How Fast Is Too Fast in Force-Probe Molecular Dynamics Simulations?

In-Silico Analyses of Molecular Force Sensors for Mechanical Characterization of Biological Systems

Mechanical forces play key roles in biological processes such as cell migration and sensory perception. In recent years molecular force sensors have been developed as tools for in situ force measurements. Here we use all-atom steered molecular dynamics simulations to predict and study the relationship between design parameters and mechanical properties for three types of molecular force sensors commonly used in cellular biological research: two peptide- and one DNA-based. The peptide-based sensors consist of a pair of fluorescent proteins, which can undergo Förster resonance energy transfer (FRET), linked by spider silk (GPGGA)n or synthetic (GGSGGS)n disordered regions. The DNA-based sensor consists of two fluorophore-labeled strands of DNA that can be unzipped or sheared upon force application with a FRET signal as readout of dissociation. We simulated nine sensors, three of each kind. After equilibration, flexible peptide linkers of three different lengths were stretched by applying forces to their N- and C-terminal Cα atoms in opposite directions. Similarly, we equilibrated a DNA-based sensor and pulled on the phosphate atom of the terminal guanine of one strand and a selected phosphate atom on the other strand in the opposite direction. These simulations were performed at constant velocity (0.01 nm/ns - 10 nm/ns) and constant force (10 pN - 500 pN) for all versions of the sensors. Our results show how the force response of these sensors depends on their length, sequence, configuration and loading rate. Mechanistic insights gained from simulations analyses indicate that interpretation of experimental results should consider the influence of transient formation of secondary structure in peptide-based sensors and of overstretching in DNA-based sensors. These predictions can guide optimal fluorophore choice and facilitate the rational design of new sensors for use in protein, DNA, hybrid systems, and molecular devices.

Probing the stability and interdomain interactions in the ABC transporter OpuA using single-molecule optical tweezers

Transmembrane transporter proteins are essential for maintaining cellular homeostasis and, as such, are key drug targets. Many transmembrane transporter proteins are known to undergo large structural rearrangements during their functional cycles. Despite the wealth of detailed structural and functional data available for these systems, our understanding of their dynamics and, consequently, how they function is generally limited. We introduce an innovative approach that enables us to directly measure the dynamics and stability of interdomain interactions of transmembrane proteins using optical tweezers. Focusing on the osmoregulatory ATP-binding cassette transporter OpuA from Lactococcus lactis, we examine the mechanical properties and potential interactions of its substrate-binding domains. Our measurements are performed in lipid nanodiscs, providing a native-mimicking environment for the transmembrane protein. The technique provides high spatial and temporal resolution and allows us to study the functionally relevant motions and interdomain interactions of individual transmembrane transporter proteins in real time in a lipid bilayer.

Complexity of Guanine Quadruplex Unfolding Pathways Revealed by Atomistic Pulling Simulations

Guanine quadruplexes (GQs) are non-canonical nucleic acid structures involved in many biological processes. GQs formed in single-stranded regions often need to be unwound by cellular machinery, so their mechanochemical properties are important. Here, we performed steered molecular dynamics simulations of human telomeric GQs to study their unfolding. We examined four pulling regimes, including a very slow setup with pulling velocity and force load accessible to high-speed atomic force microscopy. We identified multiple factors affecting the unfolding mechanism, i.e.,: (i) the more the direction of force was perpendicular to the GQ channel axis (determined by GQ topology), the more the base unzipping mechanism happened, (ii) the more parallel the direction of force was, GQ opening and cross-like GQs were more likely to occur, (iii) strand slippage mechanism was possible for GQs with an all-anti pattern in a strand, and (iv) slower pulling velocity led to richer structural dynamics with sampling of more intermediates and partial refolding events. We also identified that a GQ may eventually unfold after a force drop under forces smaller than those that the GQ withstood before the drop. Finally, we found out that different unfolding intermediates could have very similar chain end-to-end distances, which reveals some limitations of structural interpretations of single-molecule spectroscopic data.

Measuring pico-Newton Forces with Lipid Anchors as Force Sensors in Molecular Dynamics Simulations

Binding forces between biomolecules are ubiquitous in nature but sometimes as weak as a few pico-Newtons (pN). In many cases, the binding partners are attached to biomembranes with the help of a lipid anchor. One important example are glycolipids that promote membrane adhesion through weak carbohydrate-carbohydrate binding between adjacent membranes. Here, we use molecular dynamics (MD) simulations to quantify the forces generated by bonds involving membrane-anchored molecules. We introduce a method in which the protrusion of the lipid anchors from the membrane acts as the force sensor. Our results with two different glycolipids reveal binding forces of up to 20 pN and corroborate the recent notion that carbohydrate-carbohydrate interactions are generic rather than specific.

Gecko Adhesion on Flat and Rough Surfaces: Simulations with a Multi-Scale Molecular Model

A multiscale modeling approach is used to develop a particle-based mesoscale gecko spatula model that is able to link atomistic simulations and mesoscale (0.44 µm) simulations. It is used to study the detachment of spatulae from flat as well as nanostructured surfaces. The spatula model is based on microscopical information about spatulae structure and on atomistic molecular simulation results. Target properties for the coarse-graining result from a united-atom model of gecko keratin in periodic boundary conditions (PBC), previously developed by the authors. Pull-off forces necessary to detach gecko keratin under 2D PBC parallel to the surface are previously overestimated when only a small region of a spatula is examined. It is shown here that this is due to the restricted geometry (i.e., missing peel-off mode) and not model parameters. The spatula model peels off when pulled away from a surface, both in the molecular picture of the pull-off process and in the force-extension curve of non-equilibrium simulations mimicking single-spatula detachment studied with atomic force microscopy equipment. The force field and spatula model can reproduce experimental pull-off forces. Inspired by experimental results, the underlying mechanism that causes pull-off forces to be at a minimum on surfaces of varying roughnesses is also investigated. A clear sigmoidal increase in the pull-off force of spatulae with surface roughness shows that adhesion is determined by the ratio between spatula pad area and the area between surface peaks. Experiments showed a correlation with root-mean-square roughness of the surface, but the results of this work indicate that this is not a causality but depends on the area accessible.

Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics (SMD). The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jarzynski's equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the required use of very large solvent boxes. We introduce telescoping box schemes within adaptive steered molecular dynamics (ASMD) in which we adjust the solvent box between stages and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long α-helical peptide, Ala₃₀, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.

Elastic versus brittle mechanical responses predicted for dimeric cadherin complexes

Cadherins are a superfamily of adhesion proteins involved in a variety of biological processes that include the formation of intercellular contacts, the maintenance of tissue integrity, and the development of neuronal circuits. These transmembrane proteins are characterized by ectodomains composed of a variable number of extracellular cadherin (EC) repeats that are similar but not identical in sequence and fold. E-cadherin, along with desmoglein and desmocollin proteins, are three classical-type cadherins that have slightly curved ectodomains and engage in homophilic and heterophilic interactions through an exchange of conserved tryptophan residues in their N-terminal EC1 repeat. In contrast, clustered protocadherins are straighter than classical cadherins and interact through an antiparallel homophilic binding interface that involves overlapped EC1 to EC4 repeats. Here we present molecular dynamics simulations that model the adhesive domains of these cadherins using available crystal structures, with systems encompassing up to 2.8 million atoms. Simulations of complete classical cadherin ectodomain dimers predict a two-phased elastic response to force in which these complexes first softly unbend and then stiffen to unbind without unfolding. Simulated α, β, and γ clustered protocadherin homodimers lack a two-phased elastic response, are brittle and stiffer than classical cadherins and exhibit complex unbinding pathways that in some cases involve transient intermediates. We propose that these distinct mechanical responses are important for function, with classical cadherin ectodomains acting as molecular shock absorbers and with stiffer clustered protocadherin ectodomains facilitating overlap that favors binding specificity over mechanical resilience. Overall, our simulations provide insights into the molecular mechanics of single cadherin dimers relevant in the formation of cellular junctions essential for tissue function.

Mechanical force can enhance c-Src kinase activity by impairing autoinhibition

Cellular mechanosensing is pivotal for virtually all biological processes, and many molecular mechano-sensors and their way of function are being uncovered. In this work, we suggest that c-Src kinase acts as a direct mechano-sensor. c-Src is responsible for, among others, cell proliferation, and shows increased activity in stretched cells. In its native state, c-Src has little basal activity, because its kinase domain binds to an SH2 and SH3 domain. However, it is known that c-Src can bind to p130Cas, through which force can be transmitted to the membrane. Using molecular dynamics simulations, we show that force acting between the membrane-bound N-terminus of the SH3 domain and p130Cas induces partial SH3 unfolding, thereby impeding rebinding of the kinase domain onto SH2/SH3 and effectively enhancing kinase activity. Forces involved in this process are slightly lower or similar to the forces required to pull out c-Src from the membrane through the myristoyl linker, and key interactions involved in this anchoring are salt bridges between negative lipids and nearby basic residues in c-Src. Thus, c-Src appears to be a candidate for an intriguing mechanosensing mechanism of impaired kinase inhibition, which can be potentially tuned by membrane composition and other environmental factors.

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.

Gecko adhesion: a molecular-simulation perspective on the effect of humidity

Gecko adhesion is investigated by molecular dynamics simulations. It is known, that the gecko adhesion system shows increased pull-off forces in humid environments. A coarse-grained model of gecko beta keratin, previously developed in our group, is extended and used to elucidate the molecular mechanisms involved in this humidity effect on adhesion. We show that neither the change of the elastic properties of gecko keratin, nor capillary forces, can solely explain the increased pull-off forces of wet gecko keratin. Instead, we establish a molecular picture of gecko adhesion where the interplay between capillary bridges and a mediator effect of water, enhances pull-off forces, consistent with observations in AFM experiments at high humidities. We find that water density is raised locally, in molecular scale asperities of the gecko keratin and that this increase in local water density smoothes the surface-spatula interface. Water, which is absorbed into the keratin, acts as a mediator, and leads during pull-off to the dominant contribution in the van der Waals energy, because the dispersion interactions between water and surface are primarily opposing the pull-off.

Structural fluctuations and mechanical stabilities of the metamorphic protein RfaH

RfaH is a compact two-domain bacterial transcription factor that functions both as a regulator of transcription and an enhancer of translation. Underpinning the dual functional roles of RfaH is a partial but dramatic fold switch, which completely transforms the ~50-amino acid C-terminal domain (CTD) from an all-α state to an all-β state. The fold switch of the CTD occurs when RfaH binds to RNA polymerase (RNAP), however, the details of how this structural transformation is triggered is not well understood. Here we use all-atom Monte Carlo simulations to characterize structural fluctuations and mechanical stability properties of the full-length RfaH and the CTD as an isolated fragment. In agreement with experiments, we find that interdomain contacts are crucial for maintaining a stable, all-α CTD in free RfaH. To probe mechanical properties, we use pulling simulations to measure the work required to inflict local deformations at different positions along the chain. The resulting mechanical stability profile reveals that free RfaH can be divided into a "rigid" part and a "soft" part, with a boundary that nearly coincides with the boundary between the two domains. We discuss the potential role of this feature for how fold switching may be triggered by interaction with RNAP.

Advances in molecular simulations of protein mechanical properties and function

Single-molecule force spectroscopy and classical molecular dynamics are natural allies. Recent advances in both experiments and simulations have increasingly facilitated a direct comparison of SMFS and MD data, most importantly by closing the gap between time scales, which has been traditionally at least 5 orders of magnitudes wide. In this review, we will explore these advances chiefly on the computational side. We focus on protein dynamics under force and highlight recent studies that showcase how lower loading rates and more statistics help to better interpret previous experiments and to also motivate new ones. At the same time, steadily increasing system sizes are used to mimic more closely the mechanical environment in the biological context. We showcase some of these advances on atomistic and coarse-grained scale, from asymmetric membrane tension to larger (multidomain/multimeric) protein assemblies under force.

Single molecule force spectroscopy of a streptomycin-binding RNA aptamer: An out-of-equilibrium molecular dynamics study

Here, we investigate the unfolding behavior of a streptomycin-binding ribonucleic acid (RNA) aptamer under application of force in shear geometry. Using Langevin out-of-equilibrium simulations to emulate the single-molecule force spectroscopy (SMFS) experiment, we were able to understand the hierarchical unfolding process that occurs in the RNA molecule under application of stretching force and the influence of streptomycin modifying this unfolding. Subsequently, the application of the Jarzynski equality to the force profiles obtained in the pulling simulations shows that the free energies for individual systems and the difference of unfolding free energy upon streptomycin binding to the RNA free aptamer are in fair agreement with the experimental values, obtained through SMFS by Nick et al. [J. Phys. Chem. B 120, 6479 (2016)].