Vu, H. T. ; Chakrabarti, S. ; Hinczewski, M. ; Thirumalai, D. Discrete Step Sizes of Molecular Motors Lead to Bimodal Non-Gaussian Velocity Distributions under Force
. Phys. Rev. Lett. 117
, 078101. DOI:10.1103/PhysRevLett.117.078101Abstract
Fluctuations in the physical properties of biological machines are inextricably linked to their functions. Distributions of run lengths and velocities of processive molecular motors, like kinesin-1, are accessible through single-molecule techniques, but rigorous theoretical models for these probabilities are lacking. Here, we derive exact analytic results for a kinetic model to predict the resistive force (F)-dependent velocity [P(v)] and run length [P(n)] distribution functions of generic finitely processive molecular motors. Our theory quantitatively explains the zero force kinesin-1 data for both P(n) and P(v) using the detachment rate as the only parameter. In addition, we predict the F dependence of these quantities. At nonzero F, P(v) is non-Gaussian and is bimodal with peaks at positive and negative values of v, which is due to the discrete step size of kinesin-1. Although the predictions are based on analyses of kinesin-1 data, our results are general and should hold for any processive motor, which walks on a track by taking discrete steps.
Hinczewski, M. ; Hyeon, C. ; Thirumalai, D. Directly measuring single-molecule heterogeneity using force spectroscopy. Proc Natl Acad Sci U S A 113
One of the most intriguing results of single-molecule experiments on proteins and nucleic acids is the discovery of functional heterogeneity: the observation that complex cellular machines exhibit multiple, biologically active conformations. The structural differences between these conformations may be subtle, but each distinct state can be remarkably long-lived, with interconversions between states occurring only at macroscopic timescales, fractions of a second or longer. Although we now have proof of functional heterogeneity in a handful of systems-enzymes, motors, adhesion complexes-identifying and measuring it remains a formidable challenge. Here, we show that evidence of this phenomenon is more widespread than previously known, encoded in data collected from some of the most well-established single-molecule techniques: atomic force microscopy or optical tweezer pulling experiments. We present a theoretical procedure for analyzing distributions of rupture/unfolding forces recorded at different pulling speeds. This results in a single parameter, quantifying the degree of heterogeneity, and also leads to bounds on the equilibration and conformational interconversion timescales. Surveying 10 published datasets, we find heterogeneity in 5 of them, all with interconversion rates slower than 10 s(-1) Moreover, we identify two systems where additional data at realizable pulling velocities is likely to find a theoretically predicted, but so far unobserved crossover regime between heterogeneous and nonheterogeneous behavior. The significance of this regime is that it will allow far more precise estimates of the slow conformational switching times, one of the least understood aspects of functional heterogeneity. directly-measuring-single-molecule-heterogeneity-using-force-spectroscopy.pdf
Zhuravlev, P. I. ; Hinczewski, M. ; Chakrabarti, S. ; Marqusee, S. ; Thirumalai, D. Force-dependent switch in protein unfolding pathways and transition-state movements. Proc Natl Acad Sci U S A 113
Although it is known that single-domain proteins fold and unfold by parallel pathways, demonstration of this expectation has been difficult to establish in experiments. Unfolding rate, [Formula: see text], as a function of force f, obtained in single-molecule pulling experiments on src SH3 domain, exhibits upward curvature on a [Formula: see text] plot. Similar observations were reported for other proteins for the unfolding rate [Formula: see text]. These findings imply unfolding in these single-domain proteins involves a switch in the pathway as f or [Formula: see text] is increased from a low to a high value. We provide a unified theory demonstrating that if [Formula: see text] as a function of a perturbation (f or [Formula: see text]) exhibits upward curvature then the underlying energy landscape must be strongly multidimensional. Using molecular simulations we provide a structural basis for the switch in the pathways and dramatic shifts in the transition-state ensemble (TSE) in src SH3 domain as f is increased. We show that a single-point mutation shifts the upward curvature in [Formula: see text] to a lower force, thus establishing the malleability of the underlying folding landscape. Our theory, applicable to any perturbation that affects the free energy of the protein linearly, readily explains movement in the TSE in a β-sandwich (I27) protein and single-chain monellin as the denaturant concentration is varied. We predict that in the force range accessible in laser optical tweezer experiments there should be a switch in the unfolding pathways in I27 or its mutants. force-dependent-switch-in-protein-unfolding-pathways-and-transition-state-movements.pdf