Linear systems analysis of the ciliary steering behavior associated with negative-phototaxis inChlamydomonas reinhardtii

Optimal motility strategies for self-propelled agents to explore porous media

Microrobots for, e.g., biomedical applications, need to be equipped with motility strategies that enable them to navigate through complex environments. Inspired by biological microorganisms we re-create motility patterns such as run-and-reverse, run-and-tumble, or run-reverse-flick applied to active rodlike particles in silico. We investigate their capability to efficiently explore disordered porous environments with various porosities and mean pore sizes ranging down to the scale of the active particle. By calculating the effective diffusivity for the different patterns, we can predict the optimal one for each porous sample geometry. We find that providing the agent with very basic sensing and decision-making capabilities yields a motility pattern outperforming the biologically inspired patterns for all investigated porous samples.

Channelrhodopsins: From Phototaxis to Optogenetics

Channelrhodopsins stand out among other retinal proteins because of their capacity to generate passive ionic currents following photoactivation. Owing to that, channelrhodopsins are widely used in neuroscience and cardiology as instruments for optogenetic manipulation of the activity of excitable cells. Photocurrents generated by channelrhodopsins were first discovered in the cells of green algae in the 1970s. In this review we describe this discovery and discuss the current state of research in the field.

Phototaxis of Chlamydomonas arises from a tuned adaptive photoresponse shared with multicellular Volvocine green algae

A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse of micropipette-held Chlamydomonas with 3D tracking of freely swimming cells, we show that such tuning also underlies its phototaxis. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of timescales between the flagellar photoresponse and phototurning, we develop an equation of motion that accurately describes the observed photoalignment. In showing that the adaptive timescales in Volvocine algae are tuned to the organisms' rotational periods across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium, and the flagellated hemispheres of Volvox.

Photo-bioconvection: towards light control of flows in active suspensions

The persistent motility of individual constituents in microbial suspensions represents a prime example of the so-called active matter systems. Cells consume energy, exert forces and move, overall releasing the constraints of equilibrium statistical mechanics of passive elements and allowing for complex spatio-temporal patterns to emerge. Moreover, when subject to physico-chemical stimuli their collective behaviour often drives large-scale instabilities of a hydrodynamic nature, with implications for biomixing in natural environments and incipient industrial applications. In turn, our ability to exert external control of these driving stimuli could be used to govern the emerging patterns. Light, being easily manipulable and, at the same time, an important stimulus for a wide variety of microorganisms, is particularly well suited to this end. In this paper, we will discuss the current state, developments and some of the emerging advances in the fundamentals and applications of light-induced bioconvection with a focus on recent experimental realizations and modelling efforts. This article is part of the theme issue 'Stokes at 200 (part 2)'.

Motility and phototaxis of Gonium, the simplest differentiated colonial alga

Green algae of the Volvocine lineage, spanning from unicellular Chlamydomonas to vastly larger Volvox, are models for the study of the evolution of multicellularity, flagellar dynamics, and developmental processes. Phototactic steering in these organisms occurs without a central nervous system, driven solely by the response of individual cells. All such algae spin about a body-fixed axis as they swim; directional photosensors on each cell thus receive periodic signals when that axis is not aligned with the light. The flagella of Chlamydomonas and Volvox both exhibit an adaptive response to such signals in a manner that allows for accurate phototaxis, but in the former the two flagella have distinct responses, while the thousands of flagella on the surface of spherical Volvox colonies have essentially identical behavior. The planar 16-cell species Gonium pectorale thus presents a conundrum, for its central 4 cells have a Chlamydomonas-like beat that provide propulsion normal to the plane, while its 12 peripheral cells generate rotation around the normal through a Volvox-like beat. Here we combine experiment, theory, and computations to reveal how Gonium, perhaps the simplest differentiated colonial organism, achieves phototaxis. High-resolution cell tracking, particle image velocimetry of flagellar driven flows, and high-speed imaging of flagella on micropipette-held colonies show how, in the context of a recently introduced model for Chlamydomonas phototaxis, an adaptive response of the peripheral cells alone leads to photoreorientation of the entire colony. The analysis also highlights the importance of local variations in flagellar beat dynamics within a given colony, which can lead to enhanced reorientation dynamics.

Motility and phototaxis of Gonium, the simplest differentiated colonial alga

Green algae of the Volvocine lineage, spanning from unicellular Chlamydomonas to vastly larger Volvox, are models for the study of the evolution of multicellularity, flagellar dynamics, and developmental processes. Phototactic steering in these organisms occurs without a central nervous system, driven solely by the response of individual cells. All such algae spin about a body-fixed axis as they swim; directional photosensors on each cell thus receive periodic signals when that axis is not aligned with the light. The flagella of Chlamydomonas and Volvox both exhibit an adaptive response to such signals in a manner that allows for accurate phototaxis, but in the former the two flagella have distinct responses, while the thousands of flagella on the surface of spherical Volvox colonies have essentially identical behavior. The planar 16-cell species Gonium pectorale thus presents a conundrum, for its central 4 cells have a Chlamydomonas-like beat that provide propulsion normal to the plane, while its 12 peripheral cells generate rotation around the normal through a Volvox-like beat. Here we combine experiment, theory, and computations to reveal how Gonium, perhaps the simplest differentiated colonial organism, achieves phototaxis. High-resolution cell tracking, particle image velocimetry of flagellar driven flows, and high-speed imaging of flagella on micropipette-held colonies show how, in the context of a recently introduced model for Chlamydomonas phototaxis, an adaptive response of the peripheral cells alone leads to photoreorientation of the entire colony. The analysis also highlights the importance of local variations in flagellar beat dynamics within a given colony, which can lead to enhanced reorientation dynamics.

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.

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.

Evidence for a self-organized compliant mechanism for the spontaneous steady beating of cilia

Cilia or eukaryotic flagella are slender 200-nm-diameter organelles that move the immersing fluid relative to a cell and sense the environment. Their core structure is nine doublet microtubules (DMTs) arranged around a central-pair. When motile, thousands of tiny motors slide the DMTs relative to each other to facilitate traveling waves of bending along the cilium's length. These motors provide the energy to change the shape of the cilium and overcome the viscous forces of moving in the surrounding fluid. In planar beating, motors walk toward where the cilium is attached to the cell body. Traveling waves are initiated by motors bending the elastic cilium back and forth, a self-organized mechanical oscillator. We found remarkably that the energy in a wave is nearly constant over a wide range of (ATP) and medium viscosities and inter-doublet springs operate only in the central and not in the basal region. Since the energy in a wave does not depend on its rate of formation, the control mechanism is likely purely mechanical. Further the torque per length generated by the motors acting on the doublets is proportional to and nearly in phase with the microtubule sliding velocity with magnitude dependent on the medium. We determined the frequency-dependent elastic moduli and strain energies of beating cilia. Incorporation of these in an energy-based model explains the beating frequency, wavelength, limiting of the wave amplitude and the overall energy of the traveling wave. Our model describes the intricacies of the basal-wave initiation as well as the traveling wave.

Delivery of continuously-varying stimuli using channelrhodopsin-2

To study sensory processing, stimuli are delivered to the sensory organs of animals and evoked neural activity is recorded downstream. However, noise and uncontrolled modulatory input can interfere with repeatable delivery of sensory stimuli to higher brain regions. Here we show how channelrhodopsin-2 (ChR2) can be used to deliver continuous, subthreshold, time-varying currents to neurons at any point along the sensory-motor pathway. To do this, we first deduce the frequency response function of ChR2 using a Markov model of channel kinetics. We then confirm ChR2's frequency response characteristics using continuously-varying optical stimulation of neurons that express one of three ChR2 variants. We find that wild-type ChR2 and the E123T/H134R mutant ("CheTA") can pass continuously-varying subthreshold stimuli with frequencies up to ~70 Hz. Additionally, we find that wild-type ChR2 exhibits a strong resonance at ~6-10 Hz. Together, these results indicate that ChR2-derived optogenetic tools are useful for delivering highly repeatable artificial stimuli that mimic in vivo synaptic bombardment.

High-speed microscopic imaging of flagella motility and swimming in Giardia lamblia trophozoites

We report, in this paper, several findings about the swimming and attachment mechanisms of Giardia lamblia trophozoites. These data were collected using a combination of a high-contrast CytoViva imaging system and a particle image velocimetry camera, which can capture images at speeds greater than 800 frames/s. Using this system, we discovered that, during rapid swimming of Giardia trophozoites, undulations of the caudal region contributed to forward propulsion combined with the beating of the flagella pairs. It was also discovered, in contrast to previous studies with 10 times slower image sampling technique, that the anterior and posterolateral flagella beat with a clearly defined power stroke and not symmetrical undulations. During the transition from free swimming to attachment, trophozoites modified their swimming behavior from a rapid rotating motion to a more stable planar swimming. While using this planar swimming motion, the trophozoites used the flagella for propulsion and directional control. In addition to examination of the posterolateral and anterior flagella, a model to describe the motion of the ventral flagella was derived, indicating that the ventral flagella beat in an expanding sine wave. In addition, the structure of the ventrocaudal groove creates boundary conditions that determine the form of beating of the ventral flagella. The results from this study indicate that Giardia is able to simultaneously generate both ciliary beating and typical eukaryotic flagellar beating using different pairs of flagella.

Fidelity of adaptive phototaxis

Along the evolutionary path from single cells to multicellular organisms with a central nervous system are species of intermediate complexity that move in ways suggesting high-level coordination, yet have none. Instead, organisms of this type possess many autonomous cells endowed with programs that have evolved to achieve concerted responses to environmental stimuli. Here experiment and theory are used to develop a quantitative understanding of how cells of such organisms coordinate to achieve phototaxis, by using the colonial alga Volvox carteri as a model. It is shown that the surface somatic cells act as individuals but are orchestrated by their relative position in the spherical extracellular matrix and their common photoresponse function to achieve colony-level coordination. Analysis of models that range from the minimal to the biologically faithful shows that, because the flagellar beating displays an adaptive down-regulation in response to light, the colony needs to spin around its swimming direction and that the response kinetics and natural spinning frequency of the colony appear to be mutually tuned to give the maximum photoresponse. These models further predict that the phototactic ability decreases dramatically when the colony does not spin at its natural frequency, a result confirmed by phototaxis assays in which colony rotation was slowed by increasing the fluid viscosity.

Analysis of the ciliary/flagellar beating of Chlamydomonas

Eukaryotic flagella and cilia are alternative names, for the slender cylindrical protrusions of a cell (240nm diameter, approximately 12,800nm-long in Chlamydomonas reinhardtii) that propel a cell or move fluid. Cilia are extraordinarily successful complex organelles abundantly found in animals performing many tasks. They play a direct or developmental role in the sensors of fluid flow, light, sound, gravity, smells, touch, temperature, and taste in mammals. The failure of cilia can lead to hydrocephalus, infertility, and blindness. However, in spite of their large role in human function and pathology, there is as yet no consensus on how cilia beat and perform their many functions, such as moving fluids in brain ventricles and lungs and propelling and steering sperm, larvae, and many microorganisms. One needs to understand and analyze ciliary beating and its hydrodynamic interactions. This chapter provides a guide for measuring, analyzing, and interpreting ciliary behavior in various contexts studied in the model system of Chlamydomonas. It describes: (1) how cilia work as self-organized beating structures (SOBSs), (2) the overlaid control in the cilia that optimizes the SOBS to achieve cell dispersal, phototaxis steering, and avoidance of obstacles, (3) the assay of a model intracellular signal processing system that responds to multiple external and internal inputs, choosing mode of behavior and then controlling the cilia, (4) how cilia sense their environment, and (5) potentially an assay of ciliary performance for toxicology or medical assessment.

Evolution of phototaxis

Phototaxis in the broadest sense means positive or negative displacement along a light gradient or vector. Prokaryotes most often use a biased random walk strategy, employing type I sensory rhodopsin photoreceptors and two-component signalling to regulate flagellar reversal. This strategy only allows phototaxis along steep light gradients, as found in microbial mats or sediments. Some filamentous cyanobacteria evolved the ability to steer towards a light vector. Even these cyanobacteria, however, can only navigate in two dimensions, gliding on a surface. In contrast, eukaryotes evolved the capacity to follow a light vector in three dimensions in open water. This strategy requires a polarized organism with a stable form, helical swimming with cilia and a shading or focusing body adjacent to a light sensor to allow for discrimination of light direction. Such arrangement and the ability of three-dimensional phototactic navigation evolved at least eight times independently in eukaryotes. The origin of three-dimensional phototaxis often followed a transition from a benthic to a pelagic lifestyle and the acquisition of chloroplasts either via primary or secondary endosymbiosis. Based on our understanding of the mechanism of phototaxis in single-celled eukaryotes and animal larvae, it is possible to define a series of elementary evolutionary steps, each of potential selective advantage, which can lead to pelagic phototactic navigation. We can conclude that it is relatively easy to evolve phototaxis once cell polarity, ciliary swimming and a stable cell shape are present.