Cellular scale search and funneling drive bacterial penetration of extreme confinements

Abstract

Bacterial transport into micron-scale rigid pores plays an important role in microbial competition and community assembly. As the spatial dimensions of the pore approach the width of a bacterium, steric and hydrodynamic constraints sharply limit passive entry. Here, we demonstrate that motile Escherichia coli overcome these barriers via a two-step facilitated entry mechanism: cells scan flat surfaces for target openings, then pivot into alignment with the aid of flagellar thrust to penetrate them. This process effectively transforms the openings of narrow microfluidic channels into wide, dynamic funnels, dramatically expanding the range of permissible cell orientations and lateral offsets for successful entry. The mechanism increases motile cell influx into extreme confinement by ~30-50 times relative to co-axial entry. The accompanying dimensionality reduction in target search also confers a decisive transport advantage on motile bacteria over non-motile ones. These findings establish reduced-dimensionality target search at the cellular scale, a phenomenon previously thought to be exclusive to molecular enzymes undergoing facilitated diffusion.

Introduction

Bacteria inhabit environments spanning a wide range of physical confinement, from soil aggregates to mucosal layers and intestinal crypts. These habitats are often characterized by relatively planar surfaces punctuated by narrow constrictions with dimensions similar to those of the bacterium ^1–3. Access to such confined spaces can provide sustained protection from larger predators and flow-based entrainment, influencing cell survival and niche colonization. Consequently, bacterial transport into confined spaces can decisively shape microbial community structure, host-microbe interactions, and infection outcomes ^4–6.

Flagellated bacteria are well known for biasing their migration toward favorable chemical habitats ^7,8. But, even in the absence of chemical cues, flagellar motility significantly enhances dispersion, helping motile bacteria penetrate new territories faster than their non-motile counterparts ^9,10. Yet the biophysical determinants governing bacterial competition for rare and physically confining targets remain unclear. At the molecular scale, target searches often proceed through facilitated diffusion: proteins such as the RNA polymerases transiently bind to DNA to reduce the dimensionality of the promoter search and then slide one-dimensionally to amplify target association rates by two to three orders of magnitude^11–13. Whether similar dimensionality-reduction search mechanisms operate at the cellular scale and help diverse bacteria search and compete for confined niches is a fundamental biophysical question.

Here, we employed microfluidic platforms, along with live-cell imaging and quantitative modeling, to dissect how motile and non-motile E. coli penetrate micron-scale niches. Our results suggest that motile E. coli cells reduce the dimensionality of niche search by laterally scanning surfaces for openings, then pivoting to align with and penetrate narrow microfluidic channels. This two-step facilitated entry mechanism is powered by flagellar thrust, enabling the cell to transiently associate with the surface and increasing its chances of encountering a narrow opening. Based on a hydrodynamic model, we show that the probability of successful target search is entirely governed by cell geometry, specifically by a dimensionless ratio of rotational to translational drag, rather than by medium viscosity or thrust force. The inability of non-motile bacteria to generate a propulsive force limits their transport relative to motile bacteria, leading to strong motility-dependent selection and spatial organization under extreme confinement.

Results

Motile cells readily penetrate narrow, confined regions

We introduced wild-type E. coli cells at a concentration of 1 × 10⁹ cells/mL into a microfluidic trench with numerous 25 μm long orthogonal channels (Fig. 1A). The channel cross-section (1.5 x 1.5 μm) was similar to the cell width (~1.2 μm) (see Methods). Researchers usually ‘seed’ such narrow channels with single bacterial cells by employing centrifugation or extended incubation under gravitational drift ^14–16. However, we observed that individual motile cells frequently entered the orthogonal channels without any external forcing, traversing the entire length of the channels (Fig. 1B). Wild-type cells rotate their flagella counterclockwise (CCW) to propel the cell and can intermittently switch to clockwise (CW) to back out of dead-ends in porous networks¹⁷. Consistent with this, we frequently observed the cells exiting from the channels. We visually quantified channel occupancy from the phase images (Fig. S1). Approximately 2 out of 3 channels were occupied by cells within 15 min of loading (Fig. 1C).

Figure 1. Motile cells penetrate narrow constrictions.

A) Left: The microfluidic device consisted of a main trench (blue) flanked by microchannels (gray) on either side. The channel cross-section (1.5 × 1.5 μm) encloses a penetrating cell on all four sides. Right: With ~5 μm interchannel spacing, the channel area constitutes only ~0.5% of the total PDMS wall area encountered by the cells on any one side of the trench. Diagram not to scale. B) A representative motile cell trajectory as it enters a channel (red arrows) over a duration of ~3 seconds. Scale bar = 10 μm. C) Out of the total channels inspected in the phase images (n = 622 channels), 68.1 ± 5.5 % were occupied by one or more wild-type cells. Each dot indicates an independent replicate. D) The mean swimming speed decreased by ~ 70% inside the channels relative to the bulk. Swimming speeds were pooled across 3 biological replicates (pooled n = 105 cells, bulk; 25 cells, channels). Differences in means were tested using a Welch’s t-test (two-sided); asterisks indicate significance (p ~ 2.7×10⁻¹⁸). The bars represent the standard deviation in C) and D).

Next, we compared the swimming speed of individual cells in the channels with that in the bulk (trench). As the flow profile develops rapidly under low Reynolds number conditions ¹⁸, the entry length in these narrow channels is no more than a few nanometers. Hence, we calculated the time-averaged speed for the entire duration the cell was inside the channel. As shown in Fig. 1D, the cells swam approximately 3 times slower in the narrow channels, presumably due to increased wall-induced drag. The propulsive force due to the flagella, F ~ 0.5 pN ¹⁹, equals the product of the longitudinal drag coefficient and the swimming speed (V). The flagellar motor generates higher torque as the viscous loads increase^20,21, but the increase is only ~ 10% for swimmers. Therefore, we estimate that the drag coefficient within the channel increases by a factor of three, or more²².

To study the mechanism of transport into the channels at a single-cell level without kinematic complications arising from reversals, we employed a smooth-swimming strain of E. coli that perpetually rotates its motors CCW²³. Time-lapse imaging revealed that channel residency, defined as the number of occupied channels divided by the total number of available channels, increased rapidly for the smooth swimmers within 5 minutes of cell loading, then remained constant (Fig. S2). Among the occupied channels, the channel cell density plateaued within ~0.5 h (Fig. 2A), with a large percentage of channels consistently occupied across the entire range of cell concentrations we tested. Therefore, we characterized all subsequent steady-state phenomena at least 1 h after incubation. We calculated the fractional occupancy as the ratio of the total number of cells visible in the channels to the product of the number of available channels and the maximum possible cell density per channel (12 cells). A fractional occupancy of 1 corresponds to a fully saturated state in which all available channels are populated to their maximum capacity. The steady-state fractional occupancy saturated above a cell density of 2×10¹¹ cells/mL (Fig. 2B), indicating that below this concentration, cell availability limited entry.

Figure 2. Entry kinetics of motile cells.

A) The time-dependent variations in the mean channel cell-density –the number of cells per occupied channel –are shown for varying concentrations. The maximum possible channel cell density is 12 cells/channel. Cell concentrations: 3.1×10⁹ (filled, blue diamonds), 3.72×10¹⁰ (open, green triangles), 2.87×10¹¹ (filled, black squares), and 1.63×10¹² (open, red circles) cells/mL. B) The fractional occupancy after an hour of incubation with varying cell concentrations. Each mean value in A) and B) was determined from an average of n = 230 channels pooled across 2 biological replicates. The bars represent the standard error in all panels.

Cell entry is facilitated by surface scanning and dynamic funneling at the constriction

We analyzed the factors that increase the probability of motile cell entry into the channels. Analysis of the video data revealed that most motile cells approached the channels at oblique angles (Fig. 3A). Furthermore, contact was seldom at the channel opening; instead, the cells frequently collided with the impermeable PDMS wall at a distance away from the channel opening. Despite this, the cells gained entry via a two-step facilitated entry process. In the first step, the cell moved laterally upon encounter with the PDMS boundary, searching for an opening. Upon encountering a channel opening, it would frequently pivot into alignment to penetrate it (Supplementary Movie 1, 2, 3).

Figure 3. Self-propulsion creates virtual funnels.

A) Left: λ is the vertical separation between the cell and the wall, and s is the arc length of the cell trajectory (yellow curve). Scale bar = 10 μm. Right: The phase and corresponding binary images show the contact-scanning-entry of two different, representative cells at various time points. The blue dotted lines indicate the orientation of the cell body relative to the channel (red outlines). The yellow lines indicate the PDMS wall, which is perpendicular to the imaging plane. Also see representative movies 1, 2, and 3. B) The phase map shows the successful or unsuccessful (failed) entries into channels for motile cells over varying lateral separations and orientations with respect to the channel axis. The angle θ = 90° (0° or 180°) when the cell is aligned parallel (perpendicular) to the channel axis. The map was constructed over a total of 410 events (See Methods). The white curve is the prediction from equation 1, offset by the pore radius. Dark blue color indicates bins that were never visited by the cells. The parameters were $L_{\mathit{\text{cell}}}=2.5\mu \mathrm{m}$ and $w=1.2\mu \mathrm{m}$. We assumed a slightly higher translational drag, $\gamma =1.5{\gamma }_{\text{bulk}}$, to account for surface proximity effects. The white-dotted region indicates the range of orientations and contact separations where scanning and funneling are not necessary for motile cell entry. C) The derivative of the cell orientation with respect to arc length, $\frac{d\theta }{ds}$, as a function of the vertical distance from the channel/PDMS interface, $\lambda$. The inset shows the distribution of $\frac{d\theta }{ds}$ at large $\lambda \ge 6.5\mu \mathrm{m}$. Black and red curves in B and C denote approach from left and right, respectively. For $\lambda <$ $2.5\mu \mathrm{m}$, Spearman’s correlation ( $-0.4<\rho <-0.2$ ). D) The derivative of the cell orientation with respect to the lateral separation is shown for cell arrivals from the left and right. Negative values correspond to CW rotation and positive values indicate CCW rotation. The center of the channel corresponds to x = 0 μm. The total sample size (left and right) was n = 50 cells for C) and D). The red- and gray-shaded bands indicate the standard error in C) and D). E) The false-color axis-symmetric image shows averaged cell trajectories into channels captured from 10 representative successful entries. See Methods for image construction details and the original image in Fig. S3. The white lines indicate the channel. The vertical black lines show the lateral separations over which successful entries repeatedly occurred, and the white double arrows show the effective widening of the mouth. The slanting black lines indicate entry angles (θ ~ 30°) . F) A schematic of the virtual funnel from the reconstructed funnel image in E). Black lines indicate the channel, and red lines indicate the virtual funnel created by motile bacteria.

The normalized occurrences of successful or unsuccessful entry into the channel for varying initial lateral separations from the opening and cell orientations are shown in Fig. 3B. We exploited the mirror symmetry about the channel axis and collapsed the occurrence values calculated over orientations from 0 to 180° into 0 to 90° interval, where the 0-180° axis was parallel with respect to the PDMS wall. Remarkably, the cells readily penetrated even when approaching at angles as low as 15° from either left or right of the channel. They also penetrated when the distance between the opening and the initial contact site, $x_M$, exceeded 3-4 times the cell width (Fig. 3B). The entry attempts tended to be successful either when cells approached in a near-vertical orientation over a broad range of separations from the channel, or when they arrived at close separations over a wide range of orientations. When they arrived obliquely at large separations, their interactions with the PDMS wall caused them to align parallel to the wall and swim along. Thus, motile cells underwent both lateral and angular displacements during entry into narrow channels, thereby significantly increasing the likelihood of entry.

Next, we determined whether the cells required physical contact or whether they could sense the channel opening via long-range hydrodynamic interactions. We separated the trajectories of cells that successfully penetrated the channels based on whether they approached from the left or right. Then, we quantified the change in θ with the arc length, s, of the cell’s trajectory ($\raisebox{1ex}{$d\theta $}\!\left/ \!\raisebox{-1ex}{$ds$}\right.$) for varying vertical separations (λ) between the cell’s front pole and the channel openings over varying s (Fig. 3A) As observed in Fig. 3C (inset), far from the channel, the ($\raisebox{1ex}{$d\theta $}\!\left/ \!\raisebox{-1ex}{$ds$}\right.$) tended to be more negative, consistent with CW trajectories due to hydrodynamic coupling with the glass boundary^9,24. The values remained approximately constant and flat over varying λ until the point of contact with the PDMS boundary (Fig. 3C). The lack of clear trends in ($\raisebox{1ex}{$d\theta $}\!\left/ \!\raisebox{-1ex}{$ds$}\right.$) versus λ is consistent with the absence of significant long-range coupling between the swimmer and the channel opening, likely due to the strong hydrodynamic screening by the glass boundary²⁵. Thus, swimmers do not preferentially direct their movements toward channel openings from a distance, and the entry process is entirely dominated by interactions post-contact with the surface.

Once the cell contacted the PDMS, it could move only laterally, i.e., along the x-axis. Hence, we calculated ($\raisebox{1ex}{$d\theta $}\!\left/ \!\raisebox{-1ex}{$dx$}\right.$) as a function of the lateral position of the contacting pole to determine how the orientation varied before penetration. As shown in Fig. 3D, cells contacting the PDMS on the right (left) of the channel initially rotated clockwise (counterclockwise) as they probed the surface. At the channel mouth, they pivoted in the opposite direction, counterclockwise (clockwise), to enter. Thus, the motile cells employ the two-step facilitated entry mechanism from either side of the channel.

Figure 3E depicts a superimposed reconstruction of multiple lateral and angular displacements following contact with the PDMS that resulted in successful entries into the channel. The extreme orientations and separations from the channel opening produce a virtual funnel that widens the channel acceptance window. The funnel dimensions suggest an increase in channel width from 1.5 to an average of $\sim 4\mu \mathrm{m}$ (Fig. 3F).

Facilitated entry mechanism is enabled by self-propulsion

We reasoned that the mechanism of virtual funneling is driven by self-propulsion. When approaching and contacting the PDMS wall at a large lateral distance from the channel (Fig. 4A), the cell will begin to pivot and reorient parallel to the wall due to hydrodynamic interactions^26,27. Even at the closest distance, the cell is unlikely to actually touch the PDMS wall, maintaining a separation of ~100 nm or more due to electrostatic repulsion^28,29. Hence, a far-field approximation was selected, where the hydrodynamic forces realign the cell at a rotational rate $\raisebox{1ex}{$\sim F{L}_{cell}\sin \left(2\theta \right)$}\!\left/ \!\raisebox{-1ex}{$\left(\eta {\left(L_{cell}\right)}^3\right)$}\right.$²⁶. In this expression, the appropriate cell-surface separation was assumed to be ~ L_cell as only the events occurring after surface contact are pertinent. The time over which the cell reorients following contact with the PDMS can be recast in terms of the rotational drag coefficient, ${\gamma }_{\text{rot}}$, as ${\left({\Omega }^{CP}\right)}^{-1}\sim \raisebox{1ex}{$16{\gamma }_{rot}$}\!\left/ \!\raisebox{-1ex}{$F{L}_{cell}\sin \theta \cos \theta $}\right.$.

Figure 4. Non-motile cells cannot penetrate narrow constrictions.

A) Step 1 (t₁ to t₂): Schematic representation of a cell approaching and contacting the surface at a lateral offset $\left(x_{\mathit{contact}}\right)$ from the channel center and at an orientation, θ. The cell slides toward the opening while undergoing rotation that aligns it with the surface. Step 2 (t₃ to t₄): If the cell encounters the channel before it becomes parallel, its movement is obstructed by the opposing walls of the rigid opening. The transverse component of the propulsive force $\left(F_{\mathit{pivot}}\right)$ and the reaction force $\left(F_i\right)$ form a force couple that reorients the cell at the opening in the opposite direction, enabling penetration following alignment with the channel axis. B) The fractional occupancy of the channels by the non-motile is shown as red, open circles. The corresponding motile cells occupancy from Fig. 2B is shown as black, filled squares. The measurements were obtained an hour after incubating pure cultures over varying cell concentrations. Each mean value was determined from an average of n = 230 channels collected across 2 biological replicates. C) Composite image displays an overlay of the cyan and yellow fluorescence channels. Scale bar = 10μm. The non-motile cells (cyan) are mostly observed in the main trench, whereas the motile cells (yellow) occupy all available spaces within the channels. D) The channel occupancy for a 1:1 mixture of motile (filled symbols) and non-motile cells (open symbols) after an hour of incubation. The motile occupancy was ~100%, and the non-motile cells occupancy remained ~0% across all concentrations (3.1×10⁹, 3.72×10¹⁰, 2.87×10¹¹, and 1.63×10¹² cells/mL). Different symbols represent means calculated from six ROI across 3 biological replicates; each mean value was calculated over n = 96 channels. Asterisks indicate significance determined from a paired t-test (two-sided) comparing motile and non-motile cell occupancies (p ~ 3.13×10⁻⁶). The bars in B) and D) represent the standard error.

The lateral distance covered before the cell becomes parallel to the surface depends on the component of the thrust parallel to the surface: $v_x=\frac{dx}{dt}\left(=\frac{F\mathrm{c}\mathrm{o}\mathrm{s}\theta }{\gamma }\right)$, where γ is the translational drag at the surface. If the lateral distance covered $x<x_{\mathit{contact}}$, the cell reaches the channel after it has already pivoted below the minimum angle $\left({\theta }_r\right)$. In this case, no funneling is possible and the cell returns to the bulk. However, if $x>x_{\mathit{contact}}$, the cell reaches the channel at orientations $>{\theta }_r$. In that scenario, the component of the flagellar thrust parallel to the surface helps pivot the body in the opposite direction, aligning it with the channel axis and facilitating entry (Fig. 4A). We obtain the characteristic scanning distance, $\mathrm{\Gamma }$, for successful entries from $2\pi \frac{dx}{d\theta }=\frac{-16{\gamma }_{\mathit{rot}}}{\gamma L_{\mathit{cell}}\mathrm{s}\mathrm{i}\mathrm{n}\theta }$, yielding

$$\frac{\Gamma }{w}=\frac{-8}{\pi }{F}_p\ln \left|\frac{\tan \left(\raisebox{1ex}{${\theta }_r$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}{\tan \left(\raisebox{1ex}{$\theta $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}\right|$$ Equation 1

Here, $F_p=\frac{{\gamma }_{\mathit{rot}}}{\gamma L_{\mathit{cell}}w}$, is the dimensionless facilitated entry number and $w\left(=2a_{\mathit{pore}}\right)$ is the cell width. Notably, the facilitated entry number is entirely determined by the cell geometry and is independent of the thrust force or the medium viscosity.

Our measurements indicate that the ${\theta }_r\sim 15$ degrees. Below this angle, the cell rarely penetrates the channel, regardless of the initial contact separation. This minimum angle likely depends on various surface properties, including the effective roughness. As the cell can successfully scan and penetrate the channel if its initial separation from the opening is lower than Γ, the Γ versus θ defines a critical boundary that partitions the phase map shown in Fig 3B. The boundary divides the map into regimes of high probability channel entry on the left and low probability channel entry on the right, matching experimental observations with good accuracy despite the lack of fitting parameters in equation 1 and the use of the far-field approximation. Evidently, a smaller contact θ limit the scanning distances, and E. coli cells contacting the surface nearly vertically can scan almost 5 times their cell width or more (Fig. 3B).

To test the self-propulsion hypothesis, we employed a non-motile strain lacking the gene encoding the flagellar filament (fliC). We loaded the cells into the device and visualized them in the cyan fluorescence channel. Without flagellar propulsion, the cells were unable to occupy the channels for over an hour, regardless of cell concentration (Fig. 4B). When non-zero occupancies by non-motile bacteria occurred, they correlated with weak hydrodynamic flows that we were unable to eliminate.

In pure, non-motile cultures, diffusivity D ≈ 0.5-0.7 μm²/s (r)²⁸. A non-motile cell could diffusively enter a pore in 1/(C_2DD) (< 1 min), ignoring orientation constraints. Here, C_2D ~ 1 cell per 20 μm² based on experimental observations – corresponding to ~ 5 μm radial separation between cells. Instead, we rarely observed non-motile cells occupying channels, even over 24 h. Evidently, a combination of orientational constraints, steric hindrance due to other cells at the pore opening, and retardation of diffusive entry due to elevated drag within the channel decreases the penetration rates of non-motile bacteria.

Next, we tested whether mixing motile cells with non-motile cells could improve the latter’s transport into the channels, considering that the presence of active particles can increase the overall diffusivity of passive particles by several orders of magnitude ²⁹ (also see Fig. S4). We introduced mixtures of motile and non-motile cells spanning a wide range of concentrations into the device and monitored the channel occupancy. Non-motile cells remained largely excluded (Fig. 4C), and in fact, the fractional occupancy of the motile cells increased (Fig. 4D). Thus, narrow channels appear to be very effective in isolating motile cells from mixtures of motile and non-motile cells with high fidelity.

Amplification in motile cell flux due to facilitated entry mechanism

Without scanning and funneling, a hypothetical swimmer arriving precisely at the channel or pore entrance with an unfavorable orientation will spend $t\sim L_{\mathit{cell}}/V$ or less time at the opening before swimming away. During this period, the misaligned cell can reorient by ${\left(2D_{\mathit{rot}}t\right)}^{0.5}\sim 5^{\circ }$ through rotational diffusion to align with the channel axis (based on the parameters discussed in Fig. 3B, and $D_{\mathit{rot}}=0.06{rad}^2/\mathrm{s}$ ²⁸). Within this range (±5° relative to the channel axis), the hypothetical cell could directly enter the narrow channel without scanning and funneling. However, analysis of our experimental data (Fig. 3B) indicates that fewer than 1% of channel entries occurred via direct or coaxial entry within this permissible window at the channel mouth $\left(x_{\mathit{contact}}/a_{\mathit{pore}}\sim 1\right)$. The scanning-and-funneling mechanism accounted for 227 out of 229 entries.

Next, we modeled the relative contributions of diffusive and facilitated flux to motile cell transport into confined spaces. The classical result for the steady-state diffusive flux to a perfectly absorbing disk-like pore is given by $J=4a_{\mathit{pore}}D{C}_0$, where $a_{\mathit{pore}}$ is the pore radius and C₀ is the bulk concentration of the molecular species^30,31. We incorporated the orientational constraint, $J=4a{D}_{nm}{C}_0{P}_e^{\prime }$, where $P_e^{\prime }=\frac{\mathrm{\Delta }\theta }{\pi }$ and $\mathrm{\Delta }\theta =\frac{\pi }{36}$ (i.e., $85<\theta <95$ degrees).

The facilitated entry mechanism is determined by the short residence time $\left(\sim {\left({\Omega }^{CP}\right)}^{-1}\right)$ set by hydrodynamic coupling at the surface. During this time, the cell will enter a pore if it is located within a distance $\Gamma \left(\sim w{F}_p\right)$ from the point of contact. If the pore is farther than this characteristic separation, the cell orients parallel to the surface, preventing pore-entry, and eventually returns to the bulk. Hence, we assumed that the surface flux is limiting. For cells in a narrow layer of thickness w above the surface, the local density is wC₀, and the surface flux due to the cells in the annular region is approximated by: $J_{2D}\sim w\pi \left({\left(a_{\mathit{pore}}+w{F}_P\right)}^2-{a_{\mathit{pore}}}^2\right)C_0\Omega$. The combined flux is: $J_M=4a_{\mathit{pore}}{D}_M{C}_0{P}_e+w\pi \left({\left(a_{\mathit{pore}}+w{F}_p\right)}^2-{a_{\mathit{pore}}}^2\right)C_0\Omega$, where the first term signifies the flux due to direct arrivals. Here, D_M is the motile cell diffusivity and the entry probability incorporates the funneling effect: $P_e=\frac{2\left(\frac{\pi }{2}-\theta \right)}{\pi }$. The amplification, ε , due to the facilitated entry mechanism, is the ratio of the overall flux of motile cells to that of hypothetical motile cells unable to utilize the mechanism:

$$\epsilon =\raisebox{1ex}{$J_{total}$}\!\left/ \!\raisebox{-1ex}{$J^{nofunnel}$}\right.,\text{where,}{J}^{nofunnel}=4a_{pore}{D}_M{C}_0{P^{\prime }}_e.$$

As shown in Fig. 5A, the facilitated search-and-funneling mechanism is predicted to increase motile cell flux into confined spaces by a factor of ~30-50 relative to hypothetical cells incapable of facilitated entry, consistent with the observed dominance of this mechanism in channel entries (Fig. 3B). Thus, the facilitated entry mechanism dominates motile cell transport into confined regions.

Figure 5. Motile flux amplification by two-step facilitated entry.

A) The z-axis indicates the ratio of motile cell influx due to facilitated entry to that without it. The ε is plotted as a function of the cell orientations, characterized by the entry probabilities, P_e, and the dimensionless entry number, $F_p$. We assumed: $a_{\text{pore}}=0.75\mu \mathrm{m}$, $P_e^{\prime }=0.028$, $P_e=\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$, $D_M=156\mu {\mathrm{m}}^2/\mathrm{s}$, and $D_{nm}=0.16\mu {\mathrm{m}}^2/\mathrm{s}$. The encircled region indicates the predicted amplification ranges for the parametric ranges typically observed in experiments. B) The surface-scanning distance is proportional to the cell length. The two curves indicate different cell thicknesses. C) The bead radius was chosen to produce an interstitial spacing ~1.5 μm when packed as indicated. The schematic on the right shows a single cell approaching the convex bead surfaces and shifting laterally toward the interstitial space, where it penetrates the natural funnel (mesh). D) Phase image of a packed bead column with individual motile cell tracks (colored trajectories) as they exited into the reservoir. Scale bar = 10 μm. E) Representative antibiotic plates (Ampicillin, top and Kanamycin, bottom). White colonies are visible only on the Amp plates, indicating motile cells. The graph indicates the mean cell counts from the two plates over 3 technical replicates and three biological replicates (n = 18 samples). Each technical and biological replicate constitutes an independent column experiment. The bars represent the standard error.

Finally, the scanning distance, Γ, was proportional to the cell length (Fig. 5B), suggesting that longer and thinner bacterial cells likely exploit the facilitated search-funneling entry mechanism more effectively than shorter, thicker cells.

Extreme confinement helps separate pure motile cells from mixed populations

The dominant role of the facilitated-entry mechanism in enabling motile cells to penetrate narrow pores, together with the inability of non-motile cells to employ it, suggests that narrow constrictions could effectively separate motile from non-motile cells, particularly in geometries that enhance funneling. To test, we created a packed-bead column with beads of radius ~4.5 μm (see Methods). The interstitial spacing between the packed beads was ~ 1.5 μm, matching the channel width in the microfluidic chambers (Fig. 5C). In this geometry, the packed beads have the appropriate curvature to create a funnel shape, and the surface scanning is predicted to further accelerate the entry. Importantly, unlike the dead-end pore geometry in Fig. 4C, the packed-bead column could enable physical isolation of motile cells from the mixed population for downstream molecular, genetic, or functional analyses by providing a downstream collection reservoir.

The column was prepared in a tapering micro-capillary with a narrow opening of 6 μm (Fig. 5D, Fig. S5). We loaded a mixture of Ampicillin-resistant motile and Kanamycin-resistant non-motile cells onto the column and oriented it horizontally to eliminate any gravitational effects. After ~45 min, we observed several cells exiting the column outlet (Supplementary Movie 4). Cell tracking suggested these were motile cells, as they moved persistently.

We determined the cell type by centrifuging the entire contents of the reservoir where the cells had exited and plating on separate Ampicillin- and Kanamycin-containing plates. No colonies were ever observed on the Kan-plates, indicating that the non-motile bacteria failed to percolate through the column. Only the Ampicillin plates showed colony growth, indicating that the bacteria that exited the column were exclusively motile (Fig. 5E). This ~100% purity was highly reproducible (Fig. 5E, right panel). Interestingly, the search geometry in the column is effectively two-dimensional (2D) (Fig 5C, right panel), rather than quasi-1D as in the microfluidic device. Despite this, the transport differences between motile and non-motile cells remain sufficient to achieve high-purity separation.

Discussion

Funnel-shaped obstacles have been employed previously to preferentially enrich motile bacteria on one side by rectifying their motion through asymmetric surface and hydrodynamic interactions^32–36. Here, we demonstrate that effective ‘virtual’ funnels emerge dynamically through interactions between self-propelled bacteria and narrow openings on flat surfaces, facilitating cell entry into confined spaces. Single-cell imaging revealed a two-step facilitated entry mechanism: first, a bacterium arriving at a flat surface laterally scans it with its pole, reducing the dimensionality of the search for a target opening. Upon encountering a suitable opening, the cell pivots into alignment with the channel axis, effectively converting rigid pores into virtual funnels (Fig. 3E and Supplementary Movies 1, 2, 3). Although this mechanism does not rectify motile cell migration, it is the dominant mode of motile cell entry into narrow pores, amplifying their flux by ~30-50x relative to co-axial entry.

These findings establish an active, cellular-scale mechanism for faster target search, which shares key features with facilitated diffusion in protein-DNA systems, such as reduced dimensionality and elevated probabilities of successful target search ³⁷. However, unlike facilitated diffusion—which depends on weak thermodynamic interactions between RNA polymerase and DNA—the motile cells associate with the surface via persistent flagellar thrust, a fundamentally non-equilibrium, energy-dependent process^38,39. Therefore, the relative orientation of the openings with respect to the surface strongly impacts transport. Convex landscapes and narrow interstitial spacing within the bead columns enabled high-purity kinetically-driven enrichment of motile cells from mixed cultures, extending and improving upon prior observations of active–passive matter separation ^40–42. This segregation is owing to single-cell phenomenon rather than motility-induced phase separation (MIPS) or other population-level effects in motile populations^43,44. Concave geometries that, via hydrodynamic coupling, redirect individual swimmers away from openings ³² will likely inhibit facilitated entry from that direction. Further, deformable pore openings could inhibit the funneling effect, whereas increased surface roughness on the order of cell width, w, could delay the flattening of the cell against the surface, thereby extending the scanning length.

A few of the previous works that challenged motile-only cultures with geometric constraints either maintained high vertical clearances (~ 5-10 times the cell width) or imposed confinement with a single boundary ^41,45–48. Such geometries produced only modest increases in viscous drag, resulting in minor changes in swimming speed. The fully confining regimes we employed enclose the cell on all four sides at cellular dimensions, creating viscous traps that markedly decreased the swimming speed. Our flux estimates do not incorporate in-channel viscous effects; however, this is readily achieved by including an intrinsic rate constant that accounts for kinetic bottlenecking due to increased drag. Bottlenecking is expected to be particularly prohibitive for non-motile cells, as any cell that enters will naturally undergo reciprocal motion at the channel mouth, suppressing the entropically driven influx over short times. In contrast, motile cells penetrate deep in a few seconds, vacating the opening for other cells. If the pore size increased substantially (e.g., to ~10 times the cell width), geometric and hydrodynamic constraints would become negligible, and the contribution of scanning-funneling to motile cell transport would be dwarfed by the largely unhindered direct flux into the pore.

The pronounced advantage of motile over non-motile cells in penetrating extreme confinements cannot be attributed to differences in their effective diffusivities, as orientation constraints largely inhibited transport of both cell types. Instead, ~99% of the motile transport into the pores arose from facilitated entry, a mechanism unavailable to non-motile cells. The facile entry of motile bacteria into narrow channels was also reproducibly observed in other motile species, including Helicobacter pylori and Vibrio cholerae (Supplementary Movies 5, 6). These observations are consistent with prior in vivo studies showing that motile bacterial pathogens, but not flagellin-deficient mutants, effectively transmigrate across porous epithelia⁴⁹ and porous gel-like environments^50–52. The narrowest recesses in natural microbial habitats, such as intestinal crypts and mucosal interfaces, are likely to provide enhanced protection from predators such as immune cells⁵³, while strongly influencing niche colonization and initial stages of biofilm induction^54,55. Furthermore, the strong viscous effects in such narrow constrictions suppress flow-driven entrainment of the bacteria, making access to these spaces a critical determinant of microbial competition for niches. Therefore, these findings could inform future studies of spatial organization in microbial communities and infections, and suggest new avenues for enriching bacteria based on their motility phenotypes.

Methods

Strains and culturing

We used a motile strain of E. coli that swims smoothly (ΔcheY) and a non-motile strain lacking flagella (ΔfliC), along with the wild-type strain. We transformed the smooth-swimming strain with a ptrc99A vector carrying the yellow fluorescent protein (eyfp) and the non-motile strain with a ptrc99A vector carrying the cyan fluorescent protein (ecfp) allele. All the strains had an E. coli RP437 background.

We streaked fresh colonies on Luria-Bertani (LB) agar plates from frozen glycerol stocks. We grew overnight cultures and back-diluted them in fresh Tryptone Broth (TB) at a 1:100 ratio the next day to start day cultures. Where appropriate, the media was supplemented with 100 μg/mL of Ampicillin or kanamycin. To induce eCFP or eYFP expression, we added 100 μM of the inducer Isopropyl β-D-1 thiogalactopyranoside (IPTG). After about 3-4 h of incubation at 33°C on a shaker set at 170 RPM, we harvested the cells between 0.5 – 0.6 OD₆₀₀. The cells were pelleted for 5-7 min at 1500g and resuspended at various OD₆₀₀ values in motility buffer (MB). Mixtures of motile and non-motile cells were prepared by mixing equal volumes of the two at the desired OD values. In the bead-column assays, we used a wild-type with an empty ptrc99A plasmid (Amp-resistant) and a ΔfliC (non-motile strain) with an empty pBAD33 plasmid (Kan-resistant). We did not wash the cells with buffer. Instead, we directly mixed the two growth cultures in a 1:1 ratio.

Fluorescence and phase imaging

We used a Nikon TiE microscope for phase, dark-field, and fluorescence imaging. The microscope was equipped with a long-pass Chroma filter (700 LP) that filtered the phase illumination to eliminate the blue-light effect ^56–58. Microscopy videos were captured with a CCD camera (UI-3240 LE, IDS Imaging). We used a white-LED source (SOLA SE II 365 Light Engine, Lumencor) filtered appropriately with a YFP or CFP filter cube for epifluorescence illumination. We recorded emissions with a sCMOS camera (Andor Xyla, Oxford Instruments) with an exposure of 0.5-1s. We used either a 20x or a 60x oil-immersion objective for wide-field microscopy, depending on fluorescence levels. For pure cultures, phase microscopy with a 20x objective was often adequate. The different objectives yielded different channels per field of view.

Image Analysis

We analyzed the data with ImageJ. The cell counter tool was used to count the occupied and empty channels in the recorded phase and fluorescence data. We scanned several regions of interest over multiple devices per biological replicate to record occupancy. Each experiment was performed in triplicate. We obtained cell trajectories and speeds using a combination of manual and automated cell-tracking plugins. We used the line and angle tools to calculate the arc length, separations, and orientations for each trajectory.

To produce the motile cell influx phase map (Fig. 3B), we determined the θs and x_contact at the instance of initial contact for all the cell trajectories. If the cell trajectory resulted in a successful (failed) entry, we associated a label, i = +1 (0) to the corresponding θ and ${\mathrm{x}}_{\text{contact.}}$ We binned the θ and ${\mathrm{x}}_{\text{contact}}$, and in each bin, we estimated the probability of entry as ${\sum }^N\mathrm{i}/\mathrm{N}$, where N were the total events for that bin. If a particular bin had no entries, we assigned it a NaN value. We subjected the raw matrix to Gaussian smoothing (σ = 1): bins that were NaN in the raw data retained that value.

To construct the funnel image (Fig. 3E), we cropped time-lapse phase or darkfield videos into smaller single-cell motion batches, ranging from 0.5-1.5 seconds. We then shortlisted 10 representative batches in which the cell successfully entered the channel across various orientations and lateral separations. In each batch, we further cropped the image to align the entry channel, ensuring that the channel was centered both vertically and horizontally. Next, we used ImageJ to generate time-averaged projections for each batch, yielding one average image per batch showing the cell trajectory into the channel. We subsequently overlaid the 10 images to produce a composite trajectory map from which we produced a symmetric image along the vertical line of axis (Fig. 3E).

Microfluidic devices

The silicon wafer was developed according to previous protocols¹⁶. We fabricated the microfluidic device by pouring degassed PDMS onto a silicon wafer and soft baking at 60°C. We plasma-cleaned the solid PDMS and the bottom coverslips of the fluoro-dishes (Plasma Etch PE-25), subsequently bonding the two. The bonded device consisted of numerous microchannels orthogonal to the main trench, which was 1 cm × 100 μm × 100 μm (L×W×D). Each orthogonal channel was 25 μm×1.5 μm× 1.5 μm (L×W×D). We primed the device with isopropyl alcohol (IPA) (70%, VWR Life Sciences) and flushed it with DI water. We flushed the device with motility buffer (MB) prior to introducing the cells. We injected 2 μL of the cell suspension into the inlet port of the device at the beginning of the experiment and observed the cells once the flow ceased.

Bead column

We washed latex beads (4.5 ± 0.1 μm diameter, Polysciences Inc.) thrice times by pelleting and resuspending in deionized (DI) water. We placed a 50 μL drop of the bead suspension at the center of a microscopy dish. We inserted the tip of a micro-capillary (6 μm inner tip diameter and a tilt angle of 25°, Eppendorf Piezo Drill tip) into the suspension and filled the capillary with beads by applying suction using a CellTram 4r Oil manual hydraulic microinjector. Following packing under gravity, we replaced the drop with a 50 μL buffer containing 0.01 M NaCl and drew the fluid into the microcapillary to freeze the microstructure by screening out electrostatic interactions. We detached the capillary and suspended it vertically overnight at 37°C for further compaction in a chamber saturated with water vapor to prevent drying. The final bead column was ~100 μm in length.

We loaded a 1:1 mixture of motile and non-motile cells from the wide end of the capillary (1.0 mm ID) with a microloader (Eppendorf Femtotip microloader Tip, E5242956003). We carefully mounted the loaded microcapillary onto the micromanipulator holder and immersed the capillary’s narrow tip into a small petri dish containing TB using the micromanipulator (CellTram 4 oil Dr., Eppendorf). Owing to the capillary tilt, the packed bed was horizontal, and we could observe it until the first cells appeared at the capillary’s mouth, ~ 45 minutes to 1 hour later. After waiting for 30 additional minutes, we split the TB and plated it onto LB agar plates supplemented with different antibiotics (Amp-resistant and Kan-resistant). We counted the colonies after incubating the plates at 37°C for 14 hours.

Data availability

All relevant data is available from the corresponding author upon request.