The differential structural–elastic properties of molecules between their transition and initial (native or denatured) states determine force-dependent transition rates.

In spite of extensive investigations, the force-dependent unfolding/rupturing rate k(F) of biomolecules still remains poorly understood. A famous example is the frequently observed switch from catch-bond behaviour, where force anti-intuitively decreases k(F), to slip-bond behaviour where increasing force accelerates k(F). A common consensus in the field is that the catch-to-slip switch behaviour cannot be explained in a one-dimensional energy landscape, while this view is mainly built upon assuming that force monotonically affects k(F) along each available transition pathway. In this work, by applying Kramers kinetic rate theory to a model system where the transition starts from a single native state through a pathway involving sequential peeling of a polymer strand until reaching the transition state, we show the catch-to-slip switch behaviour can be understood in a one-dimensional energy landscape by considering the structural-elastic properties of molecules during transition. Thus, this work deepens our understanding of the force-dependent unfolding/rupturing kinetics of molecules/molecular complexes.

Many small protein domains or nucleic acid structures undergo two-state unfolding-refolding transitions during mechanical stretching using single-molecule techniques. Here, by applying the Jarzynski equality (JE), we analytically express the folding energy of a molecule as a function of the experimentally measured transition points ξ* obtained with two typical time-varying mechanical constraints: the force constraints F(t) and the position constraints R(t) of a Hookian spring attached to one end of the molecule. Compared to previous applications of JE based on the integration of accurately measured force-extension curves of a tether that typically contains the molecule of interest and handles, our approach just needs to accurately measure a single data point. In the case of the F(t) process, the calculation is handle-independent. The broad applications of the theory are demonstrated by measuring the folding energies of a DNA hairpin, a DNA G-quadruplex, and the titin I27 domain based on transition forces using magnetic tweezers.

The interaction between the single-stranded DNA and the homologous duplex DNA is essential for DNA homologous repair. Here, we report that parallel triplex structure can form spontaneously between a mechanically extended ssDNA and a homologous dsDNA in protein-free condition. The triplex has a contour length close to that of a B-form DNA duplex and remains stable after force is released. The binding energy between the ssDNA and the homologous dsDNA in the triplex is estimated to be comparable to the basepairing energy in a B-form dsDNA. As ssDNA is in a similar extended conformation within recombinase-coated nucleoprotein filaments, we propose that the parallel triplex may form and serve as an intermediate during recombinase-catalyzed homologous joint formation.

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