Rectified cell migration on saw-like micro-elastically patterned hydrogels with asymmetric gradient ratchet teeth

Abstract

To control cell motility is one of the essential technologies for biomedical engineering. To establish a methodology of the surface design of elastic substrate to control the long-range cell movements, here we report a sophisticated cell culture hydrogel with a micro-elastically patterned surface that allows long-range durotaxis. This hydrogel has a saw-like pattern with asymmetric gradient ratchet teeth, and rectifies random cell movements. Durotaxis only occurs at boundaries in which the gradient strength of elasticity is above a threshold level. Consequently, in gels with unit teeth patterns, durotaxis should only occur at the sides of the teeth in which the gradient strength of elasticity is above this threshold level. Therefore, such gels are expected to support the long-range biased movement of cells via a mechanism similar to the Feynman-Smoluchowski ratchet, i.e., rectified cell migration. The present study verifies this working hypothesis by using photolithographic microelasticity patterning of photocurable gelatin gels. Gels in which each teeth unit was 100-120 µm wide with a ratio of ascending:descending elasticity gradient of 1:2 and a peak elasticity of ca. 100 kPa supported the efficient rectified migration of 3T3 fibroblast cells. In addition, long-range cell migration was most efficient when soft lanes were introduced perpendicular to the saw-like patterns. This study demonstrates that asymmetric elasticity gradient patterning of cell culture gels is a versatile means of manipulating cell motility.

Figure 1. Schematic diagram showing how saw-like asymmetric elasticity patterns are hypothesized to induce rectified cell migration.

(a) Cells move randomly when substrate elasticity is homogeneously distributed. (b) On a surface with asymmetric elasticity, cells move by durotaxis towards regions with high elasticity across boundaries that have an elasticity gradient above a threshold level. Biased cell migration does not occur at boundaries that have an elasticity gradient below this threshold level. (c) Cells that migrate across the region with peak elasticity do not migrate back to the less rigid area. Instead, they enter the adjoining unit area. This process can lead to long-range cell migration via a mechanism similar to that of the Feynman ratchet.

Figure 2. Schematic diagram showing how cell adhesive hydrogels with saw-like asymmetric elasticity patterns are fabricated.

In the first step, a soft base gel is prepared by irradiation of a photocurable sol of styrenated gelatin with visible light. In the second step, the base gel is photo-irradiated through slits in a photomask for a defined period of time. The gel is continuously displaced in a perpendicular direction to the photomask at a defined speed using a computer-assisted X-Y movement stage. The duration of irradiation is set so that the StG sol surface is irradiated asymmetrically.

Figure 3. A representative gel with a saw-like asymmetric elasticity pattern.

Width of each unit: 100 µm. (a) Phase contrast microscopy image of the gel surface. (b) Cross-sectional observation of the gel surface by confocal laser scanning microscopy. (c) Distribution of Young’s modulus in a single unit. Preparation conditions: first irradiation step, 70 s; second irradiation step, stage moved at a velocity of 0.44 µm/s between 0 and 19 µm and then at 0.88 µm/s between 20 and 59 µm using a photomask with a 60 µm-wide slit and a 140 µm-wide shade.

Figure 4. Distribution of Young’s moduli in gels with different unit sizes and peak elasticities.

The width of each unit in series A and B was 100 µm and 120 µm, respectively. Series 1, 2, and 3 had a peak elasticity of ca. 100 kPa, 300 kPa, and 500 kPa, respectively. The ratio of ascending:descending elasticity gradients in each unit was 1:2, i.e., the X-position of the peak of elasticity was located at ca. 30 µm and 40 µm in series A and B, respectively. The conditions used to prepare each of the gels are described in Table 1.

Figure 5. Trajectories of 3T3 fibroblasts cultured on A1-A3 and B1-B3 gels.

Time-lapse microscopy was performed for 30 hr and images were acquired at 15 min intervals. The starting position of each cell trajectory was mapped to the origin of the graph. A band of single unit including the origin is highlighted. n=40 cells.

Figure 6. Quantitative analyses of observed cell trajectroies.

a) Time-course analysis for X trajectory of each cell observed, b) ensemble averaged displacement in the X-direction with standard deviation, c) a heat map of the regions of the gel to which cells migrated.

Figure 7. Long-range cell migration on gels with saw-like asymmetric elasticity patterns and perpendicular soft lanes (PSLs).

The conditions used to prepare the gels are described in Table 1. (a) Phase contrast microscopy image of the gel. Sale bar: 100 µm. (b) Distribution of Young’s modulus in a single unit of the gel. Unit size: 90 µm. Elasticity peak: ca. 500 kPa. (c) Trajectories of 3T3 fibroblasts cultured on gels with PSLs. Cells were observed by time-lapse microscopy for 24 hr and images were acquired at 15 min intervals. (d) Time-course of ensemble averaged trajectories with standard deviation in the presence (red) and absence (blue) of PSLs. n=30 cells.