Computation of Electron Densities of Proteins by a Classical Electrostatic Model

Principal Investigator

Jill Gready

Division of Biochemistry and Molecular Biology

John Curtin School of Medical Research

A great deal of protein research involves membrane proteins: this comprises proteins with a variable mix of substantial or minimal transmembrane and/or intracellular and/or extracellular domains. Such proteins are typified by cellular signalling proteins including immune system and cytokine receptors, ion channels and transmembrane transporters. However, high-resolution structural determination for such proteins is limited by many problems, in particular in getting crystals for X-ray crystallographic analysis. Hence, there is a strong incentive to attempt to couple protein structure prediction methods with medium resolution structural data from electron microscopy (em) in order to develop atomic level models.

The aim of this project is to develop efficient methods for the calculation of electron densities in proteins. Although such methodology has a number of possible applications, our primary purpose is to calculate densities at arbitrary resolution for comparison with em determinations at different quoted resolutions.

Co-Investigators

Drake Diedrich

Division of Biochemistry and Molecular Biology

John Curtin School of Medical Research

Projects

v54 - PC


What are the results to date and the future of the work?

Simple methods for calculating densities are implemented in standard x-ray crystallography programs such as CCP4 where gaussians of "suitable" width are placed on each atom and densities are added up. However, we are implemening a more sophisticated approach. This is classical with point charges for nuclei and charge distributions for electrons, and with the interaction energy between the components being calculated analytically. The electron distributions may be built up using either gaussian or exponential basis functions, the characteristics of which (height, width, location) can be optimized by minimising the interaction energy. As exponentials have a number of advantages and the integrals are tractable for this model, we are pursuing this approach. Both types of methods (CCP4 and ours) require inversion using fast fourier transform to convert the densities to arbitrary lower resolution.

Work so far has been in methods development and preliminary applications.

1. Energy expressions for the interaction of nuclei with exponentially decaying electron clouds have been derived and coded. Optimization procedures to find optimal parameters are being explored. Computation of low resolution Fourier transforms is very slow, due to the necessity of calculating the value of the electron density at all points on a grid. An analytical method to calculate the transform directly from the model parameters is being derived, which should yield more accurate and faster transforms for comparison with em data.

- Appendix A



2. In order to gain more experience with handling actual em data and identifying any data-related problems we would need to take into account for implementation of the new method, we undertook a study using Henderson's (3D data at two resolutions) and Mitra's em data for bacteriorhodopsin. This work was undertaken by an ANU Vacation Student, Veronique Hermann, using the CCP4 package. One important conclusion was that density maps from low resolution data may contain artifacts - one was observed and its origins investigated.

What computational techniques are used?

The types of methods we are developing as well as standard packages are described above. From the computational viewpoint: Although individual (unoptimized) energies and FFTs are quick to compute, the latter can require large core memories at higher resolutions. However, the optimization and recursive inversion will require a great many steps which is time limiting. Comparison of real data sets or comparison of such data with predicted models will require computation of densities at a relatively large number of resolutions, projections etc.