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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
free energy of binding. Using docking with MD simulations to find
structures for protein-ligand complexes. Validating complex
structures using mutation data and binding free energies. Example
from binding of ShK toxin from sea anemone to Kv1 channels.
•
Lecture 10: Rational design of a selective ShK analog for treatment
of autoimmune diseases using FEP/TI methods. Computational
study of a better candidate from the spider toxin HsTx1. Problems
and prospects for Nav channel toxins.
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 analogs 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. High Throughput
Screening) 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 main targets for autoimmune diseases
•
ShK toxin binds to Kv1.3 with pM affinity
•
But it also binds to Kv1.1 in the nervous system 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 available mutagenesis data to validate the complex model.
b) Calculate the potential of mean force for the ligand to 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 free energies (relative to the wild type) using the free energy
methods. Those with higher affinity/selectivity are candidates for new
drugs.
Proof of concept study:
Binding of charybdotoxin (ChTx) to KcsA* (Shaker Kv 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
• Agreement within 1 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
potassium 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 analogs 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 for further validation.
Use the binding mode to predict mutations that will improve the
Kv1.3/Kv1.1 selectivity.
2. Repeat the above study for ShK-K-amide (an analog with improved
Kv1.3/Kv1.1 selectivity) to rationalize the experimental results.
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.
*Breaking of this
interaction causes
shape change.
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
which can be broken during
equilibration (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 (**) is not in the complex (allosteric effect due to shape change.)
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
Average pair distances in Kv1.2–ShK from umbrella sampling
Comparison of the binding free energies of ShK and its analogs 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
Good agreement with experimental values for all channels, which
provides an independent test for the accuracy of the complex
models.
Kv1.1 complexes with ShK (transparent) and ShK-K-amide
Kv1.3 complexes with ShK (transparent) and ShK-K-amide
Computational design of Kv1.3/Kv1.1 selective analogs
The voltage-gated potassium channel Kv1.3 in lymphocytes is
overexpressed during autoimmune attacks. Thus blocking it with a high-
affinity ligand could provide a valuable therapeutic agent.
1.ShK toxin from sea anemone binds to Kv1.3 with picomolar affinity, and
has therefore attracted a great deal of attention. But lack of selectivity over
Kv1.1 prevented its use as a potential drug. Using computational methods,
new selective analogs of ShK have been predicted.
2.The scorpion toxin HsTx1 has already some Kv1.3/Kv1.1 selectivity and
could provide a better candidate for selective blocking of Kv1.3. However,
due to patenting issues, it has not been considered in the past. An HsTx1
analog with improved selectivity has been predicted from computations
and confirmed experimentally (now patented).
Application 1: Design of autoimmune drugs from the ShK toxin
• 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 Kv1.3/Kv1.1 selective analog.
• As a result, these mutations have not been considered in addressing
the selectivity problem. Instead people have been looking for analogs
with non-natural AA and adducts. Over 400 analogs of ShK were
developed at the Norton Lab (Melbourne) but only a few had some
Kv1.3/Kv1.1 selectivity.
• 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 Kv1.1–ShK or Kv1.3–ShK
complex (while R29A does). Thus first consider the K18A analog.
• 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)
Kv1.1 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)
• Simultaneous calculation of binding site/bulk avoids issues with charge
neutrality and simulation artefacts arising from using different systems.
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
Convergence of the FEP calculations for K K0 and K0  A0
Kv1.1
Kv1.3
Convergence of the TI calculations for K K0
Kv1.1
Kv1.3
The forward and backward TI calculations agree within 1 kcal/mol.
Thus there are no hysteresis effects due to inadequate sampling.
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)
ShK[K18A] enhances Kv1.3/Kv1.1 selectivity by 2.3 kcal/mol
Double and triple mutations in ShK
• The K18A mutation provides some gain in Kv1.3/Kv1.1 selectivity but
this is not sufficient for drug safety. Need to increase the selectivity
margin to > 4 kcal/mol.
• Further mutations/additions in ShK could help. Candidates:
– R29A changes the binding mode so it does not work
– Mutation of R29 to a bulky hydrophobic residue preserves the
binding mode and is likely to help
– F27 has a stronger interaction with Kv1.1, so its mutation to a
smaller hydrophobic residue could also help.
– A triple mutation that involves K18, R29 and F27 is likely to achieve
the desired selectivity margin.
Application 2: Design of drugs from the scorpion toxin HsTx1
HsTx1 toxin from scorpion has already over hundred-fold selectivity for
Kv1.3 over Kv1.1, but it is ignored because natural products cannot be
patented. We studied binding of HsTx1 to Kv channels to understand the
basis of this selectivity, and predicted a mutation that will enhance
Kv1.3/Kv1.1 selectivity.
• Prediction of Kv1.x-HsTx1 complex structures
• Validation from binding free energies
• Design of a HsTx1 analog with enhanced Kv1.3/Kv1.1 selectivity
NMR structure of HsTx1 toxin
HsTx1 toxin has four
disulfide bonds and
hydrogen bonds
between:
A1 – C29
C3 – R27
These bonds confer
HsTx1 toxin an even
more stable structure
than ShK toxin!
Pore inserting lysine
Comparison of Ca RMSDs in ShK and HsTx1
Kv1.1–HsTx1 complex
Monomers C and A
Monomers D and B
R14 makes an ionic bond with E353(B) in Kv1.1-HsTx1 complex
Kv1.3–HsTx1 complex
Monomers C and A
Monomers D and B
R14 does not interact with any Kv1.3 residues in Kv1.3-HsTx1 complex
RMSD of HsTx1 as a function of umbrella window
RMSDs of HsTx1 relative to the NMR structure – no shape change.
Convergence of the PMFs for the Kv1.x–HsTx1 complexes
Convergence of the PMF is much slower in Kv1.1 compared to Kv1.3.
This example highlights the danger of choosing an arbitrary time (e.g. 1 ns)
for equilibration in PMF calculations.
PMFs for the Kv1.x–HsTx1 complexes
Comparison of the binding free energies for Kv1.x–HsTx1
complexes to experimental values
Complex
Gb(PMF)
Gb(exp) (kcal/mol)
Kv1.1–HsTx1
-10.1 ± 0.6
-11.1 ± 0.1
Kv1.2–HsTx1
-8.9 ± 0.6
> -9.6 ± 0.1
Kv1.3–HsTx1
-14.0 ± 0.7
-14.9 ± 0.2
Good agreement with experimental values for all channels, which
provides a test for the accuracy of the complex models.
Note that there are no alanine scanning data available for HsTx1
binding to Kv1.x channels.
So we have to rely on binding free energies for validation.
Design of a HsTx1 analog with enhanced Kv1.3/Kv1.1 selectivity
The Kv1.3/Kv1.1 selectivity of HsTx1 is already ~ 4 kcal/mol.
Free energy calculations show that the R14A mutation reduces the
affinity of HsTx1[R14A] to Kv1.1 by a further 2.7 kcal/mol without
affecting its affinity to Kv1.3 (confirmed in subsequent experiments).
Thus HsTx1[R14A] provides an excellent candidate for development
of a drug for treatment of autoimmune diseases.
References (H. Rashid et al.):
ShK : J. Phys. Chem. B 116: 4812 (2012)
ShK[K18A] : PLoS One 8: e78 (2013)
HsTx1 : J. Phys. Chem. B 118: 707 (2014)
HsTx1[R14A] : Sci. Reps. 4: 4509 (2014)
Problems and prospects for Nav channel toxins
• Nav channels are even more important therapeutic targets than Kv
• Bacterial Nav structures are not very useful for modelling of
mammalian Nav channels but a reliable homology model for the
pore domain is now available.
• Pore domain of all Nav1.1 – Nav1.9 channels are very similar.
There are differences in the turret region, which could play
important roles in toxin binding. However no templates can be
found for modelling the turret regions.
• Another target is the voltage sensor. Disabling the voltage sensor
of Nav1.7 selectively by binding toxin peptides could provide novel
drugs for chronic pain.
• Finally blocking the inner cavity from inside offers treatments for
heart diseases.
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 and 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.