Fully Atomistic Simulations of Protein Unfolding in Low Speed Atomic Force Microscope and Force Clamp Experiments with the Help of Boxed Molecular Dynamics

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.

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.

Simulation of protein pulling dynamics on second time scale with boxed molecular dynamics

We demonstrate how recently developed Boxed Molecular Dynamics (BXD) and kinetics [D. V. Shalashilin et al., J. Chem. Phys. 137, 165102 (2012)] can provide a kinetic description of protein pulling experiments, allowing for a connection to be made between experiment and the atomistic protein structure. BXD theory applied to atomic force microscopy unfolding is similar in spirit to the kinetic two-state model [A. Noy and R. W. Friddle, Methods 60, 142 (2013)] but with some differences. First, BXD uses a large number of boxes, and therefore, it is not a two-state model. Second, BXD rate coefficients are obtained from atomistic molecular dynamics simulations. BXD can describe the dependence of the pulling force on pulling speed. Similar to Shalashilin et al. [J. Chem. Phys. 137, 165102 (2012)], we show that BXD is able to model the experiment at a very long time scale up to seconds, which is way out of reach for standard molecular dynamics.

ChemDyME: Kinetically Steered, Automated Mechanism Generation through Combined Molecular Dynamics and Master Equation Calculations

In many scientific fields, there is an interest in understanding the way in which chemical networks evolve. The chemical networks which researchers focus upon have become increasingly complex, and this has motivated the development of automated methods for exploring chemical reactivity or conformational change in a "black-box" manner, harnessing modern computing resources to automate mechanism discovery. In this work, we present a new approach to automated mechanism generation which couples molecular dynamics and statistical rate theory to automatically find kinetically important reactions and then solve the time evolution of the species in the evolving network. The key to this chemical network mapping through combined dynamics and ME simulation approach is the concept of "kinetic convergence", whereby the search for new reactions is constrained to those species which are kinetically favorable at the conditions of interest. We demonstrate the capability of the new approach for two systems, a well-studied combustion system and a multiple oxygen addition system relevant to atmospheric aerosol formation.

Force probe simulations using an adaptive resolution scheme

Molecular simulations of the forced unfolding and refolding of biomolecules or molecular complexes allow to gain important kinetic, structural and thermodynamic information about the folding process and the underlying energy landscape. In force probe molecular dynamics (FPMD) simulations, one pulls one end of the molecule with a constant velocity in order to induce the relevant conformational transitions. Since the extended configuration of the system has to fit into the simulation box together with the solvent such simulations are very time consuming. Here, we apply a hybrid scheme in which the solute is treated with atomistic resolution and the solvent molecules far away from the solute are described in a coarse-grained manner. We use the adaptive resolution scheme (AdResS) that has very successfully been applied to various examples of equilibrium simulations. We perform FPMD simulations using AdResS on a well studied system, a dimer formed from mechanically interlocked calixarene capsules. The results of the multiscale simulations are compared to all-atom simulations of the identical system and we observe that the size of the region in which atomistic resolution is required depends on the pulling velocity, i.e. the particular non-equilibrium situation. For large pulling velocities a larger all atom region is required. Our results show that multiscale simulations can be applied also in the strong non-equilibrium situations that the system experiences in FPMD simulations.

Mechanical Unfolding of Proteins-A Comparative Nonequilibrium Molecular Dynamics Study

Mechanical signals regulate functions of mechanosensitive proteins by inducing structural changes that are determinant for force-dependent interactions. Talin is a focal adhesion protein that is known to extend under mechanical load, and it has been shown to unfold via intermediate states. Here, we compared different nonequilibrium molecular dynamics (MD) simulations to study unfolding of the talin rod. We combined boxed MD (BXD), steered MD, and umbrella sampling (US) techniques and provide free energy profiles for unfolding of talin rod subdomains. We conducted BXD, steered MD, and US simulations at different detail levels and demonstrate how these different techniques can be used to study protein unfolding under tension. Unfolding free energy profiles determined by BXD suggest that the intermediate states in talin rod subdomains are stabilized by force during unfolding, and US confirmed these results.

Probing Single Virus Binding Sites on Living Mammalian Cells Using AFM

In the last years, atomic force microscopy (AFM)-based approaches have evolved into a powerful multiparametric tool that allows biological samples ranging from single receptors to membranes and tissues to be probed. Force-distance curve-based AFM (FD-based AFM) nowadays enables to image living cells at high resolution and simultaneously localize and characterize specific ligand-receptor binding events. In this chapter, we present how FD-based AFM permits to investigate virus binding to living mammalian cells and quantify the kinetic and thermodynamic parameters that describe the free-energy landscape of the single virus-receptor-mediated binding. Using a model virus, we probed the specific interaction with cells expressing its cognate receptor and measured the affinity of the interaction. Furthermore, we observed that the virus rapidly established specific multivalent interactions and found that each bond formed in sequence strengthens the attachment of the virus to the cell.

Direct AFM Visualization of the Nanoscale Dynamics of Biomolecular Complexes

High-speed AFM (HS-AFM) is an advanced technique with numerous applications in biology, particularly in molecular biophysics. Developed as a time-lapse AFM technique for direct imaging fully hydrated biological molecules, HS-AFM is currently capable of visualizing the dynamics of biological molecules and their complexes at a video-data acquisition rate. Spatial resolution at the nanometer level is another important characteristic of HS-AFM. This review focuses on examples of primarily protein-DNA complexes to illustrate the high temporal and spatial resolution capabilities of HS-AFM that have resulted in novel models and/or the functional mechanisms of these biological systems.

Force probe simulations using a hybrid scheme with virtual sites

Hybrid simulations, in which a part of the system is treated with atomistic resolution and the remainder is represented on a coarse-grained level, allow for fast sampling while using the accuracy of atomistic force fields. We apply a hybrid scheme to study the mechanical unfolding and refolding of a molecular complex using force probe molecular dynamics (FPMD) simulations. The degrees of freedom of the solvent molecules are treated in a coarse-grained manner while atomistic resolution is retained for the solute. The coupling between the solvent and the solute is provided using virtual sites. We test two different common coarse-graining procedures, the iterative Boltzmann inversion method and the force matching procedure, and find that both methodologies give similar results. The results of the FPMD simulations are compared to all-atom simulations of the same system and we find that differences between these simulations and the ones using the hybrid scheme are in a similar range as the differences obtained when using different atomistic force fields. Thus, a hybrid scheme yields qualitatively correct results in the strong non-equilibrium situation the system is experiencing in FPMD simulations.

A Blind Test of Computational Technique for Predicting the Likelihood of Peptide Sequences to Cyclize

An in silico computational technique for predicting peptide sequences that can be cyclized by cyanobactin macrocyclases, e.g., PatG_mac, is reported. We demonstrate that the propensity for PatG_mac-mediated cyclization correlates strongly with the free energy of the so-called pre-cyclization conformation (PCC), which is a fold where the cyclizing sequence C and N termini are in close proximity. This conclusion is driven by comparison of the predictions of boxed molecular dynamics (BXD) with experimental data, which have achieved an accuracy of 84%. A true blind test rather than training of the model is reported here as the in silico tool was developed before any experimental data was given, and no parameters of computations were adjusted to fit the data. The success of the blind test provides fundamental understanding of the molecular mechanism of cyclization by cyanobactin macrocyclases, suggesting that formation of PCC is the rate-determining step. PCC formation might also play a part in other processes of cyclic peptides production and on the practical side the suggested tool might become useful for finding cyclizable peptide sequences in general.

Adaptive free energy sampling in multidimensional collective variable space using boxed molecular dynamics

The past decade has seen the development of a new class of rare event methods in which molecular configuration space is divided into a set of boundaries/interfaces, and then short trajectories are run between boundaries. For all these methods, an important concern is how to generate boundaries. In this paper, we outline an algorithm for adaptively generating boundaries along a free energy surface in multi-dimensional collective variable (CV) space, building on the boxed molecular dynamics (BXD) rare event algorithm. BXD is a simple technique for accelerating the simulation of rare events and free energy sampling which has proven useful for calculating kinetics and free energy profiles in reactive and non-reactive molecular dynamics (MD) simulations across a range of systems, in both NVT and NVE ensembles. Two key developments outlined in this paper make it possible to automate BXD, and to adaptively map free energy and kinetics in complex systems. First, we have generalized BXD to multidimensional CV space. Using strategies from rigid-body dynamics, we have derived a simple and general velocity-reflection procedure that conserves energy for arbitrary collective variable definitions in multiple dimensions, and show that it is straightforward to apply BXD to sampling in multidimensional CV space so long as the Cartesian gradients ∇CV are available. Second, we have modified BXD to undertake on-the-fly statistical analysis during a trajectory, harnessing the information content latent in the dynamics to automatically determine boundary locations. Such automation not only makes BXD considerably easier to use; it also guarantees optimal boundaries, speeding up convergence. We have tested the multidimensional adaptive BXD procedure by calculating the potential of mean force for a chemical reaction recently investigated using both experimental and computational approaches – i.e., F + CD₃CN → DF + D₂CN in both the gas phase and a strongly coupled explicit CD₃CN solvent. The results obtained using multidimensional adaptive BXD agree well with previously published experimental and computational results, providing good evidence for its reliability.