Occupation-Dependent Access to Metabolic Energy in Fröhlich Systems

Abstract

Fröhlich systems model ensembles of electromagnetic-radiation-emitting molecular oscillators residing inside biological cells. The core piece of this theory are rate equations for the quantum-mechanical occupation numbers of the collective oscillation modes that take into account the flow of metabolic energy through the ensemble. In continuation of prior study of feedback patterns implicit in this model, oriented multigraphs representation is used to investigate the case when the pumping source—in analogy with the effect of spectral hole burning in injection lasers—exhibits depletion phenomena dependent on occupation numbers and the eigenfrequencies of the modes. As a result, in comparison with the case when all modes have equal access to pumping source, the onset of energy condensation in the fundamental mode is shifted to higher pumping levels and new feedback loops appear in the representative diagram. The modified theory provides a more realistic description of electromagnetic emission in biological cells.