Theoretical Study On Protein Folding And Misfolding Via Quantum Walk Approach

"Protein folding" is one of the important topics of biophysics in the 21st century.Based on the amino acid sequence of protein,the main task is to study how to determine the folding pathways and the final three-dimensional native structures of biological function In the traditional random-conformational-search model,the predecessors propose the hypothesis with various metastable intermediate states to solve the Levinthal paradox of folding time,who believes that the protein folding problem is extremely complicated.Chapter 1 briefly describes a recently proposed quantum simulation method,which expresses protein folding as a quantum random walk on a certain connection pattern.This is a general theoretical framework in which people no longer make more artificial assumptions.By calculating the relative folding time defined by the first passage probability,we found that the folding time obtained by the quantum walking approach is much shorter than that obtained by the classical random walk approach.This view is expected to provide more insights for future research.On the basis of the quantum method mentioned above,in Chapter 2,we further extend the protein peptide chain model to a 2-dimensional lattice model which contains 9 amino acid residues,and introduce the concept of distance space and its projection on the XY plane and several other physical feature quantities(one is called the Compactness of the protein structure and the other is called the Shortest-path-probability ratio).Among them,the method of dividing according to the subset of the shortest path and the non-shortest path after projection allows us to naturally reduce the 388×388 density matrix to a certain 2×2 matrix,and calculate the von Neumann entropy to reflect the given quantum coherence properties of the system.In our study,we use the classical random walk and quantum walk to compare the average distance and average Compactness that evolved over time,and compare the time evolution curves of Shannon entropy and von Neumann entropy.Not only can these results further affirm the fast quantum folding time,but also reveal the quantum intelligence hidden behind the choosing of protein folding pathways.In Chapter 3,we define the funnel model through different sequences of potential energy surfaces,select the funnel's stream-path under the framework of the theoretical system of quantum folding,and draw the probability and comparison with the shortest-path on the connection graph of Chapter 2.The shortest-path selection is obviously better than the calculation of the selection of the stream-path on the funnel model defined by the potential energy surface,which negates the classic funnel model proposed by the predecessors.By comparing the folding time of the two most compact structures,we proposed a physical mechanism for protein misfolding and explored the other most compact structure.We further explore the effect of the dissipation coefficient of the HP model correlation system.After deepening the potential energy or adding a part of the perturbation energy,expect to find out whether it will affect the phase transition point of the system evolution.It is hoped that by affecting the phase transition points of the above phase diagrams,these prediction will inspire people to explore some artificial measures which can interfere with the mechanism of protein misfolding.