Abstract
Cooperativity is considered to be a key organizing principle behind biomolecular assembly, recognition and folding. However, it has remained very challenging to quantitatively characterize how cooperative processes occur on a concerted, multiple-interaction basis. Here, we address how and when the folding process is cooperative on a molecular scale. To this end, we analyze multipoint time-correlation functions probing time-dependent communication between multiple amino acids, which were computed from long folding simulation trajectories. We find that the simultaneous multiple amino-acid contact formation, which is absent in the unfolded state, starts to develop only upon entering the folding transition path. Interestingly, the transition state, whose presence is connected to the macrostate cooperative behavior known as the two-state folding, can be identified as the state in which the amino-acid cooperativity is maximal. Thus, our work not only provides a new mechanistic view on how protein folding proceeds on a multiple-interaction basis, but also offers a conceptually novel characterization of the folding transition state and the molecular origin of the phenomenological cooperative folding behavior. Moreover, the multipoint correlation function approach adopted here is general and can be used to expand the understanding of cooperative processes in complex chemical and biomolecular systems.
Highlights
Biomolecular assembly, recognition and folding are complex processes in which building blocks, such as amino acids in proteins, search for favorable inter- or intra-molecular interactions in intricate manners.[1,2,3] Cooperativity has been recognized to be a key concept associated with these processes.[4,5,6] cooperativity in macromolecular systems is typically described at a phenomenological, macrostate level, and is broadly de ned as a characteristic of processes in which intermediate states are disfavored, i.e., only the extreme states are signi cantly populated
It has remained very challenging to quantitatively characterize how cooperative processes occur on a concerted, multiple-interaction basis
Cooperativity in complex systems is typically described at a macrostate level, and its characterization in molecular terms has been very challenging
Summary
Biomolecular assembly, recognition and folding are complex processes in which building blocks, such as amino acids in proteins, search for favorable inter- or intra-molecular interactions in intricate manners.[1,2,3] Cooperativity has been recognized to be a key concept associated with these processes.[4,5,6] cooperativity in macromolecular systems is typically described at a phenomenological, macrostate level, and is broadly de ned as a characteristic of processes in which intermediate states are disfavored, i.e., only the extreme states are signi cantly populated. The cooperativity concept in protein folding was introduced at the macrostate level,[8] conveying that folding proceeds in a twostate, all-or-none fashion
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