Limitations on electromagnetic communication by vibrational resonances in biological systems

Previous research in biology and physics speculates that high-frequency electromagnetic fields may be an unexplored method of cellular and subcellular communication. The predominant theory for generating electric fields in the cell is mechanical vibration of charged or polar biomolecules such as cell membranes or microtubules. The challenge to this theory is explaining how high-frequency vibrations would not be overdamped by surrounding biological media. As many of these suspected resonators are too large for atomistic molecular dynamics simulations, accurately modeling biological resonators remains an ongoing challenge. While many resonators have been studied and simulated, the general limitations on communication imposed by energy transfer arguments have not been considered. Starting with energy transfer expressions from coupled-mode theory, we derive expressions for the minimum quality factor ($Q$ factor) required to sustain communication for both near- and far-field interactions. We compare previous simulation studies and our theory. We determine the flexing mode of microtubules as an identified resonance in the literature which meets our criteria. Our results suggest the major obstacle to meeting our criteria for effective electromagnetic communication is the trade-off between the $Q$ factor and the plasma frequency: Resonators must be large enough to have a large $Q$ factor, but small enough to resonate at frequencies greater than the plasma frequency.

Figure 1

Illustration of resonators interacting with electromagnetic fields. (a) Incident field with intensity $I$ scattering off a resonator with scattering (radiative) quality factor $Q_s$ and absorption quality factor $Q_a$. (b) Two resonators with their own quality factors coupled in the near field with coupling coefficient $\kappa$.

Figure 2

Minimum $Q$ factor required for an incoming plane wave of intensity $I$ to impart more energy than $k_{B}T$ on a dipole resonator, plotted as a function of the radius of the smallest sphere enclosing the resonator. The temperature is assumed to be 300 K and the relative permittivity of the media is 80 (water).

Figure 3

Coupled spring mass resonators submerged in fluid. Each resonator has mass $m$, charge $q$, spring constant $k$, and damping coefficient $c$. The medium has permittivity $\epsilon$ and conductivity $\sigma$. At rest, both resonators are separated by a distance $r$.

Figure 4

Minimum $Q$ factor for two identical coupled resonators as a function of frequency for different interresonator coupling strengths $\kappa$. We assume that $T=300$ K and $P_t={10}^{-12}$ W. The value of $\kappa$ in the legend is attenuated as a function of frequency by a factor of $\left|A\right(\omega \left)\right|$.

Figure 5

Minimum $Q$ factor for near-field communication (blue solid line) vs frequency for varying values of $\kappa$. The red circles represent the $Q$ factor of calculated bacteria cell membrane resonances for different bacterial species computed in [14]. The green dotted line represents the calculated $Q$ factor of bending microtubule vibrations as a function of the microtubule length computed in [40]. The cyan cross represents the $Q$ factor of the slip layer radial mode calculated in [45]. Finally, the magenta diamonds represent the $Q$ factor of dipolar modes in viruses [15, 18].

Figure 6

Diagram illustrating the fundamental trade-off of cell-to-cell communication using electrically coupled mechanical resonators. Essentially, the resonator must be large enough to maintain a large $Q$ factor but not so large as to resonate at a frequency below the plasma frequency.