Force-probe Molecular Dynamics Simulations Research Articles

Adaptive resolution force probe simulations: Coarse graining in the ideal gas approximation.

The unfolding of molecular complexes or biomolecules under the influence of external mechanical forces can routinely be simulated with atomistic resolution. To obtain a match of the characteristic time scales with those of experimental force spectroscopy, often coarse graining procedures are employed. Here, building on a previous study, we apply the adaptive resolution scheme (AdResS) to force probe molecular dynamics (FPMD) simulations using two model systems as examples: One system is the previously investigated calix[4]arene dimer that shows reversible one-step unfolding, and the other example is provided by a small peptide, a β-alanine octamer in methanol solvent. The mechanical unfolding of this peptide proceeds via a metastable intermediate and, therefore, represents a first step toward a complex unfolding pathway. We show that the average number of native contacts serves as a robust order parameter for the forced unfolding of this small peptide. In addition to increasing the complexity of the relevant conformational changes, we study the impact of the methodology used for coarse graining. Apart from the iterative Boltzmann inversion method, we apply an ideal gas approximation, and therefore, we replace the solvent by a non-interacting system of spherical particles. In all cases, we find excellent agreement between the results of FPMD simulations performed fully atomistically and those of the AdResS simulations also in the case of fast pulling. This holds for all details of the unfolding pathways, such as the distributions of the characteristic forces and also the sequence of hydrogen-bond opening in case of the β-alanine octamer. Therefore, the methodology is very well suited to simulate the mechanical unfolding of systems of experimental relevance.

Discrimination between cyclic nucleotides in a cyclic nucleotide-gated ion channel.

Cyclic nucleotide-gated ion channels are crucial in many physiological processes such as vision and pacemaking in the heart. SthK is a prokaryotic homolog with high sequence and structure similarities to hyperpolarization-activated and cyclic nucleotide-modulated and cyclic nucleotide-gated channels, especially at the level of the cyclic nucleotide binding domains (CNBDs). Functional measurements showed that cyclic adenosine monophosphate (cAMP) is a channel activator while cyclic guanosine monophosphate (cGMP) barely leads to pore opening. Here, using atomic force microscopy single-molecule force spectroscopy and force probe molecular dynamics simulations, we unravel quantitatively and at the atomic level how CNBDs discriminate between cyclic nucleotides. We find that cAMP binds to the SthK CNBD slightly stronger than cGMP and accesses a deep-bound state that a cGMP-bound CNBD cannot reach. We propose that the deep binding of cAMP is the discriminatory state that is essential for cAMP-dependent channel activation.

Discrimination between cyclic-nucleotides by cyclic-nucleotide gated ion channels.

Cyclic-nucleotide-gated (CNG) ion channels play important roles throughout the entire nervous system, particularly in the signal transduction of the retina and olfactory system. They are regulated by the cyclic nucleotides cyclic adenosine monophosphate (cAMP) and cyclic guanosine monophosphate (cGMP). These two chemically very similar molecules bind to a specialized intracellular domain called the cyclic nucleotide-binding domain (CNBD). CNG channels are key in translating the chemical signal of the second messenger molecules cAMP and cGMP into an electrical response by inducing a conformational change in the CNBD that modulates the opening of the channel gate in the pore domain allowing the flow of ions across cell membranes. Functional measurements have shown that, in SthK (a prokaryotic homolog with high sequence and structural similarities to CNG channels), cGMP barely leads to pore opening while cAMP activates the channel. Here we address the question of how the CNBD can finely discriminate between the two chemically and structurally very similar ligands. Using a combination of atomic force microscopy-based single-molecule force spectroscopy (AFM-SMFS), and force probe molecular dynamics simulations, we elucidate, quantitatively and at the atomic level, the mechanism of CNBD ligand discrimination in SthK. We find that cAMP binds to the SthK CNBD with a slightly stronger affinity than cGMP, and can access a deep-bound state that is inaccessible to cGMP. We propose that the deep binding of cAMP is the discriminatory state that is essential for cAMP-dependent channel activation. We identify crucial residues and dynamic hydrogen bonding patterns within the binding pocket that give rise to this discrimination.

How Does Gecko Keratin Stick to Hydrophilic and Hydrophobic Surfaces in the Presence and Absence of Water? An Atomistic Molecular Dynamics Investigation.

We developed a united-atom model of gecko keratin to investigate the influence of electrostatic and van der Waals contributions to gecko adhesion in scenarios representing gecko's natural habitats. The keratin model assumes that only intrinsically disordered regions directly contact the surface. Contact angles of two generic substrate surfaces that we created match those previously used in AFM experiments on gecko adhesion. Force probe molecular dynamics simulations pulling the keratin from the surface show that the pull-off force increases with increased water content and is inversely related to the water contact angle of the surface. This matches experimental trends. We investigated the number and charge density of keratin and water at the surface, confirming a water-mediating effect and are able to show that keratin folds polar groups to the hydrophilic surface. We decomposed energetic contributions during pull-off, and our computational model shows that in contrast to popular hypotheses, long-range electrostatic interactions determine much of the pull-off process. The contribution of electrostatics to adhesion may be in the order of the van der Waals contributions.

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 and Structural Tuning of Reversible Hydrogen Bonding in Interlocked Calixarene Nanocapsules.

We present force probe molecular dynamics simulations of dimers of interlocked calixarene nanocapsules and study the impact of structural details and solvent properties on the mechanical unfolding pathways. The system consists of two calixarene "cups" that form a catenane structure via interlocked aliphatic loops of tunable length. The dimer shows reversible rebinding, and the kinetics of the system can be understood in terms of a two-state model for shorter loops (≤14 CH2 units) and a three-state model for longer loops (≥15 CH2 units). The various conformational states of the dimer are stabilized by networks of hydrogen bonds, the mechanical susceptibility of which can be altered by changing the polarity and proticity of the solvent. The variation of the loop length and the solvent properties in combination with changes in the pulling protocol allows to tune the reversibility of the conformational transitions.

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.

The mechano-sensing role of the unique SH3 insertion in plakin domains revealed by Molecular Dynamics simulations

The plakin family of proteins, important actors in cross-linking force-bearing structures in the cell, contain a curious SH3 domain insertion in their chain of spectrin repeats (SRs). While SH3 domains are known to mediate protein-protein interactions, here, its canonical binding site is autoinhibited by the preceding SR. Under force, however, this SH3 domain could be released, and possibly launch a signaling cascade. We performed large-scale force-probe molecular dynamics simulations, across two orders of magnitude of loading rates, to test this hypothesis, on two prominent members of the plakin family: desmoplakin and plectin, obligate proteins at desmosomes and hemidesmosomes, respectively. Our simulations show that force unravels the SRs and abolishes the autoinhibition of the SH3 domain, an event well separated from the unfolding of this domain. The SH3 domain is free and fully functional for a significant portion of the unfolding trajectories. The rupture forces required for the two proteins significantly decrease when the SH3 domain is removed, which implies that the SH3 domain also stabilizes this junction. Our results persist across all simulations, and support a force-sensing as well as a stabilizing role of the unique SH3 insertion, putting forward this protein family as a new class of mechano-sensors.

Simulating Force Response at Cellular Junctions: Desmoplakin as a Molecular Force Sensor?

Desmosomes are cell-cell junctions with a key role in mechano-sensation. However, it is currently unknown how the desmosomal complex and its proteins respond to mechanical force, transmitting chemical signals. We study desmoplakin, one of the obligate desmosomal proteins, identifying its possible role in mechanosensing. The most striking feature of this protein is the presence of an SH3 domain embedded in one of its six spectrin repeat domains. Intriguingly, the spectrin repeats hide the typical SH3 binding site, suggesting that either (i) the SH3 domain serves as a stabilizer of the protein through its interaction with one of the spectrin repeats, or (ii) it is activated only under force, initiating a signaling cascade for mechanosensing. To explore these alternatives, we performed equilibrium as well as force-probe Molecular Dynamics simulations on the central region of desmoplakin. To bridge towards physiologically relevant time scales, we repeated our simulations through a wide range of pulling velocities with a total simulation time of several tens of microseconds. We find desmoplakin to feature a clear sawtooth-like force profile, with each peak corresponding to modular spectrin repeat unfolding events followed by the final SH3 unfolding. The SH3 domain not only stabilizes desmoplakin, but also remains intact until the very last part of the trajectory, allowing interactions with downstream partners. Interestingly, we find the same behavior in the homologous plectin protein, suggesting this dual role of the SH3 domain to be conserved throughout the plakin family of proteins. However, plectin unfolds at significantly lower forces, involving an early or forceless loss of the SH3 domain-spectrin repeat interface. We identify specific mutations that promote this unfolding pathway, explaining the evolutionary adaptation of the cytosolic compared to the desmosomal mechano-sensing molecule. Our results suggest a direct role of unique SH3-insertion in spectrin repeat proteins in cellular mechanotransduction, and will be validated by direct comparison to single-molecule force spectroscopy experiments carried out by our collaborators.

Force-Sensitive Autoinhibition of the von Willebrand Factor Is Mediated by Interdomain Interactions

Von Willebrand factor (VWF) plays a central role in hemostasis. Triggered by shear-stress, it adheres to platelets at sites of vascular injury. Inactivation of VWF has been associated to the shielding of its adhesion sites and proteolytic cleavage. However, the molecular nature of this shielding and its coupling to cleavage under shear-forces in flowing blood remain unknown. In this study, we describe, to our knowledge, a new force-sensory mechanism for VWF-platelet binding, which addresses these questions, based on a combination of molecular dynamics (MD) simulations, atomic force microscopy (AFM), and microfluidic experiments. Our MD simulations demonstrate that the VWF A2 domain targets a specific region at the VWF A1 domain, corresponding to the binding site of the platelet glycoprotein Ibα (GPIbα) receptor, thereby causing its blockage. This implies autoinhibition of the VWF for the binding of platelets mediated by the A1-A2 protein-protein interaction. During force-probe MD simulations, a stretching force dissociated the A1A2 complex, thereby unblocking the GPIbα binding site. Dissociation was found to be coupled to the unfolding of the A2 domain, with dissociation predominantly occurring before exposure of the cleavage site in A2, an observation that is supported by our AFM experiments. This suggests that the A2 domain prevents platelet binding in a force-dependent manner, ensuring that VWF initiates hemostasis before inactivation by proteolytic cleavage. Microfluidic experiments with an A2-deletion VWF mutant resulted in increased platelet binding, corroborating the key autoinhibitory role of the A2 domain within VWF multimers. Overall, autoinhibition of VWF mediated by force-dependent interdomain interactions offers the molecular basis for the shear-sensitive growth of VWF-platelet aggregates, and might be similarly involved in shear-induced VWF self-aggregation and other force-sensing functions in hemostasis.

Exceptional Heterogeneous Elasticity and One-Way Valve Mechanism of the PHi29 Head-Tail Connector

The bacteriophage Φ29 DNA packaging motor, comprising ATPase, pRNA and head-tail connector, transports viral DNA inside the prohead against a maximum pressure of ∼60 atm. Two recently discussed transport models, push-and-roll (Yu et al. 2010) and one-way-revolution (Zhao et al. 2013), propose that the ATPase pushes the DNA directly into the procapsid; additionally, the latter model postulates that the connector acts as a one-way valve and restricts DNA leakage by specific loop interactions (residues N229-N246). Here, we focus on the connector's role in translocation and how it affects DNA conformation. Specifically, how such a one-way valve withstands the large pressure difference and how the connector loop-residues affect the function. To address these questions, we performed equilibrium and force-probe molecular dynamics simulations of the connector with and without DNA. We observe that the connector deforms DNA, which untwists, over-twists and compresses. Remarkably, comparison of the obtained DNA compression with FRET-FCS measurements of the T4 bacteriophage motor (Ray et al. 2010), revealed to be common characteristic of the head-tail bacteriophages. Further, the Young's modulus of the connector central region is comparable to that of structural proteins like collagen, and the obtained heterogonous connector stiffness resembles composite materials. These exceptional elastic properties enable the connector to withstand both longitudinal and lateral pressure generated by the packed DNA and the procapsid, respectively. Furthermore, pushing the DNA into the procapsid requires less force than pulling it out. Upon three loop-residue mutations (K234A.K235A.R237A), the required forces for pushing and pulling become similar, which supports the residues' essential role in the one-way-valve function. Our results corroborate the connector's one-way valve function, whereas rotation and/or revolution motions of DNA proposed in both models remain open for future investigation.

Mechanistic Explanation of Different Unfolding Behaviors Observed for Transmembrane and Soluble β-Barrel Proteins

In response to mechanical stress, membrane proteins progress through sequences of major unfolding barriers, whereas soluble proteins usually must overcome only one major unfolding barrier. To gain insight into these markedly different unfolding behaviors, we applied force-probe molecular dynamics simulations and unfolded two β-barrel proteins, the transmembrane outer membrane protein G (OmpG) and the water-soluble green fluorescent protein (GFP). The simulations mimic with high precision the unfolding experiments and show that OmpG in the absence of a membrane and GFP circumvent high unfolding barriers by rotations and explore alternative unfolding pathways. Embedding OmpG in the lipid membrane restricts this search for pathways and forces the protein to cross high unfolding barriers. Likewise, restricting the rotation forces GFP to traverse high unfolding barriers in a similar manner to membrane-embedded OmpG. These results indicate that mechanically stressed proteins search alternative unfolding pathways by rotations and explain why membrane proteins generally show higher mechanical stability compared to water-soluble proteins.View Large Image | View Hi-Res Image | Download PowerPoint Slide

Mechanistic Explanation of Different Unfolding Behaviors Observed for Transmembrane and Soluble β-Barrel Proteins

In response to mechanical stress, membrane proteins progress through sequences of major unfolding barriers, whereas soluble proteins usually must overcome only one major unfolding barrier. To gain insight into these markedly different unfolding behaviors, we applied force-probe molecular dynamics simulations and unfolded two β-barrel proteins, the transmembrane outer membrane protein G (OmpG) and the water-soluble green fluorescent protein (GFP). The simulations mimic with high precision the unfolding experiments and show that OmpG in the absence of a membrane and GFP circumvent high unfolding barriers by rotations and explore alternative unfolding pathways. Embedding OmpG in the lipid membrane restricts this search for pathways and forces the protein to cross high unfolding barriers. Likewise, restricting the rotation forces GFP to traverse high unfolding barriers in a similar manner to membrane-embedded OmpG. These results indicate that mechanically stressed proteins search alternative unfolding pathways by rotations and explain why membrane proteins generally show higher mechanical stability compared to water-soluble proteins.

Isopeptide Bonds Mechanically Stabilize Spy0128 in Bacterial Pili

Pili on the surface of Streptococcus pyogenes play a crucial role in adhesion to and colonization in human cells. The major pilin subunit, Spy0128, features intramolecular covalent isopeptide bonds that autocatalytically form between the side chains of lysine and asparagine residues and are regarded as important factors in conveying structural stability. In support of this notion, single-molecule force spectroscopy experiments with Spy0128 recently demonstrated the inextensibility of these bonds under mechanical load. However, the molecular determinants of their apparent absolute durability remain unknown. Here, we studied the impact of the isopeptide bond in the Spy0128 C-terminal domain on the mechanical properties of this subunit using force-probe molecular dynamics simulations and force distribution analysis. Even in the presence of the covalent cross-link, the pili β-sandwich domain undergoes partial unfolding, albeit at ∼50% higher rupture forces and with the ability to rapidly refold on the nanosecond timescale. We find that the isopeptide bond is located right at the point of stress concentration in the protein, leading to relative, yet not absolute, mechanical stabilization by the additional cross-link. Our findings indicate how the isopeptide bond enhances the mechanical stability and refolding capability at the molecular level, ensuring that the domain remains predominantly in a potentially adhesive conformation.

Influenza Virus Binds its Host Cell using Multiple Dynamic Interactions Revealed by Single Virus Force Spectroscopy and Force Probe Molecular Dynamics

Influenza virus belongs to a wide range of enveloped viruses. Virus-host cell binding marks the first critical step of infection. Hence, forces involved in this process are essential. The major spike protein hemagglutinin (HA) binds sialic acid (SA) residues of glycoproteins and -lipids of the cell surface of host cells with dissociation constants in the millimolar range, indicating a multivalent binding mode. Here we characterized the attachment of influenza virus to host cell receptors using three independent approaches. Optical tweezers and atomic force microscopy based single molecule force spectroscopy revealed very low interaction forces in the order of ∼10-25 pN. Further, the observation of sequential unbinding events strongly suggests a multivalent binding mode between virus and cell membrane. Force probe molecular dynamics simulations reveal a variety of unbinding pathways that indicate a highly dynamic interaction between HA and its receptor allowing to rationalize influenza virus-cell binding quantitatively at molecular level. Simulations show that the receptor-binding domain of HA is very rigid and does not show any deformations during unbinding of the ligand, which does not argue for any cooperativity between HA monomers in binding. The observed unbinding pathways are diverse and contain zipper-like as well as all-or-none unbinding events. Notably, we did not find a clear preference for binding of the probed influenza strains to one of the cell lines differing in the structure of the SA receptors.Sieben et al. (2012) Proc Natl Acad Sci USA. 09:13626-13631

Force-Dependent Platelet Binding of the Von Willebrand Factor A1-A2 Complex from Atomistic Simulations

Von Willebrand factor (VWF) is a huge multimeric extracellular protein playing a crucial adhesive role in hemostasis. In response to shear stress, VWF binds to the GP1bα receptor of platelets via its A1 domain, to build a plug that stops the bleeding of an injured blood vessel. Recent experimental studies revealed that the binding of GP1bα is altered by the presence of individual A2 subunits, suggesting that A2, adjacent to A1, interacts with A1, thereby shielding the binding site for GP1bα. In addition, electron microscopy studies measured the distance between the center of masses of A1 and A2, varying from ∼4.6 nm, in which the two subunits may be in contact, to ∼11 nm, in which the two subunits are not in contact (Zhou YF et al. EMBO J. (2011) 30: 4098-4111). Apart from these distance estimates, little is known on how A1 and A2 interact with each other and thereby modify GP1bα binding, and how this inhibition is sensitive to mechanical forces in flowing blood. We address these issues by using molecular docking, and equilibrium and force probe molecular dynamics simulations. Our study predicts a stable structure of the A1-A2 complex, in which A2 binds to the same site in A1 as GP1bα does, over a time scale of hundreds of nanoseconds. This inhibition is relieved under a stretching force, explaining how A2 can inhibit Gp1bα binding to A1 in a shear-flow dependent manner. Overall, our simulations suggest a new and intriguing mechanism on an intermolecular auto-inhibition that allows a shear-sensitive growth of blood coagulates, which reconciles previous and can be directly tested by future experiments.

Universal Relaxation Governs the Nonequilibrium Elasticity of Biomolecules

Experimental and computational dynamic force spectroscopy is widely used to determine the mechanical properties of single biomolecules. Whereas so far the focus has mainly been on rupture or unfolding forces, recent force-probe molecular dynamics simulations have revealed a strong loading rate dependence of biomolecular elasticities, which cannot be explained by the established one-dimensional transition-state treatments. We show that this nonequilibrium behavior can be explained by a theory that includes relaxation effects. For three structurally and mechanically quite diverse systems, a single relaxation mode suffices to quantitatively describe their loading-rate-dependent elastic behavior. Atomistic simulations of these systems revealed the microscopic nature of the respective relaxation modes. This result suggests a new type of "elasticity spectroscopy" experiment, which should render nonequilibrium properties of structured macromolecules accessible to single-molecule force spectroscopy.

Primary Changes of the Mechanical Properties of Southern Bean Mosaic Virus upon Calcium Removal

The mechanical properties of viral shells are crucial determinates for the pathway and mechanism by which the genetic material leaves the capsid during infection and have therefore been studied by atomic force microscopy as well as by atomistic simulations. The mechanical response to forces from inside the capsid are found to be relevant, especially after ion removal from the shell structure, which is generally assumed to be essential during viral infection; however, atomic force microscopy measurements are restricted to probing the capsids from outside, and the primary effect of ion removal is still inaccessible. To bridge this gap, we performed atomistic force-probe molecular dynamics simulations of the complete solvated icosahedral shell of Southern Bean Mosaic Virus and compared the distribution of elastic constants and yielding forces on the icosahedral shell for probing from inside with the distribution of outside mechanical properties obtained previously. Further, the primary effect of calcium removal on the mechanical properties on both sides, as well as on their spatial distribution, is quantified. Marked differences are seen particularly at the pentamer centers, although only small structural changes occur on the short timescales of the simulation. This unexpected primary effect, hence, precedes subsequent effects due to capsid swelling. In particular, assuming that genome release is preceded by an opening of capsomers instead of a complete capsid bursting, our observed weakening along the fivefold symmetry axes let us suggest pentamers as possible exit ports for RNA release.

The feasibility study of novel odor biosensor using dissociate neuronal culture expressing ion channel built-in odor receptors

Pheromone-binding proteins (PBP) supply olfactory neuron cells with pheromones by binding the ligands they are tailored for and carrying them to their receptor. The function of a PBP as an efficient carrier requires fast ligand uptake and release. The molecular basis of the ligand-binding mechanism was addressed here for the intriguing case of the PBP of the silk moth Bombyx mori. This PBP completely encapsulates its ligand bombykol without displaying any obvious ligand entrance/exit sites. Here, two opposite dissociation routes were identified as the most likely entrance/exit paths by replica-exchange molecular dynamics, essential dynamics, and force-probe molecular dynamics simulations. One of the paths runs along a flexible front lid; the other along the termini at the back. Calculated forces and energies suggest that both routes are physiologically relevant. The multiplicity of pathways may reduce or tune the entropic barrier for ligand binding.

Mechanical unfolding of bacterial flagellar filament protein by molecular dynamics simulation

Bacterial flagellum is a nano-scale motility device constructed by self-assembly. During construction of the cell-exterior filament (the ‘propeller’), subunit proteins (called flagellin) are thought to be exported through the hollow flagellum to the growing filament tip in an unfolded state. To gain insight into the unfolded state preceding any force-spectroscopy experiments on flagellin, we employed force-probe molecular dynamics simulations. Two schemes to attain an unfolded state suitable for efficient transport were examined: (i) stretching flagellin along its length; (ii) unzipping flagellin from its adjacently placed termini. Atomic-level unfolding pathways and the mechanical efforts involved under each scheme were obtained for the four-domain flagellin from S. typhimurium. Flagellin appeared stiffer and required larger unfolding forces when stretched as the relative sliding of β-strands require the breaking of multiple hydrogen bonds at once. In contrast, unzipping requires lower unfolding forces as it mainly involves unraveling β-sheets by breaking hydrogen bonds one by one.