Skip to main content

The biophysics of cytoplasmic streaming in Chara corallina

Final Report Summary - CYCLOSIS (The biophysics of cytoplasmic streaming in Chara corallina)

Cell behaviour, from unicellular organisms to complex tissues, results from the interaction between evolutionary processes shaping the cells' structures, and physical laws governing their environment. One of the best examples of direct interaction between a cell and its physical environment is given by the flagellum, a 10-20 μm long hair-like organelle highly conserved across eukaryotic species. The most evident characteristic of flagella is their incessant beating motion, by which they exert a net force on the extracellular environment. This can be used for locomotion (e.g. in sperm cells), or for active transport in ciliated tissues (e.g. mucus clearance by ciliated epithelium in mammalian respiratory tract). The resulting flows are also involved in the establishment of embryonic left-right asymmetry, and may have even played a role in the development of multicellularity. At the same time, and perhaps more surprisingly, cells use these antenna-like organelles to probe both chemical and mechanical properties of the surrounding environment.

This perceptive ability is of crucial importance: in humans, for example, malformations that cause impaired mechanosensing in ciliated cells of the kidneys lead to polycystic kidney disease. Hydrodynamics plays a key role in mediating the interaction between flagellar motion and mechanical perception. Hydrodynamic forces are certainly involved in direct interactions among individual microorganisms, for example by giving a microswimmer clues about the presence of possible preys or predators. It is conjectured that they play also a role in the establishment of interflagellar coordination, often of paramount importance to perform flagellar functions successfully. Yet, despite its importance there's still little direct experimental knowledge of the detailed hydrodynamics around flagellated microorganisms.

The project tackled this problem by studying flagellar dynamics and swimming in the Volvocales, an order of flagellated green algae. Working with species in this group presents many advantages: they are easy to grow and manipulate in the laboratory, their life cycle is short (one to two days), and it is possible to clearly follow the motion of both individual flagella and single cells for extended periods of time. Volvocalean species include the 10 μm-wide unicellular biflagellate Chlamydomonas reinhardtii (Chlamydomonas), which is the preferred model organism for biological studies of the eukaryotic flagellum. Other species consist of increasingly complex associations of Chlamydomonas-like cells, from small (4-32 cells) undifferentiated colonies, like Gonium pectorale, up to 500 µm-diameter spheroids, like Volvox carteri (Volvox), characterised by a complete tissue differentiation between an external layer of thousands of biflagellate somatic cells, responsible for locomotion, and few (∼10) non-flagellated reproductive cells in the interior.

As a first step, I studied the dynamics of the two flagella of individual cells of Chlamydomonas. Flagellar synchrony is sporadically interrupted by 'slips', short asynchronous periods lasting only a few beats, where one of the two flagella moves faster than the other. This behaviour was recognised previously, but its origin and importance was unknown. Exploring the beating dynamics of Chlamydomonas in detail, we discovered that each cell stochastically switches over the course of time between two regimes. The first is characterised by synchronous beating with occasional slips. In the second, the two flagella beat asynchronously for hundreds of cycles with a large frequency difference. We showed that the dynamics during the first regime, which includes more than 95 % of the time, is consistent with a low-dimensional model of coupled noisy phase oscillators.

Despite its simplicity, the model successfully predicts interflagellar phase-lag during synchrony, the average length of a synchronous period, and the average trajectory during a slip event. Slips correspond to noise induced phase diffusion, a well known phenomenon in the study of coupled oscillators, whose appearance in eukaryotic flagella had not been anticipated by theory. Taken together, these results show for the first time the importance of noise in the coordination of eukaryotic flagella. Furthermore, the interflagellar coupling, responsible for synchronization, is in excellent agreement with that expected from hydrodynamic interactions. This gives one of the strongest supports available to the hypothesis of a hydrodynamic origin of flagellar synchronisation, and suggests that physics plays a major role in the regulation of this behaviour.

The stochastic switching between synchronous and asynchronous regimes has clear consequences on the swimming trajectories of individual Chlamydomonas cells, and ultimately on the behaviour of a whole population. Comparing microscopic data on the beating of individual flagella with three dimensional reconstructions of swimming trajectories of isolated cells, we provided strong evidence that periods of asynchronous flagellar beating correspond to localised events of sharp reorientations in otherwise almost straight paths. This pattern should lead to macroscopic diffusion. The diffusion constant can be estimated directly from the microscopic details of individual swimming trajectories, and agrees remarkably well with the value measured from experiments on large populations, when the concentration is sufficiently low that direct interactions among individual swimmers are, on average, negligible.

As we move to suspensions with higher concentrations of swimmers, however, the flow that each creates will begin to influence the motion of others. This can have striking macroscopic effects like in the case of bioconvection, where high concentrations of swimmers on a thin layer at the water-air interface leads to the development of macroscopic downwelling plumes.

In order to understand and model the interactions among individual microswimmers it is essential to know the flow generated by a freely swimming microorganism, both in the near-field and far away. While extensively studied theoretically, these flows had not yet been measured in detail around any microorganism. In the last part of the project we performed the first such measurements.

We measured the flow field around Volvox, an example of relatively large microorganism, and around Chlamydomonas, widely regarded as a prototypical microswimmer. In the case of Volvox, our most significant finding is that the flow field is strongly dominated by a long range monopolar component, representing the effect of the weight of the organism, despite a density excess of a mere ∼0.3 %, much smaller than that of common unicellular organisms (∼5-10 %). This shows that in terms of hydrodynamic couplings a suspension of Volvox is like a sedimenting suspension, except that the velocity of each colony is the sum of a self-propelled contribution and mutual advection in the flow field of other spheroids.

The flow around Chlamydomonas can be described quantitatively by a simple model which treats the two flagella as point forces which lends experimental support to the widely used point-force approximation in modelling flagellar interactions. Our results indicate that the commonly accepted approximation of a simple force dipole is valid only at large distances, where the fluid velocity is less than 1 % of the swimming speed. We then expect interactions with other swimmers, boundaries or tracers, to be influenced mostly by the flow structure at shorter separations.