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Week 5
MD simulations of protein-ligand interactions
•
Lecture 9: Fundamental problems in description of ligand binding to
proteins: i) determination of the complex structure, ii) calculation of
binding free energies. Examples from toxin binding to potassium
channel Kv1.3. Target selectivity problem in drug design and
structure-based methods to solve the selectivity problems.
Why study proteinligand interactions?
• Quantitative description of protein–ligand interactions is a fundamental
problem in molecular biology
• Pharmacological motivation: drug discovery is getting harder searching
compound libraries using experimental methods. Using computational
methods and peptide ligands from Nature (e.g. toxins) offer alternative
methods and means for drug discovery
• Computational methods would be very helpful in drug design but
their accuracy needs to be confirmed for larger, charged peptide ligands
• Proof of concept study: Binding of charybdotoxin to KcsA* (Shaker)
Realistic case study: Binding of ShK toxin and analogues to Kv1.1,
Kv1.2, and Kv1.3 channels
Two essential criteria for development of drug leads
1. Should bind to a given target protein with high affinity
2. Be selective for the target protein
The first issue is addressed with many experimental (e.g. HTS) and
computational methods (e.g. docking), and there is a huge data base
about high affinity ligands.
The second issue is harder to address with traditional methods and would
especially benefit from a rational drug design approach.
Example: Kv1.3 is one of the the main targets for autoimmune diseases
•
ShK toxin binds to Kv1.3 with pM affinity
•
But it also binds to Kv1.1 with pM affinity
•
Need to improve selectivity of ShK for Kv1.3 over Kv1.1
Challenges in computational design of drugs from peptides
1. Apart from a few cases, the complex structure is not known.
Assuming that structures (or homology models) of protein and ligand
are known, the complex structure can be determined via docking
followed by refinement with MD simulations.
2. Affinity and selectivity of a set of ligands for target proteins need to be
determined with chemical accuracy (1 kcal/mol).
Binding free energies can be calculated accurately from umbrella
sampling MD simulations. For selectivity, one could use the free
energy perturbation (FEP) method (computationally cheaper).
The
FEP method is especially useful if one is trying to improve selectivity
via minor modifications/mutations of a ligand.
Computational program for rational drug design from peptides
1. Complex structure determination:
Find the initial configuration for the bound complex using a docking
algorithm (e.g., HADDOCK).
Refine the initial complex(es) via MD simulations.
2. Validation:
a) Determine the key contact residues involved in the binding and compare
with mutagenesis data to validate the complex model.
b) Calculate the potential of mean force for the ligand, determine the
binding constant and free energy, and compare with experiments.
3. Design:
Consider mutations of the key residues on the ligand and calculate their
binding energies (relative to the wild type) from free energy perturbation in
MD simulations. Those with higher affinity/selectivity are candidates for new
drugs.
Proof of concept study:
Binding of charybdotoxin (ChTx) to KcsA* (shaker mimic)
• Complex structure is determined from NMR, so it provides a unique
test case for MD simulations of peptide binding.
•
Using HADDOCK for docking followed by refinement via MD
simulations reproduces the experimental complex structure.
• Binding free energy of ChTx calculated from the potential of mean
force (PMF): -7.6 kcal/mol
• experimental value: -8.3 kcal/mol
Structure of the KcsA*- ChTx complex
Important pairs:
K27 - Y78 (ABCD)
R34 - D80 (D)
R25 - D64, D80 (C)
K11 - D64 (B)
K27 is the pore
inserting lysine –
a common thread in
scorpion and other
K+ channel toxins.
K11
R34
Realistic case study: ShK toxin binding to Kv1 channels
• Motivation:
–
Kv1.3 is the main target for autoimmune diseases
–
ShK binds to Kv1.3 with pM affinity (but also to Kv1.1)
–
–
Need to improve selectivity of ShK for Kv1.3 over Kv1.1
Some 400 ShK analogues have been developed for this purpose
1. Find the complex structures of ShK with Kv1.1, Kv1.2 and Kv1.3, and
validate them using mutagenesis data. Determine the PMFs and the
binding free energy and compare with experiment.
2. Repeat the above study for ShK-K-amide (an analogue with improved
selectivity) to rationalize the experimental results.
3. WT complex structures indicate that K18A mutation should improve
selectivity. Perform PMF and FEP calculations to quantify this
prediction.
NMR structure of ShK toxin
ShK toxin has three
disulfide bonds and
three other bonds:
D5 – K30
K18 – R24
T6 – F27
These bonds confer
ShK toxin an
extraordinary stability
not seen in other toxins
Homology model of Kv1.3
Can be obtained from the crystal
structure of Kv1.2 (over 90%
homology and 1-1
correspondence between
residues).
Note: care must be exercised for
the V  H404 mutation because
H404-D402 side chains cross link
(several publications have the
wrong Kv1.3 structure because
of this).
Kv1.1-ShK complex
Monomers A and C
Monomers B and D
Kv1.3-ShK complex
Monomers A and C
Monomers B and D
Pair distances in the Kv1.3-ShK complex (in A)
Kv1.3
ShK
Dock.
MD av.
Exp.
D376–O1(C)
R1–N1
5.0
4.5
S378–O(B)
H19–N
3.2
3.0
**
Y400–O(ABD) K22–N1
2.9
2.7
**
G401–O(B)
S20–OH
2.9
2.7
**
G401–O(A)
Y23–OH
3.5
3.5
**
D402–O(A)
R11–N2
3.2
3.5
*
H404-C(C)
F27-Ce1
9.7
3.6
*
V406–C1(B)
M21–Ce
9.4
4.7
*
D376–O1(C)
R29–N1
12.2
10.2
*
HADDOCK is not
very good for
hydrophobic int’s
** strong, * intermediate ints. (from alanine scanning Raucher, 1998)
R24 (**) and T13 and L25 (*) are not seen in the complex (allosteric)
Average pair distance as a function of umbrella window positions
** denotes strong coupling and * intermediate coupling
*
*
**
**
*
**
**
RMSD of ShK as a function of umbrella window
The RMSD of ShK relative to the NMR structure remains flat throughout
Overlap of the neighbouring windows
Gaussian dist: % overlap  1  erf (d / 8 ),
d : distance ,   k BT / k
For k=30 kcal/mol/A2, the overlap is about 10% in bulk, which is an
overlap
optimal value for umbrella simulations (only one extra window needed)
Convergence of the PMF for the Kv1.3-ShK complex
PMF of ShK for Kv1.1, Kv1.2, and Kv1.3
Comparison of the binding free energies of ShK and its analogues
to Kv1.x channels
Complex
Gb(PMF)
Gb(exp) (kcal/mol)
Kv1.1–ShK
-14.3 ± 0.6
-14.7 ± 0.1
Kv1.2–ShK
-10.1 ± 0.6
-11.0 ± 0.1
Kv1.3–ShK
-14.2 ± 0.7
-14.9 ± 0.1
Kv1.1-ShK-K-amide
-11.8 ± 1.0
-12.3 ± 0.1
Kv1.3-ShK-K-amide
-14.0 ± 0.4
-14.4 ± 0.1
Kv1.1-ShK[K18A]
-11.7 ± 0.7
-11.3 ± 0.1
Kv1.3-ShK[K18A]
-13.9 ± 0.6
-14.2 ± 0.1
Excellent agreement with experimental values for all channels,
which provides an independent test for the accuracy of the
complex models.
ShK[K18A] analogue should increase Kv1.3/Kv1.1 selectivity
• All the single and some double mutations in ShK have been patented
by a pharmacology company (AMGEN), which indicated that none are
useful for design of a selective analogue.
• As a result, these mutations have not been considered in addressing
the selectivity problem. Instead people have been looking for nonnatural analogues, which have other problems.
• The Kv1-ShK complex structures indicate several mutations that should
improve Kv1.3/Kv1.1 selectivity (e.g. K18A, R29A)
• The K18A mutation does not change the binding mode in either Kv1.1ShK or Kv1.3-ShK complex (while R29A does). Thus first consider the
K18A analogue
• Test case: use both the FEP/TI and PMF calculations to predict the free
energy change due to the K18A mutation.
Kv1.1 & Kv1.3 complexes with ShK[K18A] (ShK orange)
Kv1.3 complex with ShK (transparent) and ShK[K18A]
Free energy perturbation calculations for ShK[K18A]
• The K18A mutation does not change the binding mode in either
Kv1.1-ShK or Kv1.3-ShK complex. Thus one can use FEP
calculations to find the free energy change due to the mutation.
• Straightforward FEP calculation of the K18A mutation does not work.
• Split the Coulomb and Lennard-Jones parts and do a staged FEP
calculation
• In the binding site, K  K0  A0  A, while in the bulk follow the
opposite cycle, i.e., A  A0  K0  K
• Add the three contributions from K  K0 , K0  A0 and A0  A steps
to find the binding free energy difference, DDG(K  A)
Thermodynamic cycle for the FEP/TI calculations
DDGb  DGb (ShK[K18A] )  DGb (ShK)
PMF
 DDG (K  K 0 )  DDG (K 0  A 0 )  DDG (A 0  A) FEP/TI
Effect of the K18A mutation on binding free energies
Binding free energy differences for Kv1.1 and Kv1.3, and the selectivity
free energy for Kv1.3/Kv1.1. (in units of kcal/mol)
∆∆Gb(Kv1.1)
∆∆Gb(Kv1.3)
∆∆Gsel
FEP
2.1
0.5
1.6
TI
2.4
0.2
2.2
PMF
2.7
0.4
2.3
Exp.
3.1
0.8
2.3
DDGb  DGb (ShK[K18A] )  DGb (ShK )
DDGsel  DDGb (Kv1.1)  DGb (Kv1.3)
Summary
•
Reliable protein-ligand complex structures can be obtained using
docking methods followed by refinement via MD simulations.
(Complex models have been validated via mutagenesis data) .
•
Binding free energies can be determined near chemical accuracy (i.e.,
1 kcal/mol) from PMF.
•
Once a protein-ligand complex is characterized, one can study the
effects of mutations on the ligand by performing FEP calculations,
provided that the binding mode is preserved. These will be especially
useful when seeking mutations that will increase affinity or improve
selectivity of a given ligand targeting a specific protein.