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Elastic Matching

volume alignment

Since 1999 we evaluate the potential of a flexible volume representation for a fast docking algorithm in the project "Development of efficient Methods for the 1:n Protein Docking Problem with local Flexibility", placed in the context of DFG focus program "Informatikmethoden zur Analyse genomischer Daten".

The Problem of induced fit shows up if two structures, one complexed, the other unbound, are superimposed.

The project will introduce flexibility into the volume representation. Proteins will be modelled as flexible bodies as known from mechanics of elastic solids in physics. Proteins will be allowed to deform their surfaces in order to optimise complementarity.

Deformation is expressed as a vectorfield, describing the displacement of a point in the initial configuration.

The resulting internal (deformation) energy is calculated using formulae known from continuous mechanics. Using the internal energy as measure of deformation yields the advantage of frame indifference, or invariance against pure translation and rotation.

A scoring function evaluates the (improved) complementarity after the deformation on the one hand and internal energy introduced through the deformation on the other. A vectorfield is optimal if it maximises the one and minimizes the other.

System Architecture

The following issues have to be adressed in the future:

  • The global part of the vector field can be used to generate initial paramaters for a new docking hypothesis. Instead of assessing many parameter sets, only a few could be used and the docking protein would ``follow'' a path on the surface of the other towards an energy minimum.
  • Modelling not just homogenous solids, but anisotrope inhomogenous solids. This will allow to consider the specific elasticity introduced by areas that allow for hinge or shear motion. The material paranmeters which describe the solids properties are not constant anymore, but depend on the spatial coordinates. Bending at the hinge would result in way less internal energy than in the densely packed areas.
  • Optimisation should be optimised. If the cost funktion proves to be well behaved, a system of differential equations can explicitly stated and solved. Usually the Finite Element Method is employed for modelling such tasks.

This project is supported by the DFG Research focus for Analysis and interpretation of large genomic data sets.

sneumann@TechFak.Uni-Bielefeld.DE Last Update: 18 Dec 02