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Thermodynamics and Statistical Mechanics of Macromolecular Systems

Book Description

The structural mechanics of proteins that fold into functional shapes, polymers that aggregate and form clusters, and organic macromolecules that bind to inorganic matter can only be understood through statistical physics and thermodynamics. This book reviews the statistical mechanics concepts and tools necessary for the study of structure formation processes in macromolecular systems that are essentially influenced by finite-size and surface effects. Readers are introduced to molecular modeling approaches, advanced Monte Carlo simulation techniques, and systematic statistical analyses of numerical data. Applications to folding, aggregation, and substrate adsorption processes of polymers and proteins are discussed in great detail. Particular emphasis is placed on the reduction of complexity by coarse-grained modeling, which allows for the efficient, systematic investigation of structural phases and transitions. Providing insight into modern research at this interface between physics, chemistry, biology, and nanotechnology, this book is an excellent reference for graduate students and researchers.

Table of Contents

  1. Cover Page
  2. Half Title Page
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Contents
  7. Preface and outline
  8. 1 Introduction
    1. 1.1 Relevance of biomolecular research
    2. 1.2 Proteins
      1. 1.2.1 The trinity of amino acid sequence, structure, and function
      2. 1.2.2 Ribosomal synthesis of proteins
      3. 1.2.3 From sequence to function: The protein folding process
    3. 1.3 Molecular modeling
      1. 1.3.1 Covalent bonds
      2. 1.3.2 Effective noncovalent interactions and nanoscopic modeling: Toward a semiclassical all-atom representation
    4. 1.4 All-atom peptide modeling
    5. 1.5 The mesoscopic perspective
      1. 1.5.1 Why coarse-graining...? The origin of the hydrophobic force
      2. 1.5.2 Coarse-grained hydrophobic–polar modeling
    6. 1.6 Polymers
      1. 1.6.1 DNA and RNA
      2. 1.6.2 Modeling free DNA
      3. 1.6.3 Flexible, attractively self-interacting polymers
      4. 1.6.4 Elastic polymers
  9. 2 Statistical mechanics: A modern review
    1. 2.1 The theory of everything
    2. 2.2 Thermodynamics and statistical mechanics
      1. 2.2.1 The thermodynamic limit
      2. 2.2.2 Thermodynamics of closed systems: The canonical ensemble
      3. 2.2.3 Thermodynamic equilibrium and the statistical nature of entropy
    3. 2.3 Thermal fluctuations and the statistical path integral
    4. 2.4 Phase and pseudophase transitions
    5. 2.5 Relevant degrees of freedom
      1. 2.5.1 Coarse-grained modeling on mesoscopic scales
      2. 2.5.2 Macroscopic relevant degrees of freedom: The free-energy landscape
    6. 2.6 Kinetic free-energy barrier and transition state
    7. 2.7 Microcanonical statistical analysis
      1. 2.7.1 Temperature as a derived quantity
      2. 2.7.2 Identification of first-order transitions by Maxwell construction
      3. 2.7.3 Systematic classification of transitions by inflection-point analysis
  10. 3 The complexity of minimalistic lattice models for protein folding
    1. 3.1 Evolutionary aspects
    2. 3.2 Self-avoiding walks and contact matrices
    3. 3.3 Exact statistical analysis of designing sequences
    4. 3.4 Exact density of states and thermodynamics
  11. 4 Monte Carlo and chain growth methods for molecular simulations
    1. 4.1 Introduction
    2. 4.2 Conventional Markov-chain Monte Carlo sampling
      1. 4.2.1 Ergodicity and finite time series
      2. 4.2.2 Statistical error and bias
      3. 4.2.3 Binning–jackknife error analysis
    3. 4.3 Systematic data smoothing by using Bézier curves
      1. 4.3.1 Construction of a Bézier curve
      2. 4.3.2 Smooth Bézier functions for discrete noisy data sets
    4. 4.4 Markov processes and stochastic sampling strategies
      1. 4.4.1 Master equation
      2. 4.4.2 Selection and acceptance probabilities
      3. 4.4.3 Simple sampling
      4. 4.4.4 Metropolis sampling
    5. 4.5 Reweighting methods
      1. 4.5.1 Single-histogram reweighting
      2. 4.5.2 Multiple-histogram reweighting
    6. 4.6 Generalized-ensemble Monte Carlo methods
      1. 4.6.1 Replica-exchange Monte Carlo method: Parallel tempering
      2. 4.6.2 Simulated tempering
      3. 4.6.3 Multicanonical sampling
      4. 4.6.4 Wang–Landau method
    7. 4.7 Elementary Monte Carlo updates
    8. 4.8 Lattice polymers: Monte Carlo sampling vs. Rosenbluth chain growth
    9. 4.9 Pruned-enriched Rosenbluth method: Go with the winners
    10. 4.10 Canonical chain growth with PERM
    11. 4.11 Multicanonical chain-growth algorithm
      1. 4.11.1 Multicanonical sampling of Rosenbluth-weighted chains
      2. 4.11.2 Iterative determination of the density of states
    12. 4.12 Random number generators
    13. 4.13 Molecular dynamics
  12. 5 First insights to freezing and collapse of flexible polymers
    1. 5.1 Conformational transitions of flexible homopolymers
    2. 5.2 Energetic fluctuations of finite-length polymers
      1. 5.2.1 Peak structure of the specific heat
      2. 5.2.2 Simple-cubic lattice polymers
      3. 5.2.3 Polymers on the face-centered cubic lattice
    3. 5.3 The Θ transition
    4. 5.4 Freezing and collapse in the thermodynamic limit
  13. 6 Crystallization of elastic polymers
    1. 6.1 Lennard-Jones clusters
    2. 6.2 Perfect icosahedra
    3. 6.3 Liquid–solid transitions of elastic flexible polymers
      1. 6.3.1 Finitely extensible nonlinear elastic Lennard-Jones polymers
      2. 6.3.2 Classification of geometries
      3. 6.3.3 Ground states
      4. 6.3.4 Thermodynamics of liquid–solid transitions toward complete icosahedra
      5. 6.3.5 Liquid–solid transitions of elastic polymers
      6. 6.3.6 Long-range effects
    4. 6.4 Systematic analysis of compact phases
    5. 6.5 Dependence of structural phases on the range of nonbonded interactions
  14. 7 Structural phases of semiflexible polymers
    1. 7.1 Structural hyperphase diagram
    2. 7.2 Variation of chain length
  15. 8 Generic tertiary folding properties of proteins on mesoscopic scales
    1. 8.1 A simple model for a parallel β helix lattice protein
    2. 8.2 Protein folding as a finite-size effect
    3. 8.3 Hydrophobic–polar off-lattice heteropolymers
  16. 9 Protein folding channels and kinetics of two-state folding
    1. 9.1 Similarity measure and order parameter
    2. 9.2 Identification of characteristic folding channels
    3. 9.3 Gō kinetics of folding transitions
      1. 9.3.1 Coarse-grained Gō modeling
      2. 9.3.2 Thermodynamics
      3. 9.3.3 Kinetics
      4. 9.3.4 Mesoscopic heteropolymers vs. real proteins
    4. 9.4 Microcanonical effects
    5. 9.5 Two-state cooperativity in helix–coil transitions
  17. 10 Inducing generic secondary structures by constraints
    1. 10.1 The intrinsic nature of secondary structures
    2. 10.2 Polymers with thickness constraint
      1. 10.2.1 Global radius of curvature
      2. 10.2.2 Modeling flexible polymers with constraints
      3. 10.2.3 Thickness-dependent ground-state properties
      4. 10.2.4 Structural phase diagram of tube-like polymers
    3. 10.3 Secondary-structure phases of a hydrophobic–polar heteropolymer model
  18. 11 Statistical analyses of aggregation processes
    1. 11.1 Pseudophase separation in nucleation processes of polymers
    2. 11.2 Mesoscopic hydrophobic–polar aggregation model
    3. 11.3 Order parameter of aggregation and fluctuations
    4. 11.4 Statistical analysis in various ensembles
      1. 11.4.1 Multicanonical results
      2. 11.4.2 Canonical perspective
      3. 11.4.3 Microcanonical interpretation: The backbending effect
    5. 11.5 Aggregation transition in larger heteropolymer systems
  19. 12 Hierarchical nature of phase transitions
    1. 12.1 Aggregation of semiflexible polymers
    2. 12.2 Structural transitions of semiflexible polymers with different bending rigidities
    3. 12.3 Hierarchies of subphase transitions
    4. 12.4 Hierarchical peptide aggregation processes
    5. 12.5 Hierarchical aggregation of GNNQQNY
  20. 13 Adsorption of polymers at solid substrates
    1. 13.1 Structure formation at hybrid interfaces of soft and solid matter
    2. 13.2 Minimalistic modeling and simulation of hybrid interfaces
    3. 13.3 Contact-density chain-growth algorithm
    4. 13.4 Pseudophase diagram of a flexible polymer near an attractive substrate
      1. 13.4.1 Solubility–temperature pseudophase diagram
      2. 13.4.2 Contact-number fluctuations
      3. 13.4.3 Anisotropic behavior of gyration tensor components
    5. 13.5 Alternative view: The free-energy landscape
    6. 13.6 Continuum model of adsorption
      1. 13.6.1 Off-lattice modeling
      2. 13.6.2 Energetic and structural quantities for phase characterization by canonical statistical analysis
      3. 13.6.3 Comparative discussion of structural fluctuations
      4. 13.6.4 Adsorption parameters
      5. 13.6.5 The pseudophase diagram of the hybrid system in continuum
    7. 13.7 Comparison with lattice results
    8. 13.8 Systematic microcanonical analysis of adsorption transitions
      1. 13.8.1 Dependence on the surface attraction strength
      2. 13.8.2 Chain-length dependence
      3. 13.8.3 Translational entropy
    9. 13.9 Polymer adsorption at a nanowire
      1. 13.9.1 Modeling the polymer–nanowire complex
      2. 13.9.2 Structural phase diagram
  21. 14 Hybrid protein–substrate interfaces
    1. 14.1 Steps toward bionanotechnology
    2. 14.2 Substrate-specific peptide adsorption
      1. 14.2.1 Hybrid lattice model
      2. 14.2.2 Influence of temperature and solubility on substrate-specific peptide adsorption
    3. 14.3 Semiconductor-binding synthetic peptides
    4. 14.4 Thermodynamics of semiconductor-binding peptides in solution
    5. 14.5 Modeling a hybrid peptide–silicon interface
      1. 14.5.1 Introduction
      2. 14.5.2 Si(100), oxidation, and the role of water
      3. 14.5.3 The hybrid model
    6. 14.6 Sequence-specific peptide adsorption at silicon (100) surface
      1. 14.6.1 Thermal fluctuations and deformations upon binding
      2. 14.6.2 Secondary-structure contents of the peptides
      3. 14.6.3 Order parameter of adsorption and nature of adsorption transition
  22. 15 Concluding remarks and outlook
  23. References
  24. Index