Erik Lindahl

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Formulating Boltzmann • Clapeyron’s gas law: P=N k T • Potential energy (gravity): E(h)=m g h • dP/dh=(dN/dh)kT • dP=(m g N)(-dh) • dP/dh=(dN/dh)kT=-m g N • dN/dh=-(mg/kT) N • And use: (dN/dh) / N = d[ln(N)]/dh • d[ln(N)]/dh=-mg/kT • Integrate & take exponential of both sides • N ∝ exp{-m g h/kT} = exp{-E(h)/kT}
What does Boltzmann mean? • Probability of being at energy E A : pE A ∝exp{-E A /kT} • Compare with energy EB: pEA/pEB = exp{-EA/kT} / exp{-EB/kT} • Lower-energy states will be more populated • But is that everything?
Page 1: Protein Physics 2012 Lecture 2, Jan
Page 6 and 7: Natural amino acids
Page 9 and 10: α R β α L
Page 11 and 12: Outline today • More on interacti
Page 13 and 14: Semi-Empiric Modeling • Use simpl
Page 15 and 16: Bond stretching • Vibration aroun
Page 17 and 18: Torsions/dihedrals Frequently calle
Page 19 and 20: Nonbonded interactions Packing effe
Page 21 and 22: Lennard-Jones • Simpler form than
Page 23 and 24: Hydrophobic effect
Page 25: The Boltzmann Distribution ⇢ / e
Page 30 and 31: Which shape is best energy-wise? Vo
Page 32 and 33: Free Energy • Use V=exp{ln(V)}
Page 34 and 35: How many states does this correspon
Page 36 and 37: Phase Transitions Explained • Sys
Page 38 and 39: Partitioning • Consider transfer

Erik Lindahl

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