Motor shot noise explains active fluctuations in a single cilium

Mesoscopic fluctuations reveal stochastic dynamics of molecules in both inanimate and living matter. We investigate how small-number fluctuations shape the collective dynamics of molecular motors using motile cilia as model system. We theoretically show that fluctuations in the number of bound motors are sufficient to explain experimentally observed fluctuations, including correlation length and ``phase slips’’ of intra-cilium synchronization. Our findings constrain theories of motor control and establish a link between microscopic motor noise and mesoscopic non-equilibrium dynamics.

💡 Research Summary

This paper presents a comprehensive theoretical study that bridges the gap between microscopic stochasticity and mesoscopic dynamics in biological systems, using the motile cilium as a paradigm. The core thesis is that fluctuations in the small number of bound molecular motors—termed “motor shot noise”—are sufficient to explain the active fluctuations observed in the beating of a single cilium.

The research builds upon a deterministic “dry axoneme” model, which describes ciliary beating through the coupled dynamics of filament sliding and motor activity, while neglecting hydrodynamic forces due to dominant internal dissipation. The key innovation is the extension of this mean-field model into a fully stochastic framework. Here, the continuous motor binding fraction is replaced by discrete, independent Poisson processes for individual motors that randomly attach and detach with force-dependent rates. This introduces intrinsic noise stemming from the finite number of motors.

Through extensive simulations, the study maps out distinct dynamical regimes—no oscillation (NO), standing waves (SW), and traveling waves (TW)—as functions of motor activity and, crucially, motor number (N). A central finding is that motor noise actively influences pattern selection: increasing noise (decreasing N) shifts the boundary between SW and TW regimes to higher activity levels and can even suppress the TW state entirely. The quality factor (Q) of oscillations scales as Q ∝ N, directly linking macroscopic regularity to microscopic copy number.

The model is rigorously tested against experimental data from partial motor extraction experiments. It successfully reproduces the observed decrease in beat amplitude, quality factor, and intra-cilium phase correlation length upon reducing motor numbers, while the wavelength remains roughly constant. However, it fails to capture the experimental trend in beat frequency, revealing a limitation of the underlying feedback mechanism. By employing simulation-based inference on the stochastic model, the authors derive a new set of parameters that improve agreement with experimental fluctuation data.

Furthermore, the study identifies and analyzes “phase slips” or defects within a single cilium, where the local phase of oscillation becomes discontinuous along the axoneme. The rate of these topological defects increases with motor extraction, a trend corroborated by experimental observations. The model also allows estimation of the energetic cost of beating, indicating that internal dissipation dominates over hydrodynamic power output, and suggests the model may overestimate internal damping due to its low predicted susceptibility to external flow.

In summary, this work establishes that motor shot noise is a fundamental and sufficient source of active fluctuations in ciliary beating. It provides a quantitative framework connecting stochastic molecular processes to emergent, noisy oscillations at the cellular scale. The findings constrain theories of motor coordination and highlight the measurement of active fluctuations (Q, phase slips, correlation length) as a powerful tool for probing the internal control mechanisms of biological oscillators.