Folding and Binding: When the Force is Against You

Macromolecular folding and binding events are behind many cellular processes, so it is important to understand the mechanism by which they occur. Single-molecule experiments have begun to reveal details of molecular mechanisms and energy landscapes that may be very difficult to resolve via ensemble experiments (1), in particular by resolving subpopulations of molecules and unambiguously assigning the sequence of events (2). A special feature of single-molecule pulling experiments, such as those using atomic force microscopes, or optical tweezers, is that a force is applied to the same coordinate that is being observed, namely the molecular extension (3), allowing details of the molecular free energy landscape (4,5) and dynamics (6) to be elucidated. However, this introduces a requirement for attaching the molecular system to the pulling device, which has tended to limit the applications to unimolecular conformational transitions such as, for example, the folding of a nucleic acid or protein (3,5,6).

Relatively little work, either experimental or theoretical, has addressed the problem of macromolecular association in single-molecule force experiments. In recent years, practical limitations have been overcome by introducing an artificial tether between the two binding partners and by improvements in instrumental stability allowing measurements at lower forces than previously possible (7,8). These experiments have the potential to resolve different types of binding mechanism (9). However, to date there has been little corresponding theoretical work. In this issue, Pierse and Dudko (10) have published a concise statistical-mechanical theory, which culminates with an analytical solution for the key experimental observable: the distribution of folding or binding forces. The analytical nature of the theory makes it suitable for a direct fit to experimental data, unlike numerical models. The fit, in turn, yields the key determinants of folding and binding processes from mechanical pulling experiments.

At first glance, there may not seem to be much difference between the description of molecular association or refolding and that for rupture of ligand-receptor bonds or protein unfolding (4). Indeed, for molecular simulations done at a low, constant force, the same theory can be used to recover the free energy landscape parameters for protein refolding (11). However, for real experiments, the situation is more complicated:

For either refolding or binding, the effect of the stiffness of the pulling device itself cannot be ignored as it is when considering rupture or unfolding events. The reason is that in the latter case, the stiffness of the molecule in the folded or bound state is much greater than that of the pulling device, but in the former, they may be comparable, which affects the shape of the combined potential of the molecule and the device, and, hence, the transition rate.

For rebinding experiments, the tether used to link the binding partners will also alter the binding free energy landscape, and must therefore be accounted for to obtain unbiased landscape parameters.

For experiments in which the force is time-dependent, the major experimental output—the distribution of folding or binding forces—is qualitatively different, having negative skew for unbinding/unfolding, but positive for rebinding/refolding (Fig. 1). The theory of Pierse and Dudko (10) addresses all of these issues, and thus will serve as an analytical tool for quantitative interpretation of single-molecule experiments on folding, and open the way for further work on macromolecular binding.

Figure 1.

Pulling experiments in which the force is (a) ramped up (i.e., unbinding) or (b) ramped down (i.e., binding) give qualitatively different distributions of the force at which rupture or binding occurs.

Of course, there are still many interesting issues to consider, both from experimental and theoretical points of view. From a theoretical point of view, the description for protein or nucleic acid folding is well developed. However, molecular binding in the absence of a tether keeping the two molecules together is bimolecular, and an additional step is required to obtain the bimolecular rate from the pseudo-unimolecular rate in the theory being discussed here. In the design of such rebinding experiments, a number of decisions need to be made, such as how long the tethers linking the molecules should be, and where should they be attached. Most exciting will be the application of the new theory to experimental data on physiologically relevant binding events, for example for the binding of cell adhesion molecules to cell surface receptors or binding of the von Willebrand factor to glycoprotein Ibα, crucial in the formation of blood clots (8).