Microswimmer

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Microswimmers
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A microswimmer is a microscopic object with the ability to move in a fluid environment.

Given the recent nature of the field, there is yet no consensus in the literature for the nomenclature of the microscopic objects this article refers to as "microswimmers". Among the many alternative names such objects are given in the literature, microswimmers, micro/nanorobots and micro/nanomotors are likely the most frequently encountered. Other common terms may be more descriptive, including information about the object shape, e.g., microtube or microhelix, its components, e.g., biohybrid, spermbot,[2] bacteriabot,^[3] or micro-bio-robot,^[4] or behavior, e.g., microrocket, microbullet, microtool or microroller. Researchers have also named their specific microswimmers e.g., medibots,^[5] hairbots,^[6] iMushbots,^[7] IRONSperm,^[8] teabots,^[9] biobots,^[10] T-budbots,^[11] or MOFBOTS.^[12][1]

Background

In 1828, the British biologist

${\displaystyle \mathrm {Re} ={\frac {\rho ul}{\mu }}}$

Here, ρ represents the density of the fluid; u is a characteristic velocity of the system (for instance, the velocity of a swimming particle); l is a characteristic length scale (e.g., the swimmer size); and μ is the viscosity of the fluid. Taking the suspending fluid to be water, and using experimentally observed values for u, one can determine that inertia is important for macroscopic swimmers like fish (Re = 100), while viscosity dominates the motion of microscale swimmers like bacteria (Re = 10⁻⁴).^[15]

The overwhelming importance of viscosity for swimming at the micrometer scale has profound implications for swimming strategy. This has been discussed memorably by

where ${\displaystyle \mathbf {u} }$ is the velocity of the fluid and ${\displaystyle {\boldsymbol {\nabla }}p}$ is the gradient of the pressure. As Purcell noted, the resulting equation — the Stokes equation — contains no explicit time dependence.^[16] This has some important consequences for how a suspended body (e.g., a bacterium) can swim through periodic mechanical motions or deformations (e.g., of a flagellum). First, the rate of motion is practically irrelevant for the motion of the microswimmer and of the surrounding fluid: changing the rate of motion will change the scale of the velocities of the fluid and of the microswimmer, but it will not change the pattern of fluid flow. Secondly, reversing the direction of mechanical motion will simply reverse all velocities in the system. These properties of the Stokes equation severely restrict the range of feasible swimming strategies.^[16][15]

As a concrete illustration, consider a mathematical scallop that consists of two rigid pieces connected by a hinge. Can the "scallop" swim by periodically opening and closing the hinge? No: regardless of how the cycle of opening and closing depends on time, the scallop will always return to its starting point at the end of the cycle. Here originated the striking quote: "Fast or slow, it exactly retraces its trajectory and it's back where it started".^[16] In light of this scallop theorem, Purcell developed approaches concerning how artificial motion at the micro scale can be generated.^[15] This paper continues to inspire ongoing scientific discussion; for example, recent work by the Fischer group from the Max Planck Institute for Intelligent Systems experimentally confirmed that the scallop principle is only valid for Newtonian fluids.^[17][15]

Types

Different types of microswimmers are powered and actuated in different ways. Swimming strategies for individual microswimmers 

Strategies for the fabrication of microswimmers include two-photon polymerisation 3D printing, photolithography, template-assisted electrodeposition, or bonding of a living component to an inanimate one by exploiting different strategies. More recent approaches exploit 4D printing, which is the 3D printing of stimuli-responsive materials.^{[49][50][51][52]} Further functionalization is often required, either to enable a certain type of actuation, e.g., metal coating for magnetic control or thermoplasmonic responses, or as part of the application, if certain characteristics are required for e.g., sensing, cargo transport, controlled interactions with the environment, or biodegradation.^{[53][54][55][56][1]}

Natural microswimmers

Motile systems have developed in the

Apart from motor proteins, enzymes, traditionally recognized for their catalytic functions in biochemical processes, can function as nanoscale machines that convert chemical energy into mechanical action at the molecular dimension. Diffusion of various enzymes (e.g. urease, and catalase), measured by fluorescent correlated spectroscopy (FCS), increases in a substrate-dependent manner.[63]^[64] Moreover, when enzymes are membrane-bound, their catalytic actions can drive lipid vesicle movement. For instance, lipid vesicles integrated with enzymes such as transmembrane adenosine 5’-triphosphatase, membrane-bound acid phosphatase, or urease exhibit enhanced mobility correlating with the enzymatic turnover rate.^[65]

Bacteria can be roughly divided into two fundamentally different groups,

The following table, based on Schwarz et al., 2017,[68] lists some examples of natural or biological microswimmers.

Motile microorganisms

	Name	Image	Size (μm2)a	Speed (μm/s)b	Propulsion mechanism	Natural swimming habitat	Sources
bacterial swimmers (prokaryotes)	Escherichia coli		0.5 × 2	30	Peritrichous bundles	Intestinal flora	[69]
	Serratia marcescens		1 × 2	50	Peritrichous bundles	Respiratory and urinary tracts (parasitic)	[70]
	Salmonella typhimurium		0.5 × 2	30	Peritrichous bundles	Intestines (parasitic)	[71]
	Bacillus subtilis		1 × 3	20	Peritrichous bundles	Intestinal flora	[72]
	Aliivibrio fischeri		1 × 2	50	Lophotrichous flagella	Mucus (symbiotic)	[73]
	Vibrio alginolyticus		2 × 3	40	Monotrichous flagellum	Blood (parasitic)	[74][75]
	Listeria monocytogenes		0.5 × 1.5	<1	Peritrichous or amphitrichous bundles	Inter- and intracellular (parasitic)	[76][77]
	Magnetococcus marinus		2 × 2	200	Two lophotrichous bundles	Marine water	[78][79]
	Magnetospirillum gryphiswaldense		0.5 × 2	60	Two amphitrichous flagella	Freshwater sediments	[80]
	Mycoplasma mobile		0.5 × 0.5	5	Gliding via protrusions	Fish gills (parasitic)	[81]
(unicellular) eukaryotes)	Chlamydomonas		10 × 10	150	Two lophotrichous flagella	Freshwater, soil	[82]
	Tetrahymena		25 × 50	>500	Holotrichous cilia	Freshwater	[83]
	Trypanosome		3 × 20	30	Monotrichous flagellum	Blood (parasitic)	[84][85]
sperm cells	Human		3 × 5	50	Monotrichous flagellum	Reproductive tract	[86][87]
	Bovine		5 × 10	100	Monotrichous flagellum	Reproductive tract	[87][88][89]
	Murine		3 × 8	120	Monotrichous flagellum	Reproductive tract	[86][88]

Synthetic microswimmers

One of the current engineering challenges is to create miniaturized functional vehicles that can carry out complex tasks at a small scale that would be otherwise impractical, inefficient, or outright impossible by conventional means. These vehicles are termed nano/micromotors or nano/microrobots, and should be distinguished from even smaller molecular machines for energy, computing, or other applications on the one side and static microelectromechanical systems (MEMS) on the other side of this size scale. Rather than being electronic devices on a chip,

There are a variety of sensing, actuating, or pickup-and-delivery applications that scientists are currently aiming for, with local drug targeting for cancer treatment being one of the more prominent examples.[102]^[5] For applications like this, a micromotor needs to be able to move, i.e., to swim, freely in three dimensions efficiently controlled and directed with a reliable mechanism.^[68]

It is a direct consequence of the small size scale of microswimmers that they have a low

Microorganisms have adapted their locomotion to the harsh environment of low Reynolds number regime by invoking different swimming strategy.[106] For example, the E. coli moves by rotating its helical flagellum,^[107][108] Chlamydomonas flagella have a breaststroke kind of motion.^[109] African trypanosome has a helical flagellum attached to the cell body with a planar wave passing through it.^[110][111] Swimming of these kind of natural swimmers have been investigated for the last half-century.^[112] As a result of these studies, artificial swimmers have also been proposed, like Taylor sheet,^[113] Purcell's two-hinge swimmer,^[16][114] three-linked spheres swimmer,^{[115][116][117]} elastic two-sphere swimmer ^[118] and three-sphere with a passive elastic arm,^[119] which have further enhanced understanding about low Reynolds number swimmers. One of the challenges in proposing an artificial swimmer lies in the fact that the proposed movement stroke should not be reciprocal otherwise it cannot propel itself due to the Scallop theorem. In Scallop theorem, Purcell had argued that a swimmer with one-hinge or one degree of freedom is bound to perform reciprocal motion and thus will not be able to swim in the Stokes regime.^{[106][16][112]}

Purcell proposed two possible ways to elude from Scallop theorem, one is 'corkscrew' motion ^[107][104] and the other is 'flexible oar' motion.^[120][121] Using the concept of flexible oar, Dreyfus et al reported a micro swimmer that exploit elastic property of a slender filament made up of paramagnetic beads.^[31] To break the time inversion symmetry, a passive head was attached to the flexible arm. The passive head reduces the velocity of the flexible swimmer, bigger the head, higher is the drag force experienced by the swimmer. The head is essential for swimming because without it the tail performs a reciprocal motion and the velocity of the swimmer reduces to zero.^[122][112]

Another way microswimmers can propel is through catalytic reactions. Taking inspiration from Whitesides, who used the decomposition of hydrogen peroxide (H₂O₂) to propel cm/mm-scale objects on a water surface,^[123] Sen et al. (2004) fabricated catalytic motors in the micrometer range.^[92] These microswimmers were rod-shaped particles 370 nm in diameter and consisted of 1 µm long Pt and Au segments. They propelled via the decomposition of hydrogen peroxide in solution which would be catalyzed into water and oxygen. The Pt/Au rods were able to consistently reach speeds of up to 8 µm/s in a solution of 3.3% hydrogen peroxide. The decomposition of hydrogen peroxide in the Pt side produces oxygen, two protons and two electrons. The two protons and electrons will travel towards the Au, where they will be used to react with another hydrogen peroxide molecule, to produce two water molecules. The movements of the two protons and the two electrons through the rod drag the fluid towards the Au side, thus this fluid flow will propel the rod in the opposite direction. This self-electrophoresis mechanism is what powers the motion of these rods.^[93] Further analysis of the Pt/Au rods showed that they were capable of performing chemotaxis towards higher hydrogen peroxide concentrations,^[94] transport cargo,^[95] and exhibited steerable motion in an external magnetic field when inner Ni segments were added.^[95]

Responding to stimuli

Reconfigurable synthetic or artificial microswimmers need internal feedback^[125] Self-propelling microparticles are often proposed as synthetic models for biological microswimmers, yet they lack the internally regulated adaptation of their biological counterparts. Conversely, adaptation can be encoded in larger-scale soft-robotic devices but remains elusive to transfer to the colloidal scale.^[125]

The ubiquity and success of motile bacteria are strongly coupled to their ability to autonomously adapt to different environments as they can reconfigure their shape, metabolism, and motility via internal feedback mechanisms.^[126][127] Realizing artificial microswimmers with similar adaptation capabilities and autonomous behavior might substantially impact technologies ranging from optimal transport to sensing and microrobotics.^[128] Focusing on adaptation, existing approaches at the colloidal scale mostly rely on external feedback, either to regulate motility via the spatiotemporal modulation of the propulsion velocity and direction ^{[129][124][130][131]} or to induce shape changes via the same magnetic or electric fields,^{[132][133][134]} which are also driving the particles. On the contrary, endowing artificial microswimmers with an internal feedback mechanism, which regulates motility in response to stimuli that are decoupled from the source of propulsion, remains an elusive task.^[125]

A promising route to achieve this goal is to exploit the coupling between particle shape and motility. Efficient switching between different propulsion states can, for instance, be reached by the spontaneous aggregation of symmetry-breaking active clusters of varying geometry,^{[135][136][137][138]} albeit this process does not have the desired deterministic control. Conversely, designing colloidal clusters with fixed shapes and compositions offers fine control on motility ^{[139][140][141]} but lacks adaptation. Although progress on reconfigurable robots at the sub-millimeter scale has been made,^{[142][143][144][145][146]} downscaling these concepts to the colloidal level demands alternative fabrication and design. Shape-shifting colloidal clusters reconfiguring along a predefined pathway in response to local stimuli ^[147] would combine both characteristics, with high potential toward the vision of realising adaptive artificial microswimmers.^[125]

Biohybrid microswimmers

The so-called biohybrid microswimmer can be defined as a microswimmer that consist of both biological and artificial parts, for instance, one or several living microorganisms attached to one or various synthetic parts. The biohybrid approach directly employs living microorganisms to be a main component or modified base of a functional microswimmer.^[150][151] Initially microorganisms were used as the motor units for artificial devices, but in recent years this role has been extended and modified toward other functionalities that take advantage of the biological capabilities of these organisms considering their means of interacting with other cells and living matter, specifically for applications inside the human body like drug delivery or fertilisation.^{[152][153][68]}

A distinct advantage of microorganisms is that they naturally integrate motility and various biological functions in a conveniently miniaturised package, coupled with autonomous sensing and decision-making capabilities. They are able to adapt and thrive in complex in vivo environments and are capable of self-repair and self-assembly upon interaction with their surroundings. In that sense, self-sufficient microorganisms naturally function very similar to what we envision for artificially created microrobots: They harvest chemical energy from their surroundings to power molecular motor proteins that serve as actuators, they employ

In fact, the biohybrid approach can be conceived in a dualistic way, with respect to the three basic ingredients of an in vivo microrobot, which are motility, control, and functionality. Figure 1 illustrates how these three ingredients can be either realized biologically, i.e., by the microorganism, or artificially, i.e., by the synthetic component. For example, a hybrid biomicromotor based on a sperm cell can be driven by the flagellum of the sperm or by an attached artificial helical flagellum.[154]^[155] It can orient itself autonomously via biological interactions with its surroundings and other cells, or be controlled and supervised externally via artificial sensors and actuators. Finally, it can carry out a biological function, like its inherent ability to fertilize an egg cell, or an artificially imposed function, like the delivery of synthetic drugs or DNA vectors. A biohybrid device may deploy any feasible combination of such biological and artificial components in order to carry out a specific application.^[68]

Navigation

Hydrodynamics can determine the optimal route for microswimmer navigation^[156] Compared to the well explored problem of how to steer a macroscopic agent, like an airplane or a moon lander, to optimally reach a target, optimal navigation strategies for microswimmers experiencing hydrodynamic interactions with walls and obstacles are far-less understood.^[156] Furthermore, hydrodynamic interactions in suspensions of microswimmers produce complex behavior.^[157][158] The quest on how to navigate or steer to optimally reach a target is important, e.g., for airplanes to save fuel while facing complex wind patterns on their way to a remote destination, or for the coordination of the motion of the parts of a space-agent to safely land on the moon. These classical problems are well-explored and are usually solved using

There is growing interest in optimal navigation problems and search strategies [162]^{[163][164][165][166][167]} of microswimmers ^{[58][103][168][169]} and "dry" active Brownian particles,^{[170][99][171][172][156]} The general problem regarding the optimal trajectory of a microswimmer which can freely steer but cannot control its speed toward a predefined target (point-to-point navigation) can be referred to as "the optimal microswimmer navigation problem". The characteristic differences between the optimal microswimmer navigation problem and conventional optimal control problems for macroagents like airplanes, cruise-ships, or moon-landers root in the presence of a low-Reynolds-number solvent in the former problem only. They comprise (i) overdamped dynamics, (ii) thermal fluctuations, and (iii) long-ranged fluid-mediated hydrodynamic interactions with interfaces, walls, and obstacles, all of which are characteristic for microswimmers.^[99] In particular, the non-conservative hydrodynamic forces which microswimmers experience call for a distinct navigation strategy than the conservative gravitational forces acting, e.g. on space vehicles. Recent work has explored optimal navigation problems of dry active particles (and particles in external flow fields) accounting for (i) and partly also for (ii). Specifically recent research has pioneered the use of reinforcement learning ^{[173][174][175]} such as determining optimal steering strategies of active particles to optimally navigate toward a target position ^{[162][163][166][167]} or to exploit external flow fields to avoid getting trapped in certain flow structures by learning smart gravitaxis.^[176] Deep reinforcement learning has been used to explore microswimmer navigation problems in mazes and obstacle arrays ^[177] assuming global ^[163] or only local ^[164] knowledge of the environment. Analytical approaches to optimal active particle navigation ^[165][166] complement these works and allow testing machine-learned results.^{[166][167][156]}

Applications

As is the case for microtechnology and nanotechnology in general, the history of microswimmer applications arguably starts with Richard Feynman’s famous lecture There's Plenty of Room at the Bottom.^[178] In the visionary speech, among other topics, Feynman addressed the idea of microscopic surgeons, saying: "...it would be interesting in surgery if you could swallow the surgeon. You put the mechanical surgeon inside the blood vessel and it goes into the heart and <<looks>> around (of course the information has to be fed out). It finds out which valve is the faulty one and takes a little knife and slices it out. Other small machines might be permanently incorporated in the body to assist some inadequately-functioning organ." The concept of the surgeon one could swallow was soon after presented in the science-fiction movie Fantastic Voyage and in Isaac Asimov’s writings.^[1]

Only a few decades later, microswimmers aiming to become true microscale surgeons evolved from an intriguing science-fiction concept to a reality explored in many research laboratories around the world, as already highlighted by Metin Sitti in 2009.^[180][1] These active agents that can self-propel in a low Reynolds number environment might play a key role in the future of nanomedicine, as popularised in 2016 by Yuval Noah Harari in Homo Deus: A Brief History of Tomorrow.^[181] In particular, they might become useful for the targeted delivery of genes ^[182] or drugs ^[183][184] and other cargo ^[185][186] to a certain target (e.g. a cancer cell) through our blood vessels, requiring them to find a good, or ideally optimal, path toward the target avoiding, e.g., obstacles and unfortunate flow field regions.^[156]

Already in 2010, Nelson et al. reviewed the existing and envisioned applications of microrobots in minimally invasive medicine.^[187] Since then, the field has grown, and it has become clear that microswimmers have much potential for biomedical applications.^[1] Already, many interesting tasks can be performed in vitro using tailored microswimmers. Still, as of 2020, a number of challenges regarding in vivo control, biocompatibility and long-term biosafety need to be overcome before microswimmers can become a viable option for many clinical applications.^[188][1]

A schematic representation of the classification of biomedical applications is shown in the diagram on the left below. This includes the use of microswimmers for cargo transport in drug delivery and other biomedical applications, as well as assisted fertilisation, sensing, micromanipulation and imaging. Some of the more complex microswimmers fit into multiple categories, as they are applied simultaneously for e.g., sensing and drug delivery.^[1]

The design of an untethered microscopic mobile machine or microrobot to function in vivo with medical interventional capabilities should assume an integrated approach where design 3D body shape, material composition, manufacturing technique, deployment strategy, actuation and control methods, imaging modality, permeation of biological barriers, and the execution of the prescribed medical tasks need to be considered altogether, as illustrated in the diagram on the right above. Each of these essential aspects contains a special design consideration, which must be reflected at the physical design of the microrobot.^[189]

See also

• Bioinspiration
• Bio-inspired robotics
• Bio-inspired engineering
• Gray goo
• Robotic sperm
• Soft robotics
• Squirmer

References