Possible role of electrodynamic interactions in long-distance biomolecular recognition

The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is revisited within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we present a simple method to calculate the frequencies of the normal modes, which are then used to estimate the interaction potential. The possibility that such interactions play a non-negligible role in ensuring the effective functioning of the biomolecular functions is investigated. On the basis of experimental results reported in the literature and simple numerical estimates, it is found that long-range interactions involving electromagnetic fields of frequencies ${\displaystyle 0.1–1\text{THz}}$ could be temporarily activated despite radiation losses and solvent dissipation. Moreover, the theoretical background used to derive the mentioned interactions sheds light on Fröhlich's theory of selective long-range forces between biomolecules. At variance with a long-standing belief, we show that sizable resonant long-range interactions may exist only if the interacting system is out of thermal equilibrium.

Figure 1

(a) Real part of the electric susceptibility matrix elements ${\displaystyle {\chi }_{ii}^{\prime }(r,\omega )}$ computed from Eqs. (4) as a function of the distance ${\displaystyle r}$ (the index ${\displaystyle E}$ on ${\displaystyle {\chi }_{ii}}$ has been omitted to reduce the amount of notation). The parameter values are ${\displaystyle {\varepsilon }^{\prime }\left(\omega \right)=1}$ and ${\displaystyle \omega ={10}^{12}\text{Hz}}$. (b) Same as (a) except that ${\displaystyle \omega =7.24\times {10}^{15}\text{Hz}}$.

Figure 2

Absorbance of water in the terahertz domain (blue). Penetration length as a function of the frequency (red).