Thermodynamic cost of synchronizing a population of beating cilia

Abstract

Synchronization among arrays of beating cilia is one of the emergent phenomena in biological processes at meso-scopic scales. Strong inter-ciliary couplings modify the natural beating frequencies, $\omega$, of individual cilia to produce a collective motion that moves around a group frequency ${\omega }_m$. Here we study the thermodynamic cost of synchronizing cilia arrays by mapping their dynamics onto a generic phase oscillator model. The model suggests that upon synchronization the mean heat dissipation rate is decomposed into two contributions, dissipation from each cilium's own natural driving force and dissipation arising from the interaction with other cilia, the latter of which can be interpreted as the one produced by a potential with a time-dependent protocol in the framework of our model. The spontaneous phase-synchronization of beating dynamics of cilia induced by strong inter-ciliary coupling is always accompanied with a significant reduction of dissipation for the cilia population, suggesting that organisms as a whole expend less energy by attaining a temporal order. At the level of individual cilia, however, a population of cilia with $|\omega |<{\omega }_m$ expend more amount of energy upon synchronization.

6 pages, 3 figures

References in corpus (3)

• Spontaneous creation of macroscopic flow and metachronal waves in an array of cilia
• Nonequilibrium thermodynamics of coupled molecular oscillators: The energy cost and optimal design for synchronization
• Role of spatial heterogeneity on the collective dynamics of cilia beating in a minimal 1D model

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• Thermodynamic precision of a chain of motors: the difference between phase and noise correlation