STRUCTURE CALCULATIONS OF PROTEIN SURFACE SEGMENTS: MONTE CARLO SIMULATED ANNEALING

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STRUCTURE CALCULATIONS OF PROTEIN SURFACE
SEGMENTS MONTE CARLO SIMULATED ANNEALING WITH
SCALED COLLECTIVE VARIABLES AND FORCE CONSTANT
ANNEALING
Sergio A. Hassan, Ernest L. Mehler and Harel
Weinstein Dept. Physiology and Biophysics, Mount
Sinai School of Medicine, New York, NY 10029
A new algorithm for modeling segments in proteins
(in particular loops) is presented that first
finds conformations representative of segment
structures tethered to the protein at the
N-terminus only, and subsequently the free end of
the segment is driven towards its attachment
point using a reversed force constant simulated
annealing scheme with scaled collective variables
(SCV). The segment peptide is initially placed in
an extended conformation with the N-terminus
covalently bound to the attachment point in the
protein, and simulated annealing Monte Carlo (MC)
calculations 1 are carried out. The resulting
families of new conformations prepare the peptide
for attachment of the C-terminus. In the second
stage a hierachical protocol drives the segments
C-terminus towards its final position in the
protein. In this second part of the calculation
the complete force field, i.e., including the
proteins tertiary structure, is considered. The
free C-terminus is attached to a dummy residue,
identical to the target residue where the segment
will be connected. Successive MC simulations are
carried out using the SCV method 2 with
increasingly larger values of the harmonic force
constant to ensure the correct orientation of the
segment with the rest of the protein in the
attachment point. The method was evaluated for
eight different segments in the a-subunit of
transducin, using PARAM22 CHARMM and the recently
developed screened Coulomb potential based
implicit solvent model 3.
SUMMARY OF THE RESULTS The table below shows the
quantitative results of the eight segments
calculated. The results compare favorably to the
best results reported to date on loop modeling
5, except for segments s4 and s5 Differently
to the rest of the segments, s4 and s5 are not
completely solvent exposed and interact with each
other. Although the qualitative folding at the
end of these two segments is correctly
reproduced, the middle part of the segment
present a different conformation that increases
the RMSD values. In general all the segments
reproduce well the qualitative characteristics of
the native structure proper folding, correct
formation of H-bonds and proper side chain
orientation.
CALCULATION OF SEGMENTS IN THE a-SUBUNIT OF
TRANSDUCIN
INTRODUCTION Loops are important in many
biological functions of proteins and fluctuate
considerably from their equilibrium structures in
solution, which is problematic for their
structure determination by experimental methods
or for homology modeling. Structural flexibility
of loops plays an important role in
protein-protein, protein-peptide and protein-DNA
recognition by allowing adaptation of loop
conformation during interaction. In G-protein
coupled receptors, for example, the extracellular
loops are involved in binding of various ligands,
whereas intracellular loops are important for
triggering subsequent steps of the cellular
response upon activation.
One of the best-characterized G-protein
signaling pathways in humans is in the rod cells
of the retina where the conversion of light
(external stimulus) into a nerve impulse is
mediated by the a-subunit of transducin that
binds to rhodopsin, a transmembrane
photoreceptor. The a-subunit is composed of two
domains (Fig.2) one containing six b-strands
(b1-b6) surrounded by six helices (a1-a5 and aG),
and another one composed mainly of helical
structures. The two domains are connected by two
short segments, labeled linkers 1 and 2. The
eight segments considered in this study are shown
in Figures 3 and 4.
ID Seqa Nb RMSDc rmsdd
sec.structe Function s1 46-54 9
2.09 1.75 a1 aA Contains
linker 1 s2 80-90 11 1.60
0.85 aA aB s3 102-112 11 2.97
1.63 aB aC s4 132-142 11 gt10.00
lt3.00 aD aE s5 222-234 13 gt10.00
lt3.00 b4 a3 Part of the Switch III
s6 276-286 11 2.70 2.50 aG
a4 s7 301-310 10 4.20 2.70
a4 b6 Receptor binding region s8
314-321 8 2.85 1.79 b6 a5
Receptor binding region a)sequence defined in
5, PDB entry1got b)number of residues in the
segments c)root-mean-square deviations of main
chain heavy atoms of the segments, in Å note
that the proteins are superimposed, excluding the
segments. d)same as c) but superimposing the
calculated and native segments only e)elements of
secondary structure connected by the segments
(see Fig.4)
A segment is defined as a loop portion plus the
elements of secondary structure that immediately
precedes and follows it. Therefore, segment
structure prediction is a more challenging
problem since it includes the task of reproducing
the specific folding properties observed at the
ends of the segment (i.e., specific secondary
structure) and the proper H-bond interactions.
Figure 2 a-subunit of transducin (PDB entry
1got) showing the two domains connected by two
linkers (shown in black). All b-strands are
located within the domain shown at the right of
the figure. Transducin is a heterotrimeric
G-protein involved in the visual cascade in the
human retina and binds to the photoreceptor
rhodopsin the a-subunit is a 39 KDa protein.
Figure 3 Segments s1 to s8 (black ribbons) in
the a-subunit of transducin. Three segments
(s2-s4) belong to one domain of the protein and
four segments (s5-s8) belong to the second
domain Segment s1 contains (but is longer than)
the linker 1 (see Fig.2). Together, the segments
comprise about 25 of the whole protein.
The method developed here, for the calculation of
segments connecting elements of secondary
structure motifs in proteins, consists of two
successive steps 1. A simulated annealing Monte
Carlo simulation (SA-MC) of the segment peptide
tethered at its N-terminus only. 2. A Monte
Carlo simulation in the space of the scaled
collective variables (SCV-MC) of the segment,
with an increasing harmonic constraint that
drives the C-terminus towards its attachment
point.
CONCLUSIONS The method developed was shown to
reproduce the qualitative features of the
structures of the segments in the a-subunit of
transducin. Quantitative agreement with the
crystal structure, in terms of RMSD of backbone
atoms was satisfactory for s1, s2, s3, s6 and s8.
For s7 the RMSD was larger, but the overall
conformation of the calculated structure was
still in reasonable agreement with the native
structure. Notably, the known conformations in
the crystal were found to have lower energies
than any of the computed structures. This
indicates that the energy function with the
SCP-ISM is probably correct but that the sampling
method must be improved. Several option are
available to improve the quality of the results.
One approach to be explored is to introduce the
protein structure in a more gradual and
systematic way, especially for segments such as
s4 and s5 that are buried in the protein. For
these segments many steric clashes were observed
when the structures obtained in the SA-MC phase
were combined with the rest of the protein the
sudden introduction of the protein at the start
of the SCV-MC phase introduces a large
perturbation that forces the structure to leave
the initial conformation in an uncontrolled and
irreversible way. The gradual switching on of the
force field of the protein around the segment
would help avoid this problem.
The rationale for this combined process is based
on the assumption that even segments connecting
elements of secondary structural motifs have an
intrinsic propensity for a particular set of
conformations, i.e., there is a specific folding
encoded in its amino acid sequence. In addition
it is assumed that the side chains of the segment
are predominantly exposed to the solvent. The
second part of the process takes the segment from
the initially determined structures and closes it
in the presence of the rest of the protein
(Fig.1).
The calculations were carried out with the
all-atom representation of the CHARMM force field
4 and the recently proposed screened Coulomb
potential based implicit solvent model 3.
Figure 1 Schematic representation of four
successive destabilizations of a local minimum of
the energy surface by an external constraint. The
upper curve shows a minimum corresponding to a
large distance of the C-terminus from the
attachment point, obtained with a relatively
small force constant k1 of the harmonic
constraint. The lower curve represents the shift
of the minimum for complete segment closure,
achieved by a larger value k4 of the force
constant. The relaxation around each local minima
is carried out using a Monte Carlo simulation in
the space of the scaled collective variables of
the segment.
References 1 S Kirkpatrick, C D Gellat Jr and
M P Vechi Science 220, 671 (1983) 2 T Noguti
and N Go Biopolymers 24, 527 (1985) 3 S A
Hassan, F Guarnieri and E L Mehler J. Phys. Chem
B 104, 6478 (2000) ibid 104, 6490 (2000) 4 B R
Brooks et al. J. Comp. Chem. 4, 187 (1983)
MacKerell et al. J. Phys. Chem. B 102, 3586
(1998) 5 A Fiser, R Kinh Gian Do and A Sali
Protein Sci. 9, 1753 (2000) 6 D G Lambright et
al. Nature 379, 311 (1996)