3.2 Complex structures from energy optimization

The energy function is designed to have the minimum at the binding conformation. Therefore, it is possible to determine complex structures through minimizing the map interaction energy in cases where the EM complex map is not available. It should be noted that the map object assumes certain rigidity of a molecular object. Certain flexibility of loop region can be accommodated by the low-resolution characters, while large flexibilities like domain movement should be dealt with multiple map objects. Recently, this method was successfully applied in modeling of the peroxiredoxin (Prx) complex [16].

Figure 5 shows the steps to perform an energy-based conformational search to determine complex structures. In this case, no EM map is used. The TCR chains are transferred into property maps that allow interaction between map objects to be

Figure 5. Derive complex structure base on map interactions.

calculated. By searching the minimum interaction energy conformation, the complex structure is determined. The final result is only 0.57 Å away from the X-ray structure. It should be noted that this is an ideal case that the structure of the two chains is taken from the complex and there is no conformational change in this

It is interesting to see that energy-based approach to derive complex structure

Figure 6a shows the electric field of TCR α-chain and β-chain and their complex. Please notice the reduced coordinates are used for the map. The range of (1, 1) for the reduced coordinates covers the range of (∞, ∞) for the regular coordinates. The α-chain has negative field near its top-left and bottom-right areas and positive field near its lower-right and upper-left areas. Correspondingly, the β-chain has positive field at its top-right area and negative field at its bottom area, which are complementary to the α-chain. As a result, the complex map has negative field at its top and bottom areas and positive field at its left and right areas. The symmetric

Figure 6b shows the core indices of TCR α-chain and β-chain and their complex. The high values in the core indices indicate the region further away from surface and are difficult to access. The α-chain and β-chain that show complementary shape are the binding surface. Their complexes are the two maps

Figure 6c shows the electric charge distribution of TCR α-chain and β-chain and

As a further example of protein-protein docking, we show the procedure to build the pentamer of acetylcholine binding protein (AChBP). The monomers

their complex. The α-chain map shows more negative charges at the right side, while the β-chain shows more positive charges at its left side. The complex map shows the two chains come together with negative patches contacting positive patches. Overall, these map interactions provide energetic basis for protein-protein

Protein-protein docking of acetylcholine binding protein (AChBP) to build its pentamer.

takes account of molecular structure and energetic information of molecules. Figure 6a–c shows the electric field, shape, and charge maps of the two chains and their complex. Obviously, the two chains are binding together to have the low potential region matching the high potential one, to have shape complementary to

each other, and to have surface charge overlapped oppositely.

distribution of the field of the complex indicates its stability.

fitting process.

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

matching together.

Figure 7.

73

docking as shown in Figure 5.

#### Figure 6.

(a) Electrostatic field maps of TCR two chains and complexes. (b) Core-index maps of TCR two chains and complex. (c) Partial charge maps of TCR two chains and complexes.

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

calculated. By searching the minimum interaction energy conformation, the complex structure is determined. The final result is only 0.57 Å away from the X-ray structure. It should be noted that this is an ideal case that the structure of the two chains is taken from the complex and there is no conformational change in this fitting process.

It is interesting to see that energy-based approach to derive complex structure takes account of molecular structure and energetic information of molecules. Figure 6a–c shows the electric field, shape, and charge maps of the two chains and their complex. Obviously, the two chains are binding together to have the low potential region matching the high potential one, to have shape complementary to each other, and to have surface charge overlapped oppositely.

Figure 6a shows the electric field of TCR α-chain and β-chain and their complex. Please notice the reduced coordinates are used for the map. The range of (1, 1) for the reduced coordinates covers the range of (∞, ∞) for the regular coordinates. The α-chain has negative field near its top-left and bottom-right areas and positive field near its lower-right and upper-left areas. Correspondingly, the β-chain has positive field at its top-right area and negative field at its bottom area, which are complementary to the α-chain. As a result, the complex map has negative field at its top and bottom areas and positive field at its left and right areas. The symmetric distribution of the field of the complex indicates its stability.

Figure 6b shows the core indices of TCR α-chain and β-chain and their complex. The high values in the core indices indicate the region further away from surface and are difficult to access. The α-chain and β-chain that show complementary shape are the binding surface. Their complexes are the two maps matching together.

Figure 6c shows the electric charge distribution of TCR α-chain and β-chain and their complex. The α-chain map shows more negative charges at the right side, while the β-chain shows more positive charges at its left side. The complex map shows the two chains come together with negative patches contacting positive patches. Overall, these map interactions provide energetic basis for protein-protein docking as shown in Figure 5.

As a further example of protein-protein docking, we show the procedure to build the pentamer of acetylcholine binding protein (AChBP). The monomers

Figure 7. Protein-protein docking of acetylcholine binding protein (AChBP) to build its pentamer.

Figure 6.

72

(a) Electrostatic field maps of TCR two chains and complexes. (b) Core-index maps of TCR two chains and

complex. (c) Partial charge maps of TCR two chains and complexes.

Molecular Docking and Molecular Dynamics

low-energy complex structures, for example, in protein-protein docking. By replacing high-resolution atomic structure with low-resolution map objects, this work creates a convenient approach to extend the molecular modeling studies to large biomolecular machinery. This map-based approach can extend modeling and simulation objects from molecular systems to macroscopic systems like cells

This research was supported by the Intramural Research Programs of National

The authors declare there is no conflict of interest in publishing this work.

Heart, Lung, and Blood Institute (Z01 HL001027-34).

and bacteria.

Acknowledgements

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

Conflict of interest

Author details

75

Xiongwu Wu\* and Bernard R. Brooks

provided the original work is properly cited.

\*Address all correspondence to: wuxw@nhlbi.nih.gov

Laboratory of Computational Biology, NHLBI, NIH, Bethesda, MD, USA

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Figure 8. Electric field map at each docking stage to build the pentamer of acetylcholine binding protein (AChBP).

are docked one by one to form dimer, trimer, tetramer, and pentamer (Figure 7). The resulting pentamer is only 0.73 Å away from the X-ray structure, 1I9B. The electric field maps during the building process are shown in Figure 8. From the field map of the monomer, we can see the most positive field is at the top-right area and the most negative field is at the bottom-left area. A dimer is formed by matching the positive area of the second monomer with the negative area of the first one. The third monomer's positive area fits into the most negative area of the dimer to form the trimer. Similarly, the fourth and fifth monomers are docked to form the tetramer and pentamer. The map interaction limits the way of docking monomers and allows correct assemblies to be built.

Map objects cannot only be used to model rigid proteins [17], they can also be used for targeted conformational search such as flexible fitting and restrained molecular dynamics [18, 19]. Map objects provide an efficient bridge from molecular systems to large-scale bodies such as cells and organelles.

## 4. Conclusions

This work designed and developed a computational tool to manipulate map information for molecular modeling studies. Protein–protein docking can be efficiently performed with map objects. This tool is implemented into CHARMM, as a module, EMAP, and into AMBER in its SANDER program. Our design and implementation make it very flexible and efficient to perform various manipulations of map objects and to perform some routine task related to map data. This module enables user to construct macromolecular assemblies by docking high-resolution X-ray or NMR structures to low-resolution cryo-electron microscopy maps. And when there is no EM map available, this module allows user to search for

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

low-energy complex structures, for example, in protein-protein docking. By replacing high-resolution atomic structure with low-resolution map objects, this work creates a convenient approach to extend the molecular modeling studies to large biomolecular machinery. This map-based approach can extend modeling and simulation objects from molecular systems to macroscopic systems like cells and bacteria.
