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Reconciling Experimental and Theoretical Energies
Theory
Experiment
Energy Minimization (Internal
Energy)
Thermodynamic Data (ΔG, ΔH,
ΔS)
MM/GBSA (average internal
energy with solvation
included)
Kinetic Data
(KA, KD, kon, koff)
FEP/TI (relative free energies,
ΔG)
Inhibition Data (Ki, IC50)
Activity Data (EC50)
How do you compare theoretical ligand (drug) binding energies with experimental data?

What is Affinity?
Affinity: The strength of noncovalent chemical binding between two substances as
measured by the dissociation constant (KD) of the complex.
For a protein (P), binding to a ligand (L) to for a complex (PL):
the dissociation constant KD for the complex is:
KD 
[P][L]
[PL]
P
P+L
L
PL
PL
where [P], [L] and [PL] represent molar concentrations of
the protein, ligand and PL-complex, at equilibrium,
respectively. The units of KD are moles (M)
The dissociation constant is the concentration of ligand [L] at which the binding site on
a particular protein is half occupied, i.e. KD is the concentration of ligand, at which the
concentration of protein with ligand bound [PL], equals the concentration of protein
with no ligand bound [P].
KD and ΔG are Easily Related
P+L
PL
The smaller the KD , the more tightly bound the ligand is, or the
higher the affinity between ligand and protein. Or conversely,
the larger the KA, the more tightly the ligand binds
ΔGBinding = -RT lnKA = RT lnKD
What is the difference in
binding free energy for
two drugs, one that
binds with mM affinity
and one that binds with
nM affinity? Assume
room temperature (RT =
0.6).
For example: a ligand with a nanomolar (nM)
dissociation constant binds more tightly to a
particular protein than a ligand with a micromolar
(μM) dissociation constant.
1) Convert the KD units to moles: 1mM = 1x10-3 M, 1nM =
1x10-9M
2) Plug the KD values into the formula
Drug 1
Drug 2
KD
1x10-3 M
1x10-9M
ΔG
-4.1 kcal/mol
-12.4 kcal/mol
ΔΔG
-8.3 kcal/mol
Why Do Experiments Measure KD and not ΔG?
Dissociation constants can be determined from many different types of experiment. ΔG
is extremely difficult to measure experimentally.
Direct Binding
Method
KD
ΔG
Surface Plasmon Resonance
(KD, kon, koff)
Isothermal Titration
Calorimetry (ΔH, and ΔS)
NMR Spectroscopy
TitrationBased
Methods
Spectrophotometry
Potentiometry
enzyme-linked
immunosorbent assays (ELISA)
ΔGBinding = RT lnKD
What about kon and koff
Some experimental methods, notably surface plasmon resonance (SPR) can measure
the kinetic on and off rates for a binding reaction.
P+L
kon
koff
koff
KD 
k on
C
What about kon and koff
Some experimental methods, notably surface plasmon resonance (SPR) can measure
the kinetic on and off rates for a binding reaction.
Depending on the quality of the
data and the rate of the kinetics,
kon and koff can be determined by
fitting the “mass action equation”
to the SPR sensorgram
kon
koff
d[PL]
 [P][L]kon  [PL]koff
dt
What about IC50 values and Ki
The IC50 is the concentration of an inhibitor that reduces the binding of the native
ligand by half (50%). The IC50 is a measure of how well a drug (or inhibitor) competes
with the natural or native ligand for binding to a receptor.
KD
PL
P+L+I
KI
PI
IC 50
Ki 
[L]
1+
KD
Cheng Y, Prusoff WH. Relationship between the
inhibition constant (Ki) and the concentration of
inhibitor which causes 50 per cent inhibition
(IC50) of an enzymatic reaction. Biochem
Pharmacol 1973; 22:3099–108.
IC50 does not necessarily say anything about the thermodynamics of binding.
IC50 tells you how concentrated your solution with respect to ligand has to be in order
for 50%
of the receptors to be bound.
If you have poor binding, you will need a large concentration to start filling up
receptor binding sites. If you have very good binding, you won't need very much of
your inhibitor to start filling up binding sites.
What about IC50 values and ΔG
It is often easier to measure IC50 than Ki, since to measure Ki requires IC50 as well
as [L] and KD
IC 50
Ki 
[L]
1+
KD
How can we relate IC50 values
to free energies of binding?
1) If two inhibitors are assayed against the same protein with the ligand at the
same concentration then ΔΔG = -RT ln Ki,1/Ki,2
and therefore ΔΔG = -RT ln IC50,1/IC50,2

ΔΔGBCV-RTV = -RT ln 0.4x10-9/1641x10-9
= -RT ln 0.0002437
= -0.6 (-8.32)
ΔΔGBCV-RTV = 4.99 kcal/mol
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"Resistance-Associated Amino Acid Substitutions and Drug
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What about IC50 values and ΔG
It is often easier to measure IC50 than Ki, since to measure Ki requires IC50 as well
as [L] and KD
IC 50
Ki 
[L]
1+
KD
How can we relate IC50 values
to free energies of binding?
2) Alternatively, it is sometimes assumed that Ki ≈ IC50
Therefore ΔG ≈ RT ln IC50

ΔGBCV
= RT ln(0.4x10-9)
= -13.0 kcal/mol
ΔGRTV
= RT ln(1641x10-9)
= -7.99 kcal/mol
ΔΔGBCV-RTV = 5.01 kcal/mol
Example: Design of HIV Transcriptasae Inhibitors
Example: Theoretical Background
ΔGN01= RT ln(0.125x10-6)
= -9.5 kcal/mol
ΔGN14= RT ln(15.3x10-6)
= -6.6 kcal/mol
ΔΔGN01,N14 = 2.9 kcal/mol
ΔΔGN01,N14 = -RT ln IC50,N01/IC50,N14
= 0.6 ln (0.008) = 2.9 kcal/mol
Example: Computational Setup
Example: Initial Model
Example: Checking Data Convergence
Example: Comparison with Experimental Energies