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D. MODEL BUILDING AND REFINEMENT

D. MODEL BUILDING AND REFINEMENT

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Figure 6 Electron density of an a-helix at different resolutions.



amino acid side chains can be readily assigned even in the absence of

sequence information.



E. Understanding Structural Coordinates

Once a crystal structure has been determined, the information is

communicated in the form of an atomic coordinates file. In addition

to a list of the atomic positions, the coordinates file contains other information that deserves an explanation and requires attention by the

user. Some of the terms included in an atomic coordinates file are

explained briefly. It is hoped that the information will provide the reader

with insights to evaluate the quality of the structure, distinguish between

its well-defined and flexible regions, and make sensible decisions in

structural analysis.

The unit cell is the basic microscopic building block of the crystal. A

crystal can be viewed as a three-dimensional stack of identical unit cells,

each defined by three cell edges (a, b, c, in angstroms), and three angles (a,

h, g in degrees) between each pair of edges. Each unit cell may contain one

or more protein molecules related by crystal symmetry. The unique portion

of the unit cell (i.e., the portion that is not related to other portions by

crystal symmetry) is called the asymmetric unit. There are only 230 different

combinations of symmetry elements in crystals; each of these is called a

space group. However, since biological molecules are enantiomorphic,



Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.



which means that a protein crystal cannot contain mirror planes, the

number of space groups of relevance to protein crystallography is reduced

to 65. It is possible to have more than one copy of the same protein in an

asymmetric unit. However, these will be related by ‘‘noncrystallographic’’

symmetry. Therefore, all atoms of an asymmetric unit, along with the unit

cell dimensions and the space group, must be given in the coordinates file

for subsequent analysis and for regenerating the structure in any portion of

the unit cell or the crystal, which may be important for studying intermolecular ‘‘crystal packing’’ interactions.

The R-factor is probably the single most important number that

provides a sense of the overall quality of the structure. It is defined as

[A||Fobs| À k*|Fcalc||] / A|Fobs|, where Fobs is the observed structure factor

(the square root of the measured diffraction intensity or amplitude), Fcalc

is the structure factor calculated from the model, and k is a scaling

factor. The factor R is a measurement of the agreement between the

structural model and the observed diffraction data; the lower the

number, the better. For a refined crystal structure, the R factor is often

approximately 10 times its resolution (e.g., 20% for a 2.0 A˚ resolution

structure). Along with the traditional R factor, most of the recent

structures also report an Rfree value, which is obtained from the part

of the diffraction data (5–10%) set aside and not used during structural

refinement. Generally Rfree is 5–10% higher than R; larger discrepancies

between the two may indicate that there is a problem in the structure

model or diffraction data, or that the structure is overrefined against the

data. Reducing R to below 20% used to be the goal for structural

refinement; but obtaining a sensible Rfree is now considered to be more

important. Therefore, before analyzing a crystal structure on computer

graphics, one should check the R factor and Rfree values to get a sense of

the overall quality of the structure. It is important to note that these

values can be reported as percentages (20%) or as fractions (0.20).

The atomic temperature factor, or B factor, measures the dynamic

disorder caused by the temperature-dependent vibration of the atom, as

well as the static disorder resulting from subtle structural differences in

different unit cells throughout the crystal. For a B factor of 15 A˚2, displacement of an atom from its equilibrium position is approximately 0.44

A˚, and it is as much as 0.87 A˚ for a B factor of 60 A˚2. It is very important

to inspect the B factors during any structural analysis: a B factor of less

than 30 A˚2 for a particular atom usually indicates confidence in its

atomic position, but a B factor of higher than 60 A˚2 likely indicates that

the atom is disordered.



Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.



For a particular crystal, the number of diffraction data increases as

the resolution increases, which means that more experimental data will

be available for structural refinement. There are four parameters to be

refined for each atom: x, y, z (atomic position), and B (temperature

factor). If the crystal has normal solvent content (i.e., about 50%), the

number of experimental data and refinement parameters will be about the

same at 2.8 A˚ resolution. This suggests that B factors for individual

atoms should be refined only when data have a resolution better than 2.8

A˚. Refinement of atomic B factors at lower resolution will have no

physical meaning, although a lower but meaningless R factor will result.

Identification and refinement of solvent molecules (e.g., waters) become

reliable only when the structure has at least a 2.5 A˚ resolution. Even then,

before a water molecule is used in mechanistic or computational analysis,

it is always wise to check its B factor for the existence of at least one

hydrogen bond to hold the water to the protein. At times, spurious water

molecules are added (such additions will result in a meaningless lower R

factor). Unless the structure has been determined at a reasonably high

resolution, electron density and refinement often do not discriminate

between the oxygen and nitrogen atoms of asparagines and glutamines,

or the alternative conformations of histidine side chains. In a detailed

structural analysis, it may be necessary to check alternative conformations of Asn, Gln, or His side chains and decide which one makes more

sense chemically.



V. IN SILICO LEAD GENERATION

Armed with the crystal structure of the protein–ligand complex and upto-date computer modeling software, one can design additional ligands.

Numerous molecular modeling software programs are available for that

purpose. However, it is important to note that current computational

algorithms have their limitations and utilize many approximations. Therefore, while computer modeling software has been proven useful [4,18],

further testing and structural validations are required to identify the best

possible compound.



A. In Silico Screening of Virtual Compound Libraries

Starting with the crystal structure of the target, it is possible to screen for

leads in three-dimensional compound databases such as the Cambridge



Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.



Structural Database [19] or the Chemical Abstracts Service Registry [20],

or convert private databases to 3-D structures by programs such as

CONCORD [21]. Several programs are available for such screening. For

example, DOCK [22] works by using a set of overlapping spheres to create

a complementary image of the ligand binding site and essentially matching

the shape of a putative ligand with that of the image to generate a

‘‘goodness of fit’’ score that is then used to rank the hits identified. Instead

of comparing shapes, the program LUDI [23] uses parameters that

describe hydrogen-bonding potential and hydrophobic complementarity

to match the ligand and its binding site. These programs can rapidly search

through three-dimensional databases of small molecules and rank each

candidate. Typically, the 100 to 200 top-scoring compounds are examined

graphically to identify the best 10 to 50 candidates for experimental testing.

In the case of DOCK, 2 to 20% of these in silico hits may show micromolar

binding affinity [4]. Subsequently, crystallography can be used to optimize

any leads identified.



B. Building Leads from Molecular Fragments

Again starting with the crystal structure of the target, another strategy

is to dock small chemical fragments into the ligand binding site, then

grow the fragment to better complement the binding site. Programs

such as GRID [24], AUTODOCK [25], and MCCS [26] can be used

for the docking step. GRID uses small functional groups to probe the

binding site and evaluate interaction energies by using an empirical

Lennard-Jones energy function, as well as electrostatic and hydrogenbonding terms. AUTODOCK uses simulated annealing for ligand

conformational search to dock small ligands of flexible conformations

onto a rigid binding site and a standard force field for rapid grid-type

energy evaluation. MCSS (multicopy simultaneous search) places thousands of copies of functional groups in the binding site and optimizes

them simultaneously to generate energetically favorable positions and

orientations in a flexible binding site. Once selected, suitable binding

fragments can be built into a single compound by manual modeling or

by using linking programs such as CAVEAT [27], which attempts to

identify a suitable cyclic linker from a database. Alternatively, programs like GroupBuild [28] can search compound libraries for potential leads that have the functional fragments identified by the programs

just described.



Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.



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