Abstract
Understanding protein dynamics requires a comprehensive knowledge of the underlying potential energy surface that governs the motion of each individual protein molecule. Single molecule mechanical studies have provided the unprecedented opportunity to study the individual unfolding pathways along a well defined coordinate, the end-to-end length of the protein. In these experiments, unfolding requires surmounting an energy barrier that separates the native from the extended state. The calculation of the absolute value of the barrier height has traditionally relied on the assumption of an attempt frequency, υ(‡). Here we used single molecule force-clamp spectroscopy to directly determine the value of υ(‡) for mechanical unfolding by measuring the unfolding rate of the small protein ubiquitin at varying temperatures. Our experiments demonstrate a significant effect of the temperature on the mechanical rate of unfolding. By extrapolating the unfolding rate in the absence of force for different temperatures, varying within the range spanning from 5 to 45 °C, we measured a value for the activation barrier of ΔG(‡) = 71 ± 5 kJ/mol and an exponential prefactor υ(‡) ∼4 × 10(9) s(-1). Although the measured prefactor value is 3 orders of magnitude smaller than the value predicted by the transition state theory (∼6 × 10(12) s(-1)), it is 400-fold higher than that encountered in analogous experiments studying the effect of temperature on the reactivity of a protein-embedded disulfide bond (∼10(7) M(-1) s(-1)). This approach will allow quantitative characterization of the complete energy landscape of a folding polypeptide from highly extended states, of capital importance for proteins with elastic function.
Highlights
Tially with time [2]
Single molecule force spectroscopy has provided a new vista on the molecular mechanisms underlying proteinfolding at the subnanometer scale [17]
These works reported an expected decrease in the mechanical stability of the protein as the temperature was increased. It remained elusive whether the effect of temperature was uniquely to lower the height of the energy barrier, ⌬G‡, or whether the distance to the transition state, ⌬x, which determines the width of the barrier, was altered by the change in temperature. In all these studies, the absolute value of the height of the energy barrier limiting the unfolding process has been calculated assuming an attempt frequency, ‡, which has been given a value that varied over a wide range, spanning from 106 sϪ1 up to 1013 sϪ1 (29 – 31)
Summary
Tially with time [2]. Such a simplified kinetic analysis provides the framework to study the (un)folding reaction in terms of the Eyring transition state theory (TST),3 which allows quantification of the rate constant for a given chemical reaction as a function of temperature [3, 4]. We study the mechanical unfolding of the small protein ubiquitin at varying temperatures to experimentally obtain, for the first time in single molecule mechanical experiments, the attempt frequency prefactor for protein unfolding, ‡, together with the height and width of the energy barrier separating the native from the extended states of the protein.
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