### Establishing projection electrophoresis as an analytical tool

In lieu of serial interrogation and electrophoretic analysis of individual mammalian cells, projection electrophoresis (Fig. 1a) yields synchronous, concurrent analyses of hundreds of single cells. Compared to serial-cell measurements, the parallel approach reduces assay-induced protein expression heterogeneity (Fig. 1b). After in-gel immunoprobing for the protein targets glyceraldehyde 3-phosphate dehydrogenase (GAPDH, involved in glycolysis, transcription, and apoptosis) and polypyrimidine tract-binding protein 1 (PTBP1, RNA-binding protein involved in cellular processes including splicing), projection electrophoresis yields 3D data (with xy position describing the originating microwell, z-position describing protein size, Fig. 1c–g). Mean z-direction migration distances were 199 ± 9 μm for PTBP1 (57 kDa) and 346 ± 7 μm for GAPDH (37 kDa). Furthermore, the multifunctional, micropatterned polyacrylamide gel (PAG) serves as the cell isolation device, lysis vessel, separation matrix, and protein capture scaffold. This multifunctional gel thus facilitates in situ lysis, electrophoresis, and blotting, mitigating losses incurred in sample transfer steps, while synchronous analysis and fast assay times yield high assay throughput and drastically reduced sampling delays between cells in a population.

Fig. 1: Projection electrophoresis simultaneously lyses and separates both nuclear and cytosolic proteins from hundreds of single cells.

(a) Projection electrophoresis device photograph and workflow schematic. A 9 × 9 mm projection electrophoresis PAG contains > 1000 microwells that each serves as a separation lane. Cells in PAG microwells are lysed in situ using a lysis buffer-soaked hydrogel delivery matrix, and the lysate is then electrophoretically injected into the polyacrylamide and proteins are separated by size through the depth of the gel. After separation, proteins are covalently linked to the gel matrix using a UV-initiated capture. All cells are lysed and analyzed simultaneously, the active assay time (from cell lysis to photocapture) is less than 90 s, and in situ analysis reduces potential losses from transfer steps. (b) In contrast, capillary electrophoresis analyzes cells in series, with each cell lysed and proteins separated at a different time. (c–f) Different visualizations of z-directional protein separation in a single separation lane. (c) xz (y-summed) contour plots of background-subtracted protein signal within the separation lane for nuclear and cytosolic example proteins. Protein signal is visualized as peak height and false-colored. (d) z-directional intensity profiles (summed fluorescence intensity in arbitrary fluorescence units, AFU, vs. z) for PTBP1 (nuclear, blue) and GAPDH (cytosolic, green) in the same lane, revolved around the z-axis to generate a 3D rendering of fluorescence distribution. (e, f) Representative confocal xy slice images (representative of 9 confocal stacks acquired of different regions of 2 independent separation gels) for separated PTBP1 (blue) and GAPDH (green) at two z-depths into the gel ((e) at the 185 µm depth of the PTBP1 band; (f) at the 335 µm depth of the GAPDH band). Each slice image shows 4 separation lanes, 3 of which appear to have been occupied by BT474 cells prior to analysis. Overlaid squares depict xy regions of interest for the lane plotted in (c) and (d), over which fluorescence intensities were summed to yield z-directional intensity profiles. Scale bar represents 50 μm. (g) Quantified z-migration distances for PTBP1 (57 kDa) and GAPDH (37 kDa) from n = 15 (PTBP1) and n = 17 (GAPDH) separation lanes. Source data are provided as a Source Data file.

We first sought to verify the separation mechanism governing protein electrophoresis in the concurrent analyses (Fig. 2a, b). To understand the protein separation mechanism, we assessed electromigration of a ladder of well-characterized protein standards (donkey immunoglobulin anti-mouse IgG, IgG: 150 kDa; bovine serum albumin, BSA: 66.5 kDa; ovalbumin, OVA: 42.7 kDa, each labeled with AlexaFluor® dyes). When the purified protein solution is pipetted on top of the gel block (gel block face stippled with microwells), the protein solution preferentially partitions into the microwells (versus the hydrogel), thus providing a convenient, well-controlled means for sample loading into each microwell sample injector. To minimize 3D diffusional spreading during PAGE, we designed an ultra-short separation axis (1 mm, defined by the gel block thickness) and rapid (< 1 min) protein PAGE duration. Upon completion of PAGE, the multifunctional gel was toggled from the separation matrix to a protein capture scaffold using a 45-second exposure to UV illumination45.

Fig. 2: Projection electrophoresis supports protein PAGE.

(a) Confocal imaging of PAGE of fluorescently labeled protein ladder at 20 s elapsed separation time. Each ladder sample is injected from a 32 μm diameter microwell (xy plane) with PAGE along the z-axis of the gel block. Summing the background-subtracted fluorescence intensities at each pixel in the xy separation lane region of each slice image (a 300 pixel, 102 μm square region centered on each microwell) yields a z-intensity profile for each lane, with peak-to-peak displacement Δz and peak width σ (10%T PA separation gel containing 10% Rhinohide®). (b) 3D renderings and z-intensity profiles are plotted for (i) 10 s electrophoresis and (ii) 15 s electrophoresis in 10%T PAGs containing 10% Rhinohide® for comparison with the data for 20 s electrophoresis shown in (a). (c) The electrophoretic mobility of the proteins depends log-linearly on protein molecular mass. Each plotted point represents an electrophoretic mobility calculated from linearly fitting migration distance vs. electrophoresis time data from 11 to 17 segmented separation lanes in n = 5 7%T PA separation gels containing 10% Rhinohide® (5 electrophoresis times). Linear fitting yields log(Mr) = 1.7 × 104μEP + 2.25 (R2 = 0.89). (d) Electromigration distance depends linearly on electrophoresis time, thus proteins migrate at constant velocity during PAGE. Migration distances are plotted from protein bands originating from 11 to 17 nearby microwells in two independent 7%T PA gels containing 10% Rhinohide®; 33 mA constant current; 52 V/cm initial, 2 gels for each migration time. Linear fitting yields OVA migration = 16.7t-63.42; BSA migration = 12.64t-39.3; IgG migration = 3.69t-11.54. (e) Separation resolution, Rs, for BSA and OVA peaks in 10%T PAGE gels containing 10% Rhinohide®. Each point depicts the mean and standard deviation of the Rs calculation from the median migration distances and peak widths from n = 4 independent separation gels. Source data are provided as a Source Data file.

We observed (Fig. 2c) a log-linear relationship of electromigration with molecular mass, as expected in size-sieving gel electrophoresis46. Further, in this unique format, we observed constant-velocity and size-dependent electromigration for the ladder and additional protein assayed (Fig. 2d; electrophoretic mobilities of OVA: 3.3–3.7 × 10−5 cm2/Vs; BSA: 2.5–2.9 × 10−5 cm2/Vs; transferrin: 1.3–1.7 × 10−5 cm2/Vs, lectin: 0.96–1.14 × 10−5 cm2/Vs; IgG: 7.4–8.0 × 10−6 cm2/Vs). Constant-velocity migration required mitigation of deleterious effects of electrolysis (i.e., buffer pH changes, bubble formation at the electrodes), which increased the R2 of linear fits to the protein migration data from 0.87 ± 0.06 to 0.97 ± 0.03 for the three ladder protein species (Supplementary Figure 1). For BSA and OVA ladder species, both a protein monomer and dimer are resolvable, as expected in high-performance protein PAGE47,48,49. Having established the separation mechanism, we next estimated the PAGE performance by assessing the separation resolution (Rs). For two ladder proteins (OVA, BSA) in a 1 mm-thick 10%T PAG volume (Fig. 2e), the Rs reached 1.0 within 20 s of PAGE, yielding fully resolved species.

Based on the dominant separation mechanism and rapid protein separation, analysis of the purified protein ladder solution suggests that projection electrophoresis is suitable for analytical-quality protein analysis. The high performance of the rapid microfluidic protein analysis described here is in contrast to another 3D system, designed for preparatory z-direction separation performance, as previously demonstrated for bulk samples using a multilayered gel to coarsely fractionate small proteins (14–77 kDa) from large proteins (20–343 kDa)44. In terms of throughput, each purified protein projection electrophoresis gel (100 μm microwell pitch) contains >4000 microwells, facilitating >4000 parallel (replicate) purified protein separations for a total active assay throughput of 44 separations per second (not including readout time). For comparison, capillary array electrophoresis of a single sample yields a throughput of 5 separations per second15.

### Device design is informed by 3D diffusion of target proteins

Given the open microfluidic design of the projection electrophoresis device that uses a microwell array to perform sample isolation and preparation, with an abutting gel volume that performs the analytical functions (protein PAGE, immunoblotting), we sought to understand physics-based factors that set the minimum acceptable microwell-to-microwell spacing (microwell pitch, Δwell). The Δwell, in turn, sets the maximum number of concurrent protein PAGE separations per projection electrophoresis device. As illustrated schematically in Fig. 3a, the Δwell spacing is influenced by the length scale of diffusional band broadening (σxy, in the xy plane) during protein PAGE along the z-axis. As design guidelines, the throughput of each single-cell projection electrophoresis device (number of single cells assayed per device) will be a function of Δwell (sets separation lane density) and overall usable device dimensions (Fig. 3b). As Δwell depends linearly on σxy, the maximum lane density is inversely proportional to σxy2, as computed in Fig. 3c. Two design rules are plotted: at Δwell > 4σxy, we would estimate <5% protein overlap between neighboring lanes, while at the more conservative Δwell > 6σxy, we would estimate <0.3% protein overlap assuming Gaussian protein distributions.

Fig. 3: The physics of 3D diffusion dictate projection electrophoresis device design and inform image analyses.

(a) Lane density (limited by minimum spacing between separation lanes Δwell) is dependent on separated protein xy bandwidth (σxy) to avoid microwell-microwell crosstalk. σxy in turn depends on 3D diffusion of the injected protein. Simulated data shown in the left schematic; measured OVA data shown in micrograph and intensity profile (representative of two independent separation gels). Scale bar represents 100 μm. (b) Throughput is a function of both lane density and usable gel area; separated protein bands parallel to the gel edges in a cross-sectional image of the gel show uniform migration across the gel. Scale bar represents 1 mm. (c) Theoretical maximum lane density at a spacing of 4σxy (~5% overlap between lanes) and 6σxy (~0.3% overlap between lanes). Maximum lane density is inversely proportional to σxy2. (d) Measured diffusional xy band broadening (Gaussian fit peak width σxy) from purified proteins initially partitioned into 32 μm microwells, as a function of in-gel diffusion time (tdiff). Left: σxy vs. tdiff. Right: σxy2 vs. tdiff with linear fits (σxy2 = σxy,02 + 2Dtdiff). After 10 s EP, we measure σxy < 30 μm for all proteins, suggesting that 200 μm microwell spacing is sufficient. Linear fitting yields OVA σxy2 = 32.5tdiff-198 (R2 = 0.75); BSA σxy2 = 14.3tdiff + 29.8 (R2 = 0.88); IgG σxy2 = 5.41tdiff + 153 (R2 = 0.42). (e) Modeled time for ovalbumin bands to diffuse into the neighboring lane, as a function of microwell spacing Δwell. (f) Modeled separation resolution for BSA and OVA, as a function of EP time and electric field strength. (g) Modeled Péclet number (defined as the ratio of the time to reach a BSA-OVA separation resolution of 1 to the time at which the OVA band is expected to diffuse into the neighboring separation lane). (h) Physics-driven postprocessing. For each confocal slice (BSA, 7%T gel), the original image, that after physics-driven postprocessing (deconvolution of a point spread function modeling 3D diffusion), and summed pre- and post-deconvolution intensity profiles for a 100 μm region surrounding each row of protein bands are shown. Each image pair is scaled to the maximum of the (higher-intensity) deconvolved image. Scale bar represents 50 μm. Source data are provided as a Source Data file.

During electromigration, protein peaks will diffuse in three dimensions, with diffusion along the z-axis determining separation resolution (Rs) and diffusion in xy determining the minimum Δwell. Diffusional spreading of protein bands in all three dimensions depends on protein molecular mass, temperature, time, and gel density (pore size)50,51. To assess the impact of protein diffusion on setting Δwell, we assessed the well-characterized fluorescently labeled OVA/BSA/IgG protein ladder during protein PAGE in a 7%T gel projection electrophoresis device. For each time point analyzed by confocal imaging, we determined the z position of the maximum of the summed fluorescence intensity, for an xy region of interest surrounding each microwell injector. At this z position, we assessed xy resolution by Gaussian fitting x and y intensity profiles and extracting the mean fitted peak width σxy. For duplicate gels of 5 electrophoresis times, we plotted the squared peak width vs. time in gel, fitting to the expected diffusional peak spreading50:

$$\sigma_{xy} ^2 = \sigma _{xy,0}^2 + 2Dt_{diff}.$$

(1)

For each protein target, σ0 is related to the injected peak width (dictated by microwell diameter), D is the in-gel diffusion coefficient, and t is the total elapsed time since protein injection. Figure 3a shows an example confocal fluorescence data xy slice image for OVA and associated Δwell design rule. Applying the analysis to the full protein ladder (Fig. 3d), yields estimates of Δwell, across a range of protein targets and diffusion coefficients (DOVA ~ 16 μm2/s, DBSA ~ 7 μm2/s, DIgG ~ 2.7 μm2/s calculated from linear fits to the plot of σxy2 vs. diffusion time). Under the described conditions, the protein target with the largest D (OVA) suggests that a Δwell of 200 μm will satisfy the trade-off of maximizing separation lane density while minimizing separation lane overlap (7%T gels, 10 s protein PAGE). For comparison, top-down MALDI imaging mass spectrometry utilizes a protein spot pitch of 20–200 μm24.

To further understand the diffusion-driven interdependency of the microwell spacing and separation performance, for the highest diffusivity ladder protein (OVA) we modeled the maximum assay time (the time at which protein signal is expected to bleed into the neighboring lane, from the diffusional peak spreading function above) for a range of microwell spacings (Fig. 3e), as well as the Rs as a function of electrophoresis time and electric field strength (Fig. 3f). The separation resolution Rs is modeled as52:

$$R_s = \frac{{{\mathrm{{\Delta} }}z}}{{\frac{1}{2}\left( {4\sigma _1 + 4\sigma _2} \right)}} = \frac{{{\mathrm{{\Delta} }}\mu _{EP}{\mathbf{E}}t}}{{\frac{1}{2}\left( {4\sqrt {\sigma _0^2 + 2D_1t} + 4\sqrt {\sigma _0^2 + 2D_2t} } \right)}},$$

(2)

where Δz is the difference in migration distance between the two protein targets, σ1 and σ2 are the z-direction peak widths, ΔμEP is the difference in electrophoretic mobility between the two targets, E is the electric field, and D1 and D2 are the diffusion coefficients for the two targets. The diffusion coefficients for BSA and OVA (DBSA = 13.1 µm2s−1,  DOVA = 16.8 µm2s−1) were estimated at 25 ºC from the Stokes-Einstein equation50 and adjusted for in-gel diffusion51 (7%T gel) as described in the Methods. The electrophoretic mobilities were empirically determined from the results of Fig. 2d (µBSA = 2500 µm2V−1s−1, µOVA = 3300 µm2V−1s−1). We next defined a Péclet number as the ratio of the maximum assay time to the time required to reach Rs = 1, with results presented in Fig. 3g and the Péclet number given by:

$$Pe = \frac{{t_{{\mathrm{band}}\,{\mathrm{overlap}}}}}{{t_{R_s = 1}}} = \frac{{t_{{\mathrm{{\Delta} }}_{{\mathrm{well}}} \,=\, 6\sigma _{xy}}}}{{t_{R_s = 1}}}.$$

(3)

At Δwell = 200 μm (Fig. 3d), Pe ~1 for an applied electric field strength of 60 V/cm. As protein band diffusion measurements (Fig. 3d) suggest measured diffusion coefficients smaller than predicted values, our Péclet analysis is a conservative estimate of the trade-off between separation performance and achievable microwell density. Separation resolution is proportional to electric field E, thus, increasing E increases the Péclet number. E is equal to the voltage drop divided by the distance over which the voltage is dissipated. If the distance between electrodes is increased (e.g., by placing separation lanes in series between the electrodes, as configured for 2D immunoblotting30), higher driving voltages are required to reach the same E which can exceed power supply voltage limits. While we demonstrate electric fields of 43-68 V/cm in this work, future research regarding even higher operating regimes (e.g., 100 V/cm using 30 V across 0.3 cm) would shed light on limitations arising from regime-relevant physics and chemistry (i.e., Joule heating, electrolysis). Joule heating and electrolysis both increase with electric current. Joule heating reduces separation resolution and introduces nonuniformities (via nonuniform heat dissipation)52. Electrolysis generates acid and base ions and creates bubbles that can modulate the electrophoretic mobility and disrupt the electric field53 (e.g., pre-optimization projection electrophoresis system depicted in Supplementary Figure 1).

Building on an understanding of the dominant physics, namely diffusion, we next sought to investigate computational approaches to recover starting concentration distributions (here, the microwell array) from endpoint confocal fluorescence images of the protein PAGE (Fig. 3h). Recovery of starting protein concentration distributions will both enhance separation lane density, and facilitate future reconstruction of complex distributions such as those expected in adherent cells and tissue slices. In microscopy, deconvolution of an experimentally, theoretically, or computationally-determined, microscope-dependent point spread function (psf) recovers spatial resolution by image postprocessing54,55,56. Inspired by deconvolution in microscopy, we explored whether we could represent the final protein projection image (I(x, y, z, t)) as the initial protein xy pattern (p0(x, y, z); related to the spatial arrangement of cells/microwells) convolved with a ‘diffusional point spread function’ psfdiff(x, y, z, t), in turn, convolved with the imaging point spread function psfimg(x, y, z, t):

$$I(x,y,z,t) = p_0(x,y,z) \otimes {\mathrm{psf}}_{{\mathrm{diff}}}\left. {(x,y,z,t)} \right) \otimes {\mathrm{psf}}_{{\mathrm{img}}}(x,y,z,t).$$

(4)

We chose to describe the diffusional psfdiff using 3D point-source diffusion57:

$${\mathrm{psf}}_{{\mathrm{diff}}}\left. {(x,y,z,t)} \right) = \frac{M}{{(4\pi Dt)^{3/2}}} \cdot {\mathrm{exp}}\left( { – \left( {\frac{{x^2 + y^2 + z^2}}{{4Dt}}} \right)} \right),$$

(5)

where D is again the protein diffusion coefficient, t the elapsed diffusion time, and M the starting number of molecules at the point source. Although we estimated the full 3D point spread function for each protein, we performed 2D deconvolution only on the individual slice images, without using information from neighboring focal planes (as in a “no-neighbors” deconvolution imaging method58). We used this approach to simplify processing, while recognizing that the simplification limits a full 3D reconstruction and the signal intensity improvement possible from 3D deconvolution. To perform 2D processing, we deconvolved the 2D function psfdiff (through the center of the point spread function, at z = 0) from 2D confocal slice images at the z-direction migration peak for each protein (the z position at which the summed intensity for that protein in the image field of view was maximized). We neglected the effects of psfimg, as we expect that the resolution of our measurement is more limited by diffusion (tens of microns for our typical time scales, as shown in Fig. 3a) than by the resolution of confocal microscopy with high NA objectives (typically sub-micron59).

After deconvolution of the protein PAGE images, we observe a considerable improvement in spatial resolution of xy profiles of separated BSA (Fig. 3h; 5-15 s elapsed PAGE duration in (i)–(iii)). Comparing the “original” to the “deconvolved” images illustrates that spatial resolution is improved from σxy = 16 ± 2 μm to σxy = 8.4 ± 0.2 μm (47%) for 5 s electrophoresis (15 s total time until photocapture), σxy = 25.7 ± 0.6 μm to σxy = 13.1 ± 0.6 μm (49%) for 10 s electrophoresis (20 s total time), and σxy = 26.3 ± 0.6 μm to σxy = 13.3 ± 0.5 (49%) for 15 s electrophoresis (26 s total time). Further, the localization of the peak center was unperturbed by reconstruction (Δμ < 1.1 μm for all analyzed protein spots, with Δμavg = 0.38 μm) and the integrated fluorescence signal of each protein sample is minimally perturbed by the reconstruction except when visible artefacts were present in the deconvolved images as shown in the lowest electrophoresis time (i) (average AUCs after postprocessing are within 3% of the initial values in (ii-iii), but 24% in (i)). Measured errors in peak center were Δμ = 0.08 ± 0.06 μm (tdiff = 15 s), Δμ = 0.68 ± 0.3 μm (tdiff = 20 s), Δμ = 0.1 ± 0.2 μm (tdiff = 26 s); measured errors in peak AUCs were ΔAUC=23.9 ± 1.4% (tdiff = 15 s), ΔAUC = 0.5 ± 0.8% (tdiff = 20 s), ΔAUC = 3 ± 2% (tdiff = 26 s) (n = 9 ROIs). Under ideal conditions, physics-based postprocessing is expected to report a time-invariant σxy. We do observe a weak dependence of σxy on time, which we attribute to estimated model parameters (including diffusion coefficient, in-gel temperature, hydrodynamic radius, gel density, and diffusion time) and depth-dependent imaging artefacts arising from refractive index mismatch between the separation gel and immersion medium (psfimg was neglected in our analysis). Future study will benefit from refinement of the model; however, the physics-based image postprocessing introduced here offers a means to reconstruct a map of the initial sample specimen from the target concentration distributions in the 3D gel volume, all based on the endpoint fluorescence readout of protein PAGE.

### Sample preparation design for single-cell projection electrophoresis

Having considered the design of the projection electrophoresis device and assay using a well-characterized protein ladder, we next sought to identify factors important to high-performance protein PAGE of single cells (Fig. 4). We first assessed the settling of single BT474 cells in 25 μm diameter microwells within the projection electrophoresis gels. Figure 4a depicts settled Calcein-stained BT474 breast tumor cells in microwells after gravitational settling and convective wash-off of cells settled outside of microwells. A corresponding full-gel wide-field microscopy image of immunoprobed GAPDH fluorescence after the projection electrophoresis assay is also shown; probed protein bands correlate with settled cell positions. Cell settling efficiencies (populated microwells) were at 43 ± 8% with the number of settled single cells 356 ± 82 per 9 × 9 mm projection electrophoresis device (n = 5 devices). The fraction of microwells occupied by more than one cell was 10 ± 3%. Further optimization of cell settling densities, microwell geometries, settling times, and wash parameters would likely improve these values and thus assay throughput.

Fig. 4: Design and verification of sample preparation for projection electrophoresis of single mammalian cells.

(a) High-density endogenous protein bands (ii) correspond to single-cell settling in microwells (i). Scale bars represent 1 mm (left full-gel images) and 200 μm (right zoom images). (b) Illustration of top-view and side-view geometries shown in protein dilution studies (c, d). (c) Modeling and experimental quantification of diffusional dilution during lysis. Simulated and experimental top-view images of diffusional protein dilution during lysis, and side-view simulated results are shown. The simulated initial TurboGFP concentration was 2 μM. Experimental image is representative of 12 monitored cells across 3 independent lysis experiments. Scale bars represent 50 μm. (d) Modeling the impact of diffusion during electrophoresis on detectable in-gel protein concentration. Side and top view TurboGFP concentration profiles are shown at different times during electrophoresis. Simulated initial TurboGFP concentration (before lysis and electrophoresis) was 2 μM. Scale bars represent 30 μm. (e) Quantification of the percent of protein remaining in the microwell region during lysis (experiment plots mean and standard deviation of n = 12 cells across 3 lysis experiments). (f) Quantification of the change in the spatial maximum protein concentration as a function of time after protein solubilization (experiment plots mean and standard deviation of n = 12 cells across 3 lysis experiments). (g) Simulated maximum protein concentration vs. electrophoresis time, for 3 model proteins. (h) Representative β-tubulin separations from U251 glioblastoma cells lysed with different buffer formulations (2× RIPA lysis buffer and 2× RIPA including 8 M urea), both after 10 s electrophoresis. Lysis/EP buffer requires 8 M urea for fast protein solubilization and electromigration. (i) Maximum intensity projection 3D renderings and z-intensity profiles of probed GAPDH bands from single BT474 breast tumor cells. (j) Microwell packing density (impacting assay throughput) is dependent on protein band diffusion before photocapture. Protein diffusion profiles confirm that a microwell pitch of 200 μm is sufficient to resolve bands from neighboring microwells. After 10 s EP, the mean peak width (σxy) of the xy GAPDH spots is 32 ± 11 μm (mean ± standard deviation of n = 47 single-cell separation lanes across 5 replicate separation gels). The depicted confocal slice micrograph is representative of 20 confocal image stacks, across different regions of 5 replicate separation gels. At a microwell pitch of 192 μm (6σxy), <0.3% of the signal should bleed into the neighboring lane. Scale bar represents 50 μm. Source data are provided as a Source Data file.

After protein solubilization, diffusion-driven dilution of single-cell lysate occurs rapidly in the open microwell geometries. To determine how the concentration of the single-cell protein lysate changes during the lysis and electrophoresis stages of the assay, we used a combination of finite-element modeling (geometries are shown in Fig. 4b) and experimental monitoring of TurboGFP-expressing U251 cells during cell lysis (Fig. 4c) and finite-element modeling during electrophoresis (Fig. 4d). To compare simulation and experiment, we integrated the 3D protein concentrations over the full z range of the model to mimic detected wide-field fluorescence intensities (Fig. 4e, f). Using this metric, after a typical 25 s lysis time, we measure 17% ± 11% of the initial protein intensity. Our simulated profiles overestimate the diffusional dilution of protein, predicting only 2.2% of the initial intensity for in-well lysis after 25 s. We attribute the ~15% discrepancy to delayed solubilization of cellular protein (the models assumed complete solubilization at t = 0), overestimates of the predicted diffusion coefficient used in the simulation, or a possible diffusion barrier on the microwell wall surface arising from either the presence of Rhinohide® in the gel matrix or the presence of residual GelSlick® or dichlorodimethylsilane used during gel fabrication. One important consideration for projection electrophoresis is that while considerable in-gel protein dilution remains, in contrast to 2D single-cell immunoblots30,34,35, there is reduced protein ‘loss’ from the gel in the projection electrophoresis platform. While other electrophoretic cytometry assays have a fluid layer or lid gel above the thin separation gel, into which protein can diffuse and is lost, in the projection electrophoresis device most (if not all) protein is mobilized into the bulk of the 3D gel when an electric field is applied to initiate PAGE.

We then sought to quantify how the maximum protein concentration changes during the analytical single-cell PAGE stage (Fig. 4g) using finite-element modeling. From an initial protein concentration of 2 μM in a cylinder representing the cell, we estimate maximum protein concentrations of 2.1 nM (TurboGFP, 26 kDa), 4.0 nM (BSA, 66.5 kDa), and 6.8 nM (HER2, 185 kDa) after 25 s lysis and 20 s electrophoresis in Fig. 4g. We compared the expected diffusional dilution during electrophoresis to that expected in a planar system (Supplementary Figure 2) and found similar dilution during the assay steps in both systems. We note that the planar system is amenable to imaging during electrophoresis, thus our comparison (which predicts similar losses to those reported in our previous work52) serves as validation of the numerical model. Diffusional dilution of protein is dependent on both analyte size and gel density. The relatively large-pore-size gels used in this work (7%T) are optimal for large analytes (80–200 kDa), with adaptation for smaller analytes accommodated by moving to higher-density (smaller pore size) separation gels.

In optimizing the projection assay, we sought buffer chemistries to minimize lysis and solubilization times and used diffusive immunoprobing of model proteins β-tubulin and GAPDH using immunoglobulin fragments (F(ab) fragments) to assess solubilization efficacy. Here, we assessed a range of cell lysis and protein solubilization chemistries (Fig. 4h). Across a range of chemistries, we observed differences in protein electromigration and dispersion, which were dependent on buffer composition and delivery methods. We selected a dual-function lysis and solubilization buffer that utilizes the anionic detergents sodium dodecyl sulphate (SDS) and sodium deoxycholate, augmented with a strong chaotrope (8 M urea). Comparing solubilization, electromigration, and dispersion of the model protein β-tubulin from U251 glioblastoma cells lysed both without (i) and with (ii) 8 M urea in the lysis buffer, we observed rapid electromigration into the 3D gel from the microwell and lower protein peak dispersion with urea present. Without urea, the 3D protein bands exhibited a hollow, bowl-like shape (concave towards the microwell), rather than the 3D Gaussian distribution which would be expected from diffusion theory. In a sub-set of separation lanes, two β-tubulin peaks were detectable after solubilization with urea lysis buffer (Fig. 4h), suggesting delayed solubilization for a subset of the β-tubulin molecules, as might be expected depending on the intracellular state of the β-tubulin.

In formulating design guidelines for the dual-function lysis-electrophoresis buffer, we consider two additional points. First, detergents such as SDS and Triton X-100 form micelles of size on the order of nanometers60,61. Consequently, we explored the corollary hypothesis that size-exclusion partitioning62,63 of solutes hinders delivery of lysis reagents from PAG matrices. As PAG density negatively correlates with the in-gel concentration of size-excluded species62, we explored whether lower density (6%T vs. 20%T) polyacrylamide lysis gels may facilitate improved protein solubilization. By moving to 6%T lysis gels, we observed higher apparent GAPDH mobility (1.08 ± 0.03 × 10−4 cm2/V s using 6%T lysis gel, compared with 0.83 ± 0.08 × 10−4 cm2/V s using 20%T lysis gel, n = 12–14 separation lanes) and potential reduction in protein band dispersion (Supplementary Figure 3). Second, strong chaotropes like urea solubilize proteins by disrupting hydrogen bonds as well as electrostatic and hydrophobic interactions to unfold hydrophobic protein regions64. Urea-based lysis buffers can solubilize different subsets of the proteome, as compared to RIPA-like buffers65. High concentrations of urea (e.g., 8 M) can break down detergent micelles and disturb detergent-protein complexes66,67. Urea, as a small molecule, is less susceptible to size-exclusion partitioning from hydrogels. Just as in other protein separations, the ideal lysis buffer depends on the system and target of interest64. Analysis of another endogenous target protein, GAPDH, using the 8 M urea lysis buffer that better-solubilized β-tubulin also yielded protein peaks with low dispersion (Fig. 4i).

Lastly, we verified the device design suggested by analysis of the well-characterized protein ladder now for the analysis of mammalian cells using the optimized cell preparation protocol (Fig. 4j). We anticipated that the cell preparation may increase lysate diffusion from that assessed using the idealized protein ladder system in Fig. 3, both because diffusion of protein targets in each single-cell lysate occurs during the time required for lysis and solubilization and because single-cell PAGE is run at higher temperature (~37 °C vs. ~4 °C) to improve protein solubilization. As discussed above, microwell spacing dictates the achievable cell throughput on one device. After 10 s EP, we measured σxy = 32 ± 13 μm for GAPDH (36 kDa) in the xy plane. At Δwell = 192 μm (6σxy), we estimate that <0.3% of the fluorescence signal from the GAPDH in each cell lysate should bleed into the neighboring lane. Thus, Δwell = 200 μm is also sufficient to limit cross-contamination between adjacent separation lanes for GAPDH under these assay conditions.

### Immunoblotting of protein targets from hundreds of single mammalian cells

We applied projection electrophoresis to immunoblotting analyses of well-characterized endogenous proteins GAPDH and actinin across populations of individual human BT474 breast cancer cells. As depicted in Fig. 5, projection electrophoresis concurrently analyzes hundreds of single cells by parallelized separation after near-simultaneous lysis. To expedite full-gel volumetric fluorescence readout of protein immunoblots, we employed light-sheet microscopy in Fig. 5. Comparison measurements using scanning laser confocal microscopy are presented in Supplementary Figure 4. Data processing allows us to visualize immunoblot readouts as maximum intensity projection 3D renderings (Fig. 5a), 2D contour plots showing xz fluorescence peaks for each fluorescence color channel (corresponding to a target/antibody pair) (Fig. 5b), and revolved 1D z-directional fluorescence intensity plots (Fig. 5c).

Fig. 5: Projection electrophoresis permits the simultaneous analysis of hundreds of single cells by concurrent separation after simultaneous lysis.

(a) Maximum intensity projection 3D renderings of example separation lanes read out by tiled light-sheet microscopy. (b) xz (y-summed) contour plots of background-subtracted actinin and GAPDH protein signal within the lanes depicted in (a). (c) Revolved z-intensity profiles (arbitrary fluorescence units, AFU, vs. z) for the four separation lanes depicted in (a, b). Each plot depicts z-directional intensity profiles (summed fluorescence within each xy ROI vs. z) for GAPDH (magenta) and actinin (cyan), revolved around the z-axis to generate 3D rendering of fluorescence distribution. (d) Histogram quantification shows 86% of U251 cells lyse within 5 s of initiating lysis. (e) Quantified fluorescence intensity data for n = 159 separation lanes passing quality control for both the GAPDH and actinin channels. Each plot depicts revolved z-intensity profiles. (f) Full-gel wide-field fluorescence image of calcein-stained live BT474 breast tumor cells before analysis. (g) Subset of the live cells from (f), within a 1.75 × 1.75 mm light-sheet microscopy field of view (scale bar depicts 200 μm). (h) Post-separation wide-field fluorescence image of probed GAPDH signal within the same field of view as (g). (fh) are representative of n > 3 separation gels. (i) Maximum intensity projection 3D rendering (representative of duplicate separation gels) of a light-sheet microscopy image (same field of view as (g, h)), showing 3D separations of GAPDH and actinin from tens of separation lanes, each corresponding to signal from the settled cells in microwells depicted in (f, g). (j) Overlay image of segmented spots corresponding to live BT474 cells in microwells (green) and probed GAPDH bands after separation (magenta), for the same separation gel depicted in (f, i). (k) Quantification of correspondence between the segmented live cells and bands (via intensity thresholding) within the same separation lanes as (j). (l) Quantified migration distances from a total of n = 507 (GAPDH) and n = 303 (actinin) lanes passing quality control in two projection electrophoresis gels. (m) Quantified z-direction peak widths for the same bands analyzed in (l). (n-o) Map of the variation in GAPDH (n) and actinin (o) electromigration distances across the xy gel area. Source data are provided as a Source Data file.

Cells lyse nearly simultaneously (Fig. 5d). Across 4 replicate experiments, 31/36 monitored cells (86%) lysed within 5 s of placing the lysis gel on top of the microwell gel. Of the 5 remaining cells (all within the same replicate), 2 lysed during the 80 s monitoring period while 3 did not, potentially due to a bubble between the two gels. This near-simultaneous lysis, combined with parallelized electrophoretic separation over the full gel (>1000 separation lanes), facilitates concurrent analysis of hundreds of single cells. Figure 5e depicts revolved 1D intensity profiles for the 159 separation lanes within a single projection electrophoresis gel that passed R2 (>0.7 for Gaussian fit to 1D z-intensity profile) and SNR (>3) quality control in both protein channels (222 lanes passed these quality controls in the GAPDH channel; 204 lanes passed in the actinin channel). The intensity profiles show a GAPDH peak at a depth of 552 ± 54 µm and an actinin peak at a depth of 165 ± 42 µm (median ± one standard deviation). The profiles also show another peak in the actinin channel near the depth of the GAPDH peak, potentially due to off-target antibody binding and/or spectral bleed-through between the channels (optical filter sets) of the light-sheet microscope.

Projection electrophoresis is compatible with multi-modal imaging of the intact cells before separation, as well as the separated protein bands after the assay. Pre-separation live-cell imaging of intact BT474 cells (Fig. 5f, g) correlated well with detected probed bands. The in situ separations facilitated by projection electrophoresis allow comparison of live-cell fluorescence – prior to projection immunoblotting (via wide-field fluorescence microscopy in Fig. 5f, g) – and endpoint probed GAPDH signal (via wide-field fluorescence microscopy in Fig. 5h and light-sheet microscopy in Fig. 5i). The analysis revealed appreciable spatial correlation between live cell imaging prior to separation and wide-field fluorescence images of separated GAPDH (Fig. 5j–k). Comparison shows 63–74% of detected live cells are correlated with GAPDH detection. In two duplicate separations, 76 and 63% of detected live cells corresponded to probed GAPDH bands, 24 and 37% of detected live cells did not correspond to a probed GAPDH band, and 17 and 22% of probed bands did not visibly correspond to a live cell. This correlation (and potentially cell settling efficiencies and analysis throughput) could potentially be further improved in future work by encapsulating settled cells in hydrogel to mitigate cell loss/movement during manual gel transfer and electrophoresis stack setup.

We observe the expected differential in electrophoretic mobility and nearly equivalent peak widths for the GAPDH (37 kDa) and actinin (100 kDa) targets for a total of 507 (GAPDH) and 303 (actinin) single-cell separations across duplicate separation gels (Fig. 5l, m). In considering variation in electromigration, the coefficients of variation in electromigration are for GAPDH ~8.5% and for actinin ~27%. Qualitatively, we observe modestly higher electromigration on one side of the gel, on each of two gels (Fig. 5n, o, Supplementary Figure 5), which is inconsistent with Joule heating-induced electromigration nonuniformity (e.g., higher mobility in the gel center, as observed in bulk separations42). Consequently, we attribute the modest, observed electromigration variation to nonuniformities in protein solubilization or electrophoresis (e.g., E and/or temperature), or to inaccuracies in gel surface detection (z = 0) during light-sheet image analysis. Including a protein-sizing ladder in each separation lane enhances size-based protein identification, as our group has reported in similar 2D single-cell immunoblot devices (either as a ladder of well-defined, cell-endogenous proteins33 or as ladder protein-conjugated beads68). Although from diffusion theory we would expect a larger peak width for the smaller protein target, differences in peak dispersion between targets can result in wider measured peak widths.

We compared scanning laser confocal microscopy (Supplementary Figure 4) and light-sheet microscopy (Fig. 5) imaging of the same gel devices to acquire volumetric protein immunoblot readouts from the protein PAGE separation lanes. Each imaging modality presents a trade-off in field of view and z-axis resolution, but the imaging throughput of light-sheet microscopy was >10× higher than scanning laser confocal, moving from ~120 s/lane readout time down to ~8 s/lane, while retaining sufficient z-axis resolution to localize protein peaks. The laser scanning confocal imaging with 20× NA = 1.0 water immersion objective (required for high-resolution optical sectioning) supported a 425 × 425 μm field of view, while light-sheet microscopy with 5× detection objective (NA = 0.16) provided a much larger 1.75 × 1.75 mm field of view. Because its optical sectioning is facilitated by the light-sheet objectives forming a thin illumination sheet, light-sheet microscopy allows the imaging optical section thickness to be decoupled from the detection objective NA, facilitating the use of lower NA detection objectives while maintaining optical sectioning69. The light-sheet images acquired here had optical section thicknesses on the order of 10 μm, which should be sufficient to assess the diffusion-limited z-directional peak widths of tens of microns for our separated protein bands.

Further, light-sheet microscopy detected both protein targets with similar expected differential electrophoretic velocity and comparable peak widths of the immunoprobed targets to those measured with confocal (Supplementary Figure 4). Differences may be partly attributed to the impact of a slight refractive index mismatch between the hydrogel and water immersion media on apparent confocal z-depths (Supplementary Note 1). With both readout modalities, we also observe the log-linear relationship between migration distance and molecular mass for endogenous targets that would be expected for a size-sieving separation (Supplementary Figure 6). Given similar results in detection, migration location, and peak width for the model endogenous protein targets, the substantially larger field of view of light-sheet microscopy proved beneficial, allowing endpoint imaging and analysis of 10× larger number of immunoblots (imaged separation lanes passing quality control: n = 22 with confocal; n = 303 actinin and n = 507 GAPDH with light-sheet microscopy, over two separation gels).

The parallel cell analysis approach described here overcomes shortcomings of serial analysis of cells. Although synchronous cell lysis is also not instantaneous across cells (with biological variation in lysis time on the order of seconds70), serial interrogation of individual cells leads to asynchronous analysis with longer time delays between analysis of the first cell and last cell in a population. Considering one published example single-cell enzyme analysis separation, where individual cells are interrogated by a capillary sampler after cell lysis via a UV light pulse17, we estimate a 104 min delay between interrogation of the first cell and interrogation of the last cell (219 cells analyzed with an analysis throughput of 2.1 cells/min). In contrast, concurrent analysis of ~300 measurable separation lanes is completed with <10 s delay between the first and last cell, assuming a small delay in cell lysis arising during the application of the lysis and solubilization buffer. Furthermore, projection electrophoresis uses a single SDS-PAGE sieving gel for hundreds of concurrent single-cell protein-sizing separations. In contrast, serial electrophoresis separations performed in capillaries or microchannels require periodic renewal of the sieving matrix between separations to mitigate residual sample and matrix degradation71. Consequently, higher-throughput electrophoresis systems often use free solution17 or sieving polymers28. By introducing a new, rapid, and parallelized electrophoresis approach, we demonstrate simultaneous single-cell separations of hundreds of single cells with an active assay time of 2.5 cells/s (from lysis through photocapture), depending on settling efficiency — this represents a >70-fold improvement in assay throughput over serial capillary systems.

Projection electrophoresis addresses key bottlenecks in single-cell protein analysis by achieving rapid (<1.5 min active assay time), synchronous size-based protein separation for hundreds of unfixed cells in parallel, without sample transfer steps that can result in sample losses and changes in sample composition. Detection specificity combines antibody recognition with size-separation to confer proteoform-level specificity even when specific probes do not exist, and avoids the need for pre-separation tagging of proteins for detection. In situ cell lysis, separation, and photocapture of protein to the gel matrix mitigates deleterious effects of sample transfer between systems, including losses from adsorption to glassware, potential sample contamination, and sample changes between lysis and separation. Effectively synchronous analysis of hundreds of cells in parallel mitigates artifactual changes in cell population heterogeneity induced by heterogeneous lysis times, while also facilitating high assay throughput. Using rapid whole-cell lysis of unfixed cells, we demonstrate the detection of both nuclear and cytosolic proteins. We design and characterize the system by both modeling and measuring the results of microscale physics. Compared with planar (2D) single-cell western blotting, we demonstrate a 10-fold reduction in the volume of cell suspension settled (and thus the number of cells used) to assay the same number of cells, and further throughput improvements may be possible by optimizing parameters for settling efficiency. While 2D devices are conducive to immunoprobing, imaging as readout, and efficient data analysis, projection electrophoresis increases the density of single-cell analyses for the same device footprint, by shifting the separation dimension to the z-axis, while maintaining similar protein losses and outputting rich 3D information about protein band morphology and dispersion. Important beyond enhancing data density, 3D projection electrophoresis holds promise for future profiling of cellular “connectomes” by supporting analyses of complex cellular networks such as intact tissue slices and adherent cells cultured on planar hydrogel surfaces37. Looking forward, the performance of projection electrophoresis can be improved in future work by moving to larger-area gels to further parallelize analysis, and by using our understanding of the driving small-scale physics to optimize gel materials for targets of interest and thus enable the use of even higher microwell densities (or adherent cells) and improved separation performance. With a straightforward, open microfluidic format and advantages complementary to existing protein analysis tools, we anticipate that projection electrophoresis will assist in the development of proteoform-level atlases of single-cell diversity.

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