Artificial Magnetotaxis of Microbot: Magnetophoresis vs Self-swimming

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Artificial Magnetotaxis of Microbot: Magnetophoresis vs Self-swimming Wei Ming Ng, Hui Xin Che, Chen Guo, Chunzhao Liu, Siew Chun Low, Derek Juinn Chieh Chan, Rohimah Mohamud, and JitKang Lim Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01210 • Publication Date (Web): 08 Jun 2018 Downloaded from http://pubs.acs.org on June 8, 2018

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Artificial Magnetotaxis of Magnetophoresis vs Self-swimming

Microbot:

Wei Ming Ng†, Hui Xin Che†, Chen Guo§, Chunzhao Liu§, Siew Chun Low†, Derek Juinn Chieh Chan†, Rohimah Mohamud§§, JitKang Lim*,†,‡

†

School of Chemical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia.

§

State Key Laboratory of Biochemical Engineering & Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China. §§

Department of Immunology, School of Medical Sciences, Universiti Sains Malaysia, 16150 Kubang Kerian, Kelantan, Malaysia. ‡

*

Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

To whom correspondence should be addressed:

JitKang Lim School of Chemical Engineering Engineering Campus, Universiti Sains Malaysia, Seri Ampangan, 14300 Nibong Tebal, Penang, Malaysia. e-mail: [email protected] tel: +60-4-599-6423 fax: +60-4-599-1013

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ABSTRACT An artificial magnetotactic microbot was created by integrating the microalgal cell with magnetic microbead for its potential applications as biomotor in microscale environment. Here, we demonstrate the remote magnetotactic control of the microbot under a low gradient magnetic field (< 100 T/m). We characterize the kinematic behavior of the microbots carrying magnetic microbead of two different sizes, with diameter of 2 µm and 4.5 µm, in the absence and presence of magnetic field. In the absence of magnetic field, we observed a helical motion showed by the microbot as a result of the misalignment between the thrust force and the symmetry axis after the attachment. The microbot bound with a larger magnetic microbead moved with high translational velocity but rotated slowly about its axis of rotation. The viscous force is balanced by the thrust force of the microbot, resulting in a randomized swimming behavior of the microbot at its terminal velocity. Meanwhile, under the influence of a low gradient magnetic field, we demonstrated that the directional control of the microbot are based on following principles: (1) magnetophoretic force is insignificant on influencing its perpendicular motion, and, (2) its parallel motion is dependent on both self-swimming and magnetophoresis, in which this cooperative effect is a function of separation distance from the magnet. As the microbot approaching the magnet, the magnetophoretic force suppresses its self-swimming behavior, leading to a positive magnetotaxis of the microbot towards the source of magnetic field. Our experimental results and kinematic analysis revealed the contribution of mass density variation of particle-and-cell system on influencing its motion path under magnetotactic control.


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INTRODUCTION The recent decades have witnessed great progress in the design of bio-hybrid microsystems for potential applications in biomedicine, bioengineering and lab-on-a-chip devices.1 The integration of swimming bacteria,2-6 algae,7 or motile cell8 into these bio-hybrid microsystems has been proven as a promising solution in overcoming the grand challenges in the miniaturization of the on-board actuators and power sources for microsystems. Flagellated biological cells not only exhibit high motility but show huge potential to serve as on-board sensors due to their intrinsic and versatile sensing abilities.9 In this regard, different control strategies have been developed, from the cell’s sensory and behavioral response to external stimuli, in order to utilize the swimming locomotion for microscale cargo transport and delivery of microbots. These control strategies include chemotaxis,1, phototaxis,7,

15

10-12

pH-taxis,9 magnetotaxis,13-14

and electrotaxis.16 Among these strategies, magnetotaxis offers an attractive

advantage over others in which it can be used in both homogeneous and heterogeneous environments because the magnetic fields can be generated remotely. Furthermore, this method is less invasive and does not interfere with chemical and biological activities of microswimmers. In general, magnetotaxis of microbots can be achieved by the integration of magnetically responsive biological components into non-biological components, or vice versa. The primary approach is to use biological cells that are responsive to magnetic fields. Such biological cells can be either a magnetotactic bacteria13-14 which possesses naturally occurring intracellular magnetosomes, or an artificial magnetotactic cell17 with ingested magnetic nanoparticles. However, these approaches are either dependent on cells with magnetoception capability or cells that can remain viable after the ingestion of magnetic nanoparticles, limiting the type of cells that can be utilized. For the latter approach, it incorporates magnetic materials onto non-magnetic


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biological cells, creating artificial magnetotaxis for the motion control. Recently, Magdanz and co-workers presented the development of a micro-bio-robot comprising a magnetic tube driven by a spermatozoid.8 In other work, Carlsen and coworkers described the directional magnetic steering control of a superparamagnetic microbead propelled by a swarm of Serratia marcescens.18 From all these studies, the reported cell velocity driven by micron sized magnetic particle were within the range of 10 µm/s. This velocity is surprisingly low and is approaching the magnetophoretic velocity of an individual iron oxide nanoparticle with magnetic diameter at ~ 35 nm (more than 100 times smaller than those microbead used).19 For a microbead with 6 µm in diameter (exact size used in literature), by assuming only 10 % of magnetic mass, the associated magnetophoretic velocity even under the influence of extremely weak field of ~ 10 mT with low field gradient of 10 T/m is supposed to be around 162 µm/s. Hence, there is a huge mismatch between the theoretical predictions of magnetophoretic velocity with recorded velocity. In most likelihood, the thrust force associated to the self-swimming has randomized or even suppressed the migration of entire microbead-microswimmer system under artificial magnetotaxis. In addition, the effect of the magnetophoretic force is not addressed because most of the studies use a uniform magnetic field to generate magnetic torque for the direction control. Hence, it is imperative to understand the influence of self-swimming behavior towards randomizing the deterministic motion of microbots under artificial magnetotaxis. Herein, we create an artificial magnetotactic microbot by attaching magnetic material onto biological cell via electrostatic interaction between the magnetic material and the outermost layer of the biological cell. The binding of this magnetic material onto swimming microorganism imparts a positive magnetophoretic mobility to the target cell leading to rapid migration of cell to the targeted region. This method can be applied on any types of motile microorganisms. We


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demonstrate the possible use of external-attachment strategy to bind a particle directly onto the moving cell via electrostatic interaction without the need of ingestion of nanoparticles by the cell.20 This external-attachment strategy is easy to perform and less invasive to cause disruption to the biofunctionality of the microbot, especially for the biomedical and biosensing applications. This work presents a kinematic analysis on the motion trajectories of the remotely controlled microbot by low gradient magnetic field. Our work emphasizes different effects of viscous drag and magnetic forces on the self-swimming behavior of the motile cells, and reveals the dominant force for magnetic manipulation of microbot at low Reynolds number environment. This analysis is technologically important as it provides a direct evidence on the possible use of low gradient magnetic field (low energy source) to achieve motion control even though the cell is highly motile with strong thrust-force. In addition, the information collected can aid the design of magnetic separator and particles used for microalgae separation for biofuel production.21-22

EXPERIMENTAL METHODS Synthesis of Magnetic Microbeads Aliphatic amine-functionalized polystyrene latex beads were purchased from Invitrogen. We chose amine-functionalized PS (APS) beads because they were positively charged and readily to be coated with iron oxide nanoparticles. The size of the bead used were 2 µm and 4.5 µm in diameter as they can be observed clearly as compared to the size of the microalgae under the magnification used in our experiments. Co-precipitation method was employed to make a dispersion of iron oxide nanoparticles (IONPs).23-24 The IONPs synthesized via co-precipitation method had averaged size of 6.27 ± 1.28 nm as measured individually on the TEM micrograph (see Figure S1 in Supporting Information). As-received PS beads dispersion (200 µL) was mixed


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with the co-precipitated IONPs dispersion (1 mL) and left on an end-to-end rotating mixer for 1 hour, allowing the adsorption of nanoparticles onto the APS beads. Excess IONPs was removed by three centrifugation (4000 ×g)/wash/redispersion cycles. The IONPs-coated APS exhibited a negative surface charge, as determined from the electrophoretic mobility measurement. Cationic poly(diallyldimethylammonium chloride) (PDDA) with a very low molecular weight (Mw < 100,000 g/mol) was purchased from Sigma-Aldrich, Inc and used as received without modification. The IONPs-coated APS beads dispersion (200 µL) was added to deionized water (10mL) in the presence of PDDA solution (2 mL) and left on an end-to-end rotating mixer for another 1 hour to promote the deposition of cationic polyelectrolyte. Excess PDDA was removed by three repeated centrifugation (10000 ×g)/wash/redispersion cycles. The magnetic microbeads were then redispersed in deionized water (8 mL) with sonication. Culture of Chlamydomonas reinhardtii and Microscopy Study of Microbots Cultures of the microalgae were grown in Bristol’s solution subjected to continuous illumination by fluorescent light at 2000 lux. The cultivation was performed until the desired cell concentration (106 cells/mL) is achieved before the cells were harvested for experiments. The microalgal cell concentration (106 cells/mL) was fixed and the amount of magnetic microbeads added for the assembly of microbot was adjusted to maintain the consistent particle-to-cell ratio in all experiments, which is 1 magnetic microbead per cell. For instance, the magnetic microbeads dispersion (0.5mL, 107 beads/mL) was added to the cell culture (5mL, 106 cells/mL). The linkage between the microalgae and magnetic microbead was promoted through simple mixing. The physical attachment of magnetic microbead onto cell’s surface was identified through bright field optical microscope. The motion of both freely swimming microswimmer and


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Langmuir

microbot were recorded by an Olympus BX53 microscope coupled with Olympus XM10 monochrome camera used at frame rate of 15 fps. Characterization of Magnetic Microbeads The electrophoretic mobility measurement of the magnetic microbead was conducted using a Malvern Zetasize Nano-ZS. The positive electrophoretic mobility value of the PDDAIONPs-coated APS bead indicated the successful functionalization of the magnetic microbead. The magnetic property of the microbead is determined by using vibrating sample magnetometry measurement while the total Fe concentration for 2 µm and 4.5 µm magnetic microbeads were found from atomic absorption spectroscopy (AAS).

RESULTS AND DISCUSSION Synthesis and characterization of magnetic microbeads We prepared positively charged magnetic microbeads via layer-by-layer assembly approach with inner core as amine-functionalized polystyrene bead decorated with iron-oxide nanoparticles

(IONPs)

followed

by

the

outermost

layer

of

cationic

poly(diallyldimethylammonium chloride) (PDDA),25 as illustrated in Figure 1a. Figure 1b and 1c show TEM micrographs of amine-functionalized polystyrene cores at different diameters of 2 µm and 4.5 µm, respectively. Electrophoretic mobility measurement is used to provide indirect hint on the extent of the surface charge differences at each stages of preparation, as summarized in Table 1. The polystyrene core (APS) registered a positive electrophoretic mobility value due to the presence of amine group on the surface of the bead. After the attachment of IONPs, the microbead experienced surface charge reversal with a negative electrophoretic mobility value. At the final stage of the synthesis, after coated with cationic polyelectrolyte PDDA, the microbead 7 ACS Paragon Plus Environment

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recorded a positive electrophoretic mobility value, in accordance with the outermost layer being positively charged. The formation of the magnetic microbeads for 2 µm and 4.5 µm were confirmed by the TEM micrographs as shown in Figure 1d and 1e. Here we synthesized two sizes of magnetic microbeads in order to vary the magnetophoretic force used in artificial magnetotaxis experiment.

Figure 1. Preparation of magnetic microbeads. a) Schematic diagram showing the major steps involved in layer-by-layer assembly of magnetic microbeads by the mean of electrostatic interaction between opposite charged species. b-e) Transmission electron micrographs of magnetic microbeads at initial and final stages of coating process. b) 2 µm and c) 4.5 µm aminefunctionalized polystyrene beads, d) 2 µm and e) 4.5 µm magnetic microbeads after decoration of iron-oxide nanoparticles with layer of PDDA as the cationic outermost shell.

According to our vibrating sample magnetometry (VSM) measurement, the specific saturation magnetization of the IONPs is 49.6 emu/g (see M-H curve in Figure S2 in Supporting Information). Combining this information with the Fe3O4 concentration for 2 µm and 4.5 µm magnetic microbeads (determined by atomic absorption spectroscopy), the magnetic moment per magnetic microbead were 9.53 × 10-11 emu and 4.21 × 10-10 emu respectively. The calculated value of magnetic moment per magnetic microbead is the sum of the magnetic moment of individual IONPs with an assumption that all of them aligned perfectly in the same direction of


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the applied magnetic field. In the case of temporary misalignment due to thermal fluctuations, this value defines the upper bound of the magnetophoretic forces induced by the magnetic microbeads.19 Table 1. Electrophoretic mobility of magnetic microbeads at different stages of preparation recorded by Zetasizer Nano-ZS (Malvern Instruments) Electrophoretic Mobility (µm.cm/V.s) Iron oxide nanoparticles (IONPs) –2.57 ± 0.08 Amine-functionalized polystyrene bead (APS) i. 2.0 µm +1.82 ± 0.05 ii. 4.5 µm +1.98 ± 0.11 APS bead coated with IONPs i. 2.0 µm –2.65 ± 0.08 ii. 4.5 µm –2.87 ± 0.18 PDDA cationic polyelectrolyte +1.99 ± 0.15 APS-IONPs bead coated with PDDA (Magnetic microbeads) i. 2.0 µm +2.57 ± 0.07 ii. 4.5 µm +2.45 ± 0.04

Assembly of microbot We focus on the use of biflagellated unicellular microalgae Chlamydomonas reinhardtii to ferry microscale loads due to its widely investigated and welly understood swimming behavior.26-27 These microalgae are approximately spherical in shape with two anterior flagella beating synchronously to generate enough power for cell propulsion.7 They are about 5 µm in radius and due to their self-swimming behavior, and relatively large size (with approximated diffusion coefficient at 0.68 × 10-3 cm2/s), they are not susceptible to Brownian motion.27-28 The microbots in this study were assembled by attaching a positively charged magnetic microbead onto microswimmer (microalgae) by the mean of electrostatic interaction (see Figure 2).20 The cell wall of Chlamydomonas reinhardtii is a multilayered structure primarily made up


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of 4-hydroxyproline-rich glycopeptides7 and 4-hydroxyproline is a non-proteinogenic amino acid containing –COOH, and –OH functional groups (Figure 2b). The main interactions contributed to the assembly of microbots are electrostatic interactions between different charged entities: cationic polyelectrolyte PDDA (Figure 2c) on the outermost layer of the magnetic microbeads, and deprotonated carboxylic and hydroxyl functional groups present on the cell wall of the microalgae. Optical micrograph in Figure 2d illustrates the successful attachment of microbead onto the Chlamydomonas reinhardtii cell. It should be noticed that the attachment of microbead directly on to the part of cell wall where the flagellum is located has somehow suppressed its full extension into the surrounding media.

Figure 2. CR cell labelled by a microbead. a) Pictorial representation of electrostatic interaction between the cell and microbead, b) molecular structure of 4-hydroxyproline, c) molecular structure of PDDA, and, d) optical micrograph showing a 2 µm magnetic microbead was attached to a CR cell. In this work, we used microbot to represent the overall construct of microswimmer and magnetic microbead.


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Kinematic analysis of microswimmer and microbot in the absence of magnetic field We started by characterizing motility of the freely swimming microalgal cells. Bright field optical microscopy of a relatively dilute suspension of cells (106 cells mL-1) was carried out on an Olympus BX53 microscope coupled with Olympus XM10 monochrome camera used at frame rate of 15 fps. The trajectories in Figure 3 illustrate that freely swimming Chlamydomonas reinhardtii exhibits a significantly random motion. The two flagella of the microalgae beat synchronously with asymmetric power and recovery strokes at a frequency of ~ 30–60 Hz for cell propulsion.7, 29 This translates to temporal variation in swimming stroke and swimming speed of the microswimmer. Thus, the swimming speed reported here is actually averaged across the entire experimental observation duration. The swimming speed distribution (Figure 3c) determined by Gaussian fit ( g(x) =

 ( x − µ )2  1 exp−  , µ = mean = 95.9 and σ = 2σ 2  2π 

standard deviation = 14.9) shows a peak at 95.9 µm/s, compared well with other researchers’ works.7, 28

Figure 3. Self-swimming microalgae. a) Chlamydomonas reinhardtii trajectories over an interval of 1 s. The solid dots indicate the final position of the cells. b) Time lapse images showing the 11 ACS Paragon Plus Environment

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freely swimming cell which is marked by red arrow. c) Swimming speed distributions of the cells.

After the microalgal cells were mixed with the magnetic microbeads, they bound to each other via electrostatic interaction. We maintained the same particle-to-cell ratio (1:1) in all experiments. Most of the microswimmers carried one bead, but we did observed few microalgal cells transported two or more magnetic microbeads and motile cell without any bead attachment. However, under low Reynolds number, where viscous force dominates, the geometry of the swimming microbot becomes a significant factor in determining the hydrodynamic interaction with the surroundings fluid.30-31 Thus, we limited our observation and analysis to one magnetic microbead per single cell as the viscous drag experienced by multiple beads per single cell would be extremely difficult to predict due to its geometry. After the attachment, the microbots were observed under the optical microscope. The microbots carrying a magnetic microbead of 2 µm, and 4.5 µm still remained motile for at least 3 hr (see Movie S1 and S2 in Supporting Information for their mobilities over time). The trajectories of the microbots carrying different sizes of magnetic microbeads in the absence, and presence of magnetic field were observed and recorded under the optical microscope (Figure 4a). We analyzed the trajectories of 4 microbots for each size of magnetic microbead used (Figure 4b-c). Each microbot composed of a single microbead. In the absence of magnetic field (solid line trajectories shown in Figure 4b-c), the microbot carrying a magnetic microbead of 2 µm (#1-4), and 4.5 µm (#5-8) moved with two dimensional velocity of 10.9 ± 4.8 µm/s, and 8.7 ± 4.0 µm/s, respectively. In addition, we observed that the microbots possess two dimensional oscillatory trajectories when they carry a magnetic microbead, which indicates a helical motion in three dimension.18 Similarly, Edwards and co-workers observed that a 5 µm


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polystyrene bead driven by a single Serratia marcescens in the far-wall regime executes periodic, helical trajectories.32 Since the microbot showed a helical motion after the attachment of magnetic microbead, the velocity is insufficient to reflect the actual dynamical behavior of the microbot. This is because the velocity indicates the rate of change of displacement by computing the difference between the initial and final position of the microbot before the introduction of magnetic field over its travelling time in the movie captured, and it is only a characteristic of directionality of motion.33 Therefore, we estimate the apparent speed of the microbot, which is calculated as the sum of its total distance travelled divided by its total travelling time. The average apparent speeds of the microbot carrying a magnetic microbead of 2 µm (#1-4), and 4.5 µm (#5-8) were 23.7 ± 7.0 µm/s, and 18.3 ± 5.0 µm/s, respectively. Besides, we calculated the angular velocity to describe the rotational component of the helical motion for the microbot given that the dominant frequency of the motion was known. The frequency can be estimated based on the Fast Fourier Transform (FFT) for the time series of the x and y coordinates of the microbot, which are decomposed from its trajectories.32-33 From the FFT, the frequency component with the largest amplitude was selected from each series. Thus, the averaged angular velocity calculated from the frequency for the microbots carrying a magnetic microbead of 2 µm (#1-4), and 4.5 µm (#5-8) were 5.5 ± 3.2 rad/s, and 6.8 ± 2.9 rad/s, respectively. Summarized FFT analysis results and angular velocity calculations can be found in the Supporting Information. Here, it is noted that the recorded video only allows for observations in two dimensions though the helical motion analysis should be done in three dimensional domains. Under this scenario, the loss of data in the third dimension may cause the path analysis to be misleading.34 However, the two dimensional analysis done on the helical motion of the


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microbot is still sufficient to approximate its kinematic behavior in our case as long as an oscillatory motion can be observed in the two-dimensional x-y projection.

Figure 4. Magnetotaxis of microbot carrying magnetic microbead. a) Time lapse images showing the magnetotactic response of microbot under the magnetic field. The red arrows and arcs have been added to each frame to indicate the position of the microbot and magnetic source respectively. It is noted that the position of magnetic source is marked according to the direction of magnetic field and does not represent the exact position of the mu-metal tip. For the first 1 s, the microbots carrying a magnetic microbead of 2 µm, and 4.5 µm showed no magnetic response and swam helically in the absence of magnetic field. When the magnetic field was introduced at time t = 1.0 s, the microbots carrying a magnetic microbead of 2 µm, and 4.5 µm moved towards the magnetic source. These images were cropped out from the movies captured for different sizes 14 ACS Paragon Plus Environment

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of magnetic microbeads, which were provided in the Supporting Information. The complete trajectories of microbots carrying a single magnetic microbead of b) 2 µm, and c) 4.5 µm were presented for an interval of 5 s. The sector of circle drawn by red dotted line shows the position of mu-metal tip in the dispersion of microbot. Each trajectory consists of two parts: solid line represents the motion paths of microbot in the absence of magnetic field and dotted line represents their motion paths under the influences of low gradient magnetic field when the mumetal tip was magnetized by a NdFeB magnet. The solid dot indicates the final position of the microbots where their locations can still be determined precisely. The magnified view of motion paths of microbots 1 – 8 in the absence of magnetic field are provided in Supporting Information Figure S3.

We performed a kinematic analysis on the speed of the microbot. The swimming motion of Chlamydomonas reminisces the breaststroke pattern in human swimming: the flagella are pulled back in a nearly straight shape, and are then bent over and pushed forward again.26, 35 This swimming gait exerts a thrust in front of the cell, which classifies the microalgae into a pullerlike microswimmer.36 If the gravitational and buoyancy effects are neglected, the microswimmer experiences an equal but opposite drag force exerted by the surrounding fluid as it swims at terminal velocity. In addition, the flagella can beat in a time-periodic way and yet create nonzero time-averaged propulsion.37 Hence, the resulting thrust force would be taken as a timeaveraged value in our analysis. By taking into account of all aforementioned contributions, the thrust force can be estimated from the drag force exerted on part of body that does not contribute in the self-swimming (the spherical body of the microalgae cell). Under low Reynolds number environment (Re ~ 9.59 × 10-4 in our experiment) where the viscous force dominates,31 Stokes’ law can be used to evaluate the viscous drag force. Thus, the thrust force of the microalgae is 9.04pN as calculated by the equation given: F thrust = Fdrag = 6πη rc v c

(1)

where η is dynamic viscosity of water (10-3 Pa/s), rc is radius of the microalgae (5 µm), and v c is swimming velocity of the microalgae (95.9 µm/s).


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Likewise, when a magnetic microbead is attached onto the microalgae, the thrust force of the microbot can be approximated as the viscous drag force exerted on the microbot. Since the magnetic microbead is attached directly onto the microalgae, they may be considered as a single entity.30 From our observation as depicted in Figure 2d, the shape of the microbot can be approximated as a spheroid moving parallel to its major axis. Thus, the thrust forces of the microbot carrying a magnetic microbead of 2 µm and 4.5 µm are 1.06 ± 0.47 pN and 0.89 ± 0.41 pN respectively, as given by:30 Fthrust, m = Fdrag, m = 6πη Kbv m

(2)

where b is semi-minor axis of the microbot, K is a geometric correction factor to Stokes’ Law, and v m is velocity of the microbot. Please refer to Supporting Information for the definition of semi-minor axis of the microbot and equation for the geometric factor K. Here, the helical trajectories justified the approximation of microbot as a spheroid is appropriate as the motion of a spherical body will attain a steady terminal motion in which it merely translates without rotating.30 The periodic nature of the microbot’s trajectory shed new insights into the mechanism underlying its motion. Before the assembly of the microbot, the self-swimming behavior of the microbead alone would be dominated by Brownian motion as described by Stokes-Einstein equation. When the microbead was attached onto the microalgae, the microbead and the microalgae moved together as a single entity, in consequence of the irreversible attachment between them. Since the propulsion of the microbot is solely contributed by the microalgae, the off-axis of the microalgae thrust force from the microbead center will lead to the existence of torque, resulting in the helical motion of the microbot.32 Remarkably, these helical trajectories suggest that the microbot experiences both translational and rotational motions, which are


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dominated by near-constant force and torques.32 As the stroke of the flagella is time-periodic, the measured average translational and rotational velocities should be constant with respect to the microbot, and this leads to helical trajectories. In short, the helical motion of combined translation and rotation is caused by the misalignment between the mean thrust force of the microbot and the symmetry axis after the attachment of magnetic microbead. The ratio of swimming velocity to the rotation rate of the microbot (v/f) indicates the translational distance by one revolution of the microbot.38 The average v/f for the microbot carrying a magnetic microbead of 2 µm, and 4.5 µm are 16.95 µm, and 8.68 µm respectively. In other words, the microbot can move across a distance of 16.95 µm when it make a revolution about its axis of rotation if it carries a 2 µm magnetic microbead, whereas for the case of 4.5 µm magnetic microbead, the microbot could only swim for 8.68 µm per revolution. It should be noted that the microbot with the fastest rotational rate was not the fastest swimming microbot. This is because the effect of rotation increases as the misalignment of the mean thrust force from the bead center of mass (measured as moment arm) increases due to large variation in mass density distribution about the center of mass. From the conservation of energy perspective, the total kinetic energy of the microbot is constant, and hence, the translational velocity will decrease if the rotational rate increases. Thus, we could see that the microbot carrying a magnetic microbead of 2 µm move with higher translational velocity but lower rotational velocity compared to the case of 4.5 µm magnetic microbead. Artificial magnetotaxis of microbot In order to understand the influence of low gradient magnetic field on the migration pathway of the microbots, the position of the microbot with respect to the magnetic field must be determined accurately. In this study, the magnetic field gradient ∇‫ ܤ‬was generated using a 17 ACS Paragon Plus Environment

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triangular piece of mu metal sheet. The sharp end of the tip was placed in an aqueous dispersion containing the microbots while the blunt end was in contact with a 5 mm cardboard spacer (Supporting Information Figure S5). When a thin NdFeB bar magnet was brought in close contact of cardboard spacer, the mu metal tip was magnetized. We mapped out the space variation of the magnetic field from the mu metal tip by using a Gaussmeter model GM2 from AlphaLab Inc. Please refer to Figure S6 in Supporting Information for the information related to magnetic field strength and gradient used in our artificial magnetotaxis experiment. When the mu-metal tip was magnetized, producing a low gradient magnetic field (at tip edge ∇‫ ≈ ܤ‬67 T/m), all microbots migrated towards the tip. If the end of the tip acted as a point dipole, we would expect the convergence towards a single point from the microbots’ trajectories under the magnetic field.19 In our experiments, it was assumed that the absolute magnetophoretic displacement of the microbot was parallel to the field line emanating from the surface of the tip. The magnetophoretic trajectories of the microbots (the dotted line portions in Figure 4) were consistent with the assumption made. Thus, the measurement of magnetic field as a function of a single distance coordinate (distance from the mu-metal tip), ∇B ≈

dB is adequate for our dr

analysis. When the microbot was exposed to a magnetic field, magnetophoretic force Fmag was introduced on the microbot due to the presence of magnetic microbead as given by

Fmag = µ

dB dr

(3)

where µ is magnetic moment and B is magnetic flux density. Since inertia is negligible under low Reynolds number environment, it is neglected in the present analysis for simplicity.31 Thus, the kinematic equation governing the motion of the microbot can be expressed as: 18 ACS Paragon Plus Environment

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mm

dv m = Fmag + Fdrag, m + Fswim = 0 dt

(4)

where mm is the microbot’s mass and Fswim is the swimming force supplied by the microalgal cell. Please note that the thrust force term used here is the force of forward motion, which equals in magnitude but opposite in direction to the viscous drag exerted on the microbot according to Newton’s third law of motion. In the absence of magnetic field, the thrust force is originated from the self-swimming of the microbot due to the beating of the flagella. In contrast, the thrust force under a magnetic field is an outcome of combinatorial effect between the magnetophoretic force and self-swimming of the microbot. Thus, the term swimming force is used to represent the thrust force associated with the self-swimming of the microalgal cell in the presence of magnetic field. For a better quantitative analysis on the microbot’s motion, all the vectors involved in our study were resolved parallelly and perpendicularly with respect to the direction of the magnetic field gradient (main reference axis), as depicted in Figure 5. Thus, the velocity v at every time step was decomposed to v|| , the velocity parallel to the main axis (∇‫ ܤ‬direction), and v ⊥ , the velocity perpendicular to it. Similarly, the swimming and viscous drag forces were decomposed into parallel force components ( Fswim, || and F drag, || ), and perpendicular force components ( Fswim, ⊥ and Fdrag, ⊥ ).


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Figure 5. Microbot in the presence of low gradient magnetic field. a) Resolution of velocity into v|| and v ⊥ . b) Free-body diagram of the microbot visualizes the relationship of all forces acting on the microbot which dictates its motion under the influence of magnetic field. In this force balance analysis, the direction of ∇‫ ܤ‬is taking as the main reference axis where the microbot experiences Fmag. Here, we further calculate the Fmag based upon magnetophoresis equation (Eq. 3).

In order to understand the effect(s) of artificial magnetotaxis on self-swimming behavior of the microbot, we conducted a force balance analysis on the parallel force component of the microbot as the perpendicular force balance is not affected by the magnetophoretic force. The assumption made here is that all the force acting on the microbot’s center of hydrodynamic stress.30 When the microbot is moving towards the mu-metal tip due to magnetophoretic force, the viscous drag force acts in the opposite direction of the magnetophoretic force ( Fdrag, || = − 6πη Kbv || ). Upon rearrangement of Equation (4) in the direction parallel to the magnetic field, F swim, || can be calculated as follows:

Fswim,|| = 6πηKbv|| − µ

dB dr

(5)

Figure 6 illustrates the changes in F mag and Fswim, || of the microbot with respect to its distance from the tip in the magnetic field during magnetophoresis. The comparison of these two forces becomes an indicative of the deterministic motion of the microbot: self-swimming versus


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magnetotaxis. At the incipient of magnetophoresis, the microbot had a negative value parallel swimming force ( F swim, || < 0), which implies that the microbot intended to move in the direction opposed the magnetophoretic force Fmag . However, Fmag is greater in magnitude than the F swim, || and it suppresses the self-swimming of the microbot, leading to a positive magnetotaxis of the microbot. As the microbot moves closer to the tip, Fmag increases and F swim, || changes gradually from negative to positive which confirmed that the microbot had shifted its initial heading towards the direction of magnetophoretic force. We could see that the microbots carrying a magnetic microbead of 2 µm, and 4.5 µm changed their direction of swimming at about 170 µm, and 310 µm from the tip, respectively. Instead of swimming in random direction, the microbot experienced a directional magnetotactic control, as a result from the cooperative effect between F swim, || and Fmag . As F swim, || is a behavourial force of the microbot in its response to the

magnetophoretic pulling under the magnetic field, it can only be determined experimentally. Thus, the fitting of our experimental data using least squares method has suggested that F swim, || can be regressed as a logarithmic function of distance from the mu-metal tip as F swim, || ( r ) = A ln r + B . This regression equation is useful in the discussion of velocity and

acceleration in the latter section.


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Figure 6. Scatter plot of all the magnetophoretic and resolved parallel swimming forces for the microbots carrying a magnetic microbead of a) 2 µm, and b) 4.5 µm under the influence of low gradient magnetic field. The solid line represents the regression for the spatial changes of Fswim, || and the dotted line represents the 95% prediction interval of the regression.

We recorded nearly constant v ⊥ for both microbots carrying different sizes of magnetic microbeads when they approached the mu-metal tip, as illustrated in Figure 7a and 7b, respectively. In this case, v ⊥ was a result of the counterbalance between Fswim, ⊥ and Fdrag, ⊥ as there is no magnetophoretic force acting on it in the perpendicular direction of the magnetic field gradient. In contrast, their v|| increased when they moved towards to the tip. The viscous drag force should be completely independent of position while F mag and Fswim, || increases when the microbot gets closer to the tip as described by magnetophoretic force equation and regression model of Fswim, || respectively. Upon the rearrangement of Equation (5), a kinematic model of v|| can be expressed as a function of distance from the mu-metal tip r as follows:

µ v|| (r ) =

dB + Fswim,|| (r ) dr 6πηKb


(6)

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Thus, the v|| determined from the kinematic model and obtained from experiment for both size of magnetic microbeads were plotted under the same graph in Figure 7a and 7b, respectively. It was found out that the experimental trend of v|| was in good agreement with our mathematical analysis. At any distance from the mu-metal tip, v|| for the microbot carrying magnetic microbead of 4.5 were always higher than that of 2 µm as the magnetophoretic force acting on it increased with the total magnetic mass of magnetic microbead carried. In the presence of magnetic field, the microbot moved towards the mu-metal tip driven mainly by magnetophoretic force. The increasing trend of v|| as the microbot gets closer to the mu-metal tip simply implied that the microbot accerelates towards the tip. Here, the mathematical expression for acceleration of the microbot can be determined from the differentiation of v|| by applying the chain rule as follows:

a (r ) =

where

 dv||  dr   dv||    =  (− v|| ) =  dt  dr  dt   dr 

dv||

(7)

dr is the rate of change of distance from the mu-metal tip, which is equal to − v|| . Upon dt

subsitution of Equation (6) into Equation (7), the acceleration of the microbot can be expressed as a function of the distance from the mu-metal tip as:

a(r ) = −

1  d 2 B dFswim,||  dB   µ 2 +  µ + Fswim,|| (r )  6πηKb  dr dr  dr 

(8)

The comparisons on the acceleration determined from the kinematic model and those values obtained experimentally for magnetic microbeads of 2 µm, and 4.5 µm were plotted in Figure 7c and 7d, respectively. The consistency between these two results confirmed the validity of our two major assumptions/hypotheses, namely: (1) the magnetophoretic force is insignificant


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on influencing the perpendicular motion of the microbot, and, (2) the motion path of microbot under the low gradient magnetic field are collectively influenced by magnetophoresis and its self-swimming with this combinatorial effect expressed as a function of distance from magnetic source. If we compared the acceleration curves for both sizes of magnetic microbeads, the acceleration of the microbot carrying a 4.5 µm magnetic microbead is lower than that of 2 µm. This observation seems counterintuitive as the acceleration supposes to increase, hence, having larger magnetic mass should translate to greater magnetophoretic force. However, when a magnetic microbead is attached onto the microalgae, it breaks the symmetry of the microbot and this cause the relocation of center of mass with respect to the geometry of the microbot. The attachment of 4.5 µm magnetic microbead imposes a large variation in mass density distribution around its center of mass as compared to that of 2 µm, leading to a higher resistance to its acceleration.39 The microbot carrying a magnetic microbead of 2 µm that gets into this acceleration radius, about 200 µm away from the tip (Figure 7c), has increasing v|| as it approached the tip. Here, the acceleration radius is defined as the critical distance from the tip, where the microbot experienced non-zero acceleration. For the case of 4.5 µm magnetic microbead, the acceleration radius has been extended to ~400 µm (Figure 7d). Along this line of thought, when the magnetic mass of the microbot increases, we could see that the magnetophoretic force increases and this leads to the expansion of the acceleration radius (see Figure S7 in the Supporting Information). The acceleration radius defines the spatial resolution for the successful implementation of magnetotactic control. In addition, the effect of the inertial force can be evaluated from Figure 7c and 7d by multiplying the mass and the accereleration of the microbot. Given the masses of the microbot carrying a magnetic microbead of 2 µm, and 4.5 µm are 5.61 × 10-10 g, and 6.14 × 10-10


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g respectively, the inertial forces calculated would be in the magnitude of several femto-Newtons. Since these values are much smaller than other forces involved (see Figure 6), whose magnitude of pico-Newtons, the effect of inertia is negligible and Equation (4) remains valid in our analysis. In our experiment, the magnetotactic control is based on the magnetophoretic force rather than magnetic torque. The latter steering control can exploit the self-swimming behaviour of the microbot by apply a uniform magnetic field that generates magnetic torque. Instead of a random heading direction, the microbot can be steered to a desired direction by aligning their heading with the direction of the applied magnetic field. For such application, it is critical to assess the direction of motion of the microbot with respect to the polarity of the magnetic field before conducting a path following task.18 However, the magnetophoretic force based control presented here does not require a preliminary study to observe the heading direction of the microbot, which depends on the orientation of its swimming force vector with respect to the magnetic moment of the bead. Here, all we need is to make sure the magnet is located in the targeted area (direction). The magnetophoretic force introduced onto the microbot by the field gradient would suppress its randomized self-swimming, leading to a positive magnetotaxis in the desired direction.


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Figure 7. Scatter plot of v ⊥ and v|| for the microbots carrying a magnetic microbead of a) 2 µm, and b) 4.5 µm under the influence of low gradient magnetic field. Scatter plot of acceleration a for the microbots carrying a magnetic microbead of c) 2 µm, and d) 4.5 µm in its motion direction. The comparison between the experimentally measured data ( v|| and a represented by symbols) and their kinematic model calculation (solid line) were presented in each figure.

CONCLUSIONS We have revealed the transport behavior of an artificial magnetotactic controlled microbot in the absence and presence of low gradient magnetic field. The artificial magnetotactic microbot was assembled by electrostatically attaching a magnetic microbead onto a motile microalgal cell. In the absence of magnetic field, the microbot possessed helical motion as a result of the misalignment between its mean thrust force and the microbead center of pressure after the 26 ACS Paragon Plus Environment

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attachment of microbead. The increase in microbead size leads to lower translational velocity but higher rotational velocity of the microbot in its helical motion. At low gradient magnetic field, the microbot showed a positive magnetotaxis and eventually accelerated towards the magnet. The kinematic analysis on the magnetophoretic trajectories explained the underlying mechanism of magnetotaxis of the microbot. As the microbot moved closer to the tip, its self-swimming (as quantified by the parallelly resolved component of the swimming force to the direction of magnetic field) was no longer opposed to the magnetophoretic force and became a cooperative effect in the directional motion of the microbot under a magnetic field, leading to a successful magnetotactic control of randomly swim microbot. One of the most significant advantages contributed by the directional control based on the magnetophoretic force is the rapid capture of the microbot during magnetotaxis. The magnetic field gradient increases as the distance from the magnetic source decreases. When the microbot enters the acceleration zone where the acceleration become significant, the entire control scheme is achieved in real time within seconds. The use of a high magnetic mass lowers the acceleration of the microbot, but it further extend the acceleration radius, and hence, increase the effective spatial scale of magnetotactic control scheme. Moreover, this scenario has also suggested that the spatial magnetotactic control of the microbot in the magnetic field can be achieved by varying its magnetic mass. In conclusion, the bio-hybrid micro-robotic approach presented here opens up new opportunity for the integration of magnetotactic control scheme into any applications that utilized motile microorganism to do work at microscale environment. This study could provide mechanistic insight in the design and application for magnetic system involving the use of bio-hybrid microbot.


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ASSOCIATED CONTENT Supporting Information available: (Section S1) Overview of movies, (Section S2) Size distribution of IONPs synthesized via co-precipitation method, (Section S3) Magnetic moment of the magnetic microbeads produced, (Section S4) Magnified individual trajectories of all microbots in the absence of magnetic field, (Section S5) Two dimensional quantitative analysis for the helical motion of the microbots, (Section S6) Flow past a spheroid moving parallel to its major axis, (Section S7) Overview of the magnetic source used in the experiment, (Section S8) Magnetic field and magnetic field gradient generated by the magnetized mu-metal tip, (Section S9) Trajectories of all microbots under the same plot. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]. Tel: 604-599-6423. Fax: 604-594-1013. ORCID number: 0000-0002-3205-1617 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS W.M. Ng gratefully acknowledges the scholarship from Universiti Sains Malaysia (USM) Fellowship Scheme. This work was financially supported by USM Bridging Fund (#6316097) and USM RUI Grant (#8014062) and the National Natural Science Foundation of China


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(No.21476242). J.K. Lim gratefully thanks the Chinese Academy of Sciences (CAS) Fellowships for Young International Scientists to support his visit to IPE-CAS at Beijing.

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Artificial Magnetotaxis of Microbot: Magnetophoresis vs Self-swimming

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