Steering self-organisation through confinement.

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Confinement-induced accumulation and de-mixing of microscopic active-passive mixtures.

Understanding the out-of-equilibrium properties of noisy microscale systems and the extent to which they can be modulated externally, is a crucial scientific and technological challenge. It holds the promise to unlock disruptive new technologies ranging from targeted delivery of chemicals within the body to directed assembly of new materials. Here we focus on how active matter can be harnessed to transport passive microscopic systems in a statistically predictable way. Using a minimal active-passive system of weakly Brownian particles and swimming microalgae, we show that spatial confinement leads to a complex non-monotonic steady-state distribution of colloids, with a pronounced peak at the boundary. The particles' emergent active dynamics is well captured by a space-dependent Poisson process resulting from the space-dependent motion of the algae. Based on our findings, we then realise experimentally the de-mixing of the active-passive suspension, opening the way for manipulating colloidal objects via controlled activity fields.

Pelagic diatoms communicate through synchronized beacon natural fluorescence signaling.

Communication between conspecific individuals is an essential part of life both in terrestrial and marine realms. Until recently, social behavior in marine phytoplankton was assumed to rely mainly on the secretion of a variety of infochemicals that allowed population-scale collective responses. Here, we demonstrate that pelagic diatoms also use Sun-stimulated fluorescence signals for synchronizing their behavior. These unicellular microorganisms, playing a key biogeochemical role in the ocean, use photoreceptor proteins and red­far-red fluorescent radiation to communicate. A characteristic beaconing signal is generated by rhythmic organelle displacement within the cell cytoplasm, triggering coordinated population behavior. These light-based communication networks could critically determine major facets of diatom ecology and fitness and regulate the dynamics of larger-scale ocean processes.

Geometric mixing.

Mixing fluids often involves a periodic action, like stirring one's tea. But reciprocating motions in fluids at low Reynolds number, in Stokes flows where inertia is negligible, lead to periodic cycles of mixing and unmixing, because the physics, molecular diffusion excepted, is time reversible. So how can fluid be mixed in such circumstances? The answer involves a geometric phase. Geometric phases are found everywhere in physics as anholonomies, where after a closed circuit in the parameters, some system variables do not return to their original values. We discuss the geometric phase in fluid mixing: geometric mixing. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Method for the determination of preferential orientation of marine particles from laser diffraction measurements.

In situ laser diffractometry (LD) is increasingly used in oceanographic studies to estimate sediment transport, particle fluxes and to assess the concentration of marine phytoplankton. It enables an accurate characterization of the size distribution of suspended particles from the scattering signal produced by their interaction with a collimated laser beam. LD reliably reflects the sizes of suspensions dominated by nearly spherical particles; however, when complex particle morphologies dominate the suspension (e.g. phytoplankton) the resulting particle size distribution (PSD) may present significant variations attributed to different factors. In particular, the orientation of non-spherical particles - which abound in the sea - modifies LD measurements of PSDs. While this may be interpreted as a drawback for some studies (i.e. when precise measurement of the volume concentration is required), we propose that detailed analysis of this signal provides information on particle orientation. We use PDMS micropillars with prescribed elliptical cross-sections to experimentally determine the dependence between the spatial orientation of elongated particles and changes in the PSD measured with a LISST laser diffractometer. We show that LD can be used to adequately characterize the different dimensions of the non-spherical particles at specific orientations. Using this property, we describe and validate a method to infer the preferential orientation of particles in the sea. Our study opens new perspectives in the use of in-situ LD in ocean research.

Sperm chemotaxis is driven by the slope of the chemoattractant concentration field.

Spermatozoa of marine invertebrates are attracted to their conspecific female gamete by diffusive molecules, called chemoattractants, released from the egg investments in a process known as chemotaxis. The information from the egg chemoattractant concentration field is decoded into intracellular Ca2+ concentration ([Ca2+]i) changes that regulate the internal motors that shape the flagellum as it beats. By studying sea urchin species-specific differences in sperm chemoattractant-receptor characteristics we show that receptor density constrains the steepness of the chemoattractant concentration gradient detectable by spermatozoa. Through analyzing different chemoattractant gradient forms, we demonstrate for the first time that Strongylocentrotus purpuratus sperm are chemotactic and this response is consistent with frequency entrainment of two coupled physiological oscillators: i) the stimulus function and ii) the [Ca2+]i changes. We demonstrate that the slope of the chemoattractant gradients provides the coupling force between both oscillators, arising as a fundamental requirement for sperm chemotaxis.

Chemosensing versus mechanosensing in nodal and Kupffer's vesicle cilia and in other left-right organizer organs.

How is sensing carried out by cilia in the mouse node, zebrafish Kupffer's vesicle and similar left-right (LR) organizer organs in other species? Two possibilities have been put forward. In the former, cilia would detect some chemical species in the fluid; in the latter, they would detect fluid flow. In either case, the hypothesis is that an imbalance would be detected between this signalling coming from cilia on the left and right sides of the organizer, which would initiate a cascade of signals leading ultimately to the breaking of LR symmetry in the developing body plan of the organism. We review the evidence for both hypotheses. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

Light Control of Localized Photobioconvection.

Microorganismal motility is often characterized by complex responses to environmental physico-chemical stimuli. Although the biological basis of these responses is often not well understood, their exploitation already promises novel avenues to directly control the motion of living active matter at both the individual and collective level. Here we leverage the phototactic ability of the model microalga Chlamydomonas reinhardtii to precisely control the timing and position of localized cell photoaccumulation, leading to the controlled development of isolated bioconvective plumes. This novel form of photobioconvection allows a precise, fast, and reconfigurable control of the spatiotemporal dynamics of the instability and the ensuing global recirculation, which can be activated and stopped in real time. A simple continuum model accounts for the phototactic response of the suspension and demonstrates how the spatiotemporal dynamics of the illumination field can be used as a simple external switch to produce efficient bio mixing.

Turbulence induces clustering and segregation of non-motile, buoyancy-regulating phytoplankton.

Turbulence plays a major role in shaping marine community structure as it affects organism dispersal and guides fundamental ecological interactions. Below oceanographic mesoscale dynamics, turbulence also impinges on subtle physical-biological coupling at the single cell level, setting a sea of chemical gradients and determining microbial interactions with profound effects on scales much larger than the organisms themselves. It has been only recently that we have started to disentangle details of this coupling for swimming microorganisms. However, for non-motile species, which comprise some of the most abundant phytoplankton groups on Earth, a similar level of mechanistic understanding is still missing. Here, we explore by means of extensive numerical simulations the interplay between buoyancy regulation in non-motile phytoplankton and cellular responses to turbulent mechanical cues. Using a minimal mechano-response model, we show how such a mechanism would contribute to spatial heterogeneity and affect vertical fluxes and trigger community segregation.

Collective sinking promotes selective cell pairing in planktonic pennate diatoms.

Finding a partner in an inherently unsteady 3-dimensional system, such as the planktonic marine environment, is a difficult task for nonswimming organisms with poor control over their orientation. We experimentally investigate the process of cell pairing in pennate marine diatoms and present field evidence of its occurrence in the ocean. We describe the mechanism as a 3-step process in which pennate diatoms (i) vertically reorient while sinking from surface turbulent waters to a more stable environment (i.e., under the seasonal pycnocline), (ii) segregate from incompatible partners (e.g., dead or different sized cells), and (iii) pair with other partners as a result of the hydrodynamic instabilities generated by collective cell sinking. This is, eminently, a cell abundance-dependent process, therefore being more effective when population sinking is synchronized. We suggest that this selective process, enabling matching of size-compatible healthy partners, could be fundamental in understanding sexual reproduction in pennate diatoms.

Analysis of sperm chemotaxis.

In many species, sperm must locate the female gamete to achieve fertilization. Molecules diffusing from the egg envelope, or the female genital tract, guide the sperm toward the oocyte through a process called chemotaxis. Sperm chemotaxis has been studied for more than 100 years being a widespread phenomenon present from lower plants to mammals. This process has been mostly studied in external fertilizers where gametes undergo a significant dilution, as compared to internal fertilizers where the encounter is more defined by the topology of the female tract and only a small fraction of sperm appear to chemotactically respond. Here, we summarize the main methods to measure sperm swimming responses to a chemoattractant, both in populations and in individual sperm. We discuss a novel chemotactic index (CI) to score sperm chemotaxis in external fertilizers having circular trajectories. This CI is based on the sperm progressive displacement and its orientation angle to the chemoattractant source.

Phototaxis beyond turning: persistent accumulation and response acclimation of the microalga Chlamydomonas reinhardtii.

Phototaxis is an important reaction to light displayed by a wide range of motile microorganisms. Flagellated eukaryotic microalgae in particular, like the model organism Chlamydomonas reinhardtii, steer either towards or away from light by a rapid and precisely timed modulation of their flagellar activity. Cell steering, however, is only the beginning of a much longer process which ultimately allows cells to determine their light exposure history. This process is not well understood. Here we present a first quantitative study of the long timescale phototactic motility of Chlamydomonas at both single cell and population levels. Our results reveal that the phototactic strategy adopted by these microorganisms leads to an efficient exposure to light, and that the phototactic response is modulated over typical timescales of tens of seconds. The adaptation dynamics for phototaxis and chlorophyll fluorescence show a striking quantitative agreement, suggesting that photosynthesis controls quantitatively how cells navigate a light field.

Advection by ocean currents modifies phytoplankton size structure.

Advection by ocean currents modifies phytoplankton size structure at small scales (1-10 cm) by aggregating cells in different regions of the flow depending on their size. This effect is caused by the inertia of the cells relative to the displaced fluid. It is considered that, at larger scales (greater than or equal to 1 km), biological processes regulate the heterogeneity in size structure. Here, we provide observational evidence of heterogeneity in phytoplankton size structure driven by ocean currents at relatively large scales (1-10 km). Our results reveal changes in the phytoplankton size distribution associated with the coastal circulation patterns. A numerical model that incorporates the inertial properties of phytoplankton confirms the role of advection on the distribution of phytoplankton according to their size except in areas with enhanced nutrient inputs where phytoplankton dynamics is ruled by other processes. The observed preferential concentration mechanism has important ecological consequences that range from the phytoplankton level to the whole ecosystem.

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

Microscale patches of nonmotile phytoplankton.

Phytoplankton cells have evolved sophisticated strategies for actively responding to environmental signals, most notably to mechanical stresses of hydrodynamic origin. A largely unanswered question, however, is the significance of these cellular responses for the largely heterogeneous spatial distribution of cells found in the oceans. Motivated by the physiological regulation of buoyancy prevalent in nonmotile phytoplankton species, we solve here a minimal model for "active" sinking that incorporates these cellular responses. Within this model, we show how buoyancy regulation leads to intense patchiness for nonmotile species as compared to passive tracers, resulting in important variations in settling speeds and, as a consequence, determining escape rates to the deep ocean.

Microalgae Scatter off Solid Surfaces by Hydrodynamic and Contact Forces.

Interactions between microorganisms and solid boundaries play an important role in biological processes, such as egg fertilization, biofilm formation, and soil colonization, where microswimmers move within a structured environment. Despite recent efforts to understand their origin, it is not clear whether these interactions can be understood as being fundamentally of hydrodynamic origin or hinging on the swimmer's direct contact with the obstacle. Using a combination of experiments and simulations, here we study in detail the interaction of the biflagellate green alga Chlamydomonas reinhardtii, widely used as a model puller microorganism, with convex obstacles, a geometry ideally suited to highlight the different roles of steric and hydrodynamic effects. Our results reveal that both kinds of forces are crucial for the correct description of the interaction of this class of flagellated microorganisms with boundaries.

Antiphase synchronization in a flagellar-dominance mutant of Chlamydomonas.

Groups of beating flagella or cilia often synchronize so that neighboring filaments have identical frequencies and phases. A prime example is provided by the unicellular biflagellate Chlamydomonas reinhardtii, which typically displays synchronous in-phase beating in a low-Reynolds number version of breaststroke swimming. We report the discovery that ptx1, a flagellar-dominance mutant of C. reinhardtii, can exhibit synchronization in precise antiphase, as in the freestyle swimming stroke. High-speed imaging shows that ptx1 flagella switch stochastically between in-phase and antiphase states, and that the latter has a distinct waveform and significantly higher frequency, both of which are strikingly similar to those found during phase slips that stochastically interrupt in-phase beating of the wild-type. Possible mechanisms underlying these observations are discussed.

Runaway electrification of friable self-replicating granular matter.

We establish that the nonlinear dynamics of collisions between particles favors the charging of an insulating, friable, self-replicating granular material that undergoes nucleation, growth, and fission processes; we demonstrate with a minimal dynamical model that secondary nucleation produces a positive feedback in an electrification mechanism that leads to runaway charging. We discuss ice as an example of such a self-replicating granular material: We confirm with laboratory experiments in which we grow ice from the vapor phase in situ within an environmental scanning electron microscope that charging causes fast-growing and easily breakable palmlike structures to form, which when broken off may form secondary nuclei. We propose that thunderstorms, both terrestrial and on other planets, and lightning in the solar nebula are instances of such runaway charging arising from this nonlinear dynamics in self-replicating granular matter.

Brinicles as a case of inverse chemical gardens.

Brinicles are hollow tubes of ice from centimeters to meters in length that form under floating sea ice in the polar oceans when dense, cold brine drains downward from sea ice to seawater close to its freezing point. When this extremely cold brine leaves the ice, it freezes the water it comes into contact with: a hollow tube of ice-a brinicle-growing downward around the plume of descending brine. We show that brinicles can be understood as a form of the self-assembled tubular precipitation structures termed chemical gardens, which are plantlike structures formed on placing together a soluble metal salt, often in the form of a seed crystal, and an aqueous solution of one of many anions, often silicate. On one hand, in the case of classical chemical gardens, an osmotic pressure difference across a semipermeable precipitation membrane that filters solutions by rejecting the solute leads to an inflow of water and to its rupture. The internal solution, generally being lighter than the external solution, flows up through the break, and as it does so, a tube grows upward by precipitation around the jet of internal solution. Such chemical-garden tubes can grow to many centimeters in length. In the case of brinicles, on the other hand, in floating sea ice we have porous ice in a mushy layer that filters out water, by freezing it, and allows concentrated brine through. Again there is an osmotic pressure difference leading to a continuing ingress of seawater in a siphon pump mechanism that is sustained as long as the ice continues to freeze. Because the brine that is pumped out is denser than the seawater and descends rather than rises, a brinicle is a downward-growing tube of ice, an inverse chemical garden.