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Marco CecchiniLaboratoire d’Ingénierie des Fonctions Moléculaires !
ISIS (UMR7006), Faculté de Chimie!Université de Strasbourg
Computational Approaches to Protein-Ligand Binding
Lab d’Ingénierie des Fonctions Moléculaires
Joel Montalvo-Acosta
Outline
• Protein-ligand binding!
• Computational approaches to ligand-binding affinity!
• Provide a classification of methods based on stat mech!
• Results on a host-guest system
Protein-Ligand Binding
Buch, Giorgino & De Fabritiis, PNAS (2011)
Ligand Binding Affinity
P + L ↵ PL
10
�510
�210
110
4
0
0.2
0.4
0.6
0.8
1
A
B
Initial concentration
MolarFraction
µM < nM < pM
ligand potency (Kd)
[L] = Kdwhen
[PL][PL] + [P ]
=12
Kd = 1/Keq =[P ][L][PL]
Isothermal Titration Calorimetry
Canonical Approach
Keq � �µ�b � QL, QP , QPL
exp
✓��µ
�b
kT
◆=
CPL (C�)
CP CL= KeqC
�
Chemical thermodynamics
F (N,V, T ) = �kT lnQ
µ(V, T ) =✓
@F
@N
◆
V,T
= �kT✓
@ lnQ@N
◆
V,T
Classical Statistical Mechanics
Chemical Potentials
µi,v(V, T ) = �kT ln��
2�mkTh2
� 32 V
N
�+
�kT ln��
�
�
�8�2kT
h2
� 32 �
IXIY IZ
�+
�kT3n�6�
j=1
ln��
kT
h�j
��+
�De
In the limit of RRHO/BO & in vacuum
µi(V, T ) = µi,v(V, T ) + Wbulk(X0)
McQuarrie, Statistical Mechanics, New York: Harper & Row, 1976
1. Absolute Chemical Potentials
P + L ↵ PL
µ�i (T ) = µ�i,v(T ) + Wbulk(X0)
Grand Canonical Approach
µ�i (T ) = �kT ln✓Qi(p, T )
V
◆
exp
✓��µ
�b
kT
◆=
(QPL/VPL)(QP /VP ) (QL/VL)
= Keq
Qi(p, T ) ⇡QN,1QN,0
@ infinite dilution
Hill, Cooperativity Theory in Biochemistry, Springer Verlag 1985
Keq =QN,LP /QN,P
(QN,L/QN,0)/VL
& small ligand
2. Ligand Partitioning
Lfree � Lbound
Keq =QL(P )
(QL/VL)
Rigorous Approach
Keq =
Rsite dL
RdX exp (��U)R
bulk dL � (rL � r⇤)R
dX exp (��U)
Keq =QL(P )
(QL/VL)
µi(V, T ) = µi,v(V, T ) + Wbulk(X0)1. Absolute Chemical Potentials
2. Ligand Partitioning
Double Decoupling
Jorgensen et al, J Chem Phys (1988) Gilson et al, Biophys J (1997)
Keq =
Rsite dL
RdX exp (��U1)R
bulk dL � (rL � r⇤)R
dX exp (��U0)⇥
Rbulk dL � (rL � r
⇤)
RdX exp (��U0)R
bulk dL � (rL � r⇤)R
dX exp (��U1)
Keq =QL(P )
(QL/VL)
Solution
Gas phase
Alchemical RouteKeq = QL(P )(QL/VL)
Solution
Gas phase
�F = �kT ln�e��(U1�U0)
�
U0FEP
…with Restraints
Gumbart, Chipot & Roux, J Chem Theory Comput (2013)
Keq =�
site dL�
dX exp (��U1)�site dL
�dX exp [�� (U1 + uc)]
��
site dL�
dX exp [�� (U1 + uc)]�site dL
�dX exp [�� (U1 + uc + uo)]
��
site dL�
dX exp [�� (U1 + uc + uo)]�site dL
�dX exp [�� (U1 + uc + uo + up)]
��
site dL�
dX exp [�� (U1 + uc + uo + up)]�bulk dL � (rL � r�)
�dX exp [�� (U0 + uc + uo + up)]
��
bulk dL � (rL � r�)
�dX exp [�� (U0 + uc + uo + up)]�
bulk dL � (rL � r�)�
dX exp [�� (U0 + uc + uo)]�
�bulk dL � (rL � r
�)�
dX exp [�� (U0 + uc + uo)]]�bulk dL � (rL � r�)
�dX exp [�� (U0 + uc)]
��
bulk dL � (rL � r�)
�dX exp [�� (U0 + uc)]]�
bulk dL � (rL � r�)�
dX exp [�� (U1 + uc)]�
�bulk dL � (rL � r
�)�
dX exp [�� (U1 + uc)]]�bulk dL � (rL � r�)
�dX exp [�� (U1)]
Uc, Uo, Up!conformational, orientational &
positional restraints
2 alchemical transformations
Rigorous Methods
End-points Approach
MM/PBSA
Kollman et al, Acc Chem Res (2000)
Solution
Gas phase
µi(V, T ) = µi,v(V, T ) + Wbulk(X0)
MM/PBSAµi(V, T ) = µi,v(V, T ) + Wbulk(X0)
MM/PBSA assumptions
By separating out enthalpy vs entropy contributionsµi(V, T ) = (3n� 3) kT �De,v � TSi(V ) + Wsolv
Wsolv � GPBSA1.�De,v = hUi �
X 12kT2.
µi(V, T ) =32nikT + hUi + hGPBSAi � TSi(V )
implicit solvent
Force Field
MM/PBSA (HOWTO)
µi
(V, T ) = 32nikT + Ebond + Eelec + EvdW + Gpol + Gnp � TSi(V )
•Run explicit-water MD for P, L & PL!•Extract sampling & compute ensemble
averages of both the internal energy in a vacuum & the solvation free energy!
•Evaluate the configurational entropy at standard state (1M) by statistical mechanics formulas & NMA
Linear Interaction Energy (LIE)
Åqvist, Medina & Samuelsson, Protein Eng (1994)
Solution
Gas phaseKeq =
QL(P )(QL/VL)
LIEKeq =QL(P )
(QL/VL)
�µ�b = �kT log ⇣ + Wsite �Wbulk
q = qtr
qrot
qvib
qelec
In the limit of RRHO & rigid ligands:
Keq =qCM
qrock
e��Wsite
(qtr
/V ) qrot
e��Wbulk
�µ�b =12
hhUelecl/s isite � hUelecl/s ibulk
i+ ↵
hhUvdwl/s isite � hUvdwl/s ibulk
i+ �
Wnpi ⇡ ↵DUvdWl/s
EW pol
i
=12
DUelec
l/s
ELIE’s assumptions
1. 2.
LIE (HOWTO)
• Run two explicit-water MD for L & PL!• Compute ensemble averages of the
electrostatic & the Van Der Waals interaction energy of the ligand with the surroundings!
• Assign appropriate β for your ligand(s)!• Determine α,γ by fitting on experiments
�µ�b = �hhUelecl/s isite � hUelecl/s ibulk
i+ ↵
hhUvdwl/s isite � hUvdwl/s ibulk
i+ �
Guitiérrez-de-Terán & Åqvist, Computational Drug Discovery and Design (2012)
End-points Approach
Empirical Approach
virtual High-Throughput Screening (vHTS)
Molecular DockingBUT to be fast…!•Bound State!•Rigid Receptor!•Flexible Ligand!•No/Implicit solvent!•Ligand Fitness by a
Scoring Function
Force-Field Scoring
�µ�b
=protX
i
ligX
j
A
ij
r12ij
� Bijr6ij
+ 332.0qi
qj
✏ (rij
) rij
!DOCK score:
�µ�b
=h⇣
Uelecl/s
⌘
site
� 0i
+h⇣
Uvdwl/s
⌘
site
� 0i
=protX
i
ligX
j
A
ij
r12ij
� Bijr6ij
+qi
qj
✏ (rij
) rij
!
FF’s assumptions h. . . i = (. . . )⇣U
elec
l/s
⌘
bulk=
⇣U
vdw
l/s
⌘
bulk= 0
NO sampling
NO desolvation
Empirical Scoring�µ�b =X
i
Wi�µi
�µ�b = �G0 + �Ghb�
hbonds
f (�R,��) +
�Gio�
io int.
f (�R,��) +
�Glipo�
lipo cont.
Alipo +
�Garo�
aro int.
f (�R) + �Grot �Nrot
Böhm’s score:
FRESNO’s score:�µ�b = K + ↵ (HB) + � (LIPO) + � (ROT ) + � (BP ) + ✏ (DESOLV )
Montalvo-Acosta & Cecchini, Mol Inform (2016)
Summary
Host-Guest SystemCucurbit-[7]-uril (CB7)
−14.1
−11.8
−13.4
Moghaddam et al, J Am Chem Soc (2011)
AUTODOCK
LIEMM/PBSA
FEP
Benchmark
Keq =�
site dL�
dX exp (��U1)�site dL
�dX exp [�� (U1 + uc)]
��
site dL�
dX exp [�� (U1 + uc)]�site dL
�dX exp [�� (U1 + uc + uo)]
��
site dL�
dX exp [�� (U1 + uc + uo)]�site dL
�dX exp [�� (U1 + uc + uo + up)]
��
site dL�
dX exp [�� (U1 + uc + uo + up)]�bulk dL � (rL � r�)
�dX exp [�� (U0 + uc + uo + up)]
��
bulk dL � (rL � r�)
�dX exp [�� (U0 + uc + uo + up)]�
bulk dL � (rL � r�)�
dX exp [�� (U0 + uc + uo)]�
�bulk dL � (rL � r
�)�
dX exp [�� (U0 + uc + uo)]]�bulk dL � (rL � r�)
�dX exp [�� (U0 + uc)]
��
bulk dL � (rL � r�)
�dX exp [�� (U0 + uc)]]�
bulk dL � (rL � r�)�
dX exp [�� (U1 + uc)]�
�bulk dL � (rL � r
�)�
dX exp [�� (U1 + uc)]]�bulk dL � (rL � r�)
�dX exp [�� (U1)]
�µ�b =12
��Uelecl/s �site � �Uelecl/s �bulk
�+
���Uvdwl/s �site � �Uvdwl/s �bulk
�
�µ�b = Wvdwprot�
i
lig�
j
�Aijr12ij
� Bijr6ij
�+
Wele
prot�
i
lig�
j
�qiqj
� (rij) rij
�+
Whbond
prot�
i
lig�
j
�E (t)
Cijr12ij
� Dijr10ij
�+
Wsol
prot�
i
lig�
j
(SiVj + SjVi) exp
��r2ij2�2
�
µi(V, T ) =32nikT + hUi + hGPBSAi � TSi(V )
Binding Free Energy
-16
-14
-12
-10
-8
-6
-4
-16 -14 -12 -10 -8 -6 -4
Exp
erim
enta
l [kc
al/m
ol]
Calculated [kcal/mol]
FEPMM/PBSA
LIEAUTODOCK
Accuracy/Efficiency y = 0.22 3p
x
Take Home MessageOur statistical mechanics interpretation of protein-ligand binding:!• provides a useful classification of existing
methods to the binding constant!• highlights their inherent approximations and
provides guidelines for future development!• has allowed to quantify their performances
(accuracy/efficiency) on a model host-guest system
Montalvo-Acosta & Cecchini, Mol Inform (2016)
Acknowledgments
Joel Montalvo-Acosta!!
Nicolas Muzet (Sanofi)!Michael Schaefer (Novartis)
• Explicit-water MD simulations for three host-guest systems!
• Initial coordinates for the complexes obtained from the Cambridge Structural Database!
•Dodecahedron box with a layer of >14Å around the solute !
•Force-Field parameters for the guests by CGenFF!
•NPT @ 298K & 1atm!•Production runs of 20 ns with
GROMACS 5.1 compiled with PLUMED plugin
5073 atoms Simulation Setup
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