Abstract
Abstract
Force spectroscopy yields direct access to the interplay between free energy and transition kinetics of proteins and nucleic acids. Yet, complex molecules such as multi-domain proteins exhibit multiple intermediates during unfolding and refolding with different or similar stabilities and kinetics ranging from milliseconds to hours. In particular, conditions at equilibrium or near equilibrium are often impossible to find for multi-domain systems and traditional out-of-equilibrium experiments challenging to analyze. Here, we propose periodic forces to bridge different stabilities, selectively enhance intermediate populations, and a rigorous analysis framework to disentangle kinetics of multi-domain protein folding at quasi-equilibrium. Using high resolution magnetic tweezers, we apply well-defined periodic square functions of force with steady states that can be flexibly modulated. We demonstrate the analysis framework with a well-studied simple model system, the two-state folder λ
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. We show that periodic force experiments reproduce equilibrium kinetics and a simple theoretical framework opens the possibility to expand periodic force measurements to complex multidomain proteins. We apply the framework to the multi-domain protein mimic (Protein L)
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and show how periodic forces can enhance populations of distinct intermediate states by tuning their frequency and amplitude. In a last example, we show how to dissect entangled states of a hybrid two-domain protein termed λ-L, where 100-fold difference in kinetics of both domains would prevent equilibrium analysis. Expanding a two-state to a three-state periodic force protocol allowed for directed population of folding intermediates. We anticipate our method and analysis framework will expand the possibilities to decipher complex multi-domain folds and their multi-dimensional folding pathways.