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Journal of Chemical Physics / Volume 135 / Issue 23 / ARTICLES / Biological Molecules, Biopolymers, and Biological Systems

J. Chem. Phys. 135, 235102 (2011); http://dx.doi.org/10.1063/1.3666837 (12 pages)

A statistical mechanical approach to protein aggregation

John S. Schreck and Jian-Min Yuan

Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA

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(Received 20 June 2011; accepted 17 November 2011; published online 20 December 2011)

We develop a theory of aggregation using statistical mechanical methods. An example of a complicated aggregation system with several levels of structures is peptide/protein self-assembly. The problem of protein aggregation is important for the understanding and treatment of neurodegenerative diseases and also for the development of bio-macromolecules as new materials. We write the effective Hamiltonian in terms of interaction energies between protein monomers, protein and solvent, as well as between protein filaments. The grand partition function can be expressed in terms of a Zimm-Bragg-like transfer matrix, which is calculated exactly and all thermodynamic properties can be obtained. We start with two-state and three-state descriptions of protein monomers using Potts models that can be generalized to include q-states, for which the exactly solvable feature of the model remains. We focus on n × N lattice systems, corresponding to the ordered structures observed in some real fibrils. We have obtained results on nucleation processes and phase diagrams, in which a protein property such as the sheet content of aggregates is expressed as a function of the number of proteins on the lattice and inter-protein or interfacial interaction energies. We have applied our methods to Aβ(1-40) and Curli fibrils and obtained results in good agreement with experiments.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. SYSTEMS STUDIED
  3. EXPLICIT INCLUSION OF THE INTERACTIONS WITH SOLVENT
    1. Protein/solvent interfaces
    2. Average properties and thermodynamics
    3. Numerical results
  4. QUASI-1D MODELS FOR PROTOFIBRILS AND FIBRILS
  5. COMPARISON TO EXPERIMENT
  6. THREE-STATE POTTS MODEL FOR HELIX-SHEET-COIL AGGREGATES
  7. DISCUSSION AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

aggregation, biochemistry, diseases, macromolecules, molecular biophysics, nucleation, phase diagrams, physiological models, Potts model, proteins, self-assembly, statistical analysis, surface energy, thermodynamic properties

PACS

  • 87.15.R-

    Reactions and kinetics

  • 87.15.B-

    Structure of biomolecules

  • 02.50.-r

    Probability theory, stochastic processes, and statistics

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3666837

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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