NMR Structure Determination by Conformational Space
Annealing
Jinhyuk Lee 1 , Jinwoo Lee 2 and Jooyoung Lee 1
1) School of Computational Sciences and Center for In Silico Protein Science, Korea Institute
for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul 130-722, Korea.
2) Department of Mathematics, Kwangwoon University, 447-1, Wolgye-Dong, Nowon-Gu,
Seoul 139-701, Korea.
Corresponding Author : Jooyoung Lee, jlee@kias.re.kr
ABSTRACT
We have carried out numerical experiments to investigate the applicability of global optimization method to the NMR structure determination. Since the number of NMR observables is
relatively small in the early stage of NMR structure determination process and long range NOE
observables are difficult to obtain, advanced sampling techniques are greatly in need to generate
valid NMR structures from a small number of experimental restraints. By utilizing conformational space annealing method, we have determined solution NMR structures from NOE distance and backbone dihedral restraints. Several solution NMR structures are determined starting
from fully randomized conformations. We have evaluated them by measuring the qualities of
determined structures, such as structure convergence of ensemble, Ramachandran preferences,
clash scores, and the total NOE violation. These qualities are compared to those from the corresponding PDB structures.
NMR STRUCTURE DETERMINATION
In 3D structure determinations of proteins in solution by NMR (Nuclear Magnetic Resonance)
spectroscopy, the key experimental data are upper limits derived from nuclear Overhauser effects (NOEs)[1]. To extract distance constraints from a nuclear Overhauser effect spectroscopy
(NOESY) spectrum, its crosspeaks have to be assigned. The NOESY assignment is based on
previously determined chemical shift values that result from chemical shift assignment. The
calculation of the 3D structure in the condition of satisfying these distance constraints forms
a cornerston of the NMR method for protein structure determination. Briefly, Fig. 1 shows the
illustration of 3D NMR protein structure determination.
Because a protein consists of more than 1000 atoms, which are restrained by a similar number of experimentally determined constraints in addition to stereochemical and steric clashes,
it is necessary for improved sampling/search algorithms to search all of possible confromational space of conformations. Improved/efficient sampling in conforamtional space on NMR
structure calculation is expected to improve the quality of the final structures and decrease the
amount of distance constraints violated from the experiments. Since the type of various applications that can be addressed with a particular model depends on its accuracy,i.e., model quality,
high quality structures can be helpful in biology, as identifying active and binding sites, designing and improving ligands for a given binding site, modeling substrate specificity, simulating
protein-protein/ligand docking, and finally designing putative drugs.
Figure 1. Protein Structure Determination using NMR Data
GLOBAL OPTIMIZATION METHOD
The calculation of the 3D structure is formulated as a global minimization/optimization for a
target function, where in a structure calculation a potential energy function in addition of the
experimentally derived constraints, that measures the agreement between a structure and the
given set of constraints. The target function is defined such that it is zero if all experimental
distance constraints (and torsional angle constraints if necessary) are satisfied. A conformation
that satisfied the constraints more closely than another one will lead to a lower target function
value. The target function U on the 3D-structure calculation in this study is defined
U = UC + wN UN + wD UD
(1)
where UC is a general potential energy in CHARMM22 force field [2] with implicit solvation model, and wN and wD are weighting factors (or force constants) for NOE distance and
backbone dihedral angle constraints, respectively. UN is a harmonic flat-bottom NOE restraint
potential with a soft asymptote [3]. Distance summation (r = (Σj rj−6 )−1/6 ) was used for NOE
restraints that involve more than two protons. Backbone dihedral restraints were applied using
a simple periodic potential with minimum backbone dihedral angles. Weighting factors of 10
kcal/mol/Å2 for UN and 10 kcal/mol/rad2 for UD were used during CSA process.
General global optimization algorithm in NMR structure calculation is based on the idea
of simulated annealing by molecular dynamics simulation. The distinctive feature of molecular
dynamics simulation when compared to the minimization of a target function is the presence
of kinetic energy that allows overcoming barriers of the potential energy surface, which reduces greatly the problem of becoming trapped in local minima. A Monte Carlo Minimization
(MCM) method is also developed to overcome the multiple-minima problem [csa/50,csa/14].
After a random conformational change, the system energy is minimized prior to acceptance or
rejection of a trial structure. The Metropolis criterion surmounts intervening barriers in moving through successive discrete local minima in the multidimensional energy surface. The final
approach of solving a global optimization problems is conformational space annealing (CSA)
which was developed by J. Lee et.al. [4]. The CSA searches the whole conformational space
in its early stages and then narrows the search to smaller regions with low energy (“annealing
step”) as a distance cutoff, Dcut , which defined the similarity of two conformations, typically
used Hamming distance and RMSD of two conformations, is reduced. The method combines
essential aspects of the build-up procedure [5] and the genetic algorithm [6]. Instead of considering of a single conformation, attention is focused on a population of conformations, which is
called “bank”. The CSA finds not only the global minimum energy conformation but also many
other distint local minima as by-products. The CSA method were successfully applied various
optimization problems, such as finding the lowest configurations of Lennard-Jones clusters to
201 atoms [7], off-lattice protein AB models in two and three dimensions [8], and the most
stable complex consisting of a receptor and its ligand in molecular docking problem [9] and
multiple sequence alignment [10].
Recently, the CSA method has been implemented into a general molecular dynamics program, CHARMM (Chemistry at HARvard Macromolecular Mechanics) [11], which is called
CHARMMCSA. CHARMM have versatility and can utilize many modules such as molecular
dynamics, energy minimization with the physical-based potential energy and with many types
of restraints, various analyses and coordinate maninuplation routines etc. CSA will be available
in the next official version of CHARMM.
Figure 2. Comparison of two structure qualities in PDB 2kdy. Clash scores numbered below
Figs a) and b) and Ramachandran outliers numbered below Figs c) and d) in the first NMR
model deposited in PDB (two left structures) and the first model by the current study (two right
structures). The red dots in a) and b) represent atomic clashes, and the red thick lines in c) and
d) represents the regions of Ramanchandran outliers in structures. These calculations are run by
MolProbity [12].
A CASE STUDY
We performed numerical experiments to examine the applicability of CSA method to the NMR
structure determination and evaluated the final structures in terms of model qualities, such as
structure convergence of ensemble, Ramachandran preferences, clash scores (the number of
violated atoms per 1000 atoms), total NOE violations and total backbone dihedral angle violations. As a numerical case study, we determined the structures named the Meningococcal
Vaccine Candidate LP2086, PDB entry: 2kdy. It is a family of outer membrane lipoproteins
from Neisseria meningitidis, which elicits bactericidal antibodies and are currently undergoing
human clinical trials in a bivalent formulation. Compared with the structures deposited in PDB,
our determined structure shows successful result. Fig. 2 shows comparison of structure qualities: clase scores, Ramachandran outliers. The clashscore is reduced from 275 to 1 atoms and
the Ramachandran outlier is decreased from 10 to 3 percent, indicating that using identical NOE
distance and backbone dihedral angle restraints, we have generated better quality structure than
PDB structure.
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