A Kinematic View of Loop Closure
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Transcript of A Kinematic View of Loop Closure
A Kinematic View of Loop Closure
EVANGELOS A. COUTSIAS, CHAOK SEOK, MATTHEW P. JACOBSON, KEN A. DILL
Presented by Keren Lasker
Agenda
Problem definition The Tripeptide Loop-Closure Problem Generalization Applications
The Loop Closure problemFinding the ensemble of possible backbone
structures of a chain segment of a protein that is geometrically consistent with preceding & following parts of the chain whose structures are given.
SER ILE HIS ASP ALA ALA THR SER LEU ASN
R
R
R
ConstantsConstants : bond lengths, bond angles
VariablesVariables : backbone torsions
Six free rotation angles The angles form three/four rigid pairs
Special case
nC
z
y
1nC
x
R
R
R
nC
1nC
x
y
z
xy
z
iii
Moving to a coarser problem
The Tripeptide Loop-Closure ProblemC
CC
NN
Ca
CaC
CC
NN
Ca
Ca
Problem definition :
Special case
six torsion angles at three Ca atoms located
consecutively along a peptide backbone.
The atoms are fixed in space
3 variables
3 constrains
3311 ,,, CCCN
Output :
The exact position of
the loop atoms
Notation
N
C
Finding the bonds length
x
cosxn
sinxm
sincos mnx
d
r
r
ix
y
1ix y
iz
1iz
Moving to a polynomial equation
Derivation of a 16th Degree Polynomial for the 6-angle Loop Closure
iii rr cos1 ki
ji
kj
ijkiii uupuuP 1
2
0,
)(1 :),(
),,,,( 1 iiiiiip
r1
r2
0)( 3
16
0316
j
jjkuruR
0)( 3
16
0316
j
jjkuruR
iii
uuu
123 ,
Find the rotation angles
Position the atoms
Noncontiguous Ca atoms
The problem characteristic do not depend on the Ca atoms continuity
Additional Dihedral Angle
Rigid sampling coverage of the real protein structure space
resolved
unresolved
Dataset : Top500
sampling with perturbation
reso lved
unresolved
resolved
unresolved
5 degree perturbation of the
NCaC angles
10 degree perturbation of the
NCaC angles
Application to Loop Modeling Use PLOP to sample all the torsions
except for a three residue gap in the middle of the loop.
Plop -
0.29(459,0.73) 1.66(236,1.6) 3.25(42,106)
0.27(5000,8.5) 1.04 (5000,6.1) 1.89(5000,23)
Moving to a polynomial equation
Moving to a polynomial equation
1
a2
b2
3 4
a4
b4
5
a5 b5a1 b1
1
2
4
51
2
4
5
'3
o90
This extends to the orientation of Cb1
2
o111
A bimodal example
oo
o
10110
111
Theta-perturbations are not enough
oo
o
519
111
oo
o
519
111
Biological motivation
Homology modeling Monte Carlo simulation
TODO
Check that the bond angles are really constant in proteins?
Which angles do we try to find in the coarser proble m?
Why the consec helps , what is the big problem in non consecutive ?
Condtion 3 in the special case?
N
N C
C
C
R
R