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[资源] Theory of Phase Transitions in Polypeptides and Proteins (Springer Theses)2011

There are nearly 100 000 different protein sequences encoded in the human genome, each with its own specific fold. Understanding how a newly formed polypeptide sequence finds its way to the correct fold is one of the greatest challenges in the modern structural biology. The aim of this thesis is to provide novel insights into protein folding by considering the problem from the point of view of statistical mechanics. The thesis starts by investigating the fundamental degrees of freedom in polypeptides that are responsible for the conformational transitions. This knowledge is then applied in the statistical mechanics description of helix?coil transitions in polypeptides. Finally, the theoretical formalism is generalized to the case of proteins in an aqueous environment. The major novelty of this work lies in comabining (a) a formalism based on fundamental physical properties of the system and (b) the resulting possibility of describing the folding?unfolding transitions quantitatively. The clear physical nature of the formalism opens the way to further applications in a large variety of systems and processes.

Common terms and phrases:
amino acids degrees of freedom dihedral angles heat capacity molecular dynamics partition function potential energy surface protein folding random coil

Cover

Springer Theses

Theory of Phase Transitions in Polypeptides and Proteins

ISBN 9783642227318

Supervisor’s Foreword

Acknowledgments

Contents

1 Introduction

     1.1 Problems Addressed in the Thesis

     References

2 Theoretical Methods of Quantum Mechanics

     2.1 Introduction

     2.2 The Schrödinger Equation

     2.3 The Born--Oppenheimer Approximation

     2.4 Properties of the Wavefunction

     2.5 Hartree--Fock Theory

     2.6 Density Functional Theory

     2.7 Molecular Mechanics Approach: a Way to Overcome  the Complexity of Quantum Mechanics

     References

3 Degrees of Freedom in Polypeptides  and Proteins

     3.1 Introduction

     3.2 Conformational Properties of Alanine  and Glycine Chains

          3.2.1 Determination of the Polypeptides Twisting  Degrees of Freedom

          3.2.2 Optimized Geometries of Alanine Polypeptides

          3.2.3 Polypeptide Energy Dependance On the Dihedral  Angle   .

          3.2.4 Potential Energy Surface for Alanine Tripeptide

          3.2.5 Potential Energy Surface for Alanine Hexapeptide  with the Sheet and the Helix Secondary Structure

          3.2.6 Comparison of Calculation Results  with Experimental Data

     3.3 Conformational Changes in Glycine Tri- and Hexa-Peptide

          3.3.1 Optimized Geometries of Glycine Polypeptides

          3.3.2 Potential Energy Surface for Glycine Tripeptide

          3.3.3 Potential Energy Surface for Glycine Hexapeptide  with the Sheet and the Helix Secondary Structure

          3.3.4 Comparison of Calculation Results  with Experimental Data

     References

4 Partition Function of a Polypeptide

     4.1 Introduction

     4.2 Molecular Mechanics Potential

     4.3 Hamiltonial of a Polypeptide Chain

     4.4 Construction of the Partition Function

     4.5 Thermodynamical Characteristics of a Polypeptide Chain

     References

5 Phase Transitions in Polypeptides

     5.1 Introduction

     5.2 Molecular Dynamics Simulations

     5.3   a-HelixRandom  Coil Phase Transition in Polyalanine

          5.3.1 Accuracy of the Molecular Mechanics Potential

          5.3.2 Potential Energy Surface of Alanine Polypeptide

          5.3.3 Internal Energy of Alanine Polypeptide

          5.3.4 Heat Capacity of Alanine Polypeptide

          5.3.5 Calculation of the Zimm--Bragg Parameters

          5.3.6 Helicity of Alanine Polypeptides

          5.3.7 Correlation of Different Amino Acids in the Polypeptide

     5.4 Phase Transitions in Polypeptides:  Analysis of Energy Fluctuations

          5.4.1 Fluctuations of Internal Energy and Heat Capacity

          5.4.2   a-Helix Random  Coil Transition in Alanine Polypeptide

          5.4.3   p-Helix Random  Coil Transition in Valine Polypeptide

          5.4.4   p-Helix Random  Coil Transition in Leucine Polypeptide

          5.4.5 Appendix: Parameters of MD Simulation

     References

6 Folding of Proteins in Aqueous Environment

     6.1 Introduction

     6.2 Theoretical Methods

          6.2.1 Partition Function of a Protein

          6.2.2 Partition Function of a Protein in Water Environment

     6.3 Results and Discussion

          6.3.1 Heat Capacity of Staphylococcal Nuclease

          6.3.2 Heat Capacity of Metmyoglobin

     References

7 Summary and Conclusions

     References

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