Protein folding is regarded as a quantum transition between the torsion states of a polypeptide chain. According to the quantum theory of conformational dynamics, we propose the dynamical contact order (DCO) defined as a characteristic of the contact described by the moment of inertia and the torsion potential energy of the polypeptide chain between contact residues. Consequently, the protein folding rate can be quantitatively studied from the point of view of dynamics. By comparing theoretical calculations and experimental data on the folding rate of 80 proteins, we successfully validate the view that protein folding is a quantum conformational transition. We conclude that (i) a correlation between the protein folding rate and the contact inertial moment exists; (ii) multi-state protein folding can be regarded as a quantum conformational transition similar to that of two-state proteins but with an intermediate delay. We have estimated the order of magnitude of the time delay; (iii) folding can be classified into two types, exergonic and endergonic. Most of the two-state proteins with higher folding rate are exergonic and most of the multi-state proteins with low folding rate are endergonic. The folding speed limit is determined by exergonic folding.
moment of inertia, dynamical contact order (DCO), protein folding rate
Citation:Zhang Y, Luo L F. The dynamical contact order: Protein folding rate parameters based on quantum conformational transitions. Sci China Life Sci, 2011Sci, , 54: 386 -392, doi: 10.1007 Protein folding is a complex kinetic process by which a polypeptide changes from the denatured state to the native folding state. Although a great deal of theoretical work has been carried out, the fundamental physics underlying the folding remains unclear. The folding kinetics of a large number of proteins has been studied experimentally [1][2][3]. For many of these proteins, folding has been shown to be an all-or-none process with no clear intermediate state. These are called two-state proteins. However, some proteins require the accumulation of intermediates to complete the folding process. These are referred to as three-state or multi-state proteins. The rate of folding varies from milliseconds to hours. Some small proteins fold much faster, at rates in microsecond [2,3]. Experimental data has indicated that most of the ultrafast folders show a significant decrease in folding rates as the temperature is increased [4]. The wide range of folding rates and a possible folding speed limit are likely to be closely related to the inherent physics behind the phenomena. A deeper understanding of the folding mechanism and the accurate prediction of protein folding rates is an important topic in protein science. Since 1998, when the relative contact order (RCO) was proposed by Plaxco et al. [5], it has been widely accepted that folding rates and mechanisms are largely determined by the topology of the native state. Much theoretical work based on this concept has been proposed. For example, Ivankov et al. [6] pr...