1. David Minh studies constrained molecular dynamics simulations, protein-ligand binding free energies using multiple rigid receptor structures, and Bayesian analysis of isothermal titration calorimetry data. 2. Binding free energy quantifies binding strength and can be estimated using methods like alchemical free energy calculations, molecular docking, or a new method called alchemical grid docking which uses binding potential of mean force estimates. 3. Reweighting configurations from apo protein ensemble simulations using binding potential of mean forces can reproduce holo protein ensembles, validating this new type of free energy calculation method.

1. David Minh
1. Constrained molecular
dynamics as Gibbs sampling
2. Protein-ligand binding free energies
using multiple rigid receptor structures
3. Bayesian analysis of isothermal
titration calorimetry

2. The improvement score (%) is defined in the text. In the second and third column
1KK7 for Myosin), C = final (e.g. 1KK8 for Myosin), following Weiss and Levitt.
Rightmost two columns refer to Weiss and Levitt results.
aSpecific cases discussed in the text.
the
ing
thr
0.9
wh
(am
tra
oc
tid
mo
cee
of
P a
ste
Tek, A., Korostelev, A. A., & Flores, S. C. (2016). MMB-GUI: A fast morphing method demonstrates a possible ribosomal tRNA translocation trajectory. Nucleic Acids Research, 44(1), 95–
105. http://doi.org/10.1093/nar/gkv1457
Constrained dynamics can observe transitions
intractable with standard dynamics methods
but they are biased!

3. Tek, A., Korostelev, A. A., & Flores, S. C. (2016). MMB-GUI: A fast morphing method demonstrates a possible ribosomal tRNA translocation trajectory. Nucleic Acids Research, 44(1), 95–
105. http://doi.org/10.1093/nar/gkv1457

4. Monte Carlo moves can be constrained
dynamics simulationsGeneralized Coordinates Hamiltonian Monte Carlo
Avoids high energy a/empts
Avoids hard degrees of freedom
(GCHMC + CCHMC) leads to full configura?on space explora?on

5. CDHMC samples from the correct probability
distribution for torsion angles
0.0020
0.0025
0.0030
0.0035
⇢(↵)
NO FIXMAN
0.0020
0.0025
0.0030
0.0035
⇢(↵)
CDHMC
-180 -90 0 90 180
↵(degrees)
0.0020
0.0025
0.0030
0.0035
⇢(↵)
MIXED

6. CDHMC samples from the correct probability
distribution for coupled torsion angles
C5 PPII
C7eq
aL
C5 PPII
C7eq
aL

7. CDHMC improves sampling of macrocycle
conformations

8. The number of
sampled
clusters is greater

9. David Minh
1. Constrained molecular dynamics as
Gibbs sampling
2. Protein-ligand binding free
energies using multiple rigid
receptor structures
3. Bayesian analysis of isothermal
titration calorimetry

10. ΔG○ quantifies binding strength
CR
CL
C
free receptor concentration
free ligand concentration
complex concentration
standard state concentration (1 M)
CRL
Kd =
CRCL
CRL
dissociation constant
binding free energy G = 1
ln
✓
Kd
C
◆
RL⌦+R L
G
Kd MmMμMnMpMfM
0-4.1-8.3-12.4-16.6-20.8 kcal/mol
weak
biomolecular
lead compoundsgood drugshighest biological
affinity
biotin:streptavidin
lipitor:HMG-CoA
reductase ATP:kinase
WEAKSTRONG
benzamidine:
bovine trypsin

11. Millions Thousands
1st stage 2nd stage 3rd stage
<100
Alchemical pathways,
implicit solvent
(BEDAM/YANK)
We are developing a method with intermediate
accuracy between docking and “alchemical”
Accuracy
log(Computational Expense)
Alchemical pathways,
explicit solvent
End-point approximations
(MM/PBSA)
Molecular Docking
Alchemical Grid Dock
(AlGDock)

12. A binding potential of mean force is a binding free
energy between a flexible ligand and rigid receptor
1kzk,
from
docked pose

13. BPMFs can be averaged to get rigorous absolute ΔG○
• Rigorous
• Multiple rigid receptor structures
• Recyclable - thorough receptor sampling once, instead of
for every ligand
• Scalable - grid-based receptor-ligand interaction energies
are not dependent on receptor size
• Explains docking as an approximation
Minh, J Chem Phys 2012
G = 1
ln
⌦
e B
↵rR
R
+ G✏
B(rR) = 1
ln
⌦
e
↵rL,✏L
L,I
U(rX) = U(rX) + W(rX )
(rRL) = U(rRL) U(rR) U(rL)
Binding Free Energy
Binding PMF
Effective Potential Energy
Effective Interaction Energy

14. I. Sample configurations of the receptor
II. Estimate the binding PMF for each ligand
III. Estimate the binding free energy for each ligand
ˆB(rR) = 1
ln
1
N
NX
n=1
e (rRL,n)
Sample mean of exponential average
Only needs to be done once!
Does not need to be
reproduced for every ligand.
Helpful for systems with large
conformational change
New type of free energy
calculation

15. AlGDock closely reproduces YANK
c) d)
e) f)

16. FFT can be used to estimate BPMFs and therefore binding
free energies
Nguyen, T. H., Zhou, H-X, & Minh, D. D. L. currently being revised

17. 2D cross section of interaction energy
Nguyen, T. H., Zhou, H-X, & Minh, D. D. L. currently being revised

18. FFT-based BPMF estimates reasonably reproduce YANK
and AlGDock
c) d)
e) f)

19. Reweighting the apo to holo ensemble
Apo Reweighted Apo = Holo
What we would like to do:

20. Validation of BPMF-based reweighing
• Validation approach
• Run alchemical calculations to get
apo and holo ensembles
• Calculate BPMFs for snapshots from
the apo ensemble
• Compare reweighted apo and holo
ensembles
hOiRL =
⌦
O(rR)e B(rR)
↵
R⌦
e B(rR)
↵
R
Minh, JCP 2012

21. Reweighting a 1D energy landscape
ATP
AMP
Based on 400 snapshots

22. Reweighting a correlation matrix
Apo
Holo
Reweighted Apo

23. Difference Matrices
Holo - Apo Reweighted Apo - Apo

24. Difference Matrices
Reweighted Apo - Holo

25. David Minh
1. Constrained molecular dynamics as
Gibbs sampling
2. Protein-ligand binding free energies
using multiple rigid receptor structures
3. Bayesian analysis of isothermal
titration calorimetry

26. ITC experiment
The only experimental technique that measures both free
energy and enthalpy of binding.
Also allows study competitive binding, binding events in the
presence of changes in the protonation states, and in certain
cases kinetics of binding.
Measures differential power which is integrated to obtain heat.
Standard data analysis procedure is to assume a heat model
and then use nonlinear least square fitting (nonlinear
regression) to fit the heat data to the model to obtain
thermodynamic parameters.
nonlinear regression analysis
Bayesian analysis

27. Nonlinear regression data analysis

29. ΔG
ΔH
ΔG
ΔH