DNA sequences and preparationThe sequences for the DNA crosslinks and growth and shrinking activators are listed in Supplementary Table 1. DNA Sequences were designed using NUPACK 3.2.2 to have specific secondary structures and minimal undesired crosstalk64. A temperature of 25 °C and salt conditions of 0.05 M Na+ and 0.0125 M Mg2+ were used in all design programs. Designs were produced iteratively by adding new sequences to an existing set of sequences and domains (system 1–4 strands in ref.20, Supplementary Fig. 8), and we ran multiple design trials to produce several potential sets of DNA sequences. These sets of sequences were then ranked by the degrees of interaction with existing sequences predicted by NUPACK for the final selection of sequence designs. Sample scripts are at https://doi.org/10.7281/T1/WYN7FI. Unmodified and Acrydite-modified oligonucleotides were purchased in lyophilized form from Integrated DNA Technologies (IDT) with standard desalting purification. The DNA strands were solubilized in Tris-acetate-EDTA (TAE) /0.0125 M Mg2+ (TAEM) buffer (TAE buffer, Life Technologies, #24710-030; Magnesium acetate tetrahydrate, Sigma #228648). DNA concentration was verified using absorbance spectroscopy at 260 nm. 3 mM DNA crosslink complexes were annealed in TAEM from 90 °C to 20 °C at a rate of 1 °C/min using an Eppendorf Mastercycler. Growth activator strands were heated to 95 °C for 15 mins and then flash-cooled in ice for 5 mins at a concentration of 400 µM.Preparation of DNA gel pre-gel solutionThe concentrations of the components in PAAM-co-BIS-DNA pre-gel solution were: 1.41 M of acrylamide (BIO-RAD #161-0100), 5 mM of N, Nʹ-methylenebis(acrylamide) (Sigma-Aldrich, #146072), 1.154 mM DNA crosslinks, 2% v/v Omnirad 2100 (iGM Resins USA, #55924582), and 2.74 mM methacryloxyethyl thiocarbamoyl rhodamine B (Polysciences, Inc., #23591). The concentrations of the components in the PEG-co-DNA pre-gel solution were the same as those in the PAAM-co-BIS-DNA pre-gel solution except PEGDA-MW10k (Sigma-Aldrich, #729094) and PEGDA-MW20k (Sigma-Aldrich, #767549) were 10 wt%, and one of these was used in place of acrylamide and bis-acrylamide. Unless noted otherwise, PEG-co-DNA gels contain PEGDA-MW10k. Omnirad 2100 was first made into a 75% v/v butanol solution to help disperse into the pre-gel solution. When making gel bilayers, 1 mM fluorescein-O-methacrylate (Sigma, #568864) fluorescent dye was included in lieu of 2.74 mM methacryloxyethyl thiocarbamoyl rhodamine B (Polysciences Inc., #23591) in the pre-gel solution when patterning the second (upper) gel layer. The pre-gel solutions were mixed well using a pipettor and then were ultrasonically mixed for 1 min (for PAAM-co-BIS-DNA) or 3 mins (for PEG-co-DNA) before being degassed in a vacuum chamber for 15 min.Lithography chamber fabricationThe lithography chamber consisted of a chromium (Cr) mask, a glass substrate (or a Cr-coated glass substrate with patterns), and desired thickness tape serving as spacers at the left and right sides within the chamber (160 µm for monolayer gels and 60 µm for bilayer gels) to control gel thickness20,21. Plastic masks, which were then utilized for making Cr masks or Cr-coated glass substrate, were first designed using AutoCAD and then sent for printing (Fineline Imaging). Glass slides were cleaned with DI water and isopropyl alcohol (IPA), then blow-dried using nitrogen gas before being spin-coated 3 nm SC1827 (Microchem, Microposit S1800 Series) and baked on a 115 °C hotplate for 1 min. The prepared glass slides were cured through plastic masks with 180 mJ/cm2 365 nm UV light, then developed using a 1:5 w/w Microposit 351 Developer (Shipley) and washed with DI water. A 150 nm (for monolayer gel fabrication) or 300 nm (for multi-step patterning process) Cr layer was then deposited onto the glass slides through thermal evaporation. The remaining photoresist layer was washed with acetone ultrasonically and DI water. All glass slides, Cr masks, and Cr-coated glass substrate were cleaned with water and IPA and then blow-dried before each use. For multi-step photopatterning, CYTOP (Type M, Bellex International Corp.) was applied to Cr masks to prevent gels from sticking or lift-off.Photopatterning processTo pattern square-shaped, 1 mm side length monolayer gel films with a thickness of 160 µm, the pre-gel solution was injected into a chamber and then exposed to a 365 nm UV light source for 160 mJ/cm2 (PAAM-co-BIS), 800 mJ/cm2 (PEGDA-MW10K) or 1000 mJ/cm2 (PEGDA-MW20K) exposure dose. To pattern 2 mm-long, 0.5 mm-wide bilayer gel structures with each layer thickness of 60 µm, the pre-gel solution with fluorescein-O-methacrylate was first patterned using the exposure energy stated above. The first gel layer was gently washed using TAEM buffer and dried using nitrogen gas. The second 60 µm spacer was added to the gel chamber to increase the chamber height to a total of 120 µm. The mask was then aligned with the patterned gel, and the pre-gel solution containing methacryloxyethyl thiocarbamoyl rhodamine B was UV-cured. Process diagrams for the multi-step gel automata photopatterning process are shown in Supplementary Fig. 14, Supplementary Fig. 18, and Supplementary Fig. 19. Additional descriptions of the processes can be found in Supplementary Method 1. Briefly, we designed the Cr masks to have four aligning cross-shaped markers at the corners to enable alignment between gel segments. The final segment lengths of each region in the photopatterned masks for the multi-segment strips were each 1.5 times the lengths designed using computer programs. This increase in mask length was introduced to compensate for the curvature reduction in the subsequent cycle of a multi-step actuation. During the first step of multi-segment structure fabrication, a Cr-coated glass substrate with the same pattern as the photomask was used instead of a transparent glass substrate so that the aligning markers on the Cr mask could be used during subsequent patterning steps. In the following fabrication steps, gels were gently washed with TAEM and blow-dried after each patterning step, and additional spacers were added when the first layer of photopatterning was finished, as described in the bilayer gel fabrication process. All gels were washed and hydrated with TAEM buffer, gently removed from the glass substrate or Cr-coated glass substrate, and stored in TAEM in a 4 °C fridge until actuation.Characterization of monolayer DNA gel shape changeThe extent of growth and shrinking of monolayer gels were measured using time-lapse fluorescence imaging with a gel imager (Syngene EF2 G: Box) equipped with a blue light transilluminator (Clare Chemical, max emission at ≈ 450 nm) and a UV 032 filter (Syngene, bandpass 572 – 630 nm), or an automated imaging system described in the Supplementary Method 2 as Programmable imaging system (Pi-Imager) for time-lapse fluorescence image capturing (Supplementary Fig. 21). The gel samples were transferred to wells within a black-walled 96-well plate to isolate the gels from each other during actuation. Unless noted otherwise, solution composition and solute concentrations are as stated below: gels were expanded in TAEM supplemented with 0.01%v/v Tween20 (Sigma, #051M01811V) (TAEM-Tween20) to prevent gels from sticking to the well surfaces. 150 µL of TAEM-Tween20 solution containing 60 µM DNA growth activators (99% polymerizing, 1% terminating) was added to each well. After 72–100 hours of growing, the DNA solution was switched to 100 µL TAEM-Tween20 for 15 mins, and the solution was removed, and then 150 µL TAEM-Tween20 shrinking activators solution was added. The above growth/shrinking process was repeated when characterizing multiple actuation cycles. Buffer was added to clean the dish and gels between steps to maintain consistent actuation concentrations and ensure more straightforward actuation results. However, such steps are not required for reversible actuation (Supplementary Fig. 23). Images were taken every 30 mins, and the resulting photos were segmented into smaller images, each containing one gel for further MATLAB processing. All images were first transformed into gray-scale images by extracting the red channel signals from the original RGB image. Images were then contrast-stretched using MATLAB’s Image Processing Toolbox (2019a) to reduce background and simplify further feature extraction. The four side lengths of the gel in each image were measured and averaged as follows. The extrema and centroids of the objects were determined using MATLAB’s function regionprops. Eight locations provided by the extrema of a gel object (two points at the ends of each side) were used to determine the locations of the four vertices by K-means clustering. The average distance between these four clusters was used as the measure of the side length of the gel. The relative change in side length (ΔL/L0) of the gel was calculated using the measured side lengths (L) from each image in a time series relative to the side length prior to adding DNA activators (L0). PAAM-co-BIS-DNA gels were sometimes too dim to find with the MATLAB code described above. In such cases, the raw images were first treated by flat-fielding to have a brighter view and a more significant contrast against the background, in addition to the previously described process for edge-length determination. Shaded area/dotted lines enclosed the standard deviation of the mean growth value, which were smoothed using MATLAB smooth function over 50 (growing) and 10 (shrinking) points, N (sample size)= 3 or 4.Characterization of bilayer DNA gel actuationFluorescence images of the bilayer gels were captured using the gel imager, blue light, and filter stated in Characterization of monolayer DNA gel shape change. Before actuation, bilayer gels were set on their sides so that curvature could be measured from a side view of a gel. The DNA-directed actuation and solution exchange processes were the same as those described in Characterization of monolayer DNA gel shape change. Images were taken every 30 mins and were segmented into images, each containing one gel for further processing in MATLAB. Within each image, the pixels that contained the gel were first determined by selecting pixels more than 4.3 standard deviations brighter than the mean fluorescence intensity of the image to produce a binary image. The binary image was smoothed and thinned to a curve using MATLAB’s bwmorph function. The radius of curvature of the contour connecting the coordinates on the line/ring was determined using the Taubin method65. The direction of curvature of bilayer gels was distinguished using +/- (the sign of the radius of curvature). Shaded area/dotted lines enclose the standard deviation about the mean curvature value, which were smoothed using MATLAB smooth function over 20 (ascending) and 10 (flat and descending) points, N = 3.Letter gel automata designWe began creating a letter gel automaton by manually designing a three-segment gel bilayer stack, with the idea that the top and bottom portions would curve in different directions to form the top and bottom elements of the C, S, and J. To choose the lengths and systems of each gel region, we visualized the resulting curves produced by candidate bilayer strips by assuming that the segment of the bilayers would have a radius of curvature of 1.5 mm−1 based on measured curvature values in Supplementary Fig. 13 and that the composite structure of the three-segment bilayer would be formed by concatenating the shapes of each segment. The resulting design (V1.0) is shown in Supplementary Fig. 15, and the improved design (V1.1) is in Supplementary Fig. 16.Simulation of digit gel automata transformationUsing data from bilayer DNA-co-polymerized gel characterization (Supplementary Fig. 13), we developed a numeric simulation to predict the final shapes of the gel automata. We characterized the radii of curvature (RoC) of bilayer gels and the changes in contour length resulting from different actuation combinations. A lookup into the resulting table of these values, indexed by each system type, sets the radius of curvature and change in contour lengths of individual bilayers within a bilayer segment. To predict the shape of the contour of an gel automaton consisting of multiple bilayer segments, we assumed that bilayer gel segments curved independently of one another. To simulate the curvature of gel automata, we began with a 1D array segment_lengths and a 2d array identities as inputs and generated a gel automaton object. The segment_lengths array encoded the lengths of each segment, while identities encoded the types of systems in each segment. We then simulated the (up to) 16 possible states that a gel automaton could transform into, given our four switchable DNA systems to produce 16 output images as follows. We first retrieved the values of the radii of curvature and change in contour from the tables referenced above to obtain a 1d array rocs for the radius of curvature of each segment and a 1d array ctls for the change in contour length of each segment. We then produced a final shape consisting of the concatenation of the final curves of each of the bent segments. These curves were produced by generating the next point along a composite curve using a numerical contour integration scheme. Specifically, starting at (x, y) = (0, 0) and q = 0, we used delta = 20 µm as a mesh size and an iterator object to generate the next (x, y) point as follows:$$\Delta \theta=\frac{{{{\rm{delta}}}}}{{{{\rm{radius}}}}\; {{{\rm{of}}}}\; {{{\rm{curvature}}}}} \, \Longrightarrow \, \theta=\theta+\Delta \theta$$
(1)
$$\Delta x={{{\rm{delta}}}}\times \sin \theta \, \Longrightarrow \, x=x+\Delta x$$
(2)
$$\Delta y={{{\rm{delta}}}}\times \sin \theta \, \Longrightarrow \, y=y+\Delta y$$
(3)
The iterator generated new points within a given segment till the segment length limit \({segment\; length}\times \left(1+\Delta {contour\; length}\right)\) for a segment was reached. The scheme then generated points for subsequent segments by continuing along the integration path. We next compiled 28 × 28-pixel images using the x, y points and applied a Gaussian filter (with sigma value = 0.8) to each generated image so that the images appeared similar in texture to the handwritten digits in the MNIST digits library66. For additional details, refer to https://doi.org/10.7281/T1/WYN7FI.Convolutional neural network (CNN) for autonomous classifiersWe first compiled a convolutional neural network model with the TensorFlow library (Ver 2.4.3). We then trained the model with a dataset containing the MNIST digit dataset and a dataset generated by gel automaton geometry simulation. The generated dataset includes twenty-eight thousand human-labeled strip images. These images were either recognizable as one of the 0–9 digits (and thus were labeled with respective digits) or were considered random squiggles, i.e., curves not representing any numeral, and were labeled as an eleventh category. Random squiggles were included as a class so that the model could determine whether a shape resembled any digits, in addition to quantifying the resemblance of a shape to the digit. We combined the generated dataset and the MNIST dataset for model training. The combined dataset consisted of 98,000 images and was split into train and test sets, which contained 84,000 and 14,000 images, respectively. The data were normalized prior to training so that each pixel value lay between 0 and 1. The CNN model consisted of two convolutional layers with rectified linear unit (ReLU) activation and max-pooling layers. Dropout layers were included to avoid overfitting, and a flattened layer was added prior to the fully connected layers. Two fully connected layers with Relu activation and a final output layer with softmax activation were present at the end of the network for classification. The model was compiled with categorical cross-entropy loss, and trained using the Adam (Adaptive momentum estimation) optimizer with the default learning rate (0.001) from the TensorFlow library. The trained network achieved ninety-eight percent accuracy on the test set by the end of training. Scripts used can be found at https://doi.org/10.7281/T1/WYN7FI.Genetic algorithm for digit gel automata parameter searchWe developed a genetic algorithm to efficiently search through the large parameter space of bilayer gels to find designs for digit gel automata. The algorithm started with an initial population of gel automaton designs generated from a random seed. Each design within the population was then simulated to find all possible geometric outputs of each of the 16 actuation combinations. The digit that each output resembled, and its extent of resemblance were calculated using the network described in Convolutional neural network (CNN) for autonomous classifiers. During the scoring process, all images were rotated at twenty different angles, and the image with the highest score as a digit was selected to represent the final class and the score of the image. The scores for each of the 16 actuation combinations were stored in a 2d array documenting what digits were formed and the score for each digit. A custom loss function was used to evaluate the fitness of each design:$${{{\rm{loss}}}}= 5000 \times {{{\rm{number}}}} \; {{{\rm{of}}}} \; {{{\rm{digits}}}} \; {{{\rm{formed}}}} \\ \times {\sum }_{i=0}^{9}{{\mathrm{ln}}}\left(1.001-{{{\rm{score}}}}\; {{{\rm{for}}}} \; {{{\rm{digit}}}} \; {{{\rm{i}}}}\right)$$
(4)
The loss function computes the diversity and the similarity to real digits of the digits formed. Designs with output images that resembled a larger number of different, easily recognized digits were fitter according to this loss function and, therefore, more likely to be preserved in the population than those with fewer such output images. During the selection stage, 80% of the designs within the population were eliminated by selecting the designs with the 20% lowest (best) loss score to preserve. These preserved designs were sent into a mutation function to repopulate a new generation. The mutation was performed using the single-parent mutation method, where the genetic information of each descendant came from a single survived design from the previous selection. During mutation, each design had a fifty percent chance to randomly update the gel automaton segment lengths, preserving the activator pattern information. Otherwise, half of the regions in the activator pattern were mutated. Each survivor design generated four descendants, so the population returned to its original size after every round of selection and mutation. Finally, the algorithm iterated the population generation, selection, and mutation cycle until reaching the generation limit and output the optimized designs. We slightly tweaked the loss and mutation functions to obtain fabricable devices for our even digit and odd digit gel automata search. We first included an additional rule within the mutation function to ensure new designs are within reasonable patterning steps to avoid generating designs that are overly complex and thus un-patternable. The number of fabrication steps was calculated as the sum of the number of unique activator systems in each layer. Patterns that require more than six fabrication steps were eliminated from consideration and either regenerated (if part of the initial population) or re-mutated from a parent (during subsequent rounds). We used this algorithm to search for an even digit gel automaton and an odd digit gel automaton, changing the loss functions for the two searches and deriving the final optimized outputs (Supplementary Fig. 4, Supplementary Fig. 17).$${{{\rm{loss}}}}= 5000 \times {{{\rm{number}}}} \; {{{\rm{of}}}} \; {{{\rm{digits}}}} \; {{{\rm{formed}}}} \\ \times {\sum }_{i={1,3,5,7,9}}{{{\mathrm{ln}}}}(1.001-{{{\rm{score}}}} \; {{{\rm{for}}}}\; {{{\rm{digit}}}} \; {{{\rm{i}}}})$$
(5)
$${{{\rm{loss}}}}= 5000 \times {{{\rm{number}}}} \; {{{\rm{of}}}} \; {{{\rm{digits}}}} \; {{{\rm{formed}}}} \\ \times {\sum }_{i={0,2,4,6,8}}{{\mathrm{ln}}}(1.001-{{{\rm{score}}}} \; {{{\rm{for}}}} \; {{{\rm{digit}}}} \; {{{\rm{i}}}})$$
(6)
Actuation of letter and digit gel automataAs-made gel automata were transferred to a 1-inch diameter glass bottom petri dish for actuation and imaging. During monolayer and bilayer gel actuation, 1 ml of TAEM-Tween20 solution consisting of 60 µM DNA activators mix (99% growth activators, 1% growth terminators) was added to the petri dish. When further tuning of specific regions of the gel automata was needed, an additional 15 µM DNA activators mix was added to the solution. Between each actuation step, the old DNA solution was removed, and TAEM-Tween20 buffer was added for 15 mins and removed before the DNA solution for the next actuation step was added to the petri dish. Before each subsequent activation step, bright-field images were taken using a Hayear 4 K Microscope Camera (HY-1070). The actuation process was recorded using the gel imager Syngene EF2 G: Box using the imaging protocol described above for the letter gel automaton.Letter gel automata image processingImages of letter gel automata actuation results were processed using MATLAB’s Image Processing Toolbox 2022a. For each image, objects were identified using brightness thresholding followed by morphological closing. The object closest to the center of the image was then selected as the gel body. We then filtered individual images by dimming the background brightness while keeping the brightness of the gel body unchanged. Specifically, we created a binary mask covering the gel body and dimmed the region’s brightness outside the mask to zero. We then matched the image histogram of all images to the first image (in the actuation process) histogram as a reference, and the intensities of over-exposed regions were reduced by 15%.
Programming gel automata shapes using DNA instructions
