Quantum Approach to Fast Protein-Folding Time^*

Abstract

In the traditional random-conformational-search model various hypotheses with a series of metastable intermediate states were often proposed to resolve the Levinthal paradox. Here we introduce a quantum strategy to formulate protein folding as a quantum walk on a definite graph, which provides us a general framework without making hypotheses. Evaluating it by the mean of first passage time, we find that the folding time via our quantum approach is much shorter than the one obtained via classical random walks. This idea is expected to evoke more insights for future studies.Understanding how proteins fold spontaneously into their native structures is both a fascinating and fundamental problem in interdisciplinary fields involving molecular biology, computer science, polymer physics as well as theoretical physics etc.. Since Harrington and Schellman discovered that protein-folding reactions are very fast and often reversible processes[1], there has been progressively more investigations on protein folding in both aspects of theory and experiment. Levinthal [2] noted early in 1967 that a much larger folding time is inevitable if proteins are folded by sequentially sampling of all possible conformations. Thus the protein was assumed to fold through a series of meta-stable intermediate states and the random conformational search does not occur in the folding process. The questions about what are the energetics of folding and how does the denature cause unfolding motivates one to think that the protein folding proceeds energetically downhill and loses conformational entropy as it goes. Based on such a hypothesis, the free-energy landscape framework was one way to describe the protein folding [3][4][5], where the energy funnel landscape provided a first conjecture of how the folding begins and continues [6].As we known, there have been substantial theoretical models with different simplifying assumptions, such as Ising-like model [7,8], foldon-dependent protein folding model [9], diffusion-collision model [10,11], and nucleation-condensation mechanism [12, 13] etc.. Theoretical models are useful for understanding the essentials of the complex self-assembly reaction of protein folding, but till now, they often rely on various hypotheses [6,[14][15][16][17]. This often brings in certain difficulties in connecting analytical theory to experimental results because some hypotheses can not be easily put into a practical experimental measurement. As it introduces less hypotheses in comparison to those theoretical models, the atomistic simulations [18][19][20] were used to investigate the protein folding along with nowadays' advances in computer science. Recently, a high-throughput protein design and characterization method was reported that allows one to systematically examine how sequence deter-mines the folding and stability [21]. However, quantitatively achieving the folding time and accurately understanding how the sequence determines the protein folding remain to be a key challenge.Here we propose a quantum strategy to for...

Quantum intelligence on protein folding pathways*

“…Here a = 388 and c = 186 or 193. We know in a previous work that the quantum folding is faster than the classical folding with about four to six times even for the simplest model of 4 residues and it is faster than the classical folding with almost ten to hundred times or more for n = 6 [17]. Here we calculate the folding time for n = 9 that is given in Table 1.…”

“…1 as an illustration. For the structure set S 9 , the compactness of each structure is calculated and shown in the Appendix On the basis of the lattice model, we introduced previously the concept of one-step folding to describe the protein folding process [17]. The one-step folding is defined by one displacement of an amino acid in one of the lattice sites: two protein structures are connected via one-step folding if their chain conformations differ in one site only.…”

“…Then we will have a distance space D n := {s a , d ab } in which the magnitude of d ab equals to the number of steps of the shortest path connecting s a and s b in the graph G n . There has been four line-crossings already when the 22-vertex graph G 6 is plotted on a plane [17]. The G 9 contains 388 vertices and appears very complicate if it is plotted on a plane.…”

“…where τ 0 represents the time period when the first-passage probability vanishes F a,b (τ 0 ) = 0 [17]. Here a = 388 and c = 186 or 193.…”

“…Recently, we introduced a quantum strategy [17] to formulate protein folding as a quantum walk on a definite graph, which provides us a general framework without making hypotheses, where we merely studied the model with six aminoacids as toy model. We know the shortest peptide chain in nature contains more than twenty amino-acid residues.…”