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

Abstract

Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism. Especially, the temperature dependence of the folding rate remains unsolved in the literature. Starting from the assumption that protein folding is an event of quantum transition between molecular conformations, we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies. The non-Arrhenius temperature relation for 16 proteins, whose experimental data had previously been available, was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation. A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory. The statistical comparisons of the folding rates for 65 two-state proteins were carried out, and the theoretical vs. experimental correlation coefficient was 0.73. Moreover, the maximum and the minimum folding rates given by the theory were consistent with the experimental results. quantum folding, protein folding rate, temperature dependence, number of torsion mode, folding free energy Citation:Lv J, Luo LF. Statistical analyses of protein folding rates from the view of quantum transition. Sci China Life Sci, 2014Sci, , 57: 1197Sci, -1212Sci, , doi: 10.1007 It is well known that a protein chain can spontaneously fold into its unique native structure [1,2]. To paraphrase Levinthal's paradox, if a protein were to attain its correctly folded configuration by sequentially sampling all the possible conformations, it would require a period of time longer than the age of the universe to arrive at its correct native conformation [3]. Apart from theory, it is a fact that experimentally measured times for spontaneous folding of single-domain globular proteins range from microseconds [46] to tens of minutes [7]. Thus, how configurations of proteins are determined and what makes them fold so quickly are questions that constitute a longstanding puzzle in molecular biology. While two prominent models have been proposed to study the protein folding mechanism, folding nucleus [8,9] and folding tunnel [1014], the importance of topology and contact order in protein folding has been recognized over the last 15 years, and many new models to predict the protein folding rate have been published [1529]. Curiously, it is notable that the rate at which proteins fold is highly sensitive to temperature, showing non-Arrhenius behavior, i.e., the temperature dependence of the rate constant is, in fact, not exponential for these reactions. The nonlinearity of logarithm folding rate on temperature 1/T has been conventionally interpreted by the nonlinear temperature dependence of the configurational diffusion constant on rough energy landscapes [30] or by the temperature dependence of hydrophobic interaction [31,32]. Another model was proposed more recently to interpret the difference between folding and unfolding by introducing the number of dena...

Quantitative Relations in Protein and RNA Folding Deduced from Quantum Theory

“…By use of these equations we have successfully explained the non-Arrhenius temperature dependence of the folding rate for each protein. Moreover, the statistical investigation of 65 two-state protein folding rates (which were studied by Garbuzynskiy et al) shows these fundamental equations are consistent with experimental data [13] [14].…”

“…Of the 69 proteins, the folding rates of 65 two-state proteins are obtained at around 25 °C. They constitute a dataset used by us to compare the theoretical vs. experimental results [13]. Hyeon and Thirumalai collected the folding rates of 27 RNA molecules [16].…”

“…While the torsion vibration energy is 0.03-0.003 ev, the lowest in all forms of biological energies. In terms of frequency, the stretching and bending frequency is 10 14 -10 13 Hz while that for torsion is 7.5×10 12 -7.5×10 11 Hz. Interestingly, the torsion energy is even lower than the average thermal energy per atom at room temperature (0.04 ev in 25 C); the torsion angles are easily changed even at physiological temperature.…”

Experimental tests of the quantum property of protein folding

“…The particular temperature dependence reflects the quantum properties of the folding mechanism. We have proved the theoretical Eq (1) is in accordance with the experimental temperature dependence of the folding rate for all proteins whose experimental data were available [5]. This provides a strong evidence on quantum property of protein folding.…”

“…A long-standing problem is why the protein folding rate always exhibits the curious non-Arrhenius temperature dependence [4]. Our formula can explain all these experiments well [5]. Furthermore, we have succeeded in applying this theory to study RNA folding and deduced a general statistical relation between folding rate and chain length for both protein and RNA molecules [6].…”