Calculating a 3D map from topographic surface images

The atomic force microscope produces a topographic map of the surface of a specimen convolved with the shape of the tip.

A 2D image is interpreted as height data defining the edge of an envelope in 3D space. To ensure a smooth appearance when isosurfaced, this edge is generated using a function which approximates the integral of a Gaussian function:

AFM 3D eq

where σ is very similar to the Gaussian width parameter sigma, a = 1.618 and h(x,y) is the height value at pixel (x,y) in the topographic image. The expansion of a 2D image to a 3D edge or surface requires at a minimum the specification of the new z dimension (in pixels), the range of surface convolution (in Å), and the sampling (in Å/pixel):

Surface expansion

bsurf -v 7 -expand 20 -pos 13,17 -sam 1.5 -resol 3.5 -inv brcy1.tif brcy1.mrc

This command line will generate a volume, 20 voxels thick and with the minimum and maximum of the surface placed at 13 and 17 angstrom, respectively. The resolution option smooths the edge.

Bacteriorhodopsin example

The required starting files for this example:


These include the cytoplasmic and extracellular AFM topographs of bacteriorhododopsin crystals:

Bacteriorhodopsin AFM topographs

These topographs were used to generate the two surfaces:

bsurf -v 7 -expand 80 -pos 67,75 -sam 1 -ori 62,62,40 -resol 3.5 wt_cyt.tiff wt_cyt.mrc

bsurf -v 7 -expand 80 -pos 56,61 -sam 1 -ori 62,62,40 -resol 3.5 wt_ext.tiff wt_ext.mrc

The extracellular surface was then rotated to bring it into the same frame as the cytoplasmic surface:

bint -verb 7 -rot 0,1,0,180 -fill 0 wt_ext.mrc wt_ext_rot.mrc

These surfaces were then combined into one volume:

bop -verb 7 -small 1,0 wt_ext_rot.mrc wt_cyt.mrc wt_2surf.mrc

The result is a volume bounded by the two surfaces. The atomic structure of the bacteriorhododopsin trimer (1QHJ) was then position between the surfaces, with the top surface facing the cytoplasm:

A bacteriorhodopsin trimer between two surfaces