Convective Dynamics of Swarming Enzymatic Nanomotors

doi:10.21203/rs.3.rs-3999734/v1

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Convective Dynamics of Swarming Enzymatic Nanomotors

https://doi.org/10.21203/rs.3.rs-3999734/v1

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published 29 Oct, 2024

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Enzymatic nanomotors harvest kinetic energy through the catalysis of chemical fuels. When a group of self-propelled nanomotors is placed in a fuel-rich environment, they assemble into ordered groups and exhibit intriguing swarming behaviors akin to the self-organization observed in bacterial colonies, bioconvection of aerobic microorganismal suspensions, and the coordinated movements of fish, ants, and birds. This swarming behavior presents numerous advantages compared to individual nanomotors, including expanded coverage and prolonged propulsion duration. However, the physical mechanisms underlying the swarming have yet to be fully elucidated. Our study investigates the formation of enzymatic swarms using experimental analysis and computational modeling. We show that the directional movement of enzymatic nanomotor swarms is due to their solutal buoyancy. We investigated various factors that impact the movement of nanomotor swarms, such as particle concentration, fuel concentration, fuel viscosity, and vertical confinement. We examine the effects of these factors on swarm self-organization to gain a deeper understanding. In addition, the urease catalysis reaction produces ammonia and carbon dioxide, accelerating the directional movement of active swarms in urea compared with passive ones in the same conditions. The numerical analysis agrees with the experimental findings. Our findings are crucial for the potential biomedical applications of enzymatic nanomotor swarms, ranging from enhanced diffusion in bio-fluids and targeted delivery to high- efficiency cancer therapy.

Physical sciences/Nanoscience and technology/Nanoscale materials/Nanoparticles

Physical sciences/Physics/Fluid dynamics

Biological sciences/Biochemistry/Biocatalysis

Swarming behavior is widespread in nature. While individual units of a group obey simple rules, they present complex and intriguing collective behavior when assembling into highly ordered structures¹. Living organisms use distributed or swarm intelligence to accomplish sophisticated tasks to survive. Examples range from collective cell migration², honeybees adapting to repeated shaking to maintain mechanical stability of the swarm³, to emperor penguins packing in a huddle in a highly coordinated manner to survive cold winter⁴. Multiple synthetic swarming systems have been developed with inspiration from nature. The commonly used strategies for the assembly and control of swarms include: (1) applying one or multiple external forces, such as magnetic fields^5–8, light^9,10, ultrasound^11,12, electric fields^13,14, (2) utilizing chemicals as signals^15–17, (3) combining biological microswimmers, such as sperm cells and algae, into artificial moieties as a hybrid integration^18–20, (4) exploiting DNA base-pair interactions^21,22. These well-designed swarms show many advantages compared to single-unit functionalities, like enhanced coverage and fluid mixing, intelligent multitasking, and environmental adaptation.

Micro/nanomotors (MNMs) are artificial active devices achieving self-propulsion through converting various types of energy into mechanical motion²³. Enzyme-powered MNMs harnessing energy from enzymatic catalysis of chemical fuel have been proven to show directional mobility. For instance, enzyme-modified liposome motors move directionally up or down by interacting with chemical gradients²⁴; catalase-containing microcapsules exhibit enzyme-powered oxygen gas bubble-dependent buoyancy in the presence of hydrogen peroxide, a phenomenon also known as gravitaxis²⁵; enzyme-attached macroscale sheets display clockwise or counter-clockwise rotation by a solutal buoyancy mechanism arising from enzyme pump²⁶; enzyme catalysis causes fluid flow and directional transport of tracer particles on lipid membranes²⁷. Recent findings of the enzymatic nanomotors swarming behavior highlight their potential in biomedical applications, such as accelerated diffusion in viscous media²⁸, enhanced targeted payload delivery²⁹, and more effective cancer therapy³⁰. These enhancements stem from chemical reactions and the resulting asymmetrical distribution of ions in solutions. However, understanding and controlling the collective movement of enzymatic MNMs remains a challenge.

Bioconvection is a self-organized and self-sustained vortex motion that arises naturally in suspensions of microorganisms³¹. It visually resembles the Rayleigh–Bénard convection in fluid heated from below³². The bioconvection emerges due to the unstable density gradients resulting from the accumulation of buoyant microorganisms³³. Each microorganism plays a pivotal role in driving accumulation and fluid flow. Certain gravitactic algae or aerotactic bacteria exhibit upward swimming. In the presence of an upper surface, they form a thin boundary layer of microorganism-rich heavier fluid, which becomes unstable, leading to the formation of falling plumes³⁴. Inspired by the mechanisms of bioconvection, we describe enzymatic nanomotor swarms that show gravitactic behavior and collective movement in three dimensions (3D). We model a swarm as light particulates immersed in a denser fluid environment. The particulate swarm moves upward, creating a convective flow in a closed fuel-filled space. This dynamic resembles bioconvection and sheds light on the mechanism of swarming behavior observed in enzymatic nanomotors.

In our study, we view the swarming behavior of enzymatic nanomotors from the side or from the top. Control factors for directional and collective mobility of enzymatic nanomotors, such as particle and fuel concentration and media viscosity, are investigated. In addition, their swarming behavior in vertically confined chambers is studied. The enzymatic nanomotors are based on mesoporous silica nanoparticles with urease attached (UrNMs) and dispersed in phosphate buffer saline (PBS) buffer (for the characterization of UrNMs see the Supplementary Materials Fig. S1 and the Methods). From the side, upon introducing a drop of particulate in a fuel-filled chamber, the drop shows upward motion against gravity, generating a convective flow within the closed space, Fig. 1a. As the particulate reaches the upper boundary, it expands to balance the mean upward force, forming a layer of unstable particle-rich fluid. The layer then sinks in the form of falling plumes. The upward movement of a nanomotor swarm is due to buoyancy arising from the density difference between the reaction product-rich particulate and the media with fuel. We state that individual nanomotors perform urease catalysis reactions. They generate ammonia and carbon dioxide, making the particulates less dense. We conduct computational modeling based on two-fluid hydrodynamics and compare the computational results to the experiments, demonstrating a good agreement, Fig. 1b, c.

Controlling swarming behavior of UrNMs. Swarming behavior can be viewed from the side. We studied the influence of three main control factors, UrNM concentration, urea concentration, and viscosity mediated by hyaluronic acid (HA) concentration, on the swarming behavior. As illustrated in Fig. 2a, there are three stages of the swarming behavior of enzymatic nanomotors, i.e., ascending (1, 2 and 3), spreading (2 and 3), and sinking (3). When a swarm of nanomotors seeded in the bottom of the chamber that is filled with fuel, they show directional mobility against gravity. Under different conditions, they display various forms of collective behavior and velocity. Figure 2b shows the z-component of the particulate center of mass as a function of time within 32 s. The velocity difference can be deducted from Fig. S2 showing that for higher UrNM concentrations, particulates reach a lower z position in 5 s. As the UrNM concentration increases to 20 mg/mL, the majority of the nanomotor swarms cannot get to the upper boundary due to gravity (Fig. 2b, c and video S1). The velocity field was analyzed by front tracking the particulate based on custom Python code. As expected, compared with passive nanoparticles (MSNPs), active nanomotors show enhanced upward speeds, Fig. S3 and video S2. We assume that enzymatic catalysis of urea produces microbubbles³⁵ and the product, ammonia, makes this particulate less dense. Although the product quantity may be larger with higher UrNM concentration, the density of particulate increases as well when we increase the concentration of nanoparticles. We suggest that there should be a competition between the two opposite conditions, after which the effect of increased particulate density takes the lead, and the upward particulate velocity decreases with the increased UrNM concentration. Buoyancy, the main driving force, is strongly influenced by fuel concentration. Figures 2d, e show that the upward speeds increase with the fuel concentration. One can clearly observe the upward motion of particulates at concentrations of 150 mM urea and above. However, in the presence of 100 mM urea concentration, particulate almost stays at the seeding point, and there is no difference between the upward motion of active and passive swarms. We argue that this is because in low urea concentration, density difference resulting in a buoyancy force is not sufficient to lift the particulate. We added hyaluronic acid into the fuel to change the media viscosity observing that the upward speeds of particulate decreases with the increasing concentration of hyaluronic acid, Fig. 2f, g. As it was shown above, active swarms show enhanced speed compared to passive swarms in viscous media. When the concentration of hyaluronic acid increases to 3 mg/mL, both active and passive swarms remain at the seeding point because higher viscosities inhibit fluid convection. We conducted particulate velocity analysis at elevated heights in the middle of the chamber. In Fig. 2h, active particles move slightly faster in the middle of their paths and decrease their speeds when approaching the upper boundary in different groups, while passive particles keep decreasing their speeds (Fig. S4). For instance, a particulate of 5 mg/mL UrNPs moves upward at 1.74 ± 0.09 mm/s at 4 mm height, 1.93 ± 0.14 mm/s at 5 mm height, and 1.70 ± 0.08 mm/s at 7 mm/s, while a particulate of the same concentration of passive nanoparticles moves at 0.96 ± 0.03 mm/s at 4 mm height, 0.68 ± 0.02 mm/s at 5 mm height, and 0.47 ± 0.02 mm/s at 7 mm height. The acceleration process of active particulate could be due to the density changes caused by chemical reaction products.

Products of UrNMs catalysis reaction accelerate directional movement. Urease catalyzes the decomposition of urea into ammonia (NH₃) and carbon dioxide (CO₂). On the one hand, NH₃ is highly soluble in water due to the formation of hydrogen bonds with water molecules. This interaction results in a smaller density of the solution^36,37. On the other hand, the released NH₃ dissolves in water, resulting in an alkaline solution (Fig. 3a) and promoting CO₂ to dissolve. Under proper fuel concentration, the formation of NH₃ and CO₂ microbubbles can be observed³⁵. However, in acidic buffers, such as acetate buffer (pH = 4.6, Fig. 3b), CO₂ may exist because the abundant hydrogen ions inhibit the dissolution of CO₂ and the ionization of carbonic acid. Since the temperature change during chemical reactions is hard to detect (Fig. S5), we rule out heat effect on the upward movement. We conducted experiments to verify the existence of NH₃ and CO₂. In Fig. 3c, cover papers were pre-dipped in phenol red solutions, a pH indicator. Upon adding urease or UrNMs into urea solution, NH₃ is produced and evaporates until it dissolves in the cover paper that contains phenol red, the color change of which from light yellow to pink indicates the presence of NH₃. The production of CO₂ can be observed in acetate buffer, which maintains an acidic environment during the urease catalysis reaction, Fig. 3b. CO₂ bubbles produced by UrNMs reacting with urea dissolving in acetate buffer can be observed on the wall of a cuvette (video S3). In addition, the produced NH₃ and CO₂ in acetate buffer can be directly detected by a gas sensor, an optoelectronic analysis equipment that is able to accurately detect low concentration gases at ppm level, as shown in Fig. 3d, e. The enzymatic activity of UrNMs in urea solutions in both PBS buffer (Fig. 3f, S6) and acetate buffer (Fig. S7) was examined. In PBS buffer, the specific enzymatic activity of UrNMs increases from 4.08 ± 0.02 U/mg in 50 mM urea solutions to 4.82 ± 0.41 U/mg in 300 mM urea solutions. In acetate buffer, the specific enzymatic activity of UrNMs is slightly weaker, with 1.94 ± 0.05 U/mg in 50 mM urea solutions and 3.36 ± 0.45 U/mg in 300 mM urea solutions. This is because the known optimum pH for urease catalytic activity is around 7 ~ 8³⁸. The above results indicate that urease catalysis reaction produces NH₃ and dissolved CO₂ in PBS buffer, and NH₃ and CO₂ gas in acetate buffer, which are the main reasons that cause accelerated directional movement of active UrNM swarms in urea.

Vertical confinement shapes swarming behavior. Since buoyancy is the primary force that drives the self-organization of active particulates, we studied the influence of vertical confinement on their swarming behavior. As shown in Fig. 4, microfluidic chips with three different heights (1.6 mm, 0.5 mm, and 0.25 mm) were designed and filled with urea in the vertically confined chamber. Then active UrNMs were introduced and entered the chamber from the side by capillary force. In Fig. 4a and video S4, these active UrNM swarms exhibit collective movement in the chamber of 1.6 mm height. The density maps, observed from the top, show that the swarms aggregate, coarsen, and change their patterns over time. Particle image velocimetry (PIV) also confirms that the fluid flow is initially faster when the nanomotors are injected into the chamber. Fig. S8-S10 show the PIV results at 25 s time intervals in confinement with different heights. After 50 s, nanomotors keep moving and swarming behavior is still transient. After 100 s, the fluid flow keeps a relatively high speed, 1.5 µm/s on average. However, the fluid flow direction remains the same according to the arrows. As a comparison, without fuel UrNMs sink to the bottom in a confined chamber and expand along the bottom plane, Fig. S11. The convective flow is also weaker than that caused by UrNMs with fuel, Fig. S12-14. When the vertical confinement is changed to 0.5 mm, the movement of active UrNMs becomes localized. In Fig. 4b, the density map shows that the pattern of UrNMs only slightly changes over time. The PIV reveals that fluid flow velocity decreases compared to larger height values. After 50 s, the swarms barely move. When the height is further reduced to 0.25 mm, the swarms’ movement is hindered, as displayed by the unchanged shape of swarms over time and the decreased velocity of fluid flow in PIV, Fig. 4c. Active UrNMs in PBS solutions also show decreased velocity when the chamber height decreases (Fig. S14). However, compared with the active UrNMs in fuel, there are no significant differences. We also analyzed the swarm dynamics by pixel intensity distribution. A time-lapse sequence of snapshots at 12 s time intervals from video recordings is selected. As shown in Fig. S15, in a 1.6 mm-high chamber, the pixel intensity of active UrNMs in fuel is broadly distributed in the region of interest (ROI) in the initial 60 seconds, and gradually changes to narrowly distributed in 2 min. However, for the 0.5 mm-high chamber and the 0.25 mm-high chamber, pixel intensities are monodispersed in the ROI within the time durations. As a comparison, the pixel intensities of active UrNMs in PBS solutions are highly monodispersed in the three different chambers, Fig. S16. These results indicate that the vertical confinement shapes the swarms by affecting fluid convective flows.

Computational modeling shows similarity with experiments. Our starting point is two-fluid hydrodynamics³⁹. One fluid is a solvent with the kinematic viscosity η, flow velocity v, solvent pressure p, and solvent density ρ₀. Another fluid is the particulate with the volume density ρ, coarse-grained particulate velocity u, and pressure P = qρ, and the factor q depends on the temperature (as for gases). We describe the dynamics by the simplified Navier-Stokes Eq. (1), coupled to the reaction-advection equation for the concentration of chemical fuel c, Eq. (2), and a mass transport equation for the particulate density, Eq. (3):

$${\rho }_{0}\left({\partial }_{t}\mathbf{v}+\mathbf{v}\nabla \mathbf{v}\right)= \eta {\nabla }^{2}\mathbf{v}-\nabla p-{\mathbf{z}}_{0}\rho \left(g\alpha -ϵc\right)$$

$${\partial }_{t}c+\nabla \cdot \left(\mathbf{v}c\right)= {D}_{c}{\nabla }^{2}c-\gamma \rho c$$

$${\partial }_{t}\rho +\nabla \cdot \left(\mathbf{v}\rho \right)=\left(q {\nabla }^{2}\rho +\alpha g{\partial }_{z}\rho \right)/{\kappa }_{1}$$

where z_oρєc is the volume buoyancy force due to gas generation, z_o is the unit vector in the z-direction, the gas is produced due to the reaction between fuel c and particulate r with the reaction rate g. Other parameters: fuel diffusion D_c, gravity acceleration g, relative particulate/solvent density contrast a, є is the relative buoyancy coefficient that depends on the density of reaction products, and k₁ is the normalized drag coefficient. The details of model derivation are presented in Supplementary Note 1. Equations (1)-(3) were solved by the finite difference method using Matlab. We considered a two-dimensional rectangular integration domain (corresponding to the size view) with periodic boundary conditions in the x-direction and non-slip conditions in the z-direction. The primary difference with models of enzyme-generated solutal buoyancy mechanisms considered in Ref.⁴⁰ is that the enzyme distribution is not fixed but dynamically updated by the reaction-generated flow.

When buoyancy is not sufficient to counterbalance the gravity of particulates, like in the cases of high concentration of particles and low concentration of fuel, the particulate is not able to rise to the top plane and sink to the bottom after seeding, Fig. 5a, left panel. On the contrary, in the cases of low concentration of particles and high concentration of fuel, particulates rise and spread along the top plane, then descend, experiencing a similar process as in experiment, Fig. 5a, right panel, and video S5. In simulations, the volume density ρ changes from 1 to 4, chemical fuel c ranges from 0.6–1.2, and kinematic viscosity η varies from 0.1-1.0 to simulate different concentrations of particles, fuel, and HA, respectively. In Figs. 5b-d, frames at dimensionless time 2.8 are chosen from computer videos for different parameters. Figure 5b shows that in the same time frame, particulate with smaller density ρ enters the sinking stage, while particulate with larger ρ is still in the ascending or spreading stage, indicating that lighter particulates move faster. This observation agrees with the experimental results and can be further verified by Fig. 5e. The mean velocity of particulate during upward movement decreases with the increase of density ρ. In Fig. 5c, particulate settles to the bottom when chemical fuel concentration c is low (c = 0.6). Increasing the c value (c = 0.8) triggers particulate’s upward movement, yet it settles before reaching the top plane. Only relatively high fuel concentrations force the particulate to go through the three stages, and its upward speed increases with the increase of c value. In Fig. 5f, the gradual increase of the mean particulate velocity with the fuel concentration from simulations agrees with that observed in the experiments. The effect of viscosity is shown in Fig. 5d, g. Particulate in lower viscosity media enters the sinking stage earlier than for higher viscosity. Computational modeling confirms that the increased fuel viscosity slows down the particulate motion.

Computational modeling of the vertical confinement effects. We performed computational modeling of the effect of vertical confinement on swarming behavior. The details are presented in Supplementary Note 2. The model is derived from Eqs. (1)-(3) by height-averaging using the approach like in Ref.⁴¹. The corresponding two-dimensional equations in the x-y plane are solved by the quasi-spectral method in the periodic square domain using Matlab.

Parameter β is proportional to the reaction rate and parameter e ~ h², where h is the height of the chamber. We adjust the value of these two control parameters to describe the fluid flow slowdown caused by confinement. In Fig. 6a, numerical results show that in vertical confinement, particulate moves dynamically and form aggregates in the center area of the cell. A similar phenomenon has been observed in experiment, Fig. 4a. However, when the chamber’s height is reduced, the fluid flow slows, and the reaction rate decreases. As a result, particulate movement becomes more localized, and the shape formed by a particulate remains almost unchanged within the time durations, as shown in Fig. 6b-c and video S6. Furthermore, there is no significant difference between the swarm dynamics in two highly confined chambers because fluid convection is inhibited by vertical confinement.

We investigated the swarming behavior of enzymatic nanomotors from the side and from the top. We attribute their collective behavior to buoyancy-induced convection. When introducing a drop of UrNMs, dispersed in PBS buffer, into a fuel medium (high concentration of urea dissolved in PBS), the UrNMs exhibit directional upward movement due to buoyancy arising from the density difference between the particulate and the fuel medium. UrNMs decompose urea and generate carbon dioxide and ammonia, with the latter dissolving in water, further reducing the particulate density and enhancing its upward movement. When reaching the solid-air interface, UrNMs spread along the interface, form an unstable layer of front, and then sink in the form of finger-like aggregates. The process resembles natural bioconvection in microorganismal suspensions.

Particle concentration, fuel concentration, and viscosity are crucial parameters to control enzymatic swarming behavior. Specifically, increasing particle concentration, decreasing fuel concentration, or increasing viscosity can decrease the density difference between the particulate and the fuel, impeding the initiation of upward movement and subsequent convection. This phenomenon explains the settlement of nanoparticles to the bottom when observed under inverted microscopy. Furthermore, the movement of UrNMs in vertical confinement also serves as a demonstration of buoyancy-induced convection. Confinement hinders fluid convection, indicating that the swarming behavior of enzymatic nanomotors requires vertical spaces to overcome dissipation.

We performed computational modeling based on the buoyancy-driven convection mechanisms; the results align well with experimental findings. In computational modeling, particulate ascends due to buoyancy, spreads upon reaching the top, and consequently descends because of gravity. Consistent with the experimental observations, an increase in particulate density (ρ), a decrease in fuel concentration (c), or an increase in fuel viscosity (η) decreases the mean particulate velocity. Computational modeling also agrees with experimental observations for particulate moving in vertical confinement. By adjusting the parameters β and κ, corresponding to the reaction rate and the chamber height, respectively, the computational model predicts that vertical confinement shapes the swarms by controlling fluid convection.

Synthesis of MSNPs-NH₂

Mesoporous silica nanoparticles (MSNPs) serving as chassis for urease-propelled nanomotors were synthesized by the sol-gel procedure according to our previous report⁴². The surface of MSNPs was then modified for further functionalization. Briefly, 20 mg MSNPs in ethanol 99% (Panreac Applichem cat. no. 131086-1214) and 100 µL 3-aminopropyltriethoxysilane (APTES) 99% (Sigma-Aldrich cat. no. 440140) were mixed and placed in an end-to-end shaker at room temperature for 24 h. The resulting nanoparticles were then collected and washed in water by centrifugation (4000 rpm, 5 min) four times to remove residual APTES. The collected MSNPs-NH₂ nanoparticles were dried for further use.

Synthesis of UrNMs

The prepared MSNPs-NH₂ nanoparticles (2.5 mg) were resuspended in 1mL PBS 1× (Thermo Fisher Scientific cat. no. 70011-036) and activated with 100 µL GA 25 wt% (Sigma-Aldrich cat. no. G6257) in an end-to-end shaker for 2.5 hours at room temperature. The activated MSNPs-NH₂ were then collected and washed four times in PBS 1× by centrifugation (4000 rpm, 5 min), then resuspended in 1mL PBS 1× with 3 mg urease from Canavalia ensiformis (Sigma-Aldrich cat. no. U4002). The mixture reacted at room temperature in an end-to-end shaker overnight. The resulting urease-nanomotors (UrNMs) were collected and washed thrice in PBS 1× by centrifugation (4000 rpm, 5 min). Keep the supernatant of centrifugation for further quantification of the enzyme linkage. Finally, resuspend the collected UrNMs in PBS 1× (0.5 mL) and store them in the fridge at 4℃ for future use.

DLS measurements of UrNPs

Malvern Nanosizer (Zetasizer Nano ZSP) was used to measure the diffusion coefficient of UrNPs across a range of urea concentrations (0, 50, 100, 150, and 300 mM) and the surface charge of MSNPs, MSNPs-NH₂, and UrNMs. We analyzed the diffusion coefficient of UrNPs (20 µg/mL) at each urea concentration and zeta potential values of each type of nanoparticles (20 µg/mL) with three runs per experiment. Nine measurements per type of particle were performed to obtain statistically relevant data.

UrNMs characterization.

The synthesized MSNPs were characterized by scanning electron microscope (SEM), which shows a uniform particle size distribution centered at 450 nm (Fig. S1a, b). Amino groups were then grafted on the surface of MSNPs, facilitating further modification of urease on the MSNPs surface by linking GA molecules between amino groups. The surface modification process was characterized by zeta potential measurements (Fig. S1c). The introduction of amino groups results in a negative surface charge of MSNPs reversed from − 38.7 ± 4.61 mV to a positive surface charge of 27.77 ± 7.9 mV. The subsequent linking of GA molecules and urease is confirmed by particle surface charge changes due to the presence of abundant aldehyde groups and carboxyl groups, with negative surface charge reverses to -14.5 ± 9.13 mV and − 9.02 ± 4.34 mV for GA molecule and urease, respectively. DLS measurement indicates that the prepared UrNMs show an enhanced diffusion coefficient in elevated urea concentrations (Fig. S1d).

Optical video recording

The swarming behavior of UrNMs in a vertically confined space was recorded using a Leica DMi8 microscope equipped with a high-speed cooled charge-coupled device (CCD) camera from Hamamatsu and a 2.5× objective lens. Two pieces of cover glasses were separated by spacers (Silicone isolators from Grace Bio-Labs) with varying heights: 1.6 mm, 0.5 mm, and 0.25 mm. The confined space was then filled either with PBS or with a 300 mM urea solution in PBS and positioned under the microscope. A drop of UrNMs or MSNPs (3 µL) was added to the liquid-filled chamber, and videos (25 fps, 2 min) were recorded. Optical videos from side view were recorded using a digital camera (Thorlabs, DCC1240M-GL) equipped with a lens (FUJINON, HF35HA-1S). A 24×1.6×8 mm chamber was prepared by separating two pieces of cover glasses with spacers. A drop of UrNMs or MSNPs (3 µL) was added to the liquid-filled chamber and videos (15 fps, 2 min) were recorded.

Bicinchoninic acid (BCA) assay

The amount of urease linked onto the MSNP surface was quantified by BCA analysis (Thermo Fisher Scientific cat. no. 23227), table S1. Bovine serum albumin (BSA) was used as the standard for quantifying the concentration of protein concentrations. First, a series of BSA concentrations 2000, 1500, 1000, 750, 500, 250, 125, 25, 0 µg/mL were prepared, and BSA solutions and the as-prepared supernatant of UrNMs samples were added separately into a 96-multi-well plate, 25 µL for each well. Then 200 µL of working reagent (light sensitive), made with 50 parts of reagent A and 1 part of reagent B, were added to each well that has been used, either with the BSA standards or the sample. Next, shake the plate for 30 s to mix the solutions, and incubate the reaction for 30 min at 37℃. After that, the absorption of both BSA solutions and the samples after the reaction was measured at 562 nm wavelength. Comparing the protein quantity left in the supernatant, the initial quantity of proteins added, and the standard concentrations of BSA.

Enzymatic activity measurement

Urease activity was detected before and after being linked on the surface of MSNPs and was compared in PBS and acetate buffer. 0.025 mM Phenol red (Sigma-Aldrich cat. no. 114529) was added to different concentrations of urea solutions (0, 50, 100, 200, and 300 mM). The solvent of these solutions could be either PBS or acetate buffer. 2 µL PBS solution or UrNMs or urease (130 µg/mL) were added in a 96-well plate separately, followed by the addition of urea solutions. The 96-well plate was immediately placed in a multimode microplate reader (BioTek Synergy HTX). The absorption changes of phenol red were measured in real-time at 560 nm wavelength for 60 min for measurements in PBS buffer and 100 min for acetate buffer. The incubation temperature is at room temperature, the minimal time interval for measurements is 30 seconds, and the sample was orbitally shaken at a minimal frequency.

Estimation of specific enzymatic activity

The specific enzymatic activity was determined by calculating the slope of the enzymatic activity curve. According to the Beer-Lambert law,

$$A=klc$$

where A is the absorbance, k is the molar attenuation coefficient of phenol red, and l is the path length of 0.5 cm, the concentration changes c of phenol red per minute were computed. Subsequently, the specific enzymatic activity was derived based on the quantity of enzyme utilized.

Gas detection

The generated CO₂ and NH₃ were identified using a gas detector (Dräger X-am 7000). In a glass bottle filled with urea dissolved in PBS (10 mL, 200 mM) or acetate buffer (10 mL, 200 mM), UrNMs (2.5 mg) were added, and the caps were securely fastened to prevent gas release. After 30 min, the bottle caps were removed, and the probe of the gas detector was placed over the solutions to record the generated gases.

Videos analysis

To investigate the dynamics of swarms over time, the recorded videos were analyzed by pixel intensity distribution and density maps. For pixel intensity distribution, snapshots of videos were captured at 12-second intervals. Subsequently, a region of interest (ROI) measuring 300 pixels by 300 pixels was selected, and the pixel intensity distribution within the ROI was analyzed using ImageJ software. To perform density map analysis, the videos were initially processed to remove the background using ImageJ software. Then 40-second segments were extracted from these videos. The cumulative pixel intensity of these segments, consisting of 1000 frames each, was computed and visualized using the turbo colormap.

Particle image velocimetry (PIV)

The PIV of recorded videos was conducted by a custom Python code based on the OpenPIV library. The consecutive frames of videos within desired time intervals were extracted and then loaded into the code OpenPIV, with an interrogation window size of 32×32 pixels (width×height), an overlap of 16×16 pixels (horizontal×vertical), and a frame rate of 3.33 fps. The results were then reloaded into the Python code to adjust the arrow size and display particle velocities in color bars.

Acknowledgements

The research leading to these results has received funding from the grants PID2021-128417OB-I00 and PDC2022-133753-I00 funded by MCIN/AEI/ 10.13039/501100011033 and, by “ERDF A way of making Europe” and European Union Next Generation EU, (Bots4BB and BOJOS projects). This project has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 866348, iNanoSwarms) (S.S.). The IBEC team wishes to thank the CERCA programme of the Generalitat de Catalunya, the Secretaria d'Universitats i Recerca del Departament d'Empresa i Coneixement de la Generalitat de Catalunya through the project 2021 SGR 01606, and the "Centro de Excelencia Severo Ochoa", funded by Agencia Estatal de Investigación (CEX2018-000789-S). We thank Santiago Marco Colás and Eduardo Caballero Saldivar for technical support. S.S. and S.C. acknowledge the Predoctoral AGAUR-FI Joan Oró grant (2023 FI-1 00654) funded by “Secretaria d'Universitats i Recerca del Departament de Recerca i Universitats de la Generalitat de Catalunya” and by European Social Fund Plus.

Author Contributions

S.C. synthesized and characterized the nanomotors, performed the motion and velocity analysis, analyzed the data, and wrote the paper. X.P. developed python scripts for the upward velocity analysis and developed Matlab scripts for the computational modeling. A.C.B. designed the side view setup and contributed to the simulation work. F.L. analyzed the center of mass tracking and contributed to the data processing. I.S.A conceived the initial idea, developed the computational modeling, and edited the paper. S.S. conceived the initial idea, supervised the project, and edited the paper.

Competing Interests

The authors declare no competing interests.

Data Availability

The authors declare that all the raw data underlying Figs. 2b-h, 3a-b, 3d-f, as well as Supplementary Figs. 1-7 are provided as a Source Data file and available from the corresponding author upon reasonable request.

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Supplementaryinfofinalversion.docx
Supplementary info
SIVideo1Controlfactorsinfluenceenzymaticswarmingbehavior.mp4
SI Video1
SIVideo2ControlfactorsinfluenceswarmingbehaviorofMSNPs.mp4
SI Video2
SIVideo3Bubblesproducedbyenzymaticcatalysisreaction.mp4
SI Video3
SIVideo4Verticalconfinementshapesswarmingbehavior.mp4
SI Video4
SIVideo5Computationalmodelingofthecontrolfactors.mp4
SI Video5
SIVideo6Computationalmodelingoftheverticalconfinementeffets.mp4
SI Video6

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Convective Dynamics of Swarming Enzymatic Nanomotors

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Results and Discussion

Conclusion

Methods

Synthesis of MSNPs-NH₂

Synthesis of UrNMs

DLS measurements of UrNPs

Optical video recording

Bicinchoninic acid (BCA) assay

Enzymatic activity measurement

Estimation of specific enzymatic activity

Gas detection

Videos analysis

Particle image velocimetry (PIV)

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

Convective Dynamics of Swarming Enzymatic Nanomotors

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Results and Discussion

Conclusion

Methods

Synthesis of MSNPs-NH2

Synthesis of UrNMs

DLS measurements of UrNPs

Optical video recording

Bicinchoninic acid (BCA) assay

Enzymatic activity measurement

Estimation of specific enzymatic activity

Gas detection

Videos analysis

Particle image velocimetry (PIV)

Declarations

References

Additional Declarations

Supplementary Files

Status:

Journal Publication

Version 1

Synthesis of MSNPs-NH₂