Emergent Run-and-Tumble Behavior in a Simple Model of Chlamydomonas with Intrinsic Noise

Recent experiments on the green alga Chlamydomonas that swims using synchronized beating of a pair of flagella have revealed that it exhibits a run-and-tumble behavior similar to that of bacteria such as E. Coli. Using a simple purely hydrodynamic model that incorporates a stroke cycle and an intrinsic Gaussian white noise, we show that a stochastic run-and-tumble behavior could emerge, due to the nonlinearity of the combined synchronization-rotation-translation dynamics. This suggests the intriguing possibility that the alga might exploit nonlinear mechanics—as opposed to sophisticated biochemical circuitry as used by bacteria—to control its behavior.

💡 Research Summary

The paper investigates the recently observed run‑and‑tumble motion of the green alga Chlamydomonas using a minimalist, purely hydrodynamic framework. Chlamydomonas swims by beating two flagella in a coordinated stroke cycle; experimental work has shown that its trajectories consist of relatively straight “runs” punctuated by abrupt reorientations (“tumbles”), a pattern reminiscent of bacterial chemotaxis. While bacterial tumbling is usually attributed to sophisticated biochemical signaling networks, the authors ask whether a simple physical mechanism could generate comparable stochastic behavior.

To answer this, they construct a low‑dimensional model that couples three dynamical layers: (1) the flagellar beat phases, (2) the synchronization dynamics between the two flagella, and (3) the rigid‑body translation and rotation of the cell body. Each flagellum is represented by a periodic driving force (F_i(t)=F_0\sin(\omega t+\phi_i)) with phase (\phi_i). The interaction between the flagella is modeled by a Kuramoto‑type coupling term (K\sin(\phi_j-\phi_i)), which captures the hydrodynamic torque generated by the flow of one flagellum on the other. Intrinsic fluctuations in the beat cycle are introduced as additive Gaussian white noise (\sigma\xi_i(t)) acting directly on the phase equations: \