Statistical Physics Study On The Dynamics Of Polypeptides

Proteins are non-branched polymers that consist of amino acids.They are an important part of the molecular machine that performs various functions in life systems.They play an important role in many kinds of life phenomena,such as catalysis,immunity,transport,energy conversion and various life events.For example,they are molecular machine,building materials,attacking and defense weapons in cells.Proteins are usually made up of one or more polypeptides,and polypeptides are formed by dehydration condensation reaction of amino acids.The folding of proteins and polypeptides involves many kinds of interactions,such as Coulomb force,Van der Waals force,hydrophobic interaction and hydrogen bonds.Amino acids attract or repel each other due to these interactions,resulting to the folding.Some peptides fold to specific native-state structures,some fold to intrinsic disorder structures.Using physical models and molecular simulation to characterize these kinds of interactions in proteins and polypeptides,we can understand how proteins fold from a physical perspective.On the other hand,a lot of physical characteristics,such as energy transferring and dissipation,subdiffusion,slow relaxation are still not clear,which needs to be solved by using physical methods and models.Energy landscape,a widely used physical model also explains the importance of physical models in protein study.Analyzing the local interaction and conformational motion of proteins and polypeptides from a statistical physics perspective can help us better understand how proteins play their roles in biological processes,and provide a foundation for further exploration in life phenomena.Limited by the performance of experimental instruments and the current experimental measurements,there is a limitation on the time and space scale in practical research of proteins.However,molecular simulation can describe the dynamics of proteins at a smaller time and space scale.Molecular simulation is a computer simulation technique which is widely applied in biophysics,solid state physics,biochemistry and other disciplines on the physical properties of complex systems.We can get a trajectory and various kinetic information of the system by solving the kinetic equation.We can get the dynamic and thermodynamic information of the system through later statistical calculation and analysis.The data obtained by all-atom model is more accurate and reliable.In this paper,based on the molecular simulation of all-atom model,we carry out the following two topics.The internal friction of proteins is a typical dynamic phenomenon,which reflects the energy dissipation.We try to find out how energy transmit and dissipate during the folding process by analyzing the physical sources of internal friction.According to the Kramer's theory,the folding time of proteins is directly proportional to the viscosity of the external solvents.However,many theoretical simulations and experimental phenomena have found a different result.When the viscosity of the external solvent is extrapolated to zero,proteins still show a limited folding time.This is caused by the damping effect of protein itself and we call it internal friction.We use the autocorrelation function,weighted mean first passage time and Markov state model to calculate the relaxation times of two kinds of polypeptides((gly-ser)₄ and ala₈)in different solvent viscosity.Then a linear fitting and power law fitting on relaxation time and solvent viscosity are carried out to get the values of internal friction.The horizontal intercept and longitudinal intercept fitted by linear fitting,the exponential terms fitted by power law fitting are used to characterize the magnitude of internal friction.We find that internal friction exists in both peptides.We calculate the values of internal friction at different temperatures.The internal friction of(gly-ser)₄increases with temperature,while ala₈'s internal friction has a maximum value near the temperature T=315K.By analyzing the rotation of?and?angles in Ramachandran plots,we hold that the internal friction of proteins is mainly caused by its internal torsional barriers.Then we calculate the influence of torsional barriers and solvent's memory effect on internal friction.That the formation and rupture of hydrogen bonds and solvent's memory effect also contribute to internal friction.We still take(gly-ser)₄ and ala₈ in the subdiffusion topic.The trajectories of polypeptides are aligned to eliminate the influence of translation and rotation.The principal component analysis is used to avoid the deviation caused by artificial selection of reaction coordinates.We calculate the mean square displacement and relaxation time of the polypeptides.We found that the two peptide chains both show subdiffusion,similar to native proteins.The exponential terms fitted by power law fitting for(gly-ser)₄ is?=0.266,for ala₈ is?=0.314.An analysis on energy hierarchical plateau is used to characterize the source of subdiffusion.We introduce?_tto define the degree of trapping on a rugged energy landscape,?_f to define the degree of a fractal topology of the energy landscape.Our results show that the relaxation time of(gly-ser)₄ get stable quickly.Its subdiffusion is mainly caused by trapping on energy landscape.The relaxation time of ala₈ increases with observation time,similar to other native proteins.The source of the subdiffusion of ala₈ is contributed by?_f and?_t together,while?_f is more important.We conclude that the slow relaxation of proteins is caused by the subdiffusion,which is dominated by?_f.Proteins can jump to a higher hierarchical plateau in the fractal structure of energy landscape with increasing observation time,resulting to a continuous increase of relaxation time.Although internal friction and subdiffusion of proteins have been studied for years,we get innovative results in some ways.Our results reveal the effect of temperature on the internal friction of polypeptides.We discuss the source of internal friction from the view of interaction.We introduce two different values to describe the sources of subdiffusion.Finally,some possible physical source of internal friction and subdiffusion of proteins are given.All these are the breakthrough and innovation of this paper.This paper is arranged as the following.The first chapter briefly introduces the background,dynamical properties of proteins and polypeptides,and molecular simulation.The second chapter describes the research on internal friction of proteins and polypeptides,and analyses the physical source.The third chapter describes the subdiffusion and slow relaxation of proteins and polypeptides,and defines the degree of the sources of subdiffusion.The fourth chapter is a summary of this thesis,and discusses some problems for future work.