The dynamical contact order: Protein folding rate parameters based on quantum conformational transitions

Abstract

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...

Protein folding as a quantum transition between conformational states

“…C3 means the inertial moment contributed from the k-th residue is calculated relative to an axis across the k-1-th residue and perpendicular to the link between k and k-1. From Table 1 we find that the distribution of the deviation between theoretical and experimental value of folding rate has a sharp peak within the range (-2,2) irrespective of the inertial axis choice, indicating that the theory is consistent with experiments [Zhang and Luo, 2010].…”

“…Simultaneously, to make the comparison easily established the following two assumptions will be introduced. First, due to our ignorance of the angular quantum Table 1 [Zhang and Luo, 2010]. In theoretical calculations of folding rate three kinds of rotational axis of inertia moment, C1, C2 and C3, have been assumed.…”

Quantitative Relations in Protein and RNA Folding Deduced from Quantum Theory

“…The problem can be compared with the multi-state protein folding. For multi-state protein one may assume the folding is a mutual process of several quantum transitions in different domains and that some time delays exist between these transitions [36]. The similar idea might be introduced in the study of the total folding rate of the RNA molecule.…”

Statistical analyses of protein folding rates from the view of quantum transition

“…From experimental data analysis we found that F should be larger for a protein with more residues in α helix; for example, F takes a value 81 for pure α helix chain (Table 1) [42], the predicted minimum of the rate seems not conflict with any existing two-state protein data. For multi-state protein one may assume the folding is a mutual process of several quantum transitions in different domains and that some time delays exist between these transitions [40]. Therefore, it is reasonable to assume that multistate folding proceeds in a larger spatial dimension and needs more execution time.…”