A ciliate memorizes the geometry of a swimming arena

Abstract

Previous studies on adaptive behaviour in single-celled organisms have given hints to the origin of their memorizing capacity. Here we report evidence that a protozoan ciliate Tetrahymena has the capacity to learn the shape and size of its swimming space. Cells confined in a small water droplet for a short period were found to recapitulate circular swimming trajectories upon release. The diameter of the circular trajectories and their duration reflected the size of the droplet and the period of confinement. We suggest a possible mechanism for this adaptive behaviour based on a Ca(2+) channel. In our model, repeated collisions with the walls of a confining droplet result in a slow rise in intracellular calcium that leads to a long-term increase in the reversal frequency of the ciliary beat.

Keywords: Hodgikin Huxley equation; ion channel; mathematical modelling; memory; tetrahymena.

Figure 1.

Typical swimming trajectories of Tetrahymena before and after the confinement: (a1) in a wide, open space before confinement in a small space; (a2–a4) in the confined space of a spherical droplet of diameter 0.3 mm; (a5, a6) in an open space after confinement. Solid and dashed lines show the trajectories of swimming and the shape of the confined space, respectively. (b1–b3) Statistical occurrence of maximum distance (MD) in the function of τ at the diameter of droplet, 0.3 mm. Grey level indicates a normalized frequency according to the grey chart on the right. (c,d) Dependence of the diameter of circular motion on the diameter of the confined space experienced, re-drawn from (c). The left numbers in each panel of (c) indicate the diameters of the confined space (mm), and the numbers in parentheses on the right indicate the number of experiments, number of results of type (a5), (a6), number of circular trajectories count, total observation time in minute for counting the circular trajectory. The error bars in (d) represent the standard error. The dashed line indicates where the two diameters are equal. Number of results of type (a5), (a6) (diameter of droplet, mm): 15(0.3), 13(0.4), 14(0.5), 11(0.6).

Figure 2.

Schematic of mathematical description of swimming motion for free swimming (a1) and when in contact with the vessel wall (a2). Simulation of normal free swimming in the case of an excitable u₁ (b1–b3). (b1) Typical trajectory of swimming. (b2) Time course of u₁. The noise-induced spikes P1, P2 and P3 correspond to the turning events P1, P2 and P3, respectively, in (b1). (b3) A typical trajectory of a spike in the state space of u₁ and v. The solid line is the solution trajectory, and the dotted and the dashed lines are the null clines for u₁ and v, respectively.

Figure 3.

Mathematical modelling for swimming behaviour during and after confinement. Numerical simulations in the case of excitable u₁ (I = 0.0)(a1–a3) and in the case of oscillatory u₁ (I = 0.15)(b1–b3). Trajectories during (a1,b1) and after (a2,b2) the confinement. Time courses of key variables (a3,b3) and the confinement ended at time 900. The parameters for both cases were as follows: vessel size = 0.2 mm, , ɛ = 0.0001, s = 0.003, τ_u = 0.0025, τ_v = 20, a₁ = −0.3, a₂ = −1, a₃ = 4, b₀ = 1, b₁ = 5, φ₀ = 40° and . (a1,a2,b1,b2) Drawn to the same scale. (c) Simulated relationship between the diameter of the confined space and that of the circular trajectory just after confinement. The dashed line indicates where the two diameters are equal. All parameters were the same as (c). (d) Schematic of geometrical analysis of the relationship between the two diameters. See the main text for details.