Stretching single-domain proteins: Phase diagram and kinetics of force-induced unfolding

Single-molecule force spectroscopy reveals unfolding of domains in titin on stretching. We provide a theoretical framework for these experiments by computing the phase diagrams for force-induced unfolding of single-domain proteins using lattice models. The results show that two-state folders (at zero force) unravel cooperatively, whereas stretching of non-two-state folders occurs through intermediates. The stretching rates of individual molecules show great variations reflecting the heterogeneity of force-induced unfolding pathways. The approach to the stretched state occurs in a stepwise “quantized” manner. Unfolding dynamics and forces required to stretch proteins depend sensitively on topology. The unfolding rates increase exponentially with force f till an optimum value, which is determined by the barrier to unfolding when f = 0. A mapping of these results to proteins shows qualitative agreement with force-induced unfolding of Ig-like domains in titin. We show that single-molecule force spectroscopy can be used to map the folding free energy landscape of proteins in the absence of denaturants.

Low dimensionality of supraspinally induced force fields

Recent experiments using electrical and N-methyl-d-aspartate microstimulation of the spinal cord gray matter and cutaneous stimulation of the hindlimb of spinalized frogs have provided evidence for a modular organization of the frog’s spinal cord circuitry. A “module” is a functional unit in the spinal cord circuitry that generates a specific motor output by imposing a specific pattern of muscle activation. The output of a module can be characterized as a force field: the collection of the isometric forces generated at the ankle over different locations in the leg’s workspace. Different modules can be combined independently so that their force fields linearly sum. The goal of this study was to ascertain whether the force fields generated by the activation of supraspinal structures could result from combinations of a small number of modules. We recorded a set of force fields generated by the electrical stimulation of the vestibular nerve in seven frogs, and we performed a principal component analysis to study the dimensionality of this set. We found that 94% of the total variation of the data is explained by the first five principal components, a result that indicates that the dimensionality of the set of fields evoked by vestibular stimulation is low. This result is compatible with the hypothesis that vestibular fields are generated by combinations of a small number of spinal modules.

Chemically distinct transition states govern rapid dissociation of single L-selectin bonds under force

Carbohydrate–protein bonds interrupt the rapid flow of leukocytes in the circulation by initiation of rolling and tethering at vessel walls. The cell surface carbohydrate ligands are glycosylated proteins like the mucin P-selectin glycoprotein ligand-1 (PSGL-1), which bind ubiquitously to the family of E-, P-, and L-selectin proteins in membranes of leukocytes and endothelium. The current view is that carbohydrate–selectin bonds dissociate a few times per second, and the unbinding rate increases weakly with force. However, such studies have provided little insight into how numerous hydrogen bonds, a Ca2+ metal ion bond, and other interactions contribute to the mechanical strength of these attachments. Decorating a force probe with very dilute ligands and controlling touch to achieve rare single-bond events, we have varied the unbinding rates of carbohydrate–selectin bonds by detachment with ramps of force/time from 10 to 100,000 pN/sec. Testing PSGL-1, its outer 19 aa (19FT), and sialyl LewisX (sLeX) against L-selectin in vitro on glass microspheres and in situ on neutrophils, we found that the unbinding rates followed the same dependence on force and increased by nearly 1,000-fold as rupture forces rose from a few to ≈200 pN. Plotted on a logarithmic scale of loading rate, the rupture forces reveal two prominent energy barriers along the unbinding pathway. Strengths above 75 pN arise from rapid detachment (<0.01 sec) impeded by an inner barrier that requires a Ca2+ bond between a single sLeX and the lectin domain. Strengths below 75 pN occur under slow detachment (>0.01 sec) impeded by the outer barrier, which appears to involve an array of weak (putatively hydrogen) bonds.

Large vortex-like structure of dipole field in computer models of liquid water and dipole-bridge between biomolecules

We propose a framework to describe the cooperative orientational motions of water molecules in liquid water and around solute molecules in water solutions. From molecular dynamics (MD) simulation a new quantity “site-dipole field” is defined as the averaged orientation of water molecules that pass through each spatial position. In the site-dipole field of bulk water we found large vortex-like structures of more than 10 Å in size. Such coherent patterns persist more than 300 ps although the orientational memory of individual molecules is quickly lost. A 1-ns MD simulation of systems consisting of two amino acids shows that the fluctuations of site-dipole field of solvent are pinned around the amino acids, resulting in a stable dipole-bridge between side-chains of amino acids. The dipole-bridge is significantly formed even for the side-chain separation of 14 Å, which corresponds to five layers of water. The way that dipole-bridge forms sensitively depends on the side-chain orientations and thereby explains the specificity in the solvent-mediated interactions between biomolecules.