A transformation for the mechanical fingerprints of complex biomolecular interactions

Abstract

Biological processes are carried out through molecular conformational transitions, ranging from the structural changes within biomolecules to the formation of macromolecular complexes and the associations between the complexes themselves. These transitions cover a vast range of timescales and are governed by a tangled network of molecular interactions. The resulting hierarchy of interactions, in turn, becomes encoded in the experimentally measurable "mechanical fingerprints" of the biomolecules, their forceextension curves. However, how can we decode these fingerprints so that they reveal the kinetic barriers and the associated timescales of a biological process? Here, we show that this can be accomplished with a simple, model-free transformation that is general enough to be applicable to molecular interactions involving an arbitrarily large number of kinetic barriers. Specifically, the transformation converts the mechanical fingerprints of the system directly into a map of force-dependent rate constants. This map reveals the kinetics of the multitude of rate processes in the system beyond what is typically accessible to direct measurements. With the contributions from individual barriers to the interaction network now "untangled", the map is straightforward to analyze in terms of the prominent barriers and timescales. Practical implementation of the transformation is illustrated with simulated biomolecular interactions that comprise different patterns of complexity-from a cascade of activation barriers to competing dissociation pathways.complex interactions | single molecule | force spectroscopy | kinetic rate C onformational transitions in biological macromoleculessuch as the folding of nucleic acids and proteins or the binding of receptors and their ligands-usually serve as the mechanism that brings biomolecules into their working shape and enables their biological function (1). The conformational dynamics of a biomolecule are governed by its energy, which is described by a hypersurface-the energy landscape-in a space of the multitude of atomic coordinates. The energy landscapes of biological macromolecules are rough and hierarchical: the folded and unfolded (or bound and unbound) conformational states are often separated by a mountainous terrain of barriers (2-4). Remarkably, the prominent features of the landscape can be revealed by pulling the molecule apart: these features manifest themselves as nonmonotonic signatures-rips-in the force-extension curves of the molecule (5). Characteristics of the force-extension curves uniquely identify the biomolecule and thus serve as its "mechanical fingerprints" (6), in which the prominent barriers on the energy landscape are encoded. However, how can we decode the mechanical fingerprints to uncover the locations and heights of the barriers and the associated timescales of biomolecular motion (Fig. 1)? This is the central question addressed in the present paper.The realm of biomolecular interactions can be accessed in single-molecule force experiments, which apply a s...

Reconstructing Folding Energy Landscapes by Single-Molecule Force Spectroscopy

“…However, the sequential application of two-state models (36, 37, 41) to build up a piecewise picture of the landscape is not guaranteed to produce correct results, particularly when using force ramps, because the unfolding forces associated with the first (lower-force) transitions typically affect those of the later (higher-force) transitions. Put another way, only when there is no correlation between the unfolding forces of sequential transitions, that is, when such transitions can be treated as independent two-state processes, is a piecewise reconstruction valid (117). To treat the more general case, Zhang & Dudko (117) recently introduced a method for transforming the transitions in multistate force-ramp records into a map of the microscopic rates for each possible transition.…”

“…Put another way, only when there is no correlation between the unfolding forces of sequential transitions, that is, when such transitions can be treated as independent two-state processes, is a piecewise reconstruction valid (117). To treat the more general case, Zhang & Dudko (117) recently introduced a method for transforming the transitions in multistate force-ramp records into a map of the microscopic rates for each possible transition. The force dependence of each of the microscopic rates can then, in principle, be fitted to a model (such as Equation 9) to characterize each of the barriers in the landscape.…”

Mechanical unfolding pathway of a model β-peptide foldamer

“…[17][18][19] If more than one free energy well has to be taken into account due to the presence of intermediates, the individual transitions in general cannot be assumed to be independent and a modification of the simple analysis is required. 20 The fit of experimental data to model predictions allows the determination of relevant parameters characterizing the intrinsic free energy landscape of the system such as the activation free energy, the distance from the well to the barrier, and the rate at zero force.…”

Hidden dynamics in the unfolding of individual bacteriorhodopsin proteins

“…, Fig. 2), such as the formalism developed by Zhang & Dudko (30). However, given the multiplicity of unfolding trajectories through the unfolding pathway (Fig.…”