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ABSTRACT: We analyse the folding and unfolding of an RNA hairpin using a conventional zipping model that includes both the free energy for RNA binding and the elastic free energy of the system. Unfolding under isotonic conditions (where we control the applied load) is known to occur at a well-defined critical load. In marked contrast, we find that unfolding under isometric conditions (where we control the extension of the hairpin) produces a series of sharp peaks in the average load as the stem of the hairpin starts to unzip base by base. A peak occurs when the elastic energy stored in the unzipped arms of the hairpin becomes so large that it is energetically favourable for the next base pair to unzip: the consequent increase in the contour length of the unzipped arms reduces their elastic energy and causes the average load to fall abruptly. However, as the contour length of the unzipped arms increases, the peaks become less distinct. Moreover, when we include the long DNA/RNA handles that have been used in single-molecule experiments, the unzipping of individual base pairs cannot be resolved at all. Instead, with the hairpin in the folded state, the average load increases with extension until the elastic energy stored in the handles makes it energetically favourable for the hairpin to unzip over a narrow range of extensions. The resultant yield point produces a mechanical hysteresis loop with a negative slope, as observed experimentally. Unfolding of the hairpin is also affected by the elastic energy stored in a compliant force transducer. We find that short, stiff handles and a stiff force transducer could improve the resolution of mechanical experiments on single molecules.
Journal of Theoretical Biology 07/2012; 312C:96-104. · 2.21 Impact Factor
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ABSTRACT: When a two-headed molecular motor such as kinesin is attached to its track by just a single head in the presence of an applied load, thermally activated head detachment followed by rapid re-attachment at another binding site can cause the motor to 'hop' backwards. Such hopping, on its own, would produce a linear force-velocity relation. However, for kinesin, we must incorporate hopping into the motor's alternating-head scheme, where we expect it to be most important for the state prior to neck-linker docking. We show that hopping can account for the backward steps, run length and stalling of conventional kinesin. In particular, although hopping does not hydrolyse ATP, we find that the hopping rate obeys the same Michaelis-Menten relation as the ATP hydrolysis rate. Hopping can also account for the reduced processivity observed in kinesins with mutations in their tubulin-binding loop. Indeed, it may provide a general mechanism for the breakdown of perfect processivity in two-headed molecular motors.
Journal of Theoretical Biology 08/2009; 261(1):43-9. · 2.21 Impact Factor
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Advances in experimental medicine and biology 02/2003; 538:361-7. · 1.09 Impact Factor
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ABSTRACT: A key step in the processive motion of two-headed kinesin along a microtubule is the 'docking' of the neck linker that joins each kinesin head to the motor's dimerized coiled-coil neck. This process is similar to the folding of a protein beta-hairpin, which starts in a highly mobile unfolded state that has significant entropic elasticity and finishes in a more rigid folded state. We therefore suggest that neck-linker docking is mechanically equivalent to the thermally activated shortening of a spring that has been stretched by an applied load. This critical tension-dependent step utilizes Brownian motion and it immediately follows the binding of ATP, the hydrolysis of which provides the free energy that drives the kinesin cycle. A simple three-state model incorporating neck-linker docking can account quantitatively for both the kinesin force-velocity relation and the unusual tension-dependence of its Michaelis constant. However, we find that the observed randomness of the kinesin motor requires a more detailed four-state model. Monte Carlo simulations of single-molecule stepping with this model illustrate the possibility of sub-8 nm steps, the size of which is predicted to vary linearly with the applied load.
Proceedings of the Royal Society B: Biological Sciences 12/2002; 269(1507):2363-71. · 5.41 Impact Factor
