2. Method and design

We introduce map objects to represent space occupation of molecular structures. Unlike chemical description of molecules that contain atoms that are linked by

Figure 1. A map object and its properties.

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

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

### 2.1 Grid definition

On the other hand, as the development of structural biology, molecular modeling

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 effi-

We introduce map objects to represent space occupation of molecular structures.

Unlike chemical description of molecules that contain atoms that are linked by

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.

cient molecular modeling of large systems can be performed.

2. Method and design

Molecular Docking and Molecular Dynamics

Figure 1.

64

A map object and its properties.

The grid of a map object is defined by its starting position, x0, y0, and z0; grid intervals, dx, dy, and dz; and grid point numbers, nx, ny, and nz.

## 2.2 Molecular reference

Because we use map to represent a molecular structure, we use molecular reference to record which molecule this map is representing. Through reference molecule, map object and molecule coordinates become interchangeable.

#### 2.3 Distribution properties

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 experiment or properties generated from reference molecules.

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

1. Electron density maps

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.

#### 2. Electric charge maps

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.

#### 3. Electric field maps

Because electrostatic interactions are long ranged, it is difficult to have a map to cover a very large space. Instead, we propose to use transformed coordinates:

$$X = \frac{x}{|\mathbf{x}| + b},\tag{1}$$

$$\mathfrak{x} = \frac{bX}{1 - |X|},\tag{2}$$

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 space of x over ð Þ �∞; ∞ .

4. VDW core maps

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