Previously proteins are represented as a discrete object in a
continuum space:
Protein backbone structures are approximated by polygonal
chains
in R3,
where successive line segments could form any spatial conformation.
To classify local protein structures, another process of
discretization, i.e., clustering
of polygonal chains, is required.
For example, the plane curve on the left is approximated by a polygonal
chain on the right in the figure below:
Approximation by
a polygonal chain
(2) Our Approach
In our method, we quantize
the background space itself:
Local protein backbone structures are approximated by a trajectory of a vector
field
defined on a quantized space.
We could classify local protein structures simply by
computing the second
derivative, and no further quantization is required.
For example, to represent the plane curve on the left (below), the
background space is divided into a collection of triangles. And
the curve is approximated by a trajectory of
triangles as
shown on the right:
