The Role of Entropy in Biomolecular Modelling
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Transcript of The Role of Entropy in Biomolecular Modelling
The Role of Entropy in Biomolecular Modelling
Three Examples
1. Force Field Development
How to parametrise non-bonded interaction terms?
Include Entropy
=
Hydration
Hyd Hyd
G
H T S
of variety of solutes
Simulation at finite T
The Role of Entropy in Biomolecular Modelling
3. Protein-Ligand Complexation:
Ligand binding to the Estrogen Receptor:A variety of configurations (ensemble) contributes to binding, both in the protein and in waterContinuum representation of the solvent is unable to mimic binding subtleties of
individual solvent or co-solvent molecules
2. Partitioning of Solutes between various Solvent Mixtures
Solvation of small molecules:
HS Enthalpy co-act or may depending on mixture and solute
SS Entropy counteract
Continium methods will not catch these entropic effects
Four Ways to Compute Entropy Differences
( , ) ( , , ) state
( , ) ( , , ) state
a a
b b
H p r H p r
H
a
p br H p r
33333333333333333333333333333333333333333333333333333333
33333333333333333333333333333333333333333333333333333333
3( ) ln ! exp ( , , ) /NNVT b bA k T h N H p r k T dpdr
3333333333333333333333333333
Coupling Parameters approach
Hamiltonian is made function of :
Free energy depends on :
1. Entropy Difference via Thermodynamic Intergration (TI)
Free Energy Difference and End States Energy Difference
( ) ( )
( ) ( )
TI
end
end TI
T
ba
b a
ba
ba ba
ba
I
b b
b a
a a
b
b
a
a H
dA HA A A d d
d
U
U U
H
U
U AS
T
accurate
not so accurate
Four Ways to Compute Entropy Differences
,N V
AS
T
, ,N V T
S
2
1TIb
bab a
S dk T
H HH H
using
and
2. Entropy Difference directly via TI
correlation between and not so accurate
only -dependent terms all terms
H
H
3. Entropy Difference via finite Temperature Difference
using
,N T
AS
T
)
2
( ( )TI TIT ba ba
ba
T TA AS
T T
T
difference between almost equal accurate values
Four Ways to Compute Entropy Differences
4 . Solvation Entropy Difference via Solute-Solvent Entropy Difference
(using TI) and
End States Solvent-Solvent Energy Difference
,2
,,
1 1b
b a
a
ba
ba
all uv uvuv u
TI
endTI
Bv vv vv
vvu
bv
a
H HS H H d H H
k T T
US
T
accurate
only solute-solvent terms
not so accurate
all solvent terms
solvent: vsolute: u
Comparison of1. Excess Free Energy, Entropy of Water
2. Hydration Free Energy, Entropy of Water
Using four different Methods
Three Models or Hamiltonians:
1. SPC Model: Coulomb plus van der Waals interaction
2. SPCnc Model: no Coulomb interaction
3. SPCnn Model: no (non-bonded) interaction
Christine Peter
Thermodynamic Cycle System
1000 H2O moleculesperiodic boundary conditionsT = 280K, 300K, 320Ksimulations = 100-600psNVT NPT
Change:1 H2O hydration
all H2O excess more accurate
SPC (liquid)
SPCnc (liquid, no Coulomb)
SPCnn (ideal gas)
G, S, H = 0
Free Energy and Entropy of Water
Reference: J.Chem.Phys. (2004)
method2 1 4 4
Free Energy and Entropy of Water
Reference: J. Chem. Phys. (2004)
method 3
63
close
All 1000 H2O Molecules Changed
TI TI
A Single H2O Molecule Changed
A via TI S via TI Suv via TI
NVT
NPT
same patternas for 1000 H2O changed
erraticnot converged
same patternas for 1000 H2O changed