Transcript Thermodynamics slides

Thermodynamics!
Gibbs Equation: G = H - TS
Second Law: G = H - S
T
T
Entropy of the Universe??
What contributes to H?
What contributes to S?
Binding opposes motion. Motion opposes binding.
Our Mischievous Friend, Entropy
S = k lnW
S = qrev
T
Stotal = Strans + Srot + Sconf + Svib + Selec + …
k
Sx
kT << |TS|
Translational and Rotational Entropy
y
y
z
2x
z
x
Gt+r = -T(Strans + Srot)
x
Conformational Entropy
Gc = -TSconf
What about the Solvent?
Must consider IMF’s between:
Receptor  Drug
Receptor  Solvent
Drug  Solvent
Complex  Solvent
Solvent  Solvent
Total effects can be divided into two categories:
Polar interactions
Hydrophobic exclusion (effect)
The Hydrophobic Effect
Gh
G = Gt+r + nGc + A Gh + Gp
Average Parameter Values
Parameter
Physical Process
Value (kcal/mol)
Krel
Gt+r
cost of bimolecular
association
+1.3
10
Gc
cost of restricting
an internal rotor
+0.3
2
Gh
benefit of burying 33 Å2
of hydrophobic surface
-0.04
1
Gp
benefit of forming an
ideal, neutral H-bond
-1.1
7
Gionic
benefit of forming an
ideal, ionic H-bond
-2.0
28
Williams et al. Angew. Chem. Intl. Ed. 2004, 43, 6596-6616
Boltzmann Strikes Back
Remember:
G = H - S
T
T
Hopefully, you remember:
Gº = -RT lnK
which is also
K=
-Gº
e RT
which is a specialized version of
n1
=
no
-Eº
e RT
(which is the Boltzmann distribution).
Ei
E1
unbound
bound
E0
ni
Chemical Equilibrium
Drug + Receptor
(D)
(R)
Complex
(C)
1. Ka = Equilibrium Association Constant
(Binding Constant)
= [C]eq
Ka values are not usually
reported
[D]eq[R]eq
in the drug literature.
2. Kd = Equilibrium Dissociation Constant (Ka-1)
= [D]eq[R]eq
[C]eq
Kd values are usually reported
in the drug literature.
• approximate concentration at half-saturation
• convenient measure of a drug’s activity
How do we measure K?
1:1 model
Drug + Receptor
(D)
(R)
Complex
(C)
Initial conditions:
[D]total
[R]total
0
Steady state:
[D]total – x
[R]total – x
x
• We know the initial concentrations of drug and receptor.
• We need a way to measure the amount of complex formed.
• What are some observables?
• Labeling: Advantages and Disadvantages?
Okay, so how do we measure K?
• Simplest method
If you can measure [C]eq and either [R]eq or [D]eq
then you can just solve for K.
• Most common method
Fractional Occupation () = fraction of drug bound to the receptor
= [C]eq
[D]total
[D]total = [D]eq + [C]eq
(known) (unknown) (observable)
=
[C]eq
[C]eq+ [D]eq
=
Ka[R]eq
1 + Ka[R]eq
substitute from Ka = [C]eq
and rearrange
[D]eq[R]eq
Binding Isotherm
c =
Ka[R]eq
1 + Ka[R]eq
(
[C]eq = [D]total
observable
What about [R]eq?
known
Ka[R]eq
1 + Ka[R]eq
)
unknown
Choose conditions such that [R]eq ~ [R]total
Competitive Binding
Receptor  Substrate + Drug
Receptor  Substrate
Receptor + Drug
Kc
Ks
Receptor  Drug + Substrate
Receptor + Substrate
Ka
Receptor  Substrate + Drug
Kc = KsKa
Receptor  Drug
Receptor  Drug + Substrate