1. Introduction

Protein-protein docking has been a powerful approach to provide structural insights into biological procedures at atomic level [1–4]. Based on the structural information provided by X-ray and NMR, as well as constraints derived from biological data such as mutagenesis observations, protein-protein docking can produce structures and interactions of protein complexes, which helps to illustrate structural mechanism of many biological processes [5–7].

New development in experimental technologies, such as electron microscopy, provides an approach to obtain low-resolution structure information of large molecules and their assemblies [8]. Extracting structure information from these low-resolution maps and obtaining atomic interpretation of the large biomolecular assemblies become a central piece of modern structural biology [9]. This requires molecular modeling to be conducted on these low-resolution maps, as well as high-resolution atomic structures, to maximize the capability in structural biology studies.

On the other hand, as the development of structural biology, molecular modeling is applied to larger and larger biomolecular machineries. As the biology systems become larger, atomic description of molecular system becomes very inefficient and time-consuming. Millions of atoms and their chemical structural become redundant in many of modeling studies. Therefore, it would be very efficient if large biomolecules are simplified to shape objects while ignoring their internal structures. Although molecular flexibility plays important roles in biological activities, in many cases, molecular geometric shapes plus surface properties are sufficient to describe many cellular processes such as molecule assembling and protein-protein binding. In these cases, it is satisfactory to describe large molecules as rigid domains. In some cases certain internal flexibility can be simplified to the motion of several rigid fragments. Therefore, molecular modeling of large biomolecular machinery can be achieved efficiently by simplifying biomolecules with simplified shape objects.

chemical bonds, a map does not have internal chemical structures. Instead, a map represents a spatial distribution of certain properties, typically electron density. This distribution generally is described as scalar values at discrete grid points due to irregularity of the distributions and limit in storage. Figure 1 shows a cartoon of a

The grid of a map object is defined by its starting position, x0, y0, and z0; grid

Because we use map to represent a molecular structure, we use molecular reference to record which molecule this map is representing. Through reference mole-

The distribution property describes the distribution of given property over the space covered by the grid points. This can be the electron density measured in

This is the most widely used map type, which describes the electron density over the space. This type of map is often determined from electron microscopy. It can also be derived from molecular structure based on atomic coordinates and type.

This type of map is solely derived from molecular structures based on a force field. The partial charges of atoms are distributed to their nearest grid points.

Because electrostatic interactions are long ranged, it is difficult to have a map to

j j <sup>x</sup> <sup>þ</sup> <sup>b</sup> , (1)

<sup>1</sup> � j j <sup>X</sup> , (2)

cover a very large space. Instead, we propose to use transformed coordinates:

<sup>X</sup> <sup>¼</sup> <sup>x</sup>

<sup>x</sup> <sup>¼</sup> bX

where x is the real space coordinate, X is the reduced coordinate, and b is a constant controlling the reduction. X will take a range of (�1, 1) to represent a real

The VDW cores provide boundary to avoid overlapping between molecules. The core map is constructed based on the accessibility of a molecular structure. The surface has low core index, while the center has high index (the core indices are

Here are several typical types of map objects used in molecular modeling:

map object. As can be seen, a map objects contains three components.

intervals, dx, dy, and dz; and grid point numbers, nx, ny, and nz.

cule, map object and molecule coordinates become interchangeable.

experiment or properties generated from reference molecules.

2.1 Grid definition

Protein-Protein Docking Using Map Objects DOI: http://dx.doi.org/10.5772/intechopen.83543

2.2 Molecular reference

2.3 Distribution properties

1. Electron density maps

2. Electric charge maps

3. Electric field maps

space of x over ð Þ �∞; ∞ . 4. VDW core maps

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shown as the number in each grid box in Figure 1).

In this work, we introduce map objects to represent molecules with fixed structures to achieve efficient molecular modeling of large molecular systems and to efficiently derive structural information from low-resolution experimental maps. Map objects are designed to work with high-resolution atomic structures so that low-resolution maps are interchangeable with high-resolution atomic structures. A map object represents a property distribution over certain space, while a molecular structure is generally described by the coordinates of a set of atoms. This work describes an efficient approach to handle and manipulate map objects so that efficient molecular modeling of large systems can be performed.
