Nano/Micromotors in Active Matter

Nano/micromotors (NMMs) are tiny objects capable of converting energy into mechanical motion. Recently, a wealth of active matter including synthetic colloids, cytoskeletons, bacteria, and cells have been used to construct NMMs. The self-sustained motion of active matter drives NMMs out of equilibrium, giving rise to rich dynamics and patterns. Alongside the spontaneous dynamics, external stimuli such as geometric confinements, light, magnetic field, and chemical potential are also harnessed to control the movements of NMMs, yielding new application paradigms of active matter. Here, we review the recent advances, both experimental and theoretical, in exploring biological NMMs. The unique dynamical features of collective NMMs are focused on, along with some possible applications of these intriguing systems.


Introduction
From the steam engine invented by Thomas Newcomen in the 18th century to today's advanced aeroengine, a variety of motors have helped mankind to change the world. Nowadays, alongside macroscopic motors, nano/micromotors (NMMs) have attracted increasing attention due to their important applications and novel functions [1,2]. For example, myosin, dynein and kinesin that are natural NMMs can carry molecular goods along with cytoskeletal fibers [3]. Self-assembled active colloidal systems are artificial NMMs powered by light and can rotate in a liquid crystal [4]. Advances in synthetic biology, nanotechnology, and control strategies have greatly facilitated the creation and manipulation of NMMs.
Recently, active matter has become popular and is a fundamental unit for manufacturing NMMs. In general, active matter belongs to nonequilibrium-condensed systems [5]. Compared with inactive counterparts, active matter can transform ambient or stored energy into movement and drive the whole systems out of equilibrium [6,7]. This property endows active matter systems with rich collective behaviors, which can be harnessed to design and fabricate NMMs.
Common active matter includes animal groups moving collectively, reconstructed cytoskeletal filaments (RCFs), bacterial suspensions, cell tissues and artificial systems from self-propelled colloidal particles to robotic swarms [8,9]. Derived from the cell cortex, the treadmilling process of filaments and interaction between molecular motors and filaments make RCFs active [10]. In bacterial suspensions, bacteria exhibit coupling of random fluctuation and active motion [6]. These self-propelled Brownian particles can drive passive objects to move in suspensions [11] and show directed motion on an asymmetry base [12]. Cell tissues like sperm can also power NMMs [13].
In this review, we focus on NMMs in active matter and discuss several representative types of NMMs. In Section 2, we describe the concept and properties of RCF-based NMMs. We discuss the application of RCF-based NMMs in mimicking cell structure and transporting molecular cargos. In Section 3, we explain the principle of bacterium-based

Mimicking Cellular Structures via RCF-Based NMMs
When assembled in droplets or vesicles, RCF-based NMMs can form active bun [27], nematic layers [15] or cortex-like networks [28,29], which can be leveraged to m cellular structures. This type of NMMs exhibits amazingly cell-like activities. Equip with depletion agents and composite motors, MTs can form cilia-like active bundles a interface of air bubbles [27]. These MT bundles show self-oscillation, akin to the mo of flagellums of chlamysomonas. Composite motors consisting of biotin-labeled kinesin streptavidin power the entire NMMs. In the right proportions, one molecule of strep din can combine with two molecules of biotin-labeled kinesin. Such composite motors bind and move along two neighboring MTs simultaneously, resulting in relative disp ment between them [27] and this property makes composite motors widely use NMMs consisting of MT-kinesin systems.
As they are organized on the flat surface, the MT-kinesin system exhibits cohe spontaneous flows, which can drive the whole droplet to move [15]. Similarly, when capsulated into unilamellar vesicles, the microfilament-myosin system can self-orga to cortex-like networks [28,29]. Using RCF-based NMMs to mimic cellular structures tributes to an understanding of the role of structures such as cell cortex and flagellu cell movement and deformation and can also provide a basis for the making of artif cells. As they are organized on the flat surface, the MT-kinesin system exhibits coherent spontaneous flows, which can drive the whole droplet to move [15]. Similarly, when encapsulated into unilamellar vesicles, the microfilament-myosin system can self-organize to cortex-like networks [28,29]. Using RCF-based NMMs to mimic cellular structures contributes to an understanding of the role of structures such as cell cortex and flagellum in cell movement and deformation and can also provide a basis for the making of artificial cells.

RCF-Based NMMs for Self-Organizing Molecular Transport
Radial structures of MTs are very common in cells; for example, radial spindles form during mitosis to separate the chromosomes [30]. In vitro experiments showed that MT-kinesin systems can self-assemble to radial MT asters with the help of central anchored molecules [31] or polymer-stabilized microfluidic droplets [32], which are unique biotemplates for the assembly of NMMs. When combining with MT asters, functionalized composite cytoskeletal motors can carry molecular cargo along MTs to implement specific functionalities. This kind of RCF-based NMMs can be used for a self-organizing molecular transport.
For example, using NMMs consisting of the MT-kinesin system, a fish melanophorelike optical device can be assembled [31] (Figure 2). Powered by kinesin motors, MTs in the chamber arrange to an aster with minus ends located in the center and plus ends located in the edge. Dynein motors can transport pigment granules along such MT aster to its center, which can change the chamber's color pattern. This principle is similar to the color-changing mechanism of zebrafish pigment cells. When designed DNA molecules are added, these motors can achieve more complex functions [26]. Specific instructions are encoded in DNA sequences, which can be used to control the assembly and disassembly of MT asters, or to load and unload cargos. A self-organizing molecular transport system makes it possible to fabricate complex functional NMMs.
like optical device can be assembled [31] (Figure 2). Powered by kinesin motors the chamber arrange to an aster with minus ends located in the center and plus cated in the edge. Dynein motors can transport pigment granules along such MT its center, which can change the chamber's color pattern. This principle is simila color-changing mechanism of zebrafish pigment cells. When designed DNA m are added, these motors can achieve more complex functions [26]. Specific instruct encoded in DNA sequences, which can be used to control the assembly and disa of MT asters, or to load and unload cargos. A self-organizing molecular transpor makes it possible to fabricate complex functional NMMs.

RCF-Based NMMs as Bioshuttle
If we attach the motor molecules to the substrate, the cytoskeletal filament pushed to glide along the substrate (Figure 1b). In this experiment system, RCFs assemble into nanowire and nanospool structures [33] (Figure 3a). On a large sca can arrange to polar and nematic order states, which can coexist and transition other [17]. These interesting phenomena motivate us to modify and optimize suc imental systems to manufacture NMMs, and so bioshuttles come into being [34ure 3b). Cytoskeletal filaments are used as shuttles and powered by cytoskeletal on the plane or in well-designed micro-tracks. Nitta et al. [35] analyzed the dispe active transport by bioshuttles and found that it is comparable to the transport troosmotic flow. Protein linkers are attached on cytoskeletal filaments, so RCF-bas tles can carry cargo molecules [37,38]. Besides carrying goods, this kind of NMM used in parallel computation and biosensors [39,40]. By photoetching, combinator lems are encoded into the structure of networks. Propelled by molecular motors, c etal filaments explore the nanostructured network and solve the mathematical p independently. With the help of bioshuttles, Fischer et al. [40] designed a smart d sensor to monitor the environment in organisms or public spaces. In order to de bioshuttles rationally, Nitta et al. [36] simulated the transport properties of micr by the Monte-Carlo method. The emergence of bioshuttles explores the potential tion of RCF-based NMMs in cargo deliver, biosensors and biocomputation.

RCF-Based NMMs as Bioshuttle
If we attach the motor molecules to the substrate, the cytoskeletal filaments can be pushed to glide along the substrate (Figure 1b). In this experiment system, RCFs can self-assemble into nanowire and nanospool structures [33] (Figure 3a). On a large scale, RCFs can arrange to polar and nematic order states, which can coexist and transition to each other [17]. These interesting phenomena motivate us to modify and optimize such experimental systems to manufacture NMMs, and so bioshuttles come into being [34][35][36][37][38] (Figure 3b). Cytoskeletal filaments are used as shuttles and powered by cytoskeletal motors on the plane or in well-designed micro-tracks. Nitta et al. [35] analyzed the dispersion in active transport by bioshuttles and found that it is comparable to the transport by electroosmotic flow. Protein linkers are attached on cytoskeletal filaments, so RCF-based shuttles can carry cargo molecules [37,38]. Besides carrying goods, this kind of NMM can be used in parallel computation and biosensors [39,40]. By photoetching, combinatorial problems are encoded into the structure of networks. Propelled by molecular motors, cytoskeletal filaments explore the nanostructured network and solve the mathematical problem independently. With the help of bioshuttles, Fischer et al. [40] designed a smart dust biosensor to monitor the environment in organisms or public spaces. In order to design the bioshuttles rationally, Nitta et al. [36] simulated the transport properties of micro-tracks by the Monte-Carlo method. The emergence of bioshuttles explores the potential application of RCF-based NMMs in cargo deliver, biosensors and biocomputation.

NMMs Consisted of Bacterial Suspensions
Bacteria are a common kind of active particles which achieve active movement through motor organelles such as flagella and cilia [41,42]. In suspensions, bacteria can not only self-organize to form patterns such as bacterial membrane and bacterial chain [43], but also have the property of self-propulsion, which can drive passive particles to a directed motion [6]. These properties of bacteria make them ideal materials for synthesizing or propelling NMMs. In this Section, we review the NMMs composed or powered by bacteria.

Bacterium-Driven Directed NMMs
Back in the 1960s, Feynman pointed out that in nonequilibrium systems, a directed motion can arise from the chaotic dynamics of molecules [44]. Even on asymmetry substrate, Brownian particles show random disordered motion. However, when nonequilibrium conditions such as external periodic drive, particles show spontaneously directed motion which known as ratchet effect [6,45,46]. These unique and directional motions derived from nonequilibrium and asymmetry open the way to assemble bacterium-driven directed NMMs. In this type of NMM, micro-shuttles and micro-gears act as motors, and bacteria propel the whole NMMs by colliding with the motors.
Bacterium-driven directed NMMs often display ratchet effect. The breaking in spatial symmetry and time symmetry is essential for supporting directed motion [47]. Through experiments and simulations, arrow-shaped [11] and wedge-shaped [48] micro-shuttles spontaneously perform directed motions in bacterial suspensions. Motion speed shows dependence on the shuttle-shape [11]. Once the shape of the structures is determined, their motion speed increases and then decreases with the bacterial density in the suspensions

NMMs Consisted of Bacterial Suspensions
Bacteria are a common kind of active particles which achieve active movement through motor organelles such as flagella and cilia [41,42]. In suspensions, bacteria can not only self-organize to form patterns such as bacterial membrane and bacterial chain [43], but also have the property of self-propulsion, which can drive passive particles to a directed motion [6]. These properties of bacteria make them ideal materials for synthesizing or propelling NMMs. In this Section, we review the NMMs composed or powered by bacteria.

Bacterium-Driven Directed NMMs
Back in the 1960s, Feynman pointed out that in nonequilibrium systems, a directed motion can arise from the chaotic dynamics of molecules [44]. Even on asymmetry substrate, Brownian particles show random disordered motion. However, when nonequilibrium conditions such as external periodic drive, particles show spontaneously directed motion which known as ratchet effect [6,45,46]. These unique and directional motions derived from nonequilibrium and asymmetry open the way to assemble bacterium-driven directed NMMs. In this type of NMM, micro-shuttles and micro-gears act as motors, and bacteria propel the whole NMMs by colliding with the motors.
Bacterium-driven directed NMMs often display ratchet effect. The breaking in spatial symmetry and time symmetry is essential for supporting directed motion [47]. Through experiments and simulations, arrow-shaped [11] and wedge-shaped [48] micro-shuttles spontaneously perform directed motions in bacterial suspensions. Motion speed shows dependence on the shuttle-shape [11]. Once the shape of the structures is determined, their motion speed increases and then decreases with the bacterial density in the suspensions [48]. This is because, at low density, the more bacteria there are, the greater the co-propelling force is. In the case of high density, things become different. The system shifts into the jamming state, where the more bacteria there are, the less able the object is to move. Besides wedge-like structures, asymmetric structures such as micro-gears can also be used as NMMs in bacterial suspensions [49][50][51]. Angelani et al. [49] numerically proved that it is possible to assemble bacterium-driven directed gears. The key point of this kind of NMMs is trapped bacteria in corners so that bacteria can provide continuous torque for the directional rotation of gears. Di Leonardo et al. [50] and Sokolov et al. [51] fabricated several kinds of chiral micro-gears which can spontaneously rotate in bacterial baths (Figure 4a,b). Vizsnyiczai et al. [52] created more efficient 3D micro-gears ( Figure 4c). Ramp structures are designed to guide bacteria into the rotor chamber in the right direction, through which the efficiency and stability of the NMMs are improved obviously. These studies suggest that we can extract energy from bacterial suspensions through well-designed machines, providing promising route towards engineering new NMMs.
Micromachines 2022, 13, x 6 of 19 [48]. This is because, at low density, the more bacteria there are, the greater the co-propelling force is. In the case of high density, things become different. The system shifts into the jamming state, where the more bacteria there are, the less able the object is to move. Besides wedge-like structures, asymmetric structures such as micro-gears can also be used as NMMs in bacterial suspensions [49][50][51]. Angelani et al. [49] numerically proved that it is possible to assemble bacterium-driven directed gears. The key point of this kind of NMMs is trapped bacteria in corners so that bacteria can provide continuous torque for the directional rotation of gears. Di Leonardo et al. [50] and Sokolov et al. [51] fabricated several kinds of chiral micro-gears which can spontaneously rotate in bacterial baths (Figure 4a,b). Vizsnyiczai et al. [52] created more efficient 3D micro-gears (Figure 4c). Ramp structures are designed to guide bacteria into the rotor chamber in the right direction, through which the efficiency and stability of the NMMs are improved obviously. These studies suggest that we can extract energy from bacterial suspensions through well-designed machines, providing promising route towards engineering new NMMs.

Bacterium-Based NMMs Applying to Particles Transport and Separation
In addition to converting energy into directional motion, bacterium-based NMMs can also apply to particles transport. In these NMMs, bacteria act as motors to drive cargo molecules. Some numerical works have investigated the flow of bacteria in channels and the interactions between bacteria and particles [53][54][55]. Based on these simulation, Turiv et al. [56] used streams of bacteria to deliver glass sphere. Nguyen et al. [57] assembled a liposomal bacterium-based NMM to delivery anti-cancer drug. The liposomes loaded with paclitaxel are connected with bacteria via streptavidin-biotin binding mechanism. Driven by bacteria, these NMMs can reach the lesion and release the drugs that target at

Bacterium-Based NMMs Applying to Particles Transport and Separation
In addition to converting energy into directional motion, bacterium-based NMMs can also apply to particles transport. In these NMMs, bacteria act as motors to drive cargo molecules. Some numerical works have investigated the flow of bacteria in channels and the interactions between bacteria and particles [53][54][55]. Based on these simulation, Turiv et al. [56] used streams of bacteria to deliver glass sphere. Nguyen et al. [57] assembled a liposomal bacterium-based NMM to delivery anti-cancer drug. The liposomes loaded with paclitaxel are connected with bacteria via streptavidin-biotin binding mechanism. Driven by bacteria, these NMMs can reach the lesion and release the drugs that target at tumor. With similar binding mechanism, Suh et al. [58] bound poly(lactic-co-glycolic acid) nanoparticles to a tumor-targeting bacterium. They prove that compared with passive diffusing drug particles, these drug delivery NMMs can penetrate deeply in poorly vascularized tumor tissue.
Bacterium-based NMMs can also be used in particle separation. Particle separation is a current research hotspot and has been applied in mature fields. For example, Wang et al. [59] prepared anisotropic structural color particles by phase separation of graphene oxide and silica nanoparticles in droplets. These particles are endowed with specific functions and can be used in cell culture, sensing and other aspects. When well-designed barriers are placed in a bacterial bath, particle separation can also occur in this kind of NMM. A wealth of simulations [60,61] and experiments [12,62,63] confirmed that bacteria can be guided to directional motion by microstructures. Funnel-shaped walls in the flow cell can be used to rectify the flow state of initially uniform bacterial suspension [62] (Figure 5a) or to concentrate bacteria [63]. Reichhardt et al. [60] numerically proved that the strength of ratchet effects in these NMMs are dependent on the barrier geometry and the topological property and density of bacteria. tumor. With similar binding mechanism, Suh et al. [58] bound poly(lactic-co-glycolic acid) nanoparticles to a tumor-targeting bacterium. They prove that compared with passive diffusing drug particles, these drug delivery NMMs can penetrate deeply in poorly vascularized tumor tissue. Bacterium-based NMMs can also be used in particle separation. Particle separation is a current research hotspot and has been applied in mature fields. For example, Wang et al. [59] prepared anisotropic structural color particles by phase separation of graphene oxide and silica nanoparticles in droplets. These particles are endowed with specific functions and can be used in cell culture, sensing and other aspects. When well-designed barriers are placed in a bacterial bath, particle separation can also occur in this kind of NMM. A wealth of simulations [60,61] and experiments [12,62,63] confirmed that bacteria can be guided to directional motion by microstructures. Funnel-shaped walls in the flow cell can be used to rectify the flow state of initially uniform bacterial suspension [62] (Figure 5a) or to concentrate bacteria [63]. Reichhardt et al. [60] numerically proved that the strength of ratchet effects in these NMMs are dependent on the barrier geometry and the topological property and density of bacteria. NMMs-mediated particles transport and separation have a wide range of applications. Active particles can be separated in terms of their swimming modes or chirality [6,64,65]. If funnel-shaped walls are arranged along designed structures, the NMM can be used to display specific patterns [63]. Koumakis et al. [12,61] confirmed that bacteria can spontaneously and efficiently deliver and store colloidal beads in designed asymmetry 3D structures. Figure 5b shows the main geometric features of asymmetric barriers. At the same barrier height, if ab  , bacteria can transport beads into the centers of barrier; if ab  , the barrier centers are the forbidden zones of beads. A generalized effective temperature has been introduced to explain the property of this motor [61]. Bacterium-driven directed motors and NMMs-mediated particles transport and separation demonstrate that bacterium-based NMMs have wide applications for fabrication and use in bio-machines. NMMs-mediated particles transport and separation have a wide range of applications. Active particles can be separated in terms of their swimming modes or chirality [6,64,65]. If funnel-shaped walls are arranged along designed structures, the NMM can be used to display specific patterns [63]. Koumakis et al. [12,61] confirmed that bacteria can spontaneously and efficiently deliver and store colloidal beads in designed asymmetry 3D structures. Figure 5b shows the main geometric features of asymmetric barriers. At the same barrier height, if a > b, bacteria can transport beads into the centers of barrier; if a < b, the barrier centers are the forbidden zones of beads. A generalized effective temperature has been introduced to explain the property of this motor [61]. Bacterium-driven directed motors and NMMs-mediated particles transport and separation demonstrate that bacterium-based NMMs have wide applications for fabrication and use in bio-machines.

NMMs Consisted of Cells
Cells can also be used to manufacture NMMs. On the one hand, cell populations exhibit polarization and alignment [66,67], and the kinetic energy and enstrophy of cell monolayer collective flows obey q-Gaussian distribution [68]. These findings shed light on the potential biomedical applications of assembling cell-based NMMs. On the other hand, properties as diverse as self-propulsion and biocompatibility enable the NMMs a wide application prospect. In this Section, we will review NMMs consisted of different types of cells.

NMMs Powered by Sperm Cells
Like the bacteria described above, sperm cells are also flexible micro-swimmers, which offers a route to make NMMs. Taking the human sperm cell as an example, it consists of a disc-like head containing genetic information and a long tail which provides a powerful boost to the movement [69]. Biocompatibility, efficient locomotion in the low Reynolds number flow and manipulability make sperm cells become an ideal power source for NMMs [70]. The most common sperm-based NMMs are composed of well-designed microcap and the sperm cell [13,[71][72][73][74] (Figure 6). The microcap provides the object for functionalizing the NMM, while the sperm cell serves as the motor for the power. Khalil et al. [73,75] simulated the hydrodynamic effects of NMMs in a low Reynolds number heterogeneous viscous medium and provided theoretical support for the manufacture of NMMs powered by sperm cells.

NMMs Consisted of Cells
Cells can also be used to manufacture NMMs. On the one hand, cell populations exhibit polarization and alignment [66,67], and the kinetic energy and enstrophy of cell monolayer collective flows obey q-Gaussian distribution [68]. These findings shed light on the potential biomedical applications of assembling cell-based NMMs. On the other hand, properties as diverse as self-propulsion and biocompatibility enable the NMMs a wide application prospect. In this Section, we will review NMMs consisted of different types of cells.

NMMs Powered by Sperm Cells
Like the bacteria described above, sperm cells are also flexible micro-swimmers, which offers a route to make NMMs. Taking the human sperm cell as an example, it consists of a disc-like head containing genetic information and a long tail which provides a powerful boost to the movement [69]. Biocompatibility, efficient locomotion in the low Reynolds number flow and manipulability make sperm cells become an ideal power source for NMMs [70]. The most common sperm-based NMMs are composed of well-designed microcap and the sperm cell [13,[71][72][73][74] (Figure 6). The microcap provides the object for functionalizing the NMM, while the sperm cell serves as the motor for the power. Khalil et al. [73,75] simulated the hydrodynamic effects of NMMs in a low Reynolds number heterogeneous viscous medium and provided theoretical support for the manufacture of NMMs powered by sperm cells. The design of materials and structures of the microcap will give NMMs specific properties and functions. Magdanz et al. [72] fabricated thin ferromagnetic microtubes and coupled them to bull spermatozoa (Figure 6c). An external magnet can direct the motion of these NMMs. Xu et al. [71] designed a tetrapod ferromagnetic microstructure, and the can protect against oxidative stress that may damage sperm cells [74]. Together, NMMs driven by sperm cells have a good prospect in cargo delivery and targeted therapy and have become a potential treatment for gynecological diseases and cancer.

NMMs Consisted of Somatic Cells
Somatic cells are collections of all cells except for germ cells. Somatic cells can also apply for manufacturing NMMs. Herein, we mainly introduce the NMMs composed of red blood cells (RBCs) and cardiomyocytes.
RBCs are natural molecular vehicles in the body. The typical shape of mammals' RBCs is the biconcave disk. When maturing, RBCs of mammals lose nuclei and all other cellular organelles that improve cargo and deformation capacities [76]. According to the propulsion mode, RBC-based NMMs can be divided into self-propulsion NMMs [77] and field-driven NMMs [78][79][80]. For self-propulsion RBC-based NMMs, RBCs are assembled with bacteria into hybrid NMMs, in which bacteria provide propulsion force and RBCs are responsible for loading cargos. For field-driven RBC-based NMMs, the outfield drive is realized by loading specific particles in RBCs. Alapan et al. [77] designed bacteriumpropelled biohybrid NMMs (Figure 7a). RBCs loaded with anticancer drug molecules and magnetic nanoparticles are bound with bacteria, which provide autonomous propulsion for NMMs. Dreyfus et al. [79] assembled an artificial flagellum to drive RBC-based NMMs. The magnetic particles are coated with streptavidin and particles are linked with doublestranded DNA with biotin at each end. A uniform magnetic field is used to align these flagella and another orthogonal magnetic field can drive flagella to oscillate to produce the driving force. Wu et al. [80] and Gao et al. [78] encapsulated molecule cargos and magnetic nanoparticles into RBC-based NMMs (Figure 7b). These NMMs can move spontaneously in ultrasonic field and the direction of motion is controlled by magnetic field. Guo et al. [81] rebuilt RBCs that mimic the properties of native RBCs. Via loading ATP biosensors in rebuild RBCs, this NMM can be used to sense toxin. Due to biocompatibility and ability to travel throughout the body with the circulatory system, RBC-based NMMs are ideal systems for drug delivery.  Muscle cells can also power NMMs because of the ability of powerful contraction [82][83][84][85]. Williams et al. [82] engineered self-propelled sperm-like NMMs. These NMMs are composed of polydimethylsiloxane filaments, which are akin to the sperm cells in shape. Cardiomyocytes are cultured on the tail. The contraction of cardiomyocytes drives the periodic deformation of filaments to power the NMM movement. Guided by bionics and optogenetics, Park et al. [83] created a stingray-like artificial animal. The architecture of this NMM includes a golden skeleton, a muscle layer and two elastomer layers. Through muscle circuits, light stimulation can be used to activate muscle to drive the whole NMM. Inspired by the color changing mechanism of chameleons, Fu et al. [84] developed living structural color hydrogels. Cardiomyocytes drive the periodic changes of inverse opal structure to achieve self-regulation. Chen et al. [85] found that when cultured on Morpho butterfly wings, cardiomyocytes recovered their autonomous beating ability through cell orientation and good contractility. They used cardiomyocytes to cause the wings to periodically deform, giving rise to the corresponding structural color. Similar self-powered hybrid NMMs have also been used to make bionic fish [86] and caterpillar-like soft robots [87]. These NMMs, with the help of bionics, not only reveal the mechanisms of the corresponding life processes, but also explore technical routes for the construction of intelligent actuators and soft robots.

Regulation and Control of NMMs
For motors in daily life, we control them by encoding in order to function better. Likewise, we are eager to stimulate the potential of NMMs based on active matter. In this Section, we review a variety of methods that are used to regulate and control the NMMs.

Physical Field
Although NMMs are capable of converting stored energy to mechanical movement, most of them still require external factors to accomplish a more controllable motion [88]. External physical fields as diverse as light and magnetic field are widely used to regulate and control the behaviors of NMMs.

Light
In the 1980s, Jean-Marie Lehn proposed the light-coupled transport process [89], which is the source of light-regulated NMMs [88]. In recent years, with the rapid development of optogenetics and photocatalysis, the light source has been explored in-depth to regulate the behaviors of NMMs based on active matter [31,52,83,90,91].
Introducing light-activated proteins into the NMM systems is one of the control routes. Ross et al. [92] achieved light-controlled formation, fusion and motion of MT asters via synthetic motors assembled by fusing kinesin motors to optically dimerizable iLID proteins. When exposed to light, the synthetic motors form dimers that can bind and move along two neighboring MTs. Zhang et al. [93] used light-sensitive myosin motors to control the movement of defects. Qu et al. [94] proposed a similar method to control the flow field. Ahamd et al. [95] synthesized light-driven energy vesicles containing bacteriorhodopsin, a light-driven proton pump that can actively transport proton across the cell membrane [96] and EF 0 F 1 -ATP synthase, which can use proton gradient to synthesize ATP. They adopted light-powered vesicles to control the beating frequency of flagella and the contraction of MT networks (Figure 8a).
Activation and deactivation of light-controlled chemical material release are another approach to control and regulate NMMs. This method is common in inactive matter-based NMMs, represented by tiny spheres coated with specific chemicals [97]. Shao et al. [90] introduced this approach in RBC-based NMMs. With the metal sputter-coating method, they produced Janus polymeric particles half covered with gold. In order to move efficiently in the biological environment, erythrocyte membranes are coated on these particles. When exposed to the light, a thermal gradient is generated due to asymmetric distribution of Au, which makes it possible to drive these NMMs to move. Hess et al. [91] controlled the motion of bioshuttle via UV-induced release of caged ATP (Figure 8b). The artificial optical device is activated in a similar way [31].
Light can control the motion direction and velocity of NMMs. Park et al. [83] used the relative intensity among light sources to guide the stingray-like NMM maneuver through constraints. Vizsnyiczai et al. [52] controlled the rotational speed of bacterium-based NMM via light intensities. They designed E. coli bacteria, which express bacteriorhodopsin on the membrane. The bacteria can move continuously under the light source, achieving continuous operation of NMMs. The rotational speed can be modulated by adjusting the speed of bacteria and by changing the light intensity. Light can also control the density of bacteria to display patterns. Frangipane et al. [98] introduced genetically modified bacteria, whose motion speeds are controlled by light. They display patterns by changing the density of bacteria in local areas, and can switch between different patterns (Figure 8c).

Magnetic Field
Since Dreyfus et al. [79] assembled magnetically driven and controlled NMMs, magnetic fields have been widely used in the control of NMMs. For different active matter-based NMMs, the implementation of magnetic control is different. For sperm cell-based NMMs, introducing ferromagnetic structure is the main way to realize magnetic control [13,71,72]. Sperm cells can produce powerful thrusts, while ferromagnetic microcaps surrounding their heads regulate the direction of the movement in the magnetic field (Figure 8d). Guided by a magnetic field, sperm cell-based NMMs can navigate through complex passageways to the desired location. For RBC-based NMMs, magnetic control can be achieved by wrapping magnetic nanoparticles or magnetic hemoglobin in RBCs [78,80]. The existence of magnetic nanoparticles also makes it possible for magnetic resonance imaging. Magnetic control shows great potential in RCF-based NMMs. At the oil-water interface experiments, Guillamat et al. [99,100] introduced octyl-cyanobiphenyl(8CB) molecules in the oil layer. 8CB molecules align with the direction of the magnetic field. In orthogonal magnetic field, topological defects can be arranged along the magnetic field [99]. Under the rotating magnetic field, some novel defect structures are generated in active nematic swirls [100]. Zhang et al. [101] explored the general mechanism of pattern synthesis and control in the active system using an electromagnetic field to regulate the active time. In order to improve the application value of magnetic control, more effects need to be realized in the accurate fabrication methods and the make of degradable magnetic materials.
Micromachines 2022, 13, x 12 of 19 [99]. Under the rotating magnetic field, some novel defect structures are generated in active nematic swirls [100]. Zhang et al. [101] explored the general mechanism of pattern synthesis and control in the active system using an electromagnetic field to regulate the active time. In order to improve the application value of magnetic control, more effects need to be realized in the accurate fabrication methods and the make of degradable magnetic materials.

Topological Constraint
In recent years, the effects of topological constraint on active matters have attracted extensive attention. Sipos et al. [102] showed that bacteria can swim along convex wall for a long time, which is called wall entrapment behavior. Bianchi et al. [103,104] studied the mechanism underlying wall entrapment in bacteria suspensions. Experiments and numerical studies showed that the size, topological structure and anchoring properties of constraints have marked influences on RCF systems [105][106][107]. Motivated by these behaviors, topological constraints become a method to regulate and control the behaviors of NMMs. As mentioned before, the ratchet effect promotes the emergence of bacteriumdriven NMMs [50,51]. Mahmud et al. [108] used micropatterned ratchets to control the cell motions. They realized non-movement, random movement and directional movement through adjusting the shape of the micro-structure. Hess et al. [109] introduced a ratchet effect in RCFs. In pinwheel patterns, MT-based shuttles can be sorted by the motion direction. Doot et al. [110] generated RCF networks in ratchet channels. Motors can move along the networks to transport cargos directly.
Topological constraints can control the motion of RCFs and regulate the assembly of self-organizing structures [111][112][113]. Clemmens et al. [111] designed a complex track including reflector function, crossing function and circular concentrator to sort and collect bioshuttles. Inoue et al. [112] found that RCFs can form dynamic adaptive patterns according to constraints. Thijssen et al. [113] controlled the motion and number of topological defects in active nematic flow by submersed micropatterns. Clemmens et al. [114,115] analyzed the principles of MTs guiding in the microchannels. They demonstrated that the edges combine both topography and chemistry to attain the highest guiding efficiency, which provides theoretical support for the design of bioshuttles.
The design and arrangement of constraints enable NMMs to achieve a variety of functions. Nicolau Jr. et al. [39] designed a pass junction and a split junction to guide the motion of actin filaments and MTs. By properly arranging these microstructures, RCF-based parallel computation can be realized (Figure 9). Saper et al. [116] adopted kinesin motors and constraints to accelerate the assembly of MTs. Hess et al. [117] merge the images of MTs gliding on the substrate to explore the surface properties. A piconewton forcemeter is assembled with the RCF-based NMM [118]. These brilliant ideas open up the possibility of building smart nanorobots in the future. edges combine both topography and chemistry to attain the highest guiding efficiency, which provides theoretical support for the design of bioshuttles. The design and arrangement of constraints enable NMMs to achieve a variety of functions. Nicolau Jr. et al. [39] designed a pass junction and a split junction to guide the motion of actin filaments and MTs. By properly arranging these microstructures, RCFbased parallel computation can be realized (Figure 9). Saper et al. [116] adopted kinesin motors and constraints to accelerate the assembly of MTs. Hess et al. [117] merge the images of MTs gliding on the substrate to explore the surface properties. A piconewton forcemeter is assembled with the RCF-based NMM [118]. These brilliant ideas open up the possibility of building smart nanorobots in the future.

Chemical Field
Chemical field can also control and regulate NMMs in active matter. Most active matter-based NMMs require fuel consumption during operation, so the movement of these NMMs can be controlled by tuning the level of chemical substances such as ATP and oxygen [119]. Sokolv et al. [51] regulated the rotation speed of bacterium-driven gears by tuning the amount of oxygen available to the bacteria. The chemical gradient field can be used to control the direction of the NMMs' movement. Using chemotaxis, bacteriumbased NMMs can induce deflection or directional motion under specific substance concentration gradients [120][121][122]. Singh et al. [123] explored the use of concentration gradi-

Chemical Field
Chemical field can also control and regulate NMMs in active matter. Most active matter-based NMMs require fuel consumption during operation, so the movement of these NMMs can be controlled by tuning the level of chemical substances such as ATP and oxygen [119]. Sokolv et al. [51] regulated the rotation speed of bacterium-driven gears by tuning the amount of oxygen available to the bacteria. The chemical gradient field can be used to control the direction of the NMMs' movement. Using chemotaxis, bacterium-based NMMs can induce deflection or directional motion under specific substance concentration gradients [120][121][122]. Singh et al. [123] explored the use of concentration gradient-guided bacterium-based NMMs to deliver anticancer drugs. A glucose gradient is created on the Transwell membrane, and bacterium-based NMMs move towards cancer cells under the guidance of glucose concentration gradient. Other chemicals can also affect the movement of NMM. Liu et al. [124] designed logic gates through multilink 3D printing of bacteria. Three kinds of logic gates including AND, OR and NAND can be obtained by changing the biochemical molecular compositions in the hydrogel at the inputs. Keya et al. [125,126] controlled the collective behavior of RCF-based NMMs via introducing DNA molecules into the systems. They devised photoresponsive DNA to control the NMM switching between solitary and swarm. Genetic engineering has expanded the application of biochemical molecular control. Curatolo et al. [127] introduce engineered E. coli to realize complex dynamic behaviors such as phase separation, oscillation and co-location of different populations.

Algorithmic Navigation and Control
The experimental realization of various control strategies paves the way for NMMs to serve as micro/nanoscopic robots that are capable of performing instructed tasks in complex micro-environments. Among the various potential real-world applications ranging from drug delivery to precision surgery to environmental remediation, one fundamental task is to navigate an NMM between two points in an environment. Challenges arising from this task include long-distance travel on the scale magnitudes larger than an NMM, unknown or dynamically changing environment with obstacles and dead-ends. There have been efforts directed towards developing various navigation strategies, including decision rules derived from heuristics [128,129], from the Markov decision process framework [130], as well as from data-driven learning-based methods [131,132]. Particularly, state-of-the-art learning-based method leverages the learning capacity and generalizability of deep neural networks to derive decision rules that enables robots to navigate in unknown environments. Beyond single NMM, collectively controlled NMM swarms can form intelligent systems that carry out non-trivial tasks such as cargo capture and transport in micro-structured environments [133,134].

Conclusions
In this review, we introduce three kinds of NMMs consisting of active matter including RCF-based NMMs, bacterium-based NMMs and cell-based NMMs. We also discuss the methods to control and regulate NMMs, including physical field, topological constraint, and chemical field, as well as algorithmic control and navigation. Biocompatibility, robustness, and ease of handling make active matter-based NMMs, promising applications. Cargo delivery is one of these applications. Active matter-based NMMs can be guided by the field or self-controlled to carry goods to designated areas. The propulsive force even allows these NMMs to penetrate the membrane structures of the cell and deliver cargos to the interior. Biomedical therapy is another application. At the cellular scale, cargo delivery application allows active matter-based NMMs to acquire targeted drug delivery capability, which can improve the therapeutic efficiency. At the tissue level, these NMMs can be applied to wound healing, thrombolysis and tissue imaging. Environmental detection and nano/micro sensing are also potential applications of active matter-based NMMs. Algorithmic control and navigation address controller design challenges when employing these NMMs as futuristic robots at the microscopic scale.
Despite great progress, active matter-based NMMs still face many challenges before they can enter daily life. First, the process of preparing NMMs in large quantities needs to be explored. In this process, quality control of the products as well as production costs need to be considered. Second, current functions are relatively simple and unitary. How to assign complex functionality to active matter-based NMMs is a problem when it comes to solving real problems. Third, developers must demonstrate the efficiency and reliability of the active matter-based NMMs before it can be put to use.
In summary, active matter-based NMMs have a wide application prospect. The research and development of NMMs provide technological paths for the manufacture of nanorobots, bio-machines and even artificial life. The 1966 movie Fantastic Voyage depicts the future of nanomachines: astronauts perform brain surgery in a tiny submarine that penetrates into a patient's bloodstream [135]. Perhaps in the near future, a similar scenario will appear in life, with the slight difference that doctors will control the active matter-based NMMs to be implemented.