Just Keep Swimming: Structure, Movement, and Light Interactions of Unicellular Green Algae

Ai-Lan Ji-Eun Nguyen, Tesnim Obey, Anders Schwarz, Jackson Yu

Abstract

Popular scientific theory suggests that life on earth originated in a primordial ocean billions of years ago. Basic prokaryotic cells allegedly diverged into eukaryotes, and chloroplasts that produce oxygen later appeared. The first organisms with functioning chloroplasts are presumed to be a kind of marine algae. The genus of interest in this essay, Chlamydomonas, is known to be among these first algae ancestors. It comprises an important range of species across a wide range of environments. The species that will be primarily investigated in this essay is Chlamydomonas reinhardtii, an intensely studied species of Chlamydomonas considered to be a ‘model organism' by the scientific community. The essay will analyze Chlamydomonas through  mechanics and physical phenomena, in an attempt to understand how this ancient organism has succeeded in thriving on earth with its interactions with the surrounding environment.

Introduction

The natural world is a dynamic system subject to constant change across a variety of aspects. For life forms living within this system, this implies making use of the environment in every way possible, and this is best exemplified in organisms that have survived, relatively unchanged, throughout vast periods of time.. A perfect example of this is Chlamydomonas, a genus of unicellular green algae encompassing more than 500 species. Requiring little space for growth and a relatively short regeneration time, Chlamydomonas are found in a wide range of habitats from soil to oceans and lakes.(Sass S et al., 2018).

Chlorophytes including Chlamydomonas diverged from streptophytes (land plants) over a billion years ago, and comparative genomic suggests that Chlamydomonas genes date back to the original green-plant or plant-animal ancestor. Therefore, an analysis of Chlamydomonas helps to further our understanding of the ancestral eukaryotic cell, especially the key components of flagella and photosynthetic function (Merchant et al., 2007). To survive and thrive in varying habitats for such a time range, Chlamydomonas employ a variety of physical phenomena uniquely utilizing the properties of their surroundings to promote their interests. This essay deals with the mechanical and optical phenomena linked to Chlamydomonas' structure, movement, and responses to light.

Chlamydomonas reinhardtii

Chlamydomonas reinhardtii refers to the small (around 10 μm in diameter), unicellular, biflagellate eukaryotic organism, which is part of the larger genus of green algae, Chlamydomonas; these organisms are colloquially known as “unicellular green algae” (Maul et al., 2002). They come in a variety of rounded shapes (spherical, oval, pyriform), and have two flagella projecting from the surface of the cell at its anterior pole (see Figure 1), which they use to “swim” around in a manner similar to the breaststroke (Ringo, 1967). Unlike most other green algae, Chlamydomonas do not have a cell wall containing cellulose (Imam et al., 1985). Rather, the Chlamydomonas cell wall consists of a multi-layered made from proteins and glycoproteins (Imam et al., 1985). One experiment found that the cell wall of Chlamydomonas reinhardtii is comprised of seven layers (Roberts et al., 1974).

Fig. 1 Structure of a Chlamydomonas reinhardtii cell (in microns) and its key components, including flagella, cell wall, and eyespot (Bodenes, 2017). Note the location of both flagella on the cell's anterior pole. The cell's singular eyespot is located to the side, closer to one flagellar than the other.

While the Chlamydomonas are largely bilaterally symmetric organisms, as most of the cell's organelles are symmetrically positioned along their length, they are slightly asymmetric due to their singular eyespot (Holmes & Dutcher, 1989). This photosensory organelle serves as an antenna of sorts, communicating information to the photoreceptor within the cell (Holmes & Dutcher, 1989). Typically, each Chlamydomonas cell has a single eyespot positioned slightly closer to one flagellum than the other (Holmes & Dutcher, 1989). As such, the asymmetric position of the eyespot can be used to conventionally distinguish the cell into two halves: cis, containing the eyespot, and trans, without the  eyespot (Holmes & Dutcher, 1989). The cis and trans halves can be divided by drawing an imaginary line passing between the two basal bodies of the cell (Holmes & Dutcher, 1989).

A Model Organism

Chlamydomonas reinhardtii is commonly used by researchers as a reference organism (Salomé & Merchant, 2019). Generally, a reference organism (also called a model organism) is a non-human, biological organism that has suitable, easily observable qualities (including structure, and response to certain stimuli), that allow for the study of a specific trait or phenomenon (Leonelli, 2013). The end goal is to standardize experimental knowledge accumulated from the model organism on a broad scale and then create a reference point for comparative studies involving other (typically more complex) biological species (Leonelli, 2013). A model organism is selected based on appropriate, useful characteristics: the cell has a simple life cycle, and it can easily be manipulated and mutated (and these mutations are easily isolated from the reference group) (Harris, 2001). With the addition of the ever-evolving array of methods and technologies used for studying genetics at the molecular scale, Chlamydomonas is thus a very helpful organism when studying the behavior of eukaryotic cells under different stresses, as well as plant cells (Harris, 2001). To date, the Chlamydomonas have been employed to study such things as the process of photosynthesis, the biology related to chloroplasts, cell-to-cell recognition, as well as the mechanisms related to sensory and motor flagella (Salomé & Merchant, 2019). On the other hand, Chlamydomonas has also been applied to understand light perception and how light interacts with certain organisms (Harris, 2001).

Chlamydomonas as a lens

A biological organism, such as Chlamydomonas reinhardtii needs to be able to perceive (or “see”) its surroundings, however, its cell body is too small and simple to allow for the organism to have eyes. One study found that the cell body of the Chlamydomonas can behave as a convex lens (Ueki et al., 2016). In a typical lens, light rays that enter the medium (lens) are refracted twice: upon entry and exit of the medium. As a result, light exits a lens in a different direction from the incident (entering) ray. Convex lenses are generally used to condense light as they make incident light rays converge, as opposed to a concave lens which diverges light. This study observed that light that was shone across the Chlamydomonas reinhardtii cell had converged and formed a small bright spot on the other side (Ueki et al., 2016), which will be discussed later in the essay. When studying the lens effect of the Chlamydomonas cell body, it is estimated that this organism has a refractive index of around 1.47 (Ueki et al., 2016) The refractive index is a value that indicates the refractive strength of a given medium, or rather how much light bends (change direction) in a medium. As a reference, the refractive index of water at room temperature for visible wavelengths is about 1.33 (Hosoda, Haruki et al., 2004). Typically, when light enters a medium with a higher refractive index (from water to the cell body, in this case), the light travels at a slower velocity within the medium of higher refractive index, bends, and eventually exits the medium at a different angle than the incident angle.

The refractive properties of the Chlamydomonas reinhardtii cell body, paired with replicable experimental conditions, make this organism a suitable model for studying light refraction and the behavior of light with lenses. These results also demonstrate Nature's design solution for Chlamydomonas' lack of eyes: the Chlamydomonas cell body has evolved to have a refractive index suitable to make it function as a lens. This solution allows Chlamydomonas reinhardtii to focus light that enters through its eyespot, onto the photoreceptor within the cell.

Cell clumping

Despite being a unicellular organism, green algae Chlamydomonas can survive very extreme environmental conditions through acclimation, but also via the formation of multicellular structures (de Carpentier et al., 2019). The latter process requires socialization amongst multiple Chlamydomonas cells (de Carpentier et al., 2019). When this occurs, Chlamydomonas cells will either form palmelloids or cell aggregates (de Carpentier et al., 2019). The palmelloid phenomenon occurs when around 4 to 16 cells come together as a result of one cell undergoing multiple cell divisions without degrading its cell wall; these 4 to 16 cells end up surrounded by the same cell wall (de Carpentier et al., 2019). This process is triggered by a stress event (either biotic or abiotic) and ensures that no harm comes to the cells within the shared cell wall (de Carpentier et al., 2019).

Fig. 2 As a response to certain stress conditions, Chlamydomonas renhardtii form palmelloid structures (bottom right). Note that the shared outer cell wall of the palmelloid hatches once stress conditions improve, thus releasing the daughter cells. Under harsher stress conditions, Chlamydomonas will form temporary cell aggregates instead (top right image) (de Carpentier et al., 2019).

With more extreme conditions, palmelloid structures may yet be too weak to withstand the stressors; in this case, the Chlamydomonas will form cell aggregates (de Carpentier et al., 2019). These structures can contain up to 100,000 individual Chlamydomonas cells. Cell aggregation (or cell clumping) is thus one of the primary defensive mechanisms employed by Chlamydomonas reinhardtii (Zhang et al., 2023). Aggregate Chlamydomonas cells demonstrate increased resistance to both biotic and abiotic stressors, as well as an overall decrease in photosynthesis activity, thus decreasing the risk of damage due to photo and thermal stress (Zhang et al., 2023). This response to stress is only temporary, however, as the cells eventually return to their unicellular state of being once the perceived stressor is no longer present (Zhang et al., 2023). As this stress response demonstrates that multicellular structures can, in fact, be generated as a result of severe conditions, many researchers have proposed that there exists a link between survival, stress responses, evolution, and an eventual transformation from unicellular organisms to the existence of multicellular organisms (de Carpentier et al., 2019).

Thermal Stress

Of the many environmental disturbances faced by living organisms, temperature fluctuations are the most common, especially in recent times due to human activity. Extremely high and low temperatures have been known to limit the growth and development of plant-like cells such as the Chlamydomonas (Ermilova, 2020). In order to reduce damage done to the cell, and to maintain homeostasis, Chlamydomonas produces various heat-stress responses (HSRs), thus allowing it to acclimate to high temperatures and survive (Schroda et al., 2015).

Photo stress

While Chlamydomonas reinhardtii requires light to perform photosynthesis, like other algae and plant cells, if too much light is absorbed at a given moment in time, it can be harmful and lead to adverse effects on the photosynthetic apparatus of the cell (Erickson et al., 2015). Photosynthesis in the Chlamydomonas works most efficiently in limiting light conditions, such as the darker shaded areas that this organism is more accustomed to (Erickson et al., 2015). Given these ideal conditions, the rate of of light is in step with the rate of photosynthesis (Erickson et al., 2015). The issue presents itself when the intensity of light continues to increase past the cell's threshold of light intensity required for the photosynthetic process to function (Erickson et al., 2015). As light intensity increases, photosynthesis rate also increases, but excess light absorption can overexcite the cell's photosynthetic molecules, causing harmful byproducts and photo-oxidative damage (Erickson et. al., 2015). The absorption of excess light can therefore be harmful, as it can lead to photoinhibition (continuous decrease in the efficiency of the photosynthetic apparatus, paired with an overall decreased capacity to perform photosynthesis) (Demmig-Adams & Adams, 2003).

One method employed by the Chlamydomonas reinhardtii is to swim away from the source of light once its photosensor detects excess light; this mechanism is discussed later on in this essay. In order to dissipate the excess light energy absorbed, another one of Chlamydomonas' defense mechanisms against photo-oxidative damage is a non-chemical photo quenching (NPQ) mechanism (Gabilly et al., 2019). The purpose of the NPQ is to de-excite the over-excited molecules (in this case, the excited chlorophyll), and thus avoid the potential for producing harmful chemical byproducts (Gabilly et al., 2019).

Mechano-transduction

It is known that, depending on their nature, living organisms adapt to changing environmental stressors by applying various strategies and solutions (Félix de et al., 2021). Distortion to the cellular membrane, such as compression stress, can provoke changes in the physiology of a cell (Min et al., 2014). In other words, external mechanical stress can trigger mechano-transduction (a cellular response to mechanical stimulus), which in turn results in intracellular changes, or remodeling.

In an experiment by Posten and Wagner, it is observed that Chlamydomonas algal cells continue to grow at their typical rate, even when subjected to extreme pressure changes (up to a certain threshold, 300 mbar) (Wagner & Posten, 2017). This therefore demonstrates the capability of Chlamydomonas to withstand sudden pressure changes, which may be a beneficial survival tactic when, for instance, the organism travels into deeper depths of the sea (and therefore into areas with higher pressure). While the rate of development is seemingly unperturbed by pressure changes, it is also noted that compared to their radius at atmospheric pressure (around 10 μm), Chlamydomonas also exhibit swelling when subject to higher pressure differences (see Fig. 3) (Wagner & Posten, 2017).

Fig. 3 Light microscopic photos (bright field, 400x magnification) of Chlamydomonas reinhardtii cells, taken under different pressure conditions. Image (1): microscopic picture of Chlamydomonas cells at atmospheric pressure, (0 mbar, no applied pressure) where the length L of a randomly selected cell, measured down from the apex of the cell, is 10.19 μm. Image (6): microscopic picture of Chlamydomonas taken at 300 mbar of pressure (after multiple stepwise increases in pressure are performed), where the length L of Chlamydomonas under these conditions include 17.54 μm, 9.69 μm, and 18.29 μm. An overall increase in the physical size of Chlamydomonas cells is observed in the case of high pressure changes. Adapted from Wagner & Posten, 2017.

Cilia and flagella

Did You Know? Cilia and flagella are structurally distinct components of the cell, as cilia are shorter and much more numerous than the longer flagella (of which there are only two on Chlamydomonas reinhardtii). Motile cilia and flagella both contribute to the movement of the cell, however, differ in their beating (Gilpin et al., 2020)

Chlamydomonas both have flagella (on the anterior pole of the cell) and cilia, short hair-like structures, along the surface of the cell (Meng & Pan, 2017). These cilia are used to direct the motion of the cell, as well as for signaling (Meng & Pan, 2017). As previously mentioned, Chlamydomonas reinhardtii is a biflagellate unicellular organism. A flagellum is a whip or tail-like appendage, employed by cells to propel their motion (Höög et al., 2014). This microtubule-based organelle also serves as a sensor of external, environmental cues (Höög et al., 2014). The flagella of the Chlamydomonas contain the motor protein dynein as well as motor enzymes known as kinesin, which are two crucial components allowing for cell movement (Bernstein & Rosenbaum, 1994). At the base of cilia and flagella are the basal bodies, also known as the kinetosomes, which are anchored to the cell membrane of the Chlamydomonas. These basal bodies control the growth and organization of the flagella (Geimer & Melkonian, 2004). The two basal bodies affixed by a formation of microtubules and fibers, along with two pro-basal bodies, make up the basal apparatus of the cell (Geimer & Melkonian, 2004). As such, these flagella are mainly composed of the basal body, the hook, and the filament (Vonderviszt & Namba, 2008). The filament is long and helically shaped and connects to the basal body through the hook, which is a short and very curved element (see Fig. 4).

Fig. 4 Schematic of a locomotive flagellum and its three main components: the basal body (anchors to the cell membrane), the hook (joint between the basal body and filament), and the filament (Vonderviszt & Namba, 2008).

Wavelike motion

There are two types of motions that Chlamydomonas cilia use for propulsion. The “Forward” and the “Reverse“ motion. The forward motion involves the cilia moving away from the longitudinal axis of the cell body. And the reverse motion will involve the curvature of each cilium. We can quantify these beating patterns by beat frequency and waveform curvature.

Fig. 5 Chlamydomonas forward (A) and reverse (B) waveforms, over one beat cycle. Arrows show the direction of cell movement (Woodhams et al., 2023).

The movement of cilia is orchestrated through the regulated sliding of neighboring outer Doublet Microtubules (DMTs) within the axoneme. The dynein protein motors harness energy from the hydrolysis of adenosine triphosphate (ATP) to produce this sliding action, which is then transformed into a bending motion to form the waveform. If every ciliary dynein were active simultaneously, the cilia would enter a rigor state or a tug-of-war scenario, leading to zero net movement or bending. For an effective bend to occur, the functioning of dynein motors needs to be regulated both longitudinally along the axoneme and circumferentially around it, across a designated axis (Dutcher, 2020).

Forward propulsion

Chlamydomonas propels itself forward by exerting force on the surrounding fluid. In its power stroke, the dual cilia beat and shift the fluid around the body, pulling it towards its rear end. The movement of the fluid around such a free-moving cell has been quantified using particle imaging velocimetry. In this method, the fluid is infused with inert marker particles, which help in determining both the direction and strength of flow across varied locations (Drescher et al., 2010). Within the principal beat plane of the cilia, the flow pattern is characteristic of a “puller” type of micro swimmer, similar to the locomotion observed in ciliates like Paramecium (Guasto, Rusconi, & Stocker, 2011). This creates a unique stress pattern in the fluid, drawing flow in the direction of its movement and pushing it away from its sides (Figure 6). This “pulling” mechanism contrasts sharply with the propulsion of other micro swimmers such as spermatozoa and flagellated bacteria like E. coli, which operate as “pushers,” exerting force in a manner that propels them forward by pushing the fluid backward (Fauci & Dillon, 2005). The flow pattern exhibited by cilia-propelled organisms closely mirrors that created by a model swimmer applying point in the fluid—at each cilium and at the cell body—adhering to the force-free and torque-free prerequisites essential for swimming at low Reynolds numbers. This results in a forward propulsion that enables organisms such as Chlamydomonas to move along their anterior–posterior axis. Despite the complex dynamics of cilia, this streamlined perspective is often adopted as a representative model for Chlamydomonas's swimming behavior, effectively encapsulating the essential mechanics while bypassing the intricacies of the cilia's dynamic shape (Woodhams et al., 2023).

Fig. 6 (A) The flow pattern surrounding a swimming cell within the average beat-plane displays a distinct streamline configuration, as observed in PIV studies (Drescher, Goldstein, & Tuval, 2010). (B) A simpler model of the swimmer mimics the helical swimming path of the organism. (C) The left-handed helical rotation, when observed from the front, results from the nonplanar beating motion of the two cilia (Cortese & Wan, 2021). (D) The rotation is linked to photoreception and plays a crucial role in the cell's phototactic behavior, which might vary depending on the strain. While some strains lean towards positive phototaxis, others exhibit negative phototaxis, even when exposed to the same light stimulus (Woodhams et al., 2023).

Asymmetries of the cilium

The orchestrated control of dynein-driven microtubule sliding is vital for the regulation of ciliary and flagellar movement (Viswanadha, Sale, & Porter, 2017). Yet, the mechanisms for dictating the location and of dynein proteins activity remain only partially known. The observed asymmetries in the Chlamydomonas cilium seem pivotal for both the initiation and regulation of the waveform. Such control demands both proximal and radial asymmetries since waveform initiation takes place in the proximal area. The diversity in dynein proteins arms, combined with the modifications in DMT1 and DMT2 in the proximal axoneme, might be instrumental in waveform onset (Dutcher, 2020). In Chlamydomonas, DMT1–2 is positioned almost perpendicularly to the plane of bending and displays minimal interdoublet sliding (Nakano et al., 2003).

The influence of the central pair and radial spokes in directing dynein proteins is further illustrated by the identification of suppressor mutations that reintroduce some mobility to paralyzed mutants resulting from flaws in the CPC/RS and radial spokes (Porter, Power, & Dutcher, 1992). These mutations impact both the exterior and interior dynein arms and the N-DRC, which adjusts dynein activity. The absence of the N-DRC can activate the dynein function without CPC/RS prompts (Dutcher, 2020). Another model posits that the interactions between dynein and the axoneme's passive elements can yield coordinated propelling oscillations. Distributed axial forces exerted in counter directions on interconnected beams within a viscous medium induce a dynamic structural imbalance, giving rise to oscillatory, wave-like movement (Bayly & Dutcher, 2016).

However, when wild type Chlamydomonas is exposed to strong light, it triggers the symmetrical waveform by prompting an influx of calcium ions into the cells (Holland et al., 1997). Multiple studies hint that the outer dynein arms might be influenced by the central pair–radial spoke system in producing this symmetrical waveform (Wargo & Smith, 2003).

Ciliary beating kinematics

The shape of a cilium is typically described by the tangent angle, Ψ, in reference to a specific axis, frequently using the tangent at the cilium's base since it offers a practical point of reference. This tangent angle is determined by the arc length, s, and time, t. By integrating this tangent angle over the cilium's length, one can derive the x and y positions of the cilium, as shown in Figure 7. It is often beneficial to express local forces and velocities using their respective components in the local tangent, T, and normal, N, orientations.

Fig. 7 Kinematic equations of the Chlamydomonas cilium. (A) The parameters determining the shape of the cilium are influenced by its arc length, denoted as s, and by time, denoted as t. In the Cartesian coordinate system, the coordinates x and y can be derived by integrating the cosine and sine, respectively, of the tangent angle, denoted as ψ, along the cilium's arc length, s. The local curvature of the cilium, represented by κ, is derived from the tangent angle with respect to the arc length. (B) The Cartesian coordinate system is positioned so that it aligns with the base of a trans cilium. Here, the arc length, s, starts at zero at the cilium's base and extends to L at its tip. The angle ψ indicates the angle between the local tangent vector, represented by T, and the x axis. The local normal vector, represented by N, is positioned perpendicular to T and is oriented in the direction of curvature. An arc's radius, denoted as R, corresponds to that of any chosen point on the cilium, illustrated with a dotted line. This radius of curvature, R, is determined by the inverse of the curvature κ (Woodhams et al., 2023).

A key feature of ciliary form is the curvature, denoted as κ. This curvature is obtained by differentiating the tangent angle, Ψ, based on the arc length, s. It's also equivalent to the inverse of the radius of curvature R. Two contrasting directions of planar curvature can be observed: the “principal bend” and the “reverse bend.” In the context of Chlamydomonas, the main bend that drives the effective stroke causes the cilium to curve outwards towards the 5–6 doublets. Conversely, the reverse bend makes the cilium curve in the opposing direction. (Johanningmeier & Howell, 1984)

Cell body kinematics and kinetics

The linear and angular displacement (θ, X, and Y) of the cell's body are analyzed to determine the cell's linear and angular speeds. These kinematic metrics are employed to outline the forces impacting the cell body in relation to the Gxy frame, which momentarily aligns with the fixed frame Gx' y' of the body. However, this Gxy frame does not possess its own linear or angular momentum. By employing a simple coordinate transformation, the cell body's speeds within the Gxy frame can be ascertained. The x-axis corresponds to the primary axis, while the y-axis aligns with the secondary axis of the ellipsoid depicted in the visual representation. At every point in time, the Gxy frame starting point matches the cell center, and its axes are in line with Gx' y'. The linear speed components of the cell body in relation to the Gxy frame are showcased in Equation (1) (Bayly et al., 2011).

v_x = v_x \cos(\theta) + v_y \sin(\theta) \quad v_y = -v_x \sin(\theta) + v_y \cos(\theta) \qquad \qquad (1)

The initial velocity is sorted to align with the flagellum's position at the same moment. This organized data is then refined using a low-pass filter. Much like the flagellum, the outcomes provide a continuous evaluation of the cell  linear and angular speeds throughout a typical beat, boasting high time resolution. The related viscous forces acting on the cell body can be deduced using the equations that dictate the movement of either a sphere or an ellipsoid under Stokes flow. Stokes flow equations are linear, meaning that the resultant force and moment for a specific set of linear and angular velocities can be determined through superposition. Equations suitable for ellipsoids have been formulated for various situations, outlining the viscous and rotational force on an elongated ellipsoid based on viscosity, the major axis a, the minor axis b, and the eccentricity, given by:

e = \sqrt{\frac{1 - b^2}{a^2}}

F_x = 6\pi\mu av_x \times CF_1,
F_y = 6\pi\mu av_y \times CF_2,
M_G = 8\pi\mu a b^2\omega \times CF_3,

where

C_{F1} = \frac{8}{3} e^{3} \left[ -2e + (1 + e^2) \ln\left(\frac{1 + e}{1 - e}\right) \right]^{-1},

C_{F2} = \frac{16}{3} e^{3} \left[ 2e + (3e^2 - 1) \ln\left(\frac{1 + e}{1 - e}\right) \right]^{-1},

C_{F3} = \frac{4}{3}e^{3}\frac{2 - e^{2}}{1-e^{2}} \left[- 2e + (1 + e^{2})\ln\left(\frac{1+e}{1-e}\right)\right]^{-1}.

Fx and Fy describe the x and y components of linear drag on ellipsoid at low Reynolds numbers. MG shows the connection between torque and rotation of the prolate ellipsoid about its minor axis (Bayly et al., 2011).

Effect of viscosity

At the microscopic level of Chlamydomonas cilia, the surrounding fluid viscosity poses a greater resistance than the forces required to surpass the inertia of both the cell and its adjacent fluid (Bray, 2000). Due to the properties of motion in viscous environments, the waveform needs to be unbalanced relative to the axis perpendicular to the swimming direction. If the power and recovery strokes of the Chlamydomonas cell were perfect reflections of each other, then the cell would not move forward. Similarly, during photo shock, the cell would not retreat if the waveform did not travel from the base to the tip of the cilium.

The Reynolds number is a dimensionless quantity used in fluid mechanics to predict the flow regime of a fluid, especially the transition between laminar and turbulent flow. It represents the ratio of inertial forces to viscous forces and describes the relative importance of these two types of forces for given flow conditions. It is defined as:

Re = \frac{\rho u L}{\mu}

In the equation, ρ is the fluid density (in kg/m3), u is the fluid velocity (in m/s), L is a characteristic linear dimension (in m) — often the diameter of a pipe for pipe flow, and μ is the dynamic viscosity of the fluid (in Pa·s or N·s/m2). In cilia, the Reynolds number typically falls between 10-5 and 10-3; this range of values is extremely low. Therefore, the flow around cilia is considered laminar, and viscous forces dominate over inertial forces in the fluid flow around the cilia. This makes it possible to use the resistive force theory to model the viscous forces acting on the cilium, wherein the force directly corresponds with velocity, as shown in Figure 6.

Fig.8 Resistive force theory for the cilium (Woodhams et al., 2023).

In models that consider significant deformations of ciliary beating, different coefficients are assigned for resistance in directions tangent and perpendicular to the ciliary axis. The resistance encountered during the cell body translation and rotation can be addressed using Stokes' Law (Bayly et al., 2011), as shown in Figure 9.

Fig 7. (A) Equations of motion for Chlamydomonas cells. (B) Resulting forces and torques on the cilium (Woodhams et al., 2023).

Light response

Algae utilize light as both an energy source for photosynthesis and as a regulatory signal for biological processes such as initiation of enzyme activity and gene expression (Johanningmeier, 1984). This highlights the importance of having the cell respond to light effectively. Many studies focus on the species Chlamydomonas reinhardtii, as it provides an array of mutants with impaired mobility, and the defects can be analyzed to understand the function of the mutated components (Harris, 2001). These organisms demonstrate remarkable sensitivity to light cues making them suitable for studying optical mechanisms governing phototaxis, adhesion, and environmental responses. Many attribute the photoresponsivity of the green algae to its eyespot. This organelle found in the chloroplast is formed by two carotenoid layers close to photoreceptor proteins called rhodopsins.

Light and movement

Phototaxis occurs when a whole organism moves towards or away from light (Kreimer, 1994). While the complete mechanism that dictates the movement of the Chlamydomonas remains unknown, some key elements that might explain how this phenomenon occurs in Chlamydomonas have been studied. In the context of recent research, it has been proposed that the Chlamydomonas phototactic pathway comprises four stages (Ueki et al., 2016). First, the absorption of a photon by rhodopsins initiates a change in the molecule structure due to the photon energy. This change allows for the rhodopsin to function as a protein channel, transporting a photon through the cellular membrane. This creates a potential difference in the cellular membrane, creating an action potential, initiating intraflagellar transport of cation (Litvin, 1978) (Holland et al., 1997). Consequently, either of the flagella are stimulated, steering the cell in a negative phototaxis (away from the light source) or in a positive phototaxis (towards the light source). During the first stage, the eyespot seemingly plays a significant role in determining the linear direction of the algae (Ueki et al., 2016).  Rhodopsins, the light receptors of the eyespot, are localized at the plasma membrane above the carotenoid layers. The carotenoid rich fat cells of the eyespot are efficient in the scattering of light due to their high lipid composition (Li-Beisson et al. 2015).  So, the lipid layer serves to scatter, thereby amplifying, incoming light signals from the external environment while preventing the detection of light passing in the cell from the back, as depicted in Figure 10 (Ueki, 2016).

Fig. 10 Diagram of eyespot and photoreceptor interaction with light in Chlamydomonas (Ueki et al., 2016).

Fluctuations in light intensity are caused by varying factors such as light absorption by carotenoids stored in lipid globules and chloroplast pigments in the eyespot. As a result, when the eye point is away from the light source, shadowing occurs in the photoreceptor, which means that the cell must respond to these changes in the environment through its swimming pathway (Kreimer, 1994; Kreimer et al., 2023). This adaptive response allows Chlamydomonas to maintain its trajectory and avoid deviations due to changes in light intensity (Kreimer et al., 2023). As the Chlamydomonas cell undergoes rotational motion during swimming, this interplay of light reflection and blocking at the carotenoid layers results in a sinusoidal variation in the light intensity reaching the photoreceptor when the cell swims perpendicular to the direction of the light (Sineshchekov & Govorunova, 2001; Ueki et al., 2016).  To further understand the importance of the lipid layer, a study investigates how mutants without that layer behave. It is found that, despite missing the carotenoid layer in the eyespot, they still navigate along phototaxes but inversely to non-mutated species. (Lamb, Mary Rose et al., 1999).  This phenomenon is due to the lens-like properties of the Chlamydomonas reinhardtii.

While phototaxes concern the orientation of the Chlamydomonas in relation to the light, photophobic responses relate to the change of direction of the cell (Kreimer et al., 2023). Photophobic responses involve a change in the cell's motion triggered by a change in light intensity above a certain threshold of photon influx (Bennett, 2015). The helical swimming motion of Chlamydomonas, a typical pattern for unicellular algae, creates a periodic change in photon fluence rate (Kreimer et al., 2023). When traveling along a phototaxis, this periodic change is regular and can be modeled through a sinusoidal function, as mentioned previously. However, that is not the case when the cell is not moving parallel to the light source, which signals the cell to correct its orientation (Sineshchekov & Govorunova, 2001).  Photophobic responses determine the cell phototaxis. As mentioned previously, Chlamydomonas phototaxis varies with light intensity preventing cellular damage from overexposure to sunlight while still being able to seek it to perform photosynthesis. That might explain why the eyeless mutants described in Figure 11 are not found in nature as they tend to swim towards high intensity light, damaging the cell, and inhibiting the species survival. However, little is known about the signals that determine the phototactic direction.

Fig. 11 Difference in light and interactions between wild type Chlamydomonas possessing an eyespot and mutant Chlamydomonas lacking an eyespot, showing the effects of the eyespot (red) and the lens properties of the cell body on photopsin (blue) excitation and flagella activation (C and T). The model shows that the side receiving most light signals (orange arrows) in the mutant is opposite to that of the wild type, leading to an inversion of the flagella activated (shown by the flagella in bold). This leads to opposing movement directions (showed by the black arrows). The diagram considers movement in high intensity light, which leads to a negative phototaxis in the wild type and a positive phototaxis in the mutant species. (Ueki et al., 2016)

Indeed, the back-side light which travels through the cell converges towards the photoreceptor, making that light more significant than the light coming from the outside that does not converge. The missing eyespot allows the back-side light to reach the photoreceptor instead of being reflected as depicted in Figure 11. The carotenoid rich lipid layer seems to be the Chlamydomonas simple solution to make navigation efficient and prevent cellular damage by high intensity light. As mentioned earlier, the lipid layer amplifies the light signal by scattering it while not allowing backlight to reach the photoreceptors. This solution is, at first, energy consuming; the accumulation of fat globules requires the Chlamydomonas to fix carbon during photosynthesis and convert that to lipid.  However, the cell sees this as an investment in energy as the outcome allows it to seek light efficiently and perform photosynthesis (Goold et al. 2016). An alternative solution would be to somehow make the photopsins initiate an opposite response.  However, this would require major changes to the whole system.

Moreover, just as most mammals accumulate adipose tissue during periods of high energy consumption, Chlamydomonas produce excess lipid globules once its energy needs are met. As a result, in arduous conditions, such as low CO2, the organism uses the fat as an energy reserve, allowing it to survive until conditions allow for energy production (Abreu et al., 2020).

The future of algae: Chlamydomonas can be used as a source of lipid for biofuel! The amount of CO2 released when the fuel is burned is equal to the amount of CO2 required for the algae to develop and produce the fuel. Thus, the net CO2 emission is zero, the same as it would have been had the algae never been cultivated. A renewable fuel source that doesn't harm the environment could be available thanks to algae! (Scranton 2015)

The process which converts absorption of light into work is partly due to the two types of proteins that exist in the photoreceptor: Chlamydomonas sensory rhodopsin A (CSRA) and B (CSRB).  Data shows that CSRB absorbs the most light at 510 nm with a shoulder at 490 nm while CSRA has absorption maximum around 470 nm and a minor band around 490 nm (Fig. 12) (Sineshchekov et al., 2002). The differentiation of photoreceptors may have allowed the Chlamydomonas to respond to different wavelengths of light. This phenomenon is seen in several species, such as in humans, where the three different types of cones are sensitive to different wavelengths as depicted in Figure 12. The similarities between cones and rhodopsin hints at the correlation between the eyespot in green algae and the evolution of the eye.

Fig. 12 Similarities between rhodopsin and cones in mammals. Left: Sensitivity of photoreceptors CSRA (red) and CSRB (blue) at different wavelengths (Sineshchekov et al., 2002). Right: Sensitivity of green, red, and blue cones in humans at different wavelengths (MacLeod & Johnson, 1993).

Adhesion

Flagellar adhesion in Chlamydomonas plays a pivotal role in the organism ability to survive within its habitats, which include complex and confining environments such as soil and temporary pools (Kreis et al., 2018). The adhesive properties of the Chlamydomonas flagella allow it to remain on the surface of water or otherwise polarized substances, where photosynthesis is most likely to occur.  A study measured adhesion forces in various Chlamydomonas cell types  in different conditions (Kreis et al., 2018). From previous research, it is known that the adhering property is nonexistent when the flagella are treated with protease, which hydrolyses peptide bonds, suggesting that the property is a result of intermembrane proteins (Bloodgood et al., 2019).  Moreover, the regulation of flagellar adhesiveness in Chlamydomonas is especially sensitive to blue light at a range of 470 nm at which there is a photon fluence rate threshold for the activation of the photoproteins responsible for the adhesion at around 3.32 to 8.30 micromoles of photons per square meter per second. That is a measure of the number of photons that reach the surface of the Chlamydomonas photoreceptors which can be thought of as the “current of photons”. Like the current in an electrical circuit, the photon flux density considers the number of particles which pass an intersection per second. The particles, i.e. photons, carry energy which can be used for work. This process involves creating an action potential by exciting the photoprotein, which acts like an ion channel.

Interestingly, the adhesive property is almost non-existent in red light  (Fig. 13) (Kreis et al., 2018). This is sensible as rays in the red range barely penetrate the water. That is due to Rayleigh scattering which states that shorter wavelengths of light, like blue and violet light, are more prone to scattering when interacting with particles smaller in dimension than the wavelength of light itself. In the context of bodies of water, the solvent molecules, which are more abundant, contribute to the scattering. When sunlight traverses the water surface, the relatively small size of water molecules results in pronounced scattering of the shorter blue wavelengths in all directions. This scattering phenomenon fundamentally contributes to the perceivable blue coloration of water. As for the absorption of red light, water molecules selectively absorb wavelengths of light within the red range which excites them. Water during the process of selective absorption acquires energy from the red light, prompting them to oscillate and generate thermal energy.  The connection between Rayleigh scattering and the blue hue of water is underscored by the Rayleigh scattering formula, which describes the scattering intensity as inversely proportional to the fourth power of the wavelength of light (i.e. 𝜆-4) (Zhang et al., 2021). In practice, this means that shorter wavelengths, such as blue, experience more pronounced scattering while not getting absorbed, making blue visible light waves abundant in bodies of water. As seen previously with rhodopsin, photoproteins tend to be sensitive to a small range of wavelengths. So, considering the lack of red light in water, there is no need for green algae to produce adhesive photoproteins sensitive to red light despite it being almost as effective as blue light in initiating photosynthesis (Li et al., 2020; Richardson et al., 1983).

Fig. 13 Adhesive force of flagella in response to red light (c) and to irradiance with blue light depicting rapid increase at 2 to 5 x 1018 photons per square meter per second (f) (Sineshchekov et al., 2002).

These specific light sensitivity values align with several other photoreceptors that trigger various photoresponses in Chlamydomonas such as rhodopsins and phototropins. The latter is notable for its presence in the flagellum of Chlamydomonas and its involvement in governing various aspects of the cell's life cycle and mating processes (Huang, 2004).  As for rhodopsins, they can direct the flagella causing displacement as mentioned previously. Curiously, the flagellar adhesion is sensitive at 470 nm, which corresponds to the maximum sensitivity of CSRB. A correlation between the protein type and adhesion could be further explored (William, 2016).

Cell life cycle

Reproduction in Chlamydomonas has been shown to necessitate light.  Gametes are generated from haploid vegetative cells and have the potential to fuse to form diploid zygotes that undergo mitosis to produce 4 haploid cells (Fig. 14).

Fig. 14 Life Cycle of Chlamydomonas reinhardtii (Sasso et al., 2018).

Light in this process is necessary for transforming pre-gametes into gametes, for maintaining the reproductive abilities of these gametes, and for germination (Huang & Beck, 2003) (Sasso et al., 2018). This process is believed to be facilitated by phototropins that get excited by photons, starting a chain reaction involving intermembrane proteins, but the specifics of the phenomena remain unclear.

One of the critical aspects of Chlamydomonas reproduction influenced by light is gametogenesis, i.e. the maturation of pre-gametes (Huang, K. et al., 2003). Gametogenesis is initiated by nitrogen starvation. When vegetative cells are subjected to nitrogen starvation in the absence of light, they undergo a transformation into mating-incompetent pregametes (Beck, C. F. et al., 1992). Then, the second signal, blue light, promotes the maturation of these pregametes into functional gametes. The sensitivity of Chlamydomonas to blue light during pregamete-to-gamete conversion is remarkable. Experimental data demonstrates that even at low blue-light fluence rates such as 10-11 mol of photons per meter squared over 90 minutes, a significant conversion of pregametes to gametes can be observed (Huang, K. et al., 2003). Furthermore, light not only induces their maturation but also maintains their mating competence. Indeed, incubating gametes in the dark results in a rapid loss of their mating ability. However, exposure to blue light restores their mating competence, which allows for the algae to travel freely without affecting its reproductive capacities (Huang, K. et al., 2003). In other words, this allows the Chlamydomonas to avoid light at high intensity and interrupt their ability to reproduce as the conditions are not favorable, but to regain the ability once the Chlamydomonas finds more favorable conditions.  Finally, it has been demonstrated that light is required for the formation of zygotes. These mechanisms ensure that light is available once the cells have formed.  It could also be to encourage reproduction and a higher population density in sunlit environments.

Phototropin, known to control various blue-light-dependent processes in other organisms, is likely responsible for initiating these reproductive events in Chlamydomonas (Stoelzle et al., 2003).  Interestingly, mutants that do not possess phototropins are rare, if not non-existent, which supports this hypothesis, as it implies that their chances of survival are low since they do not reproduce exclusively in lit environments.  A study which utilizes mutated Chlamydomonas lacking phototropins also demonstrates their inability to reproduce.  The study also reveals that phototropins are very sensitive to even a significant reduction in phototropin levels, less than a 10% variation of light intensity does not abolish the organism's ability to respond to blue light, even during reproduction (Huang, K. et al., 2003). This could explain how the species can populate poorly lit environments such as soil. However, which factors and organic molecules work in tandem with phototropins during cellular multiplication are currently undetermined.

Conclusion

          The Genus Chlamydomonas employs many unique physical techniques to both persist and proliferate across a variety of environments subject to varying conditions. When subject to sudden changes including thermal and photo stressors, Chlamydomonas can form palmelloid structures, with a cell undergoing multiple divisions without degrading the cell wall, or aggregates of neighboring cells. Both serve to maintain homeostasis through insulation. These processes could be a hint regarding the formation of multicellular organisms from unicellular life forms, demonstrating the potential role of stress responses. When the external stressors prove to be unbearable, Chlamydomonas utilize their cilia and flagella along the outside of the cell to propel themselves forward or backward through the aqueous environment in which they reside. This is achieved by dynein motor proteins which slide microtubules within the axenome, causing cilia bending in a waveform cycle such that each ciliary dynein is periodically active at different times. These organelles then draw flow in the direction of movement, pushing fluid away from its sides. This results in point forces being applied to the surrounding liquid, effectively achieving a force and torque-free system of movement that is essential for controlled motion at low Reynolds numbers. 

          Chlamydomonas also move to achieve an optimal phototaxis in response to changes in intensity of light perceived through an eyespot apparatus, an organelle capable of measuring the intensity of light to promote movement when photon influx is detected above or below a certain threshold. Light is of utmost importance for unicellular green algae as it allows them to perform photosynthesis, thus making them produce their own energy source.

Chlamydomonas' conundrum revolves around how to efficiently seek light for photosynthesis while keeping the solutions simple and non-energy intensive. One of the ways to do so is through the lipid globule layer in the eyespot. As described earlier, the scattering properties of lipids amplifies the signal coming from the front of the eyespot and blocks the converging light coming from behind without compromising the body's structure and physical properties. This allows for the Chlamydomonas to move towards medium and low intensity light for photosynthesis and avoid high intensity, damaging, light. The fat layer also serves as energy storage, which makes this solution twice as effective.  Another way in which it enhances its light seeking abilities is by broadening the spectrum to which its photoreceptors react to. As previously stated, instead of broadening the range of a single type of photoreceptor, the organism derives another photoreceptor most sensitive to another wavelength. The superposition of these sensitivities allows the Chlamydomonas to react to a broader range of light wavelengths, especially in the blue spectrum. Photoproteins perform best under blue light radiation and worst under red light despite photosynthesis being very effective in both wavelengths, potentially due to red light failing to reach deep bodies of water due to its absorption by water. Therefore, the development of photoproteins to seek blue light ensured the survival and the functioning of the species.  Finally, the adhesive properties of the flagella initiated by photoproteins allows for the Chlamydomonas to stay on surfaces which light reaches, where photosynthesis can occur.  Like other photoproteins in the cell, they do not respond to red light. This may indicate that the Chlamydomonas uses receptors found in the eyespot to initiate the adhesive response. The cell would rather keep its components as constant as possible and implement small changes, for instance by adding lipids in the eyespot structure and shifting rhodopsin sensitivity. In other words, the cell would rather remain as simple and efficient as possible. After all, it is minimalism that saves it from unnecessary expenditure of energy and from the risk of change.

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