Mapping the energy landscape of biomolecules using single molecule force correlation spectroscopy (FCS): Theory and applications

In the current AFM experiments the distribution of unfolding times, P(t), is measured by applying a constant stretching force f_s from which the apparent unfolding rate is obtained. To describe the complexity of the underlying energy landscape requires additional probes that can incorporate the dynamics of tension propagation and relaxation of the polypeptide chain upon force quench. We introduce a theory of force correlation spectroscopy (FCS) to map the parameters of the energy landscape of proteins. In the FCS the joint distribution, P(T,t) of folding and unfolding times is constructed by repeated application of cycles of stretching at constant fs, separated by release periods T during which the force is quenched to f_q<f_s. During the release period, the protein can collapse to a manifold of compact states or refold. We show that P(T,t) can be used to resolve the kinetics of unfolding as well as formation of native contacts and to extract the parameters of the energy landscape using chain extension as the reaction coordinate and P(T,t). We illustrate the utility of the proposed formalism by analyzing simulations of unfolding-refolding trajectories of a coarse-grained protein S1 with beta-sheet architecture for several values of f_s, T and f_q=0. The simulations of stretch-relax trajectories are used to map many of the parameters that characterize the energy landscape of S1.Comment: 23 pages, 9 figures; accepted to Biophysical Journa

Probing protein-protein interactions by dynamic force correlated spectroscopy (FCS)

We develop a formalism for single molecule dynamic force spectroscopy to map the energy landscape of protein-protein complex ($P_1$$P_2$). The joint distribution $P(\tau_1,\tau_2)$ of unbinding lifetimes $\tau_1$ and $\tau_2$ measurable in a compression-tension cycle, which accounts for the internal relaxation dynamics of the proteins under tension, shows that the histogram of $\tau_1$ is not Poissonian. The theory is applied to the forced unbinding of protein $P_1$, modeled as a wormlike chain, from $P_1$$P_2$. We propose a new class of experiments which can resolve the effect of internal protein dynamics on the unbinding lifetimes.Comment: 12 pages, 3 figures, accepted to Phys. Rev. Let

Mechanistic Basis for the Binding of RGD- and AGDV-Peptides to the Platelet Integrin αIIbβ3

© 2017 American Chemical Society.Binding of soluble fibrinogen to the activated conformation of the integrin αIIbβ3 is required for platelet aggregation and is mediated exclusively by the C-terminal AGDV-containing dodecapeptide (γC-12) sequence of the fibrinogen γ chain. However, peptides containing the Arg-Gly-Asp (RGD) sequences located in two places in the fibrinogen Aα chain inhibit soluble fibrinogen binding to αIIbβ3 and make substantial contributions to αIIbβ3 binding when fibrinogen is immobilized and when it is converted to fibrin. Here, we employed optical trap-based nanomechanical measurements and computational molecular modeling to determine the kinetics, energetics, and structural details of cyclic RGDFK (cRGDFK) and γC-12 binding to αIIbβ3. Docking analysis revealed that NMR-determined solution structures of cRGDFK and γC-12 bind to both the open and closed αIIbβ3 conformers at the interface between the αIIb β-propeller domain and the β3 βI domain. The nanomechanical measurements revealed that cRGDFK binds to αIIbβ3 at least as tightly as γC-12. A subsequent analysis of molecular force profiles and the number of peptide−αIIbβ3 binding contacts revealed that both peptides form stable bimolecular complexes with αIIbβ3 that dissociate in the 60-120 pN range. The Gibbs free energy profiles of the αIIbβ3-peptide complexes revealed that the overall stability of the αIIbβ3-cRGDFK complex was comparable with that of the αIIbβ3−γC-12 complex. Thus, these results provide a mechanistic explanation for previous observations that RGD- and AGDV-containing peptides are both potent inhibitors of the αIIbβ3-fibrinogen interactions and are consistent with the observation that RGD motifs, in addition to AGDV, support interaction of αIIbβ3 with immobilized fibrinogen and fibrin

Atomic Structural Models of Fibrin Oligomers

© 2018 Elsevier Ltd The space-filling fibrin network is a major part of clots and thrombi formed in blood. Fibrin polymerization starts when fibrinogen, a plasma protein, is proteolytically converted to fibrin, which self-assembles to form double-stranded protofibrils. When reaching a critical length, these intermediate species aggregate laterally to transform into fibers arranged into branched fibrin network. We combined multiscale modeling in silico with atomic force microscopy (AFM) imaging to reconstruct complete atomic models of double-stranded fibrin protofibrils with γ-γ crosslinking, A:a and B:b knob-hole bonds, and αC regions—all important structural determinants not resolved crystallographically. Structures of fibrin oligomers and protofibrils containing up to 19 monomers were successfully validated by quantitative comparison with high-resolution AFM images. We characterized the protofibril twisting, bending, kinking, and reversibility of A:a knob-hole bonds, and calculated hydrodynamic parameters of fibrin oligomers. Atomic structures of protofibrils provide a basis to understand mechanisms of early stages of fibrin polymerization. Zhmurov et al. used 27 relevant crystal structures to computationally reconstruct the full-atomic models of fibrin oligomers and protofibrils, which correlate with high-resolution atomic force microscopy images. The structures contain much valuable information for understanding the early stages of fibrin polymerization

Regulatory element in fibrin triggers tension-activated transition from catch to slip bonds

© 2018 National Academy of Sciences. All Rights Reserved. Fibrin formation and mechanical stability are essential in thrombosis and hemostasis. To reveal how mechanical load impacts fibrin, we carried out optical trap-based single-molecule forced unbinding experiments. The strength of noncovalent A:a knob-hole bond stabilizing fibrin polymers first increases with tensile force (catch bonds) and then decreases with force when the force exceeds a critical value (slip bonds). To provide the structural basis of catch–slip-bond behavior, we analyzed crystal structures and performed molecular modeling of A:a knob-hole complex. The movable flap (residues γ295 to γ305) containing the weak calcium-binding site γ2 serves as a tension sensor. Flap dissociation from the B domain in the γ-nodule and translocation to knob ‘A’ triggers hole ‘a’ closure, resulting in the increase of binding affinity and prolonged bond lifetimes. The discovery of biphasic kinetics of knob-hole bond rupture is quantitatively explained by using a theory, formulated in terms of structural transitions in the binding pocket between the low-affinity (slip) and high-affinity (catch) states. We provide a general framework to understand the mechanical response of protein pairs capable of tension-induced remodeling of their association interface. Strengthening of the A:a knob-hole bonds at 30- to 40-pN forces might favor formation of nascent fibrin clots subject to hydrodynamic shear in vivo

Conformational Flexibility and Self-Association of Fibrinogen in Concentrated Solutions

© 2017 American Chemical Society. We studied the hydrodynamic behavior of fibrinogen, a blood plasma protein involved in blood clotting, in a broad 0.3-60 mg/mL range of concentration and 5-42 °C temperature using pulsed-field gradient 1 H NMR-diffusometry. Arrhenius plots revealed the activation energy for fibrinogen diffusion E d = 21.3 kJ/mol at 1.4 mg/mL and 28.4 kJ/mol at 38 mg/mL. We found a dramatic slowdown in fibrinogen self-diffusion with concentration beginning at 1.7-3.4 mg/mL, which deviated from the standard hard-particle behavior, suggesting a remarkable intermolecular entanglement. This concentration dependence was observed regardless of the absence or presence of the GPRP peptide (inhibitor of fibrin polymerization), and also in samples free of fibrin oligomers. By contrast, diffusivity of fibrinogen variant I-9 with truncated C-terminal portions of the Aα chains was much less concentration-dependent, indicating the importance of intermolecular linkages formed by the αC regions. Theoretical models combined with all-atom molecular dynamics simulations revealed partially bent fibrinogen solution conformations that interpolate between a flexible chain and a rigid rod observed in the crystal. The results obtained illuminate the important role of the αC regions in modulating the fibrinogen molecular shape through formation of weak intermolecular linkages that control the bulk properties of fibrinogen solutions

Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N [subscript G] is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε ε[subscript s] with slow internal dynamics. The cohesion strength ε[subscript s] of this freezing transition depends on N G . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N [subscript G] . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi