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Statistical Model of an Order-Disorder Transition in Peptides Gregory G. Wood

Statistical Model of an Order-Disorder Transition in Peptides Gregory G. Wood Mathematics Graduate Seminar October 25 2006. Statistical Mechanics Peptides Statistical Model of Peptides An Optimization Problem.

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Statistical Model of an Order-Disorder Transition in Peptides Gregory G. Wood

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  1. Statistical Model of an Order-Disorder Transition in Peptides Gregory G. Wood Mathematics Graduate Seminar October 25 2006 • Statistical Mechanics • Peptides • Statistical Model of Peptides • An Optimization Problem

  2. “The Boltzmann factor is one of the most important quantities in the physical sciences” McQuarrie, DA and Simon, JD “Physical Chemistry” (University Science Books, Sausalito, 1997) p. x and p. 694. Two reasonably good derivations: http://en.wikipedia.org/wiki/Maxwell-Boltzmann_statistics Three reasonably good text books on the topic: Kittel, C Elementary Statistical Physics (Dover, 2004) Tolman, RC Principles of Statistical Mechanics (Dover, 1980) Reif, F Fundamentals of Statistical and Thermal Physics (McGraw-Hill, 1965) Example: Dilute paramagnet (non-interacting paramagnets).

  3. Relationship of Probabilities to Thermodynamic Quantities (connection of theory to experiment) Where:

  4. Experimental Data of Curie Law (χα 1/T) Sucksmith, W. and R. R. Pearce Proc. Royal Soc. (London) A, 167 p. 189-204 (1938). Graph is for Nickel (pure?) above about 9500C it is linear, below linear w/ diff slope…

  5. Comparison of Simple Calculations With Experiment Specific heat of diamond (McQuarrie, p. 704) Specific heat of oxygen (O2) gas (McQuarrie, p.702) Note: theory is solid line, experiment dashed line.

  6. Peptides:

  7. The Alpha Helix (i to i+4 bonding)

  8. Ramachandran Plot

  9. Experimentally Derived Helix Propensity Δ(ΔE-TΔS) (kcal/mol) Pace, C.N. and J. M. Scholtz, Biophysical Journal 75 422 (1998)

  10. Relative Helix Propensity Δ(ΔG) (arbit units) w/ Gly set to one Pace C.N. and J. M. Scholtz, ibid. Note: Avg* and AvgDev* toss out high and low value.

  11. “Hidden Thermodynamics” • Free energies are, in general, non-additive. • Historically this has been called the “hidden thermodynamics” • Free energies do add over independent degrees of freedom. “…additivity principles appear to be few and limited in scope in biochemistry…if thermodynamic additivity principles can be found having variances smaller then about 0.1 kcal/mol, they may be as important to biochemistry as the great symmetry principles are to physics” K. A. Dill J. Biol. Chem 1997

  12. Non-Additivity: Simple Example Reference State • Square with two identical fluctuating bonds: energy -ε, entropy -s. Our model (approximation): sum only over the strongest (lowest entropy) independent bonds! ΔE≡0 ΔS≡0 ΔE= -ε ΔS= -s ΔE= -ε ΔS= -s ΔE= -2ε ΔS= -s Δ S = Σ (si)indep. Δ E = Σεi

  13. Latest fits (unpublished):

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