Collective Dynamics of Urease‐Based Nanomotors in a Chemical Gradient

Abstract

Gradients are widespread in nature, including within the human body, making the study of nanomotors’ collective dynamics in gradients crucial to advancing biomedical applications and deepening the understanding of natural active matters. However, the comprehensive understanding of nanomotors’ collective dynamics under gradients remains underexplored, particularly. This study employs urease‐based nanomotors (UrNMs) as a model system to explore their collective dynamics within a urea gradient, revealing three fundamental principles that govern their behavior: density‐driven convection, UrNMs’ response to the urea gradient, and a coupling effect between UrNMs and their environment. Initially, migration is dominated by convection‐induced motion arising from the steep gradient. As convection gradually diminishes, UrNMs' positive response to the urea gradient becomes the dominant factor governing their migration. Notably, the coupling effect between nanomotors and the gel, plays a crucial role in the migration process. This coupling effect arises from hydrogen bonding between product anions and the gel, which generates ionic gradients. The dominant influence of electric force is validated by pH‐controlled experiments. These insights advance the fundamental understanding of gradient‐responsive nanomotor behavior and offer inspiration for the design of intelligent, environment‐sensitive active systems.

This study investigates the collective migration of urease‐based nanomotors in a urea gradient. It identifies three governing mechanisms: density‐driven convection, chemotactic response to urea, and a coupling effect arising from ion–gel interactions. The coupling effect induces self‐generated ionic gradients that modulate migration through electric forces. These findings provide insights into active matter behavior under physiochemical gradients and contribute to the design of intelligent, responsive nanomotor systems.

1. Introduction

The collective behavior of chemically propelled nanomotors, often referred to as “active particles” or “active colloids,”^{[ 1 ]} provides valuable insights into natural phenomena such as vortex formation, swarming, and clustering.^{[ 2} , ³ , ^{4 ]} Beyond their fundamental significance, the unique non‐equilibrium properties of nanomotors offer potential breakthroughs in biomedical applications, particularly in targeted delivery and enhancing diffusion at localized sites.^{[ 5} , ⁶ , ^{7 ]} However, most studies on the collective behavior of nanomotors have focused on homogeneous systems with uniform physiochemical parameters, conditions that are far removed from the complex, gradient‐driven environments commonly found in nature.^{[ 8 ]} In biological and other natural systems, various chemical gradients, such as pH gradient,^{[ 9 ]} oxygen gradient,^{[ 10 ]} and reactive oxygen species gradient^{[ 11 ]} are prevalent. These gradients arise from the localized sources, such as tissues and cell clusters, and are shaped by reaction‐diffusion processes. Understanding nanomotors’ collective migration in such gradient environments is therefore essential for uncovering active matter dynamics and advancing the design of intelligent, environmentally responsive nanomotors for applications.

Current research on the collective migration of nanomotors under chemical gradients generally follows a common methodology: 1) establishing a mesoscale gradient (10² µm–10² mm) using microfluidic^{[ 12} , ¹³ , ^{14 ]} or static diffusion^{[ 15} , ¹⁶ , ^{17 ]} techniques, 2) capturing periodic images at fixed locations (typically at intervals of 0.5–2 h over a spatial range of ≈10² µm), and 3) analyzing fluorescence intensities to calculate migration displacement. A range of systems, including those powered by catalase,^{[ 13 ]} urease,^{[ 16 ]} ATPase,^{[ 18 ]} glucose oxidase,^{[ 19 ]} Zinc oxide,^{[ 20 ]} and nanozymes,^{[ 21 ]} have demonstrated directional migration (often referred to as “chemotaxis”) along fuel gradients. The prevailing explanation is that nanomotors accumulate in regions where substrate binding lowers the chemical potential.^{[ 22 ]} Additional mechanisms, such as particle geometry‐induced torque,^{[ 15} , ^{18 ]} phoretic mobility differences,^{[ 23 ]} differential diffusivity between bound and free states,^{[ 24} , ^{25 ]} and fluctuation‐induced hydrodynamic effects,^{[ 26} , ^{27 ]} are also invoked to explain these positive responses. For urease‐based nanomotors (UrNMs), Sen's group observed negative migration in urease‐coated liposomes and attributed it to the effect of ions on the surface energy of the UrNMs.^{[ 13 ]} Later, Golestanian et al. suggested that a competition between phoresis and enhanced diffusion governs migration:^{[ 25 ]} at high substrate concentrations, phoretic forces dominate, while at lower concentrations, enhanced diffusion prevails. These findings shed light on the importance of surface energy of particles and hydrodynamic forces on particles’ migration, and they focus primarily on the one‐way impact of chemical gradients on nanomotors, emphasizing the environment's influence on the particles.^{[ 16} , ²⁸ , ²⁹ , ^{30 ]} Despite these advancements, a comprehensive understanding of nanomotor dynamics under gradients remains lacking. Two key challenges persist: 1) a lack of dynamic observations at short time intervals to capture the full migration features of nanomotors and 2) limited consideration of multi‐factor interactions, including convection and particle‐environment coupling. This coupling effect—where the environment influences nanomotor dynamics and, conversely, nanomotors modify their surroundings, potentially generating new gradients that further regulate their behavior—has been widely observed in nature, as exemplified by bacterial quorum sensing^{[ 31 ]} and self‐generated gradients in cellular systems.^{[ 32 ]}

In this study, we employ UrNMs as a model type of nanomotor, a well‐characterized system powered by ionic diffusiophoresis,^{[ 33} , ³⁴ , ^{35 ]} to investigate their collective dynamics in a urea gradient. By utilizing a microchip embedded with agarose gel in the central channel, we establish a controlled gradient while minimizing bulk flow effects. We identify three critical components in collective migration under a urea gradient: 1) density‐driven convection, 2) the UrNMs’ positive response to the urea gradient, and 3) the coupling effect between UrNMs and their environment. Specifically, the anion products of the enzymatic reaction diffuse asymmetrically via hydrogen bonding with hydroxyl groups inside the gel, generating ionic gradients. By controlling the pH of urea solution, we confirm the critical role of the electric field generated by ionic gradients. This study presents a comprehensive analysis of the collective dynamics of UrNMs in a urea gradient. We highlight the importance of considering density‐driven convection, which can lead to particle accumulation near high‐concentration regions, even in the absence of active mobility. Additionally, the coupling effect, previously overlooked, offers new insights into the nanomotors’ behaviors under chemical gradient. These findings pave the way for the development of intelligent, gradient‐responsive nanomotors for both fundamental research and practical applications.

2. Results and Discussion

2.1. Design of the Experimental System and Analysis Methods

We investigated the collective migration of UrNMs using a three‐channel microchip with 1% w/w agarose gel in the middle channel (Figure 1 ). The gel was fully filled with substrate using microfluidic syringe pump (10 µL min⁻¹ for 30 min) in the two side‐channels (further discussed in Note S1, Supporting Information). The UrNMs suspension was introduced in the right‐side channel after substrate removal, with gradient control achieved by varying substrate concentration in the gel (details are shown in Figure S1, Supporting Information and Experimental Section). Optical images were captured across the three channels to monitor fluorescence intensity (FI) profiles, exhibiting the distribution of UrNMs. Particle shifts were quantified over time using the area ratio (AR) (Figure S1, Supporting Information), calculated as the ratio of FI between the left and right regions of interest (ROIs) (details in Experimental Section). An increasing AR indicates positive migration (toward the regions with high urea concentration), while a decreasing AR indicates negative migration. As shown in Figure S2 (Supporting Information), measurements confirm the absence of bulk flow, a common concern in gel systems,^{[ 36 ]} demonstrating the suitability of this setup for studying nanoparticle migration. To enhance visualization, we generated pseudo‐colored images, with the color bar shown at the bottom of Figure 1. The microchip's geometry and thickness cause it to scatter the incident laser, resulting in a faint green fluorescence. This artifact was removed during image processing. In the pseudo‐colored images, whiter regions with higher FI indicate a higher particle concentration.

Figure 1.

A schematic of the experimental setup used to study the collective migration of UrNMs. A three‐channel microchip, containing agarose gel in the middle channel and UrNMs in the right channel, is observed continuously by inverted fluorescent microscopy. Images are captured at 1‐min intervals, with fluorescence imaging tracking particle distribution (green), which is then analyzed by pseudo color mapping to enhance the features.

2.2. Positive and Negative Migration of UrNMs in a Urea Gradient

The UrNMs we used have been extensively explored in our previous studies, with a diameter of 400 nm and a zeta potential of −9.84 mV (Figure S4, Supporting Information). We began with a classic system featuring a 300 mm urea gradient and monitored the collective migration at 25× magnification (Video S1, Supporting Information) to capture the global features in the x‐y plane. The observed collective behavior combines both negative and positive migration, as illustrated in Figure 2A. During the initial 5 min, the rightward shift of the leading edge of migration (gray dashed line in Figure 2B) indicates the negative migration of UrNMs. This behavior is further supported by the reduction in the AR variation of UrNMs from 1 to 0.91 (Figure 2C). Subsequently, accumulation is observed in regions with high urea concentration, and the AR increases from 0.91 (t = 4 min) to 1.06 (t = 30 min), signifying a positive migration. This positive response to the fuel gradient is consistent with previous reports.^{[ 30} , ³⁷ , ^{38 ]} In comparison, the control group of inactive UrNMs, prepared by heating at 80°C for 2 h (Figure S5, Supporting Information), exhibits only negative migration without a subsequent positive phase (Figure 2C), and its leading edge remains stable after 8 min. Interestingly, accumulation at the boundary with high urea concentration occurs even in the absence of active mobility (Figure S6 and Video S2, Supporting Information), as it will be discussed later. An important aspect for the chemotaxis community is that focusing solely on FI changes of boundaries or near the regions (typically ≤ 10⁴ µm²) with high substrate concentration^{[ 17} , ³⁰ , ^{39 ]} is insufficient, as global FI observation, or setting more observations points, is necessary.

Figure 2.

Negative and positive migration of UrNMs under urea gradient (c_urea = 300 mm). A) Schematics illustrate the negative and positive migration of UrNMs over time. B) Density map from fluorescence images of active UrNMs showing migration direction; the arrows indicate migration direction, and dashed lines mark the leading edges of migration. C) Time evolution of area ratio (AR) of active and inactive UrNMs. The data are shown as mean AR ± standard deviation (SD) of three independent experiments (n = 3). D) Displacement of UrNMs along the x‐axis over time (for ≈3 min) at the top and bottom of the microchannel, highlighting migrations away from the gel (bottom) and toward the gel (top) resulting from convective flows. The data are analyzed by fifteen particles (n = 15). E) Logarithmic plot of mean squared displacement in the x‐direction (MSD_x ) over time, illustrating the slopes (k) of UrNMs displacement at different channel z‐positions and in the homogenous environment (without gradient). F) Displacement of UrNMs along the x‐axis over time (at ≈7 min) at the bottom of the microchannel, highlighting negative migrations of inactive particles and positive migration of UrNMs. The data are analyzed by thirty particles (n = 30).

We subsequently explored the origin of the negative migration by using 200× magnification to capture detailed views in the z‐axis planes. Videos S3 and S4 (Supporting Information) exhibit migration (in the first 3 min) at the top and bottom planes of the microchip, respectively, and the z‐distance between them is 0.213 mm. Particle migration occurs mainly in two directions: transverse (x‐axis) and parallel (y‐axis) to the channel's main axis. As the parallel movement is attributed to injection, our focus is on the transverse (x‐axis) migration. In Figure 2D, UrNMs at the bottom exhibit positive displacement (Δx > 0, away from the gel), while those at the top move in the opposite direction (Δx < 0, toward the gel). In a homogenous 300 mm urea environment (without gradient), the x‐axis position of UrNMs remains largely unchanged over time (Figure S7, Supporting Information). Furthermore, the mean squared displacement (MSDx) along the x‐axis was calculated (Figure S8, Supporting Information) and analyzed using a logarithmic method (Figure 2E), which converts the power‐law characteristics into a slope. In the homogenous environment, the slope is 0.95, close to 1, indicating diffusion behavior. In the chip gradient environment, the slopes of 1.67 (top) and 1.46 (bottom) suggest “super diffusion,” which typically indicates either enhanced diffusion or convection. However, for UrNMs (diameter ≈ 400 nm) nanoparticles observed at 25 fps, true super diffusion is unlikely because the rotational relaxation time of such particles (τ_R ≈ 0.048 s) is comparable to the minimum observation time interval (Δt = 0.04 s), pointing instead to convection. Considering the flow directions at different layers, this resembles an anticlockwise density‐driven flow consistent with heavier solute‐induced convection.^{[ 40} , ^{41 ]} Furthermore, the change in AR (∆AR) over 30 min, under various urea concentrations was quantified (Figure S9, Supporting Information). The results show that a urea gradient consistently induces negative migration, even at low concentrations where the density difference is minimal. The linear relationship between ∆AR and urea concentration highlights the concentration‐dependent nature of negative migration, and supports the density‐driven convection mechanism, as further discussed in Note S2 (Supporting Information). This density‐driven flow explains the accumulation of the inactive group at the gel boundary: UrNMs on the top were transported toward regions of higher fuel concentration. However, due to the sedimentation of UrNMs (with less than 10% of particles remaining at the top after 5 min) and the lack of a positive response to the urea gradient, inactive particles do not exhibit continuous increases in AR. To further validate the role of density‐driven convection, we performed a control experiment using H₂O₂ (20 mm) instead of urea, as shown in Figure S10 (Supporting Information). In the absence of active catalysis, no significant collective migration was observed. When catalase‐based nanomotors (CatNMs) were introduced, only positive migration was detected under the H₂O₂ gradient, with no evidence of negative migration. Since the density difference between the H₂O₂ solution and PBS is negligible, this result further supports that density‐driven convection is the primary mechanism underlying the initial negative migration observed in the urea system.

Furthermore, the single particle tracking at ≈7 min shows that the particles at the bottom (both UrNMs and inactive particles) change from “super diffusion” into normal diffusion, with the slope ≈0.98 (Figure S11, Videos S5 and S6, Supporting Information), indicating the weakening of density‐driven convection. UrNMs at the bottom change from negative to positive migration, showing the positive response of UrNMs to the urea gradient. In contrast, inactive particles maintain their negative migration (Figure 2F). The positive migration here can be explained by many microscopic theories, such as including dissipation toward regions more favorable for substrate‐enzyme binding to lower free energy,^{[ 24 ]} stronger phoretic flows driven by higher urea concentration,^{[ 25 ]} and fluctuation‐induced hydrodynamics effects.^{[ 26 ]}

2.3. Coupling Effect Induced by Non‐Equilibrium Transport of Anions

To explore the details of the collective migration process of UrNMs, we monitored real‐time pH changes (an important feature of urease reaction) using a pH‐sensitive fluorescent dye, Solvent Green 7 (HPTS), which exhibits increased fluorescence intensity at higher pH values (Figure 3A). To enhance contrast, we applied pseudo‐chromatization to the image, where red represents higher fluorescence intensity. Prior to the experiments, the gel was filled with a solution containing 300 mm urea and 100 µm HPTS. And the particle suspension in the right channel, which did not exhibit fluorescence, also contains 100 µm HPTS. The FI on both sides of the microchip was recorded over time. As shown in Figure S12 and Video S7 (Supporting Information), the inactive group exhibits no significant changes in FI over time on either side, with the FI levels on both sides remaining nearly identical (Figure S13, Supporting Information). In the active group, after introducing UrNMs into the right channel, the pH increases due to the enzymatic reaction:

$$\begin{array}{c}\hfill {\left(\mathrm{N}{\mathrm{H}}_2\right)}_2\mathrm{CO}+3{\mathrm{H}}_2\mathrm{O}\stackrel{\mathrm{Urease}}{\to }2\mathrm{N}{\mathrm{H}}_3+\mathrm{C}{\mathrm{O}}_2\stackrel{{\mathrm{H}}_2\mathrm{O}}{\to }2{\mathrm{NH}}_4^{+}+{\mathrm{HCO}}_3^{-}+\mathrm{O}{\mathrm{H}}^{-}\end{array}$$ (1)

Figure 3.

Mass transport dynamics in agarose gel. A) A schematic of the experimental setup showing the three‐channel system and the preferential transport of OH⁻ ions across the gel, leading to a pH increase in the left channel. B) Pseudo‐colored images showing the progression of ionic transport over time. FI variation of HPTS C) in the left channel and D) in the right channel over time. E) AR analysis between the left and right channels. The data are shown as mean AR ± SD of three independent experiments (n = 3). F) A schematic of RhB transport across the gel. G) Fluorescence images depicting RhB transport over time in the UrNMs group. FI variation of RhB H) in the left channel and I) in the right channel with UrNMs over time. J) AR analysis between left and right channels for the UrNMs group and the inactive UrNMs group over time. The data are shown as mean AR  ± SD of three independent experiments (n = 3).

Instead of symmetrical diffusion, OH⁻ diffuse preferentially across the gel, raising the pH and FI in the left channel (Figure 3B; Video S8, Supporting Information), meaning a non‐equilibrium diffusion. Compared with right channel, left channel has the faster and larger pH increasing (Figure 3C,D). Figure 3E shows the AR of HPTS fluorescence between the left and right channels. For inactive UrNMs, AR decreased slightly over time. For active UrNMs, AR first decreases as pH increased locally in the right channel, followed by a rapid increase in AR after 3 min, indicating the preferential diffusion of OH⁻ towards the left channel. After 8 min, the slight decrease in AR implied saturation in the left channel, and OH⁻ shows higher diffusion flux toward right channel (as indicated by the arrows in Figure 3B), compared with left channel. This non‐equilibrium OH⁻ transport intensified the pH asymmetry between the two sides of the microchip, which indicates the bidirectional coupling between UrNMs and their environment. Two hypotheses may explain this non‐equilibrium process: 1) nonspecific forces, like convection, or 2) specific forces acting on ions.

If convection is plausible, while facilitating the OH⁻ transport toward the left channel, it would also hinder the diffusion of other species to the right channel. To test this hypothesis, we introduced 100 µm pH‐insensitive dye Rhodamine B (RhB) to the left channel and monitored its transport (Figure 3F).^{[ 42 ]} As shown in Figure 3G–I and Video S9 (Supporting Information), RhB diffuses from the left (high concentration) to the right (low concentration) over ≈30 min, with FI decreasing on the left and increasing on the right. Furthermore, the diffusion of RhB in the active group is similar to that in the inactive group (Figures S14–S15 and Video S10, Supporting Information). AR analysis indicates that the enzymatic reaction only slightly affects RhB diffusion (Figure 3J). These results show that convection is not the primary mechanism behind the long‐term preferential transport of OH⁻.

Regarding the specific forces acting on ions, we propose a potential hypothesis: enhanced anion transport mediated by hydrogen bonding. Agarose gel, composed of repeated sugar units linked by glycosidic bonds, consists of D‐galactose and a 3,6‐anhydro‐L‐galactose derivative. These components are structurally similar to glycosaminoglycans and glycoproteins found in the extracellular matrix and cell membranes.^{[ 43} , ^{44 ]} The hydrogen atoms in hydroxyl groups of the gel readily interact with the oxygen atoms in the negatively charged OH⁻ and HCO₃⁻, both of which carry lone pairs of electrons and are highly electronegative.^{[ 45 ]} This hydrogen bonding interaction facilitates preferential anion binding and provides an additional driving force for anion diffusion, thereby driving the observed non‐equilibrium transport of base species (Figure 4A). Hydrogen bond‐mediated ions transport is widely used in the design of ion‐exchange membranes^{[ 46} , ^{47 ]} and in ions transport across biological membranes.^{[ 48} , ^{49 ]} We performed contact angle measurements to support our hypothesis. To prevent the complete spreading of the droplet caused by direct contact with the gel, a composite film was fabricated (Figure S16, Supporting Information), with details provided in the Experimental Section. As shown in Figure 4B, compared to the pure cellulose acetate membrane (“C” in Figure 4B) without the gel, the composite film exhibited a stronger affinity for NH₄HCO₃ solution. Notably, when NH₄HCO₃ was replaced with NH₄Cl (red column in Figure 4B), the smaller contact angle of NH₄HCO₃ suggested a higher affinity, providing indirect evidence of potential hydrogen bonding between HCO₃⁻ and the gel. Similarly, increasing the pH of the NH₄HCO₃ solution, which increases the concentration of OH⁻, resulted in a smaller contact angle, further suggesting an interaction between OH⁻ and the gel.

Figure 4.

Proposed mechanism of non‐equilibrium ion transport. A) A schematic show that hydrogen bonds between anions and agarose gel promote the non‐equilibrium anions transport. B) Contact angles between composite film and different solutions. C) A schematic of the experimental setup for measuring the diffusion potential of ions. D) The OCV under different conditions. CC: cellulose acetate membrane – cellulose acetate membrane; CAC: cellulose acetate membrane – agarose gel (thin) – cellulose acetate membrane. The data is shown as mean value ± SD of five independent experiments (n = 5).

To further investigate the relative diffusion differences among product ions, we measured the open circuit voltage (OCV), which represents the potential difference in the absence of an external current. As depicted in Figure S17 (Supporting Information), urea and UrNMs were positioned on opposite sides of diffusion chambers, separated by composite membranes consisting of cellulose acetate (C) and agarose gel (A). In the inactive group, where no chemical reaction occurred, the urea gradient failed to induce a potential difference (Figure 4D). In the reactive UrNMs system (CC membrane), differential ionic mobilities ($D_{N{H}_4^{+}}$ = 1.98 × 10⁻⁹ m² s⁻¹, $D_{O{H}^{-}}$ = 5.3 × 10⁻⁹ m² s⁻¹, $D_{HC{O}_3^{-}}$ = 1.2 × 10⁻⁹ m² s⁻¹) generated a diffusion potential between the chambers, albeit lower than the theoretical prediction (+ 6.2 mV, the voltage in left chamber is set to 0 V, see Note S3, Supporting Information) The positive OCV indicates faster diffusion of anions compared to cations. Incorporating agarose gel into the membrane (CAC configuration with a thin agarose gel film in the middle) results in a slight increase in diffusion potential. Extending the length of the agarose gel (Figure 4C) significantly amplifies the diffusion potential, underscoring the enhanced preferential transport of anions across the gel due to the longer effective range of the hydrogen bond effect. These results confirm that agarose gel enhances differences in ionic diffusion coefficients, promoting selective anion transport. The induced electric field may exert an additional effect on the migration of UrNMs.

Based on the non‐equilibrium anion transport, we qualitatively simulated ion gradients using the diffusion‐convection equation (details provided in Note S4, Supporting Information). The non‐equilibrium transport of anions was simulated using a virtual flow, with the Peclet number ($Pe=\frac{Lu}{D}$) set to 1 × 10⁻² to minimize the influence of diffusion. As shown in Figure S18 (Supporting Information), anions migrate across the gel preferentially, creating an ion gradient in the right channel. For cations (NH₄ ⁺), enzymatic reaction in the right channel initially generates a gradient directed toward regions of lower urea concentration (Figure S19, Supporting Information). However, this gradient is transient (<2 min). As the continued production of NH₄⁺ and the restricted diffusion caused by the microchip's wall, the gradient reverse direction, ultimately pointing toward regions with higher urea concentration (Figure S20, Supporting Information).

These ionic gradients reveal a bidirectional coupling between UrNMs and their environment, rather than a unidirectional gradient‐driven effect on the particles. Ion gradients affect the collective migration of UrNMs through two potential mechanisms: 1) surface energy modulation and 2) electric field interactions. Regarding surface energy modulation, UrNMs exhibit negative migration under a 100 mm NH₄HCO₃ gradient (Figure 5A), consistent with previous reports.^{[ 13 ]} NH₄⁺ and HCO₃⁻ increase the surface energy of proteins, lowering their solubility and inducing negative migration.^{[ 50 ]} Additionally, the asymmetric ion distribution generates an electric field in the right channel, akin to those observed in ionic diffusiophoresis.^{[ 51} , ^{52 ]} The resulting volumetric charge density (ρ_e ) and the corresponding electro‐hydrodynamics (u) were analyzed to assess their impact on particle migration. As depicted in Figure 5B, the electric field points toward regions of higher urea concentration, same direction with experimental results (Figure 4D), generating electrical forces around UrNMs (inset, Figure 5B) that hinder their positive migration.

Figure 5.

Potential effects of ion gradients. A) AR variation of UrNMs over time under 100 mm NH₄HCO₃. The data are shown as mean AR ± SD of three independent experiments (n = 3). B) Simulated distribution of normalized electrical potential (V) in the right channel. The arrows indicate the direction of the electric field, and the inset shows the velocity field of particles (|u| =   − |u _electro |) provided by this electric field.

2.4. Validation of the Dominated Effect of Ion Gradients

We investigated the role of ion gradients by modulating non‐equilibrium ion transport within the gel, achieved through adjusting the pH of the urea solution inside the gel (pH 6 and 8). Acidic pH introduces a neutralization reaction, increasing the attraction between anions and the gel matrix, while alkaline pH reduces ions transport by diminishing the OH⁻ concentration gradient (Figure 6A). Under acidic pH, there are opposing effects in the right channel: the enhanced electric field reduces positive migration (view of electric field), while the decrease in HCO₃⁻ concentration promotes positive migration (view of surface energy). In contrast, under alkaline pH, the electric field is weakened, and HCO₃⁻ concentration increases, exhibiting effects opposite to those under acidic conditions. So we can validate the dominated effect of ion gradients by the collective dynamics under different pH.

Figure 6.

The impact of ion gradients on nanomotor migration validated through pH variation. A) A schematic illustration of the ionic fields established in the microchannel under different pH conditions. B) The FI profiles of HPTS in left channels and right channels over time under different pH conditions. C) AR of HPTS between the left and right channels of the microchip changes over time. The data are shown as mean AR ± SD of three independent experiments (n = 3). D) The absorbance of standard phenol red solutions with different pH values (6–10) at 560 nm (A₅₆₀ ) and the absorbance of solutions in the right channel after 30 min reaction under urea with pH 6, 7, 8, incubated with phenol red. The dashed line is the fitting standard line. The data are shown as mean value ± SD of three independent experiments (n = 3). E) AR variation of UrNMs under PBS at different pH values. The data are shown as mean value ± SD of three independent experiments (n = 3). F) MSD of UrNMs at a 1 s interval in homogenous urea environment with pH 6–8. The data are shown as mean value ± SD (n = 30). G) Fluorescence images showing the directional migration of colloids under different pH conditions. H) AR variation of UrNMs during the positive migration phase under different pH conditions. I) The migration velocity of UrNMs (V_migration ) calculated as the first derivative of AR with respect to time.

To confirm this pH‐dependence of ion transport, we monitored real‐time pH dynamics in both channels. As shown in Figure 6B, the pH 6 group exhibits the most rapid and pronounced pH changes, while the pH 8 group shows only minor variations (Video S11 and S12, Supporting Information). Moreover, the steep slope of AR variation in pH 6 group (Figure 6C) highlights enhanced transport of basic anions from the right to the left channel. Final pH measurements in the right channel, determined via phenol red absorbance at 560 nm (A₅₆₀), reveals a pH‐dependent increase in basic ion transport (Figure 6D). Relative A₅₆₀ absorbance increased by 153.8%, 253.8%, and 323.1% for the pH 6, 7, and 8 groups, respectively, compared to a standard solution at pH 7. These findings validate the hypothesized pH‐dependent modulation of ion transport.

The pH of the gel could potentially influence collective dynamics indirectly by altering fluid properties or enzyme activity. However, we rule out this possibility. While pH influences the surface tension of the salt solution (Figure S21, Supporting Information),^{[ 53 ]} which could theoretically impact UrNMs migration through tension‐driven convection, experiments with gels filled with PBS solutions at different pH values reveal negligible differences in UrNM migration (Figure 6E). This indicates that the pH gradient alone does not significantly affect particle migration. Additionally, previous studies reveal that pH 8 is optimal for immobilized urease activity,^{[ 54 ]} suggesting heightened sensitivity to urea gradients at this pH. Tracking‐based mobility analysis of single UrNMs were conducted in homogenous 300 mm urea solutions at pH 6, 7, and 8, in the absence of gel and any chemical gradients, thus eliminating ion‐gel coupling effects. Under there uniform conditions, where particle dynamics are primarily governed by surface chemical reaction, only minor variations in diffusion coefficients were observed: 1.19 ± 0.21, 1.12 ± 0.43, and 0.92 ± 0.39 µm² s⁻¹, respectively (Figure 6F). These results confirm that the effects of pH on UrNMs mobility are negligible and that pH primarily influences ions transport.

The collective migration of nanomotors under pH‐dependent modulation of ion transport is evaluated (Videos S13 and S14, Supporting Information), focusing on the phase of positive migration (after 5 min). Compared to the neutral pH 7 group, UrNMs in the pH 8 group exhibits the strongest positive accumulation in the regions with high urea concentration (Figure 6G). AR analysis (Figure S22 and Figure 6H, Supporting Information) confirms enhanced positive migration in the pH 8 group. Moreover, the differential of the AR curve reveals a higher migration velocity (V_migration =  dAR/dt) under pH 8 conditions (Figure 6I). These observations indicate that weaker ions gradient enhances positive migration, demonstrating that ionic fields operate primarily via electric mechanisms. Additionally, we validate these findings through numerical simulations, modeling the effect of pH on ions transport by adjusting the Péclet number (Pe) (Note S5, Supporting Information). Boundary integral calculations of electro‐hydrodynamics around particles (${\int }_{\mathrm{\Gamma }}|\mathbf{u}|\mathrm{d}l$) reveal significant changes: pH 8 and pH 6 groups exhibit 61% and 158% variations, respectively, relative to the pH 7 group, showing the weaker resistance in the group pH 8. These simulated trends closely align with experimental results, underscoring the role of pH in regulating ion transport and collective migration. To further validate this coupling mechanism, we introduced a non‐ionic enzyme, catalase, which produces neutral molecules (O₂ and H₂O) as reaction products, eliminating any potential for an enzyme‐induced electric field. According to previous studies, immobilized catalase exhibits optimal activity at pH 7.^{[ 55 ]} We analyzed the diffusion coefficient under different pH conditions, as shown in Figure S23 (Supporting Information). The pH 7 group exhibited the highest diffusion coefficient, while the pH 6 and pH 8 groups showed similar diffusion behavior. In terms of collective migration, the pH 7 group demonstrated the strongest positive migration, whereas the pH 6 and pH 8 groups exhibited similar migration patterns. The correlation between single particle dynamics and collective migration further supports our proposed mechanism.

3. Conclusion

This manuscript provides a comprehensive framework of UrNMs’ collective dynamics in a urea gradient, identifying three critical factors governing their behavior: density‐driven convection, positive response to the urea gradient, and coupling effect between UrNMs and their environment. We found that UrNMs in a urea gradient initially show a negative migration away from the fuel source due to density‐driven convection. Over time, UrNMs exhibit a positive migration towards regions of higher urea concentration. A key finding of this study is the significant role of the coupling effect, which was previously overlooked in directing UrNMs migration. This effect arises from hydrogen bonding between product anions and hydroxyl groups within the gel that separates the channels, resulting in ion gradients that influence migration. The dominant influence of electric force is validated by pH‐controlled experiments. This work emphasizes the importance of considering density‐driven convection, which can lead to particle accumulation near high‐concentration regions, even in the absence of active mobility. Moreover, the coupling effect offers new insight into the collective behavior of nanomotors. This also inspires further explorations of interactions between nanomotors and biological materials, such as hydrogel, extracellular matrices, and membranes, which will offer a broader perspective on active matter dynamics in natural and biomimetic systems.

4. Experimental Section

Materials

Ethanol (EtOH, 99%), methanol (MeOH, 99%), hydrochloric acid (HCl, 37%), tetraethylorthosilicate (TEOS, 99%), triethanolamine (TEOA, 99%), cetyltrimethylammonium bromide (CTAB, 99%), 3‐aminopropyltriethoxysilane (APTES, 99%), glutaraldehyde (GA, 25% in water), fluorescein isothiocyanate (FITC, 90%), urease (from Canavalia ensiformis, type IX, powder, 50 000–100 000 units per gram of solid), urea (99.9%), ammonium bicarbonate (NH₄HCO₃), phenolsulfonphthalein (Phenol Red), solvent green 7, rhodamine 6G, cellulose acetate membrane were purchased from Merck. Electrical insulating compound silicone grease (DC4) was purchased from Dow Corning. All reagents were used as received without any further purification. The water used for the experiments was of type I ultrapure quality, obtained from a purification system (18.2 MΩ cm).

Synthesis of Fluorescein Isothiocyanate‐Labeled Mesoporous Silica Nanoparticles (FITC‐MSNPs)

To obtain FITC‐MSNPs, a mixture of FITC (2 mg), EtOH (5 mL), and APTES (400 µL) was prepared and stirred for 30 min at room temperature. Mesoporous silica nanoparticles (MSNPs) with an average diameter of 450 nm were synthesized following a sol–gel process based on the Stöber method, with some modifications. Briefly, a solution of CTAB (570 mg) and TEOS (35 g) in MilliQ‐water (20 mL) was heated to 95°C in a silicon oil bath, using a three‐neck round‐bottom flask under reflux and constant stirring for 30 min. After homogenization, TEOS (1.25 mL) and APTES‐FITC (0.25 mL) were added dropwise using a Pasteur pipette. The reaction was left for 2 h under the same conditions of reflux, temperature, and stirring. Then, the resulting silica NPs were collected by centrifugation (1350 g, 5 min). MSNPs were created using an acidic MeOH solution under reflux to remove the CTAB. For this, MSNPs were suspended in MeOH (30 mL), adding hydrochloric acid (1.8 mL). The mixture was placed in a one‐mouth round‐bottom flask in a silicon oil bath at 80°C for 15 h. Finally, the resulting MSNPs were collected by centrifugation (1350 g, 5 min) and washed three times in EtOH, sonicating for 10 min between each centrifugation. The final concentration of MSNPs obtained was calculated by dry weighing.

Amine Modification of FITC‐MSNP

APTES (6 µL mL⁻¹) was added to a suspension of MSNPs (1 mg mL⁻¹) in 70% EtOH solution. The mixture was heated to 70°C in a silica oil bath while stirring for 1 h. In the following step, MSNP‐NH₂ were collected by centrifugation and washed in EtOH (three times, 1150 g, 5 min) and in ultrapure water (three times, 1500 g, 5 min) with vortex vibration for 30 s and sonicating for 10 min between each centrifugation.

Enzyme Linking

UrNMs were fabricated using GA as a linker molecule between primary amino groups and proteins, enabling covalent binding. For this, MSNP–NH₂ (900 µL, 1 mg mL⁻¹ in PBS 1×) were activated by adding GA (100 µL). The mixture was reacted for 2 h at room temperature while mixing in a rotary shaker. Then, the particles were collected by centrifugation and washed in PBS 1× (three times, 1150 g, 5 min), vortex vibration for 30 s, and sonicated for 10 min between each centrifugation. Finally, the GA–FITC‐MSNP were resuspended in a solution of PBS 1× containing urease (3 mg mL⁻¹), to obtain UrNMs. The mixture was placed on a rotary shaker and kept at room temperature overnight. The resulting UrNMs were collected by centrifugation and washed with PBS 1× (three times, 1150 g, 5 min), vortexing for 30 s between each centrifugation.

Preparation of Experimental Setup

The commerical microchannels (idenTx 3) used in experiments were purchased from Aimbiotech (https://aimbiotech.com/product/identx‐3‐chip/). This chip consists of three interconnected channels, where agarose gel was injected into the middle channel to separate them. To obtain the agarose gel, 1% w/w agarose PBS solution was heated to 100°C until the solution turned transparent under stirring. Subsequently, 10 µL agarose solution was filled into the middle channel of the chip (Figure S1, Supporting Information). Place the gel‐filled chips under room temperature to allow polymerization. Before measurement, the substrate solution was flown into both the side channels at a flow rate of 10 µL min⁻¹ for 30 min to fully fill the gel. The urea solution was carefully removed using a pipette prior to the injection of the particle suspension. The suspension was then gently introduced to minimize any tangential force exerted on the gel.

Analysis of Fluorescence Images

After pre‐processing images by Fiji, the normalized transverse distributions of fluorescence intensity (FI_normalized (x_i )) in the regions of interest (ROIs) were calculated by:

$$F{I}_{average}\left(x_i\right)=\frac{{\sum }_{j=0}^{j=n_{yROI}}F{I}_{x_i}\left(y_j\right)}{N_{pixel}}$$ (2)

$$F{I}_{normalized}\left(x_i\right)=\frac{F{I}_{average}\left(x_i\right)-\min \left(F{I}_{average}\left(x_i\right)\right)}{\max \left(F{I}_{average}\left(x_i\right)\right)-\min \left(F{I}_{average}\left(x_i\right)\right)}$$ (3)

where n_yROI is the maximum of y coordinate for a given x coordinate, N_pixel is the number of pixels in this line perpendicular to x‐axis.

After getting the FI_normalized profiles, area ratios (AR) between the profiles on the left side and right side were calculated to evaluate the migration‐induced shifts:

$$S_{totalleft}=S_{left}+S_1$$ (4)

$$S_{totalleft}=S_{right}+S_2$$ (5)

$$AR=\frac{S_{left}}{S_{right}}$$ (6)

The FI_normalized in the locations of gel interfaces were chosen to be the baseline, and AR _0min was set as the standard value (1). The other data in the same group was scaled equally. The ΔAR  =  AR _{t + Δt} − AR_t were used to quantify the shifts. As time develops, if AR is increasing, ΔAR is greater than 0, and the migration is positive (towards “source”). By contrast, migration is negative (away from the source).

In terms of the analysis of real‐time pH variation and RhB diffusion, the AR is obtained by calculating the quotient of FI_normalized in left channels with right channels of microchips.

UrNMs Single Particle Tracking and Mean Squared Displacement (MSD) Analysis

Observation and video recording of the UrNMs were performed in a THUNDER optical microscope (Leica). For the homogenous environment, 5 µL of UrNMs in PBS were placed on the center of a 9 mm diameter and 0.12 mm deep Secure‐Seal spacer (Thermo Fisher Scientific) stuck onto a glass slide and thoroughly mixed with the urea solutions in PBS at the desired concentrations. Then, the mixture was covered using a coverslip to avoid artifacts caused by the drifting effect. Videos of 30 s were recorded using a Hamamatsu camera at a frame rate of 25 fps under bright field. The analysis of motion was performed with a homemade Python code to obtain the tracking trajectories, and MSD analysis was conducted by:

$$MSD\left(\mathrm{\Delta }t\right)=⟨{\left(x_i\left(t+\mathrm{\Delta }t\right)-x_i\left(t\right)\right)}^2⟩=4D\mathrm{\Delta }t+2v^2\mathrm{\Delta }{t}^2$$ (7)

where D and v are the diffusion coefficient and translation speed of particles, respectively. The ROIs were selected as 250 × 250 µm squares, positioned ≈100 µm away from the gates, with their centerlines aligned as closely as possible with the centerline of the gel. This selection principle helps minimize statistical errors caused by variations in ROI selection. Figure S24 (Supporting Information) illustrates the ROIs used in video analysis.

Preparation of Composite Membranes

For contact angle measurements, a composite film was prepared on a glass slide (Figure S16, Supporting Information). Specifically, a sealing washer (≈100 µm thick) coated with adhesive on both sides was first affixed to the slide. Then, 10 µL of agarose gel solution was deposited inside the washer. To prevent direct contact between the measurement droplet and the gel surface, a porous cellulose acetate membrane (the same type used in the OCV measurements) was placed on top of the gel before polymerization. Direct contact would otherwise lead to immediate spreading of the droplet, due to the highly hydrophilic nature of the gel. Placing the membrane prior to gelation allows the formation of an agarose–cellulose acetate composite surface. After gelation, the surface was gently blotted with dust‐free paper to remove residual moisture. For OCV measurement, two types of composite membranes were prepared: the CC membrane, composed of two cellulose acetate membranes layered together, and the CAC membrane, which incorporated an agarose gel layer. To fabricate the CAC membrane, 100 µL of 1% w/w agarose in PBS at 60°C was applied to a cellulose acetate membrane. A second cellulose acetate membrane was then placed on top of the solution, allowing the agarose gel to solidify, forming a stable, sandwiched structure.

Filling the Chamber Neck with Agarose Gel

The chamber necks were inverted and positioned in a petri dish, filled with 1% w/w agarose PBS solution at 60°C, and left to cool and solidify. Silicone grease was applied around the edges to provide mechanical stability and prevent slippage.

Open Circuit Voltage Measurement

The assembled chambers were secured with clamps, and the agarose gel was equilibrated by soaking in a urea solution (500 mm with 10 µm NaCl) for 2 h. This process was repeated three times. Prior to measurement, the urea solution (500 mm with 10 µm NaCl) in one chamber was replaced with a 0.5 mg mL⁻¹ UrNMs suspension (with 10 µm NaCl). Ag/AgCl electrodes were positioned, with the working electrode in the urea solution chamber. The electrodes were connected to an Autolab PGSTAT302 electrochemical workstation, and open‐circuit voltage was recorded after 15 min of reaction.

Measuring the Final pH in the Microchip

Firstly, absorbances of phenol red aqueous (40 µL) with PBS with different pH (10 µL) were measured at 560 nm (A₅₆₀ ) as the standard curve. Then, we replaced the PBS with solutions in the right side after 30 min reaction to measure the A₅₆₀ .

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Supplementary Video 1

Supplementary Video 2

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Supplementary Video 14

Lin J., Chen S., Lezcano F., Li Z., Xu L., Guan J., Sánchez S., Collective Dynamics of Urease‐Based Nanomotors in a Chemical Gradient. Small 2025, 21, 2502212. 10.1002/smll.202502212

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.