Geometric phase shifts in biological oscillators

Many intracellular processes continue to oscillate during the cell cycle. Although it is not well-understood how they are affected by discontinuities in the cellular environment, the general assumption is that oscillations remain robust provided the period of cell divisions is much larger than the period of the oscillator. Here, I will show that under these conditions a cell will in fact have to correct for an additional quantity added to the phase of oscillation upon every repetition of the cell cycle. The resulting phase shift is an analogue of the geometric phase, a curious entity first discovered in quantum mechanics. In this letter, I will discuss the theory of the geometric phase shift and demonstrate its relevance to biological oscillations.