Peter Vingaard Larsen
Ph.D. in Applied Mathematics
Valdemarsgade 83,
1665 Copenhagen V
Telephone (Direct): (+45) 6171 0927
E-mail:  peter.vingaard(a)


I have investigated the effect of some geometrical aspects of the DNA molecule in relation with dipole-dipole interaction between base pairs (base pairs can be though of as the building blocks of DNA). This is only possible using a nonlocal description, because dipole-dipole interaction is a long-range interaction in the sense that is occurs between all base pairs and as such it cannot be described by a local model, where only, say, neighboring interactions are considered.

One important feature of the DNA molecule is its ability to separate the two strands of which it consists. This is crucial for protein processing and cell reproduction. The process requires the breaking of hydrogen bonds, but no chemical energy is consumed during it. It turns out that the dipole-dipole interaction together with geometry suggests another way for the needed energy to appear.

The strength of the dipole-dipole interaction is governed by both the relative direction of the dipoles as well as the distance between them (the distance dependence is inversely cubic). Therefore, the twist of the dipoles in the (usually helically shaped) DNA molecule and the curvature of the DNA molecular chain becomes important. This may locally change the energy potential and provide an energy funnel, that may trap the thermal fluctuations that arise due to the body temperature - and thus a sufficient energy level may be provided without chemical energy! We show that this occurs in regions where both the twist and curvature is strong, in accordance with experimental results.

We use an augmented version of the renowned Peyrard-Bishop (PB) model of the DNA molecule. The original PB model did not consider dipole-dipole interaction, but has previously been used to show that strand separation is possible on a straight, untwisted chain - but only at temperatures well above body temperature. Our augmented model with dipole-dipole interaction shows that separation may be initiated at a physically reasonable temperature, when the geometry is favorable.

The physics of the Peyrard-Bishop model results in a set of coupled discrete nonlinear partial differential equations. The solutions were computed with a 4th order Runge-Kutta solver, implemented with C++ and MatLab.