Title: Protein Physics
1Protein Physics
- A. V. Finkelstein
- O. B. Ptitsyn
- LECTURE 8/9
- www.nd.edu/aasztalo
Andrea Asztalos, 2007 August 3
2Recap Topics
- Secondary structures are concatenated by coiled
regions - - helices
- - sheets
- - turns
- Stability of these
- structures
- Transitions in
- proteins
- Kinetics of these transitions
-
3Why Statistical Mechanics?
The polymer is formed by an N number of
monomers, N gtgt1
Assume 2 configurations/monomer -gt 2N possible
configurations
The protein has zillions of configurations
100-link protein has 2100 1030 possible
configurations
1ns/configuration gt 3x1013 years to consider all
of them
- the average number of configurations is between 8
and 10
S, T, E, F
4Separation of Variables
Kinetic Energy - does not depend on
coordinates
Potential Energy - it depends only on
coordinates
Further on we refer at
Energy Epot Entropy Spot Free Energy
Fpot Microstates Wpot
5Stability at temperature T
Tangent at (E1, S1)
STABLE
F1 Constant
UNSTABLE
UNSTABLE
Unphysical Condition
6Conformational Changes
Gradual
Abrupt 1st order phase transition
(all-or-none)
7Kinetics of Transitions
t time taken to jump from the barrier
Rate of transition from 0 to 1
Vant Hoff-Arrhenius equation
Transitions with trap X
Transition Time ( 0 -gt 1) Sum of the times ( 0
-gt X X -gt 1)
8Parallel Transitions
Sequential Transitions
- transition rate
- for the ith pathway
- transition time to overcome
- barrier i, if it were only one
- on the pathway from 0 to M
k(lowest barrier)
t(larger barrier)
9k0-gt1 Diffusion Rate
Stokes law
Damping occurs till
Friction stops molecules in water within
PICOseconds
10Theoretical Background
- Configurational energy, entropy, etc
- Stable states at T convexity of S(E)
- Coexistent states are unstable
- Transition time to cross a ?F barrier
- A molecule loses initial velocity in PicoSec
- Characteristic diffusion time Nanosec
- tgttdiff -gt existence of ?F barrier
Apply it for helices and sheets
11Stability of alpha helices
Homo-polypeptides
n residues are fixed by n-2 H-bonds
Remark
fH is not just the energy as would be the
case in vacuum, but it also includes
both the energy and entropy of the
subsequent H-bond rearrangement in the
aqueous environment
- free energy of helix initiation
- free energy of helix elongation/residue
12Denote
helix initiation parameter, s ltlt 1 ( 10-3)
helix elongation parameter, s 1 (Ala 2, Gly
0.2)
Is coil -gt helix a 1st order phase transition?
No
Can we talk about different phases?
No
change in molecular conformation
13Characteristic chain length for mixing
N residue sequence,
At mid-transition T, Felong0
- Number of end points kN/n
Experimentally determined
n030
14How fast do alpha helices form?
Rewritten
In any of n0 places
To extend the helix
Initiation of the helix requires overcoming an
activation barrier
Overall time taken
t helix elongation by one residue
t200 ns