deletion, which reduces the catch bond response, and simulations with in silico mutant peptides further support the observed behaviors. The present results highlight the combined role of interdomain motion, fluctuating forces, and interfacial contacts in determining the mechanical response and fine peptide discrimination by a TCR, thereby resolving the conundrum of nearly identical crystal structures of TCRαβ-pMHC agonist and antagonist complexes.

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.

Multifaceted folding-unfolding landscape of the TrpZip2 β-hairpin and the role of external sub-piconewton mechanical tensions

Proteins can experience uneven tensions of the order of tens of piconewtons when exposed to different solvent environment due to the thermal motion of the solvent. It is also true that biomolecules, especially proteins, are subjected to a variety of mechanical tensions generated by several factors, including mechanically assisted translocation and pressure gradients within living systems. Here, we use metadynamics simulations to revisit the folding-unfolding of the TrpZip2 β-hairpin and redefine it from the perspective of an external force of a sub-piconewton magnitude acting on the ends of the hairpin. The chosen forces, while preserving the morphology of the β-hairpin chain when it is pulled, are capable of influencing the conformational behavior of the chain during folding and unfolding. Our investigations confirm that the TrpZip2 β-hairpin exhibits a zipper (zip-out) mechanism for folding-unfolding in both mechanically unbiased and biased (with a 30 pN end force) situations. However, it is important to note that they present marked differences in their folding and unfolding paths, with the mechanically biased system capable of becoming trapped in various intermediate states. Both unbiased and biased scenarios of the hairpin indicate that the hairpin turn is highly stable during the folding-unfolding event and initiates folding. More importantly we confirm that the existing heterogeneity in the TrpZip2 β-hairpin folding-unfolding is a consequence of the wide range of conformations observed, owing to the different trapped intermediates caused by the uneven forces it may experience in solution.

Cellular force-sensing through actin filaments

The actin cytoskeleton orchestrates cell mechanics and facilitates the physical integration of cells into tissues, while tissue-scale forces and extracellular rigidity in turn govern cell behaviour. Here, we discuss recent evidence that actin filaments (F-actin), the core building blocks of the actin cytoskeleton, also serve as molecular force sensors. We delineate two classes of proteins, which interpret forces applied to F-actin through enhanced binding interactions: 'mechanically tuned' canonical actin-binding proteins, whose constitutive F-actin affinity is increased by force, and 'mechanically switched' proteins, which bind F-actin only in the presence of force. We speculate mechanically tuned and mechanically switched actin-binding proteins are biophysically suitable for coordinating cytoskeletal force-feedback and mechanical signalling processes, respectively. Finally, we discuss potential mechanisms mediating force-activated actin binding, which likely occurs both through the structural remodelling of F-actin itself and geometric rearrangements of higher-order actin networks. Understanding the interplay of these mechanisms will enable the dissection of force-activated actin binding's specific biological functions.

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.

Cubic Nanogrids for Counterbalance Contradiction among Reorganization Energy, Strain Energy, and Wide Bandgap

Molecular cross-scale gridization and polygridization of organic π-backbones make it possible to install 0/1/2/3-dimensional organic wide-bandgap semiconductors (OWBGSs) with potentially ZnO-like fascinating multifunctionality such as optoelectronic and piezoelectronic features. However, gridization effects are limited to uncover, because the establishment of gridochemistry still requires a long time, which offers a chance to understand the effects with a theoretical method, together with data statistics and machine learning. Herein, we demonstrate a state-of-the-art 3D cubic nanogridon with a size of ∼2 × 2 × 1.5 nm³ to examine its multigridization of π-segments on the bandgap, molecular strain energy (MSE), as well as reorganization energy (ROE). A cubic gridon (CG) consists of a four-armed bifluorene skeleton and a thiophene-containing fused arene plane with the Csp³ spiro-linkage, which can be deinstalled into face-on or edge-on monogrids. As a result, multigridization does not significantly reduce bandgaps (E_g ≥ 4.03 eV), while the MSE increases gradually from 4.72 to 23.83 kcal/mol. Very importantly, the ROE of a CG exhibits an extreme reduction down to ∼28 meV (λ⁺) that is near the thermal fluctuation energy (∼26 meV). Our multigridization results break through the limitation of the basic positively proportional relationship between reorganization energies and bandgaps in organic semiconductors. Furthermore, multigridization makes it possible to keep the ROE small under the condition of a high MSE in OWBGS that will guide the cross-scale design of multifunctional OWBGSs with both inorganics' optoelectronic performance and organics' mechanical flexibility.

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.