Dead-End Elimination for Protein Design with Flexible Rotamers
description
Transcript of Dead-End Elimination for Protein Design with Flexible Rotamers
Dead-End Eliminationfor Protein Design
with Flexible Rotamers
Ivelin Georgiev
Donald Lab
02/19/2008
protein design protein design algorithmalgorithm
energy function rotamer
library
inputinputstructurestructure
stabilityspecificity
novel function
drug designdrug design
wildtypewildtype
mutantmutant
Computational Design
…
CCCC
MinDEE
qqqq q*q*q*q*
partition functionε-approximation algorithm
redesign for Leu
Contributions
provable energy minimization
ensembles
Traditional-DEE
E lowerbound
E upperbound
itir
rotamer pruning
Enumerate
fixed backbone/side-chains
Desmet et al., 1992
GMECGMEC
ir
it
conformations
E
O(qO(q22nn22))
Traditional-DEE with Rigid Rotamers/Backbone
Conformations
Ene
rgy
it
Traditional-DEE with Side-chain Dihedral FlexibilityConformations
Ene
rgy
min
max
it
Traditional-DEETraditional-DEE
CCCC
E minimizationE minimization
Xnot provably-correct
CCCC
√
MinDEEMinDEE
E minimizationE minimization
provably-correct
Traditional-DEETraditional-DEE
CCCC
rigid energiesrigid energies
√provably-correct
CCCC
√
MinDEEMinDEE
E minimizationE minimization
provably-correct
continuousside-chain
dihedral space
voxelsvoxelsbound rotamer
movement
MinDEE
lowerlower / / upperupper energy boundsenergy boundsir
js
it
χir
Energy
MinDEE
E(ir , js)
ir
js
js
ir
χjs
MinDEE:
pruning candidate
competitor
witness
not in trad-DEElowerlower boundbound
on on ir conformation conformationenergiesenergies
-upperupper boundbound
on on it conformation conformationenergiesenergies
-possible energypossible energychanges due tochanges due to
rotamer movementrotamer movement
> 0
lowerlower / / upperupper energy boundsenergy boundsir
js
it
traditional-DEE
MinDEE
MinDEEMinDEE: Side-chain Dihedral Flexibility
MinDEE Applications
∫1Z
K*: provably-accurate approximation to the binding constant via conformational
ensembles
JCB’05
min
GMEC-basedGMEC-based
singlelowest-energyconformation
weightedaverage
Ensemble-basedEnsemble-based
a
sequence K*
TIAAIC 7.3
GIRMQM 3.1
TGIAIV 2.9
LMLAIS 1.7
TWAIGY 0.3
MinDEE Applications
MinDEE/A*: GMEC-based Method
full Eminimization
CC
C’C’
MinDEEpruning
A* search(E lower bounds)
MinDEE/A*: GMEC-based Method
O(nO(n22rr22))
full Eminimization
CC
C’C’
MinDEEpruning
A* search(E lower bounds)
MinDEE/A*: GMEC-based Method
O(nO(n22rr22))
full Eminimization
CC
C’C’
MinDEEpruning
A* search(E lower bounds)
…
…
MinDEE/A*: GMEC-based Method
O(nO(n22rr22))
full Eminimization
CC
C’C’
MinDEEpruning
A* search(E lower bounds)
……
… …
MinDEE/A*: GMEC-based Method
B(c) > E(best)B(c) > E(best)
O(nO(n22rr22))
minGMEC
Hybrid-K*: Ensembles Method
Hybrid-K*: Ensembles Method
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
Volumefilter
seq1
p’
…
Hybrid-K*: Ensembles Method
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
Volumefilter
seq1
p’
…
Hybrid-K*: Ensembles Method
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
p’
q* < (1-ε)q
Hybrid-K*: Ensembles Method
CC
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization p’
q* ≥ (1-ε)q
repeat search
C’C’
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
p’
q* < (1-ε)q
…
Hybrid-K*: Ensembles Method
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
Volumefilter
seq1
CC
C’C’
DEEpruning
…
q*
full Eminimization
seqn
…
p’
A* search(E lower bounds)
…
q* ≥ (1-ε)qq* ≥ (1-ε)q
Hybrid-K*: Inter-mutation Pruning
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
Volumefilter
seq1
CCseqn
p’
q* ≥ (1-ε)q
Hybrid-K*: Inter-mutation Pruning
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
Volumefilter
seq1
CC
C’C’
DEEpruning
…
q*
full Eminimization
seqn
…
p’
A* search(E lower bounds)
K*i
p’
Ķ*n<
Hybrid-K*: Inter-mutation Pruning
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
Volumefilter
seq1
CC
C’C’
DEEpruning
…
q*
full Eminimization
seqn
…
p’
A* search(E lower bounds)
K*i
p’
Ķ*n
…
>>>
q* < (1-ε)q
Hybrid-K*: Intra-mutation Pruning
CC
C’C’
DEEpruning
A* search(E lower bounds)
…
q*
full Eminimization
Volumefilter
seq1
CC
C’C’
DEEpruning
…
q*
full Eminimization
seqn
…
p’
A* search(E lower bounds)
…
q* ≥ (1-ε)qq* ≥ (1-ε)q
E minimizationE minimization
Results
rigid energiesrigid energies single structuresingle structure
ensemblesensembles
MinDEE: EnsemblesMinDEE: Ensembles
Traditional-DEETraditional-DEE
MinDEE: GMEC-basedMinDEE: GMEC-based
K* (RECOMB’04)K* (RECOMB’04)
this workthis work previousprevious
Structural Model
GrsA-PheA Active Site
235 236 239 278 299 301 322 330 331
D A W T I A A I C
• 1AMU (Conti et al., 1997)• Residues: 39
• flexible: 9• steric shell: 30
• Flexible ligand• AMP• Richardsons’ rotamer library• AMBER (vdW,elect,dihed) + EEF1• 2-point mutation search for Leu• GAVLIFYWM allowed
Comparison to Traditional-DEE
• trad-GMEC ranked 397th
• E(minGMEC) < E(rigid-GMEC) by ≈ 6 kcal/mol
minGMEC:
* minGMEC rotamer pruned by traditional-DEE
235 236 239 278 299 301 322 330 331
D M W T I A* M I C
2 5 3 3 6 - 9 6 2
-150
-148
-146
-144
-142
-140
-138
-136
-134
0 1000 2000 3000 4000 5000 6000 7000
Conformation Rank
En
erg
y
minGMEC
trad-GMECtrad-GMEC
Hybrid-K*
Predictions • T278M/A301G (Stachelhaus et al., 1999) ranked 3rd
• G301 in all known natural Leu adenylation domains• Experimental verification
Computational • 9 hrs. on 24 processors• Original K* fully-evaluated 30%
more conformations• K* w/o filters: ≈ 3,263 days
Conf. Remaining
Pruning Factor (%)
Initial 6.8 x 108 -
Volume Filter 2.04 x 108 3.33 (70.0)
MinDEE Filter 4.13 x 106 49.43 (98.0)
Steric Filter 3.86 x 106 1.07 (6.5)
A* Filter 7.82 x 104 49.41 (98.0)
Top 40 Mutations – Hybrid-K*
0
0.001
0.002
0.003
0.004
0.005
0.006
0 5 10 15 20 25 30 35 40 45 50
Log K* Score
Fra
ctio
n E
valu
ated
Co
nfs
(B
ou
nd
)
• Ew = 12.5 kcal/mol• 4 days on a single processor• 206 of 421 rotamers pruned• over 60,000 extracted conformations• 7,261 conformations (221 unique sequences) within Ew
• minGMEC: A236M/A322M
MinDEE/A*Top 40 Mutations – MinDEE/A*
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
D235 M236 W239 T278 I299 M322 I330 C331
AS Residue
Ro
tam
er F
req
uen
cy (
no
rmal
ized
)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-150 -148 -146 -144 -142 -140 -138 -136 -134
Energy
RM
SD
Rotamer Diversity for A236M/A322MRotamer Diversity for A236M/A322MConf Energies vs. RMSD for A236M/A322MConf Energies vs. RMSD for A236M/A322M
Conclusions and Future Work• Traditional-DEE not correct with energy minimization
• MinDEE provably-correct and efficient
• MinDEE capable of returning lower-energy conformations
• Ensemble-based and GMEC-based redesign predictions are substantially different
• MinDEE: Ensembles Method successfully predicts both known and novel redesigns
• Improve MinDEE pruning efficiency
• Improve model accuracy
• Marriage of MinDEE and BD
Top 40 Mutations – Hybrid-K*
Acknowledgments
• Bruce Donald
• Ryan Lilien
• Amy Anderson
• Serkan Apaydin
• John MacMaster
• Tony Yan
• All members of Donald Lab FundingFunding:: • NIHNIH• NSFNSF