Homology recognition funnel

Abstract

The recognition of homologous sequences of DNA before strand exchange is considered to be the most puzzling stage of homologous recombination. A mechanism for two homologous dsDNAs to recognize each other from a distance in electrolytic solution without unzipping had been proposed in an earlier paper [A. A. Kornyshev and S. Leikin, Phys. Rev. Lett. 86, 366 (2001)]. In that work, the difference in the electrostatic interaction energy between homologous duplexes and between nonhomologous duplexes, termed the recognition energy, has been calculated. That calculation was later extended in a series of papers to account for torsional elasticity of the molecules. A recent paper [A. A. Kornyshev and A. Wynveen, Proc. Natl. Acad. Sci. U.S.A. 106, 4683 (2009)] investigated the form of the potential well that homologous DNA molecules may feel when sliding along each other. A simple formula for the shape of the well was obtained. However, this latter study was performed under the approximation that the sliding molecules are torsionally rigid. Following on from this work, in the present article we investigate the effect of torsional flexibility of the molecules on the shape of the well. A variational approach to this problem results in a transcendental equation that is easily solved numerically. Its solutions show that at large interaxial separations the recognition well becomes wider and shallower, whereas at closer distances further unexpected features arise related to an abrupt change in the mean azimuthal alignment of the molecules. The energy surface as a function of interaxial separation and the axial shift defines what we call the recognition funnel. We show that it depends dramatically on the patterns of adsorption of counterions on DNA.