The introduction of disulfide bonds into proteins creates additional mechanical barriers and limits the unfolded contour length (i.e., the maximal extension) measured by single-molecule force spectroscopy. Here, we engineer single disulfide bonds into four different locations of the human cardiac titin module (I27) to control the contour length while keeping the distance to the transition state unchanged. This enables the study of several biologically important parameters. First, we are able to precisely determine the end-to-end length of the transition state before unfolding (53 Angstrom), which is longer than the end-to-end length of the protein obtained from NMR spectroscopy (43 Angstrom). Second, the measured contour length per amino acid from five different methods (4.0 +/- 0.2 Angstrom) is longer than the end-to-end length obtained from the crystal structure (3.6 Angstrom). Our measurement of the contour length takes into account all the internal degrees of freedom of the polypeptide chain, whereas crystallography measures the end-to-end length within the "frozen" protein structure. Furthermore, the control of contour length and therefore the number of amino acids unraveled before reaching the disulfide bond (n) facilitates the test of the chain length dependence on the folding time (tau(F)). We find that both a power law scaling tau(F) lambda n(lambda) with lambda = 4.4, and an exponential scaling with n(0.6) fit the data range, in support of different protein-folding scenarios.
In particulate materials, such as emulsions and granular media, a "jammed" system results if particles are packed together so that all particles are touching their neighbours, provided the density is sufficiently high. This paper studies through experiment, theory and simulation, the forces that particles exert upon one another in such a jammed state. Confocal microscopy of a compressed polydisperse emulsion provides a direct 3D measurement of the dispersed phase morphology within the bulk of the sample. This allows the determination of the probability distribution of interdroplet forces, P(f) where f is the magnitude of the force, from local droplet deformations. In parallel, the simplest form of the Boltzmann equation for the probability of force distributions predicts P(f) to be of the form e(-f/p), where p is proportional to the mean force f for large forces. This result is in good agreement with experimental and simulated data.
Statistical theories of protein folding have long predicted plausible mechanisms for reducing the vast conformational space through distinct ensembles of structures. However, these predictions have remained untested by bulk techniques, because the conformational diversity of folding molecules has been experimentally unapproachable. Owing to recent advances in single molecule force-clamp spectroscopy, we are now able to probe the structure and dynamics of the small protein ubiquitin by measuring its length and mechanical stability during each stage of folding. Here, we discover that upon hydrophobic collapse, the protein rapidly selects a subset of minimum energy structures that are mechanically weak and essential precursors of the native fold. From this much reduced ensemble, the native state is acquired through a barrier-limited transition. Our results support the validity of statistical mechanics models in describing the folding of a small protein on biological timescales.force-clamp spectroscopy ͉ protein folding M ore than 2 decades ago statistical theories of protein folding, developed from simplified models of proteins (1) and scaling laws borrowed from polymer physics (2), offered an appealing framework for how proteins fold (3-5). These pioneering studies laid down the foundation of the ''new view'' of the protein folding theory (6-8). From this viewpoint, a polypeptide exposed to folding conditions is thought to go through progressively smaller conformational ensembles along a rough, funnel-like energy surface leading to the native state topology (8, 9). The envisaged stages of folding involve an initial hydrophobic collapse into a large set of nonspecific globular structures, which then select a few minimum energy collapsed conformations that fold via activated all-or-none transitions (4,5,(10)(11)(12)(13)(14). Time scales for each one of these phases were estimated from simplified models to range from microseconds for the collapse to seconds for the final fold (2,12). Although theoretical models propose physical mechanisms underlying protein folding (12,(15)(16)(17), their experimental verification has been inaccessible. Observing the multitude of trajectories and folding structures using bulk techniques averages out the ensembles predicted by the statistical theories of protein folding. Much of the literature studying bulk denaturation and refolding of proteins therefore reports 2-state folding reactions where even the presence of single folding intermediates is controversial (18,19). Indeed, as pointed out by Dill and Chan (15) in their seminal review, the predictions made by the statistical theories are in conflict with the view that folding proceeds through a well defined pathway that crosses a single energy barrier to the native state. This longstanding debate can only be addressed by sampling the conformational diversity of a single protein along its folding trajectory.Here, we demonstrate that single protein force-clamp spectroscopy using the AFM captures the diversity of the collapsed conforma...
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