Synthesis

DNA-GPS: A theoretical framework for optics-freespatial genomics and synthesis of current methods
Graphical abstract

Authors
Laura Greenstreet, Anton Afanassiev,
Yusuke Kijima, ..., Samuel King,
Nozomu Yachie, Geoffrey Schiebinger

Correspondence
nozomu.yachie@ubc.ca (N.Y.),
geoff@math.ubc.ca (G.S.)

In brief
While single-cell sequencing methods
capture genomic profiles at the cellularlevel, they lose spatial context. In the past
decade, over a dozen spatialtranscriptomics methods have beendeveloped. Greenstreet et al. highlighttrade-offs and synergies in existing
methods and propose DNA-GPS, aframework for large-scale optics-freespatial transcriptomics.

Highlightsd

Spatial transcriptomics methods exhibit trade-offs inresolution and scaledThey can be split into optical imaging, positional indexing,
and mathematical cartographyd

DNA-GPS combines ideas from positional indexing andmathematical cartographyd

It provides a mathematical framework for large-scale opticsfree spatial transcriptomics

Greenstreet et al., 2023, Cell Systems 14, 844–859
October 18, 2023 ª 2023 The Authors. Published by Elsevier Inc.
https://doi.org/10.1016/j.cels.2023.08.005ll

ll
OPEN ACCESS

Synthesis

DNA-GPS: A theoretical framework for optics-freespatial genomics and synthesis of current methods
Laura Greenstreet,1,7 Anton Afanassiev,1,7 Yusuke Kijima,2,3,7 Matthieu Heitz,1,7 Soh Ishiguro,2 Samuel King,2Nozomu Yachie,2,4,5,6,8,* and Geoffrey Schiebinger1,2,9,10,*
1Department of Mathematics, The University of British Columbia, Vancouver, BC, Canada
2School of Biomedical Engineering, The University of British Columbia, Vancouver, BC, Canada
3Department of Aquatic Bioscience, The University of Tokyo, Tokyo, Japan
4Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan
5Premium Research Institute for Human Metaverse Medicine (WPI-PRIMe), Osaka University, Suita, Osaka, Japan
6Graduate School of Media and Governance, Keio University, Fujisawa, Japan
7These authors contributed equally
8X (formerly Twitter): @nzmyachie
9X (formerly Twitter): @geoffschieb
10Lead contact*Correspondence: nozomu.yachie@ubc.ca (N.Y.), geoff@math.ubc.ca (G.S.)
https://doi.org/10.1016/j.cels.2023.08.005

SUMMARY

While single-cell sequencing technologies provide unprecedented insights into genomic profiles at thecellular level, they lose the spatial context of cells. Over the past decade, diverse spatial transcriptomics
and multi-omics technologies have been developed to analyze molecular profiles of tissues. In
this article, we categorize current spatial genomics technologies into three classes: optical imaging, positional indexing, and mathematical cartography. We discuss trade-offs in resolution and scale, identify
limitations, and highlight synergies between existing single-cell and spatial genomics methods. Further,
we propose DNA-GPS (global positioning system), a theoretical framework for large-scale optics-freespatial genomics that combines ideas from mathematical cartography and positional indexing. DNAGPS has the potential to achieve scalable spatial genomics for multiple measurement modalities,
and by eliminating the need for optical measurement, it has the potential to position cells in three-dimensions (3D).
INTRODUCTION
Understanding the cellular architecture of tissues is a major
challenge with tremendous potential impacts across thelife sciences. Single-cell measurement technologies haveenabled high-dimensional, unbiased measurements of transcriptomic, proteomic, genomic, or epigenomic informationin large populations of cells.1–4 However, these technologies
lose spatial context. Spatial genomics has made it possible
to chart the spatial distribution of transcriptional states,5 chromatin accessibility,6 and other elements of cell state.7,8 This
article first categorizes current spatial genomics technologies
into three groups, identifying gaps and synergies, then introduces a theoretical framework for optics-free spatial genomics called DNA-GPS (global positioning system) that combines ideas from mathematical cartography and positional
indexing to overcome the gaps in the current technologies.
While DNA-GPS could be implemented with small modifications to existing positional indexing methods, it has the potential for further extensions to multi-modal measurement andthree-dimensional (3D) volumes.

Optical imaging
Since Hooke’s discovery of cells in the 1660s, the microscope
has been an indispensable tool for biological discovery. Today,
gene expression can be imaged through a variety of opticsbased approaches (Figure 1A).
In situ hybridization (ISH) is an imaging system wherereporter probes hybridize to a specific target nucleotide
sequence, enabling the spatial localization of the target
sequence in a histologic section under a microscope.29 Expression of a target gene over a tissue section can be quantified
from the intensity of the reporter. Fluorescent ISH (FISH) using
fluorescent probes has enabled multiplexed measurements,30
but its scalability has classically been limited to the numberof distinct fluorescent probes that can be imaged simultaneously. Recent advances in single-molecule FISH (smFISH)
with super-resolution imaging have enabled localization andcounting of individual RNA molecules over the tissue space,and combinatorial indexing strategies have expanded thenumber of targets to the genomic scale.9–11 In the multiplexed
smFISH approach, each RNA molecule is imaged multiple
times over cycles of different probe hybridizations and

844 Cell Systems 14, 844–859, October 18, 2023 ª 2023 The Authors. Published by Elsevier Inc.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

llSynthesis

OPEN ACCESS

A

B

C

Figure 1. Overview of spatial genomics(A) Optical imaging. MERFISH,9 seqFISH+,10 and EEL-FISH11 fall into smFISH category. FISSEQ,12 STARmap,13 and ExSeq14 fall into in situ sequencing category.
(B) Positional indexing. 103 Visium,15 DBiT-seq,16 Spatial-ATAC-seq,6 XYZeq,17 and sci-Space18 fall into a priori indexing category. HDST,19 Slide-seq,20 SeqScope,21 Pixel-seq,22 Stereo-seq,23 and Slide-DNA-seq24 fall into a posteriori indexing category.
(C) Mathematical cartography. DNA microscopy,25 PARSIFT,26 and IPL27 fall into DNA sequencing-based microscopy category. NovoSpaRc28 is a gene
expression cartography method.

fluorophore quenching, where a unique fluorescent color code
appearing through the imaging cycle is assigned to each RNA
species.9 Scalable fluorescent indexing of many RNA species
has been enabled by two-step smart encoding approaches,
where the first gene specific probes with common anchor sequences are further probed by secondary common fluorophore
probes, minimizing the cost of fluorescent probes.9–11 However, due to its reliance on super-resolution imaging, smFISH
greatly sacrifices field of view to observe large numbers ofgenes. A new technology called EEL-FISH, which transfers tissue RNAs onto a positively charged glass slide by electrophoresis, has improved scalability by reducing imaging effort. Yet,it still takes more than 2 days to process 500 genes over1 cm2.11 Furthermore, smFISH probes designed for one species cannot be utilized for other species.
In situ sequencing has been coupled with super-resolution imaging to enable genome-scale spatial transcriptomics.12–14 In
this approach, after fixing a tissue section, RNAs are reverse transcribed into complementary (c)DNAs, which are then circularized
and amplified by rolling circle amplification (RCA). Next, theamplified cDNA sequences are sequenced in situ by
sequencing-by-ligation (where specific fluorescent signals are
spatially obtained over cycles along with the template directed
elongation of sequence strand by short probe ligation). Similar
to smFISH, this approach requires high-resolution imaging, resulting in a small field of view. Expansion microscopy (ExM), atechnology to physically expand tissue using a swellable polymer
gel,31 has also been applied to in situ transcriptomics andachieved high scalability with better signal separation and reagent penetration. Coupling in situ sequencing of short generegions as well as ex situ sequencing of longer gene regions,this expansion sequencing (ExSeq) approach has enabled spatial
mapping of long sequencing reads.14 As the expansion process
preserves the intact tissue structure, ExSeq has also demonstrated spatial transcriptomics of a 3D volume; however, theexpansion approach has only be demonstrated in soft tissues.32
Scalable optical imaging has also been developed for other
non-transcriptomic modalities. Multiplexed smFISH and in situ
sequencing have been applied to locate genomic sequences
together with epigenetic marks at molecular resolution, enabling
the identification of high-resolution chromatin structures, butthey are limited to few thousands of cells.33–35 Tissue clarification approaches and light-sheet microscopy have also enabledmultiplexed 3D localization of proteins at whole organ scale using fluorescent-conjugated antibodies, but for a limited numberof protein species.36 In summary, optical imaging technologies
can profile the 3D distribution of molecules across cells or
tissues, but the use of optics introduces fundamental tradeoffs between field of view, resolution, and the number of molecular species to be profiled.
Positional indexing
Positional indexing (Figure 1B) is a category of spatial genomics methods whose concept has been derived from thewidely applied idea of cellular indexing in single-cell genomics
technologies (Box 1). In cellular indexing, cellular materials are
Cell Systems 14, 844–859, October 18, 2023 845

ll
OPEN ACCESS

Synthesis

Box 1. Cellular indexing approaches for single-cell genomics

Single-cell RNA sequencing (scRNA-seq) was originally demonstrated in microwells, where individual cells are physically isolated
in wells. In each well, polyadenylated (poly(A)ed) RNA products are captured and reverse transcribed by primers having poly(thymine) (poly(T)) on their 30 ends together with well-specific barcodes. This reverse transcription (RT) reactions fuse the producing
complementary (c)DNA products to the well-specific barcodes. After high-throughput sequencing, single-cell gene expression
profiles can be reconstructed from read counts of genes sorted by the well-specific barcodes.37–39 In 2015, water-in-oil
droplet-based approaches revolutionized scRNA-seq, where single cells are each encapsulated into droplets together withmicrobead anchoring poly(T) RT primers encoding a unique bead-specific barcode.40,41 Following microfluidic high-throughput
generation of droplets, single-cell transcriptomes are captured on the beads, and their 30 sequences are fused to the bead-specific(i.e., cell-specific) barcodes by RT for high-throughput sequencing. Similar to the microwell-based approaches, the total
sequencing reads for gene expression counts are sorted into single cells according to the unique cell-specific barcodes fusedto them. This approach has been widely adopted by the community today and is still under significant development.42–45
Recently, split-and-pooling was proposed to achieve scalable single-cell genomics with no single-cell compartmentalization.4,46–48
In split-and-pooling, single cells are first fixed with their genomic materials and split into a handful of wells where their transcriptome
sequences are reverse transcribed and conjugated to well-specific DNA barcodes in situ. The cell populations are then pooled andsplit again into multiple wells where their transcriptome sequences are further conjugated to barcodes specific to the second-roundwells. The iterations of this split-and-pooling procedure enable transcripts of every single cell to be tagged with a unique combinatorial array of barcodes. This approach has been demonstrated to achieve profiling multiple millions of single cells.46,49
Single-cell measurements of molecular profiles that can be converted into a form of DNA sequences have been enabled by thesecellular indexing approaches. For example, similar to the modality of transcriptome measurements achieved by converting RNA
to DNA with the conjugation to cell-specific barcodes, single-cell surface proteome measurement has also been enabled by labeling surface proteins using a cocktail of antibodies tethered to their specific DNA barcodes followed by poly(T) sequence.2 This
enabled the simultaneous single-cell measurement of transcriptome and surface proteome profiles. Genomic sequences,3 epigenetic modifications,50,51 and chromatin structures4,52 have also been measured at the single-cell resolution with the same concept.

translated into a form of DNA, if needed, and fused to cell-specific DNA barcodes. The barcoded DNA sequences are identified by high-throughput sequencing. DNA sequences associated with single cells are later sorted computationallyaccording to the cell-specific DNA barcodes.
In positional indexing for spatial genomics, DNA barcodes areused to index the spatial pixels of an image. For example, inspatial transcriptomics a tissue slice is first stamped on a pixelated surface of barcoded poly(thymine) (poly(T)) primers forreverse transcription (RT) of polyadenylated (poly(A)ed) RNAs.
Tissue RNAs are captured and reverse transcribed by their proximal RT primers, resulting in the fusion of positional barcodes to
cDNAs. After sequencing, the gene expression profile of eachpixel is reconstructed computationally from the positional barcodes. This approach has great potential scalability because it
allows for reading out the transcriptome in a highly multiplexedmanner by high-throughput DNA sequencing without the needfor a specific probe set or in-tissue optical imaging. Somemethods in this category have already reached single-cell resolution at whole-body scale for organisms such as mice.23
846 Cell Systems 14, 844–859, October 18, 2023

There are two types of indexing approaches to encode positional information to DNA barcodes: a priori indexing and a posteriori indexing. In a priori positional indexing, as seen in 103 Genomics Visium,15 a set of known DNA barcodes are deposited topreassigned positions. After applying a tissue slice on the barcoded surface, DNA sequences representing molecular profiles
are fused to the positional barcodes and analyzed bysequencing. The density, size, and number of barcoded spots
determine the field of view and resolution of the spatial genomics
image being obtained. While its scalability has been limited to thenumber of DNA barcodes that can be synthesized separately
and deposited to unique spatial positions, combinatorial indexing seen in DBiT-seq has broken this linear scalability.16 DBiTseq uses a microfluidics device that can create two sets ofunidirectional massively parallel flows on a tissue slice. The first
set of flows provides DNA barcodes of primary (row) coordinates
to the tissue-derived DNA. The second set of flows are
90 -rotated from the first and provide secondary (column) coordinates. The two barcodes are ligated together to encode bothrow and column information. This combinatorial row-column

llSynthesis

OPEN ACCESS

Box 2. Slide-seq

Slide-seq20,53 is a pioneering method for spatial transcriptomics using a posteriori positional indexing strategy that has many similarities with Drop-seq,40 a droplet-based method for scRNA-seq (Box 1). Slide-seq also employs barcoded beads that are 10 mmdiameter, made of polystyrene, and surfaced by poly(T) RT primers encoding unique bead-specific barcodes. The barcoded beads
are first densely and randomly deposited on a class surface. The bead layer is then subjected to optical in situ sequencing of asequencing-by-ligation method to identify barcode sequences and their locations. After the identification of barcodes and theircoordinates, tissue section is applied on their surface, where released RNAs are captured by their proximal barcoded RT primers
on the beads. Finally, the sequencing library is prepared by RT, followed by PCR amplification. The sequencing reads are analyzed
similarly to that of scRNA-seq, where gene expression profiles of positional barcodes are sorted with their two-dimensional coordinates. Slide-seq has been demonstrated for a range of mouse tissues including hippocampus, cerebellum, liver, and kidney
and revealed the spatial cell state distribution and their molecular profiles across the tissue substructures.
The field of view of Slide-seq is a 3-mm diameter circle since the current protocol uses a 3-mm gasket to distribute barcoded
beads. The same group reported an updated version, Slide-seq V2, in 2020 with an improved bead synthesis strategy, sequencing
method, and library preparation protocol.53 Although it largely improved the transcriptome yields compared with the initial version,
the limitation in scale remains. Additionally, like other positional indexing approaches, transcripts from multiple cells may be
captured by the same bead.

indexing of spatial genomic products has achieved more scalable position indexing with minimized barcode members and aspot size of 10 mm square per side.
In a posteriori positional indexing, clusters of unidentified
monoclonal DNA barcodes are first distributed on a two-dimensional (2D) surface and then later identified by in situ sequencing
or smFISH. In Slide-seq20,53 (Box 2) and HDST,19 barcoded
poly(T) RT primer beads are randomly distributed in space andthen identified by in situ sequencing and smFISH, respectively.
Seq-Scope21 and Pixel-seq22 use an approach similar to Illumina
sequencing: spatially distributed monoclonal DNA barcode clusters are prepared by bridge PCR amplification of sparsely immobilized DNA barcode molecules on a 2D surface. The sequencesof clonal sequence clusters are then identified via sequencing bysynthesis. Similarly, in Stereo-seq,23 barcoded DNA nanoballs
are generated by RCA, deposited spatially, and then identified
by DNBSEQ sequencing.54 Stereo-seq has achieved unparalleled scalability, positioning reads over a 13.2 cm 3 13.2 cm
area at subcellular resolution.
Positional indexing links genomic products to a single spatial
pixel, but these pixels can capture information from multiple cells
because the pixel boundaries do not align with cell boundaries.
Further, genomic products of single cells are likely to diffuse
before they bind to positional barcodes, blurring the image. To

address this issue, several approaches have been developed
to extend cellular indexing from single-cell genomics to spatial
genomics. In XYZeq17 and sci-Space,18 a tissue sample is firststamped on a surface of positional barcodes prepared by a prioriindexing. In this approach, the positional barcode molecules are
not fused to the genomic products of cells but to the cells themselves. Cells are then dissociated, and their genomic products
and positional barcodes are both indexed by cellular barcodes
using split-and-pooling indexing (Box 1). Both the spatial positions and genomic profiles of cells can be decoded by highthroughput sequencing. However, the cells are not localizedwith extreme precision: sci-Space has achieved a higher resolution with a pixel size of 73.2 mm compared with XYZeq with apixel size of 500 mm. For precise localization of single cells, thisapproach would require smaller positional barcode pixels.
Further, because split-and-pooling loses a significant fractionof cells, this approach cannot exhaustively scan single-cellgenomic profiles across a tissue section.
Positional indexing has also enabled the measurement ofdiverse modalities of molecular profiles in a spatial context. For
example, DBiT-seq has demonstrated simultaneous spatial
profiling of the transcriptome and cell surface proteome.7,16
Slide-seq has enabled spatial genome sequencing by applying
Tn5 transposase that fragments genomic DNA and concatenates
Cell Systems 14, 844–859, October 18, 2023 847

ll
OPEN ACCESS

the fragments to adapter sequences.24 Similarly, DBiT-seq has
also recently been demonstrated for different genomic modalities
to identify open chromatin regions, chromatin modifications, andtheir combinations with gene expression profiles across a tissue
space.6,8,55
Positional indexing has scaled 2D spatial genomics to the levelof whole organs and small organisms. A priori approaches arelikely reaching the limit of their scalability due to technical limitations in precisely depositing many positional barcodes to corresponding small areas. While a posteriori indexing approaches
have the potential to scale with the growth of massively parallel
sequencing technologies, they require optical in situ sequencing
to retrospectively identify positional barcodes. Therefore, these
positional indexing approaches cannot benefit from advancesin non-optics-based DNA sequencers, such as nanopore
sequencers. Further, the need for optical imaging limits positional indexing approaches to 2D tissue sections.
Mathematical cartography
The last emerging family of spatial genomics techniques ismathematical cartography (Figure 1C), where an image is reconstructed by solving an inverse problem. This eases the experimental burden of directly profiling transcriptional states at precise positions over large areas and relies only on DNA
sequencing. Mathematical cartography approaches have thepotential to elegantly increase in scale as DNA sequencing technologies improve, but none of them currently have practicallarge-scale demonstrations. In principle, these techniques are
not limited to two dimensions. Currently, this class is represented by sequencing-based microscopy and gene expression
cartography methods. However, we present a theoretical framework for mathematical cartography, DNA-GPS, which is morescalable than existing approaches and synergizes with positional indexing methods while not relying on optical imaging.
DNA microscopy25 offers an alternative to both optical imaging and positional indexing approaches. Similar to positional indexing, it is a sequencing-based approach. However, while
positional indexing technologies require an experimental procedure to determine their spatial locations, in DNA microscopy,
the locations of spatially distributed molecules are inferred only
from DNA sequencing data where each sequencing readencodes the information needed to reconstruct its position. Its
first implementation reconstructed the spatial distribution of
RNA molecules over an estimated 250–700 cells. After fixing
cells, target RNA species are reverse transcribed in situ withprimer molecules encoding random short sequences as uniquemolecular identifiers (UMIs). The resulting UMI-tagged cDNAs
are then amplified in situ by PCR and their products are allowed
to diffuse spatially. As this in situ PCR step is performed withprimers encoding common sequences and random nucleotides,
the cDNA amplicons are fused with proximal amplicon products
through overlap-extension, resulting in two UMI-tagged geneproducts fused with primer-derived random nucleotide segments at the junction. The resulting random nucleotide pair at
the junction is called a unique event identifier (UEI). The cDNA
sequences, UMIs, and UEIs are readout by high-throughput
DNA sequencing. This sequencing data collectively represent
the physical proximities between every single RNA molecule,which originally served as a source template for spatially diffused
848 Cell Systems 14, 844–859, October 18, 2023

Synthesis
cDNA amplicons. The spatial positions of the RNA molecules
can be reconstructed with a maximum likelihood procedure,
based on pairwise proximities.
In theory, this reaction can be performed at a tissue scale witha single readout of high-throughput sequencing. However, thismolecular cartography has only been demonstrated to datewith images consisting of less than a thousand cells due to therequired sequencing depth. Since molecules must be densely
sequenced to reconstruct positions using collisions, bothsequencing and computational efficiency would be needed toapply this method at a large scale. For example, with 105 molecules per cell and 106 cells/cm2, reconstructing 100 cm2 oftissue would require sequencing 1013 molecules and, even if asparse binary matrix could be constructed with only 10 neighbors per molecule, would still require storing and processing
100 terabyte (TB) of data. This illustrates the benefit of localizing
cells instead of molecules: while single-molecule resolution may
eventually be useful, there will still be much to be gained fromstudying tissue architecture at the level of cells, rather than individual molecules within cells. Indeed, some recent single-molecule studies have analyzed their data by aggregating them to thelevel of cells.10,23
PARSIFT26 and IPL27 are two theoretical mathematical
cartography approaches.56 In these approaches, a 2D surfaceof DNA sequences is charted by planar graph embedding
where the nodes of the graph represent DNA sequence locations and adjacent sequences are connected by an edge.
The two methods propose different methods for measuring
this adjacency graph, roughly based on concatenating adjacentbarcodes and sequencing. Similar to the first method, both ofthese methods would require tremendous sequencing depth
to cover large spatial areas. Further, practical implementationsof spatial genomics based on these approaches remain to be
proposed.
Gene expression cartography is a mathematical frameworkthat predicts cellular locations directly from single-cell gene
expression profiles obtained by single-cell RNA sequencing(scRNA-seq). One of the earliest methods in this category is
Seurat,57 which has been demonstrated on zebrafish embryos.
However, it requires additional FISH spatial expression patternsof several marker genes collected from independent embryos ofthe same developmental stage. Therefore, this approach can beused only when rich spatial gene expression datasets of thesame species at the same biological condition are available.
NovoSpaRc28 is another approach that does not theoretically
rely on auxiliary FISH datasets. Instead, this method relies on
the strong assumption that cells located in spatially close
positions have similar gene expression profiles. This assumption
enables setting up an optimization problem to identify the locations of cells from their gene expression profiles. Although
NovoSpaRc demonstrated reconstructions of spatial gene
expression profiles from a range of datasets to some degree, images that were similar to the biological ground-truth samples
could not be obtained unless spatial gene expression patterns
for marker genes were provided to constrain the image reconstruction process. This is likely because the key assumption of
nearby cells sharing similar transcription profiles fails to hold insome locations, such as at tissue boundaries. Accordingly,
gene expression cartography is a scalable approach but still

llSynthesis
requires direct measurement of spatial expression patterns for atleast several genes with FISH.
DNA GPS
We now propose DNA-GPS, a theoretical framework for largescale optics-free spatial genomics. Similar to other mathematical
cartography methods, DNA-GPS localizes positions using
sequencing information alone. However, DNA-GPS greatly increases scalability by incorporating positional barcodes insteadof resolving individual molecules. These barcodes can be associated with spatial pixels, as is done in positional indexing, or with thecellular barcodes used in single-cell genomics. DNA-GPS localizes positional barcodes using manifold learning (Box 3). The
data required for this spatial genomics can be collected entirely
through DNA sequencing, without optics at any stage. Based on
simulations presented below, only 30–500 additional reads per
barcode would need to be sequenced to position each barcode
at 10–30 mm resolution. The majority of mammalian cells are 10–
100 mm in diameter,58–70 though a few cell types are slightly below
10 mm.71–76 Therefore, in principle, DNA-GPS should scale as asmall overhead on total sequencing at the near-single-cell resolution as DNA sequencing technologies improve.
Our key idea is to introduce an artificial set of ‘‘satellite DNA
barcodes,’’ each of which diffuses in a spatially coherent way
from a random initial position (Figure 2A). The spatially distributed satellite barcodes can be captured in the same way as
the cellular genomic contents and tagged by positional barcodes. Therefore, the positional barcodes provide ‘‘informationanchoring’’ between the satellite barcodes and the cellular
genomic contents from the same position. For example, DNAGPS can determine the positions and sequences of positional

OPEN ACCESS

bead barcodes used in Slide-seq (Box 2) with no a priori or a posteriori indexing process. Below, we explain and demonstrate
the idea through simulations. In these simulations, we focus on
one concrete realization of DNA-GPS related to Slide-seq. We
then discuss the broad applicability of DNA-GPS and its potential synergies with other spatial and singe-cell genomics
methods.
To apply DNA-GPS to determine locations of positional beadbarcodes, similar to those used in Slide-seq, tissue transcriptome and satellite barcodes would both be captured by theirproximal RT primers encoding positional barcodes on spatiallydistributed beads and fused to the positional barcode sequences by RT and polymerase extension, respectively (Figure 2B). The locations of bead barcodes could then be reconstructed using manifold learning to learn the underlying 2D
positions of beads from their satellite barcode count profiles.
This is similar to the GPS used in navigation systems for carsand cell phones, where devices determine their precise location
on Earth using their distance to multiple satellites. The core principle of DNA-GPS is that neighboring points in physical space
will collect similar counts of satellite barcodes because they
are distributed in a spatially coherent way. In mathematicalterms, the measurement process can be understood to embed
the physical 2D positions of bead barcodes into a high-dimensional ‘‘satellite barcode space,’’ where each point is represented by its vector of satellite barcode counts, similar to how
a transcriptome profile is represented by a high-dimensional
gene expression vector (Figure 2C). The embedded bead layer
forms a low-dimensional manifold, or surface, in high-dimensional satellite barcode space. We provide a precise theorem
statement in the supplemental information (see Method S1 andBox 3. Manifold learning

Manifold learning aims to learn a low-dimensional structure embedded in a higher dimensional space. It can be thought of as a formof dimensionality reduction, with the stronger assumption of an underlying low-dimensional structure.
Principal-component analysis (PCA) can exactly capture linear structures such as lines and planes by decomposing the data intolinear, uncorrelated components.77 PCA has high computational complexity, as it is calculated by performing a spectral decomposition on the covariance matrix. However, a small number of linear components can be found more efficiently by performing
truncated singular value decomposition (SVD). Classic or metric multidimensional scaling (MDS) is another popular linear manifold
learning approach that uses the pairwise distances between data points.78 It similarly has a high computational complexity byrelying on a spectral decomposition.
Many times, we want to capture non-linear structures. Non-linear spectral methods generally share a three-step process ofcreating a graph on the data by connecting neighboring points, converting the graph to a matrix, and taking a spectral embeddingof the resulting matrix via a spectral decomposition, where the methods differ in the process used to convert the graph to a matrix.79 Spectral methods include locally linear embeddings (LLEs), Isomap, and Laplacian and Hessian eigenmaps.80–83 The spectral decomposition is computationally intensive, but some methods, such as LLE, are more scalable as they consider small areas
instead of global structure.
Force-directed layout embedding methods offer more scalability, as naively they only require pairwise comparisons and using approximations can be scaled to millions of data points. t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold
approximation and projection (UMAP) are two popular force-directed layout methods. t-SNE represents the similarity between
points as probabilities and minimizes the divergence between the high and low-dimensional probability distributions.84,85
UMAP uses topological structures to capture properties of the data in the high-dimensional space and then uses a force-based
method to find a low-dimensional Euclidean representation that approximates the high-dimensional topological structure.86
Autoencoders are a class of deep learning models for dimensionality reduction that can capture complex non-linear relationships.87 Autoencoders are neural networks with internal layers that are a lower dimension than the original data, forcing the
network to learn a low-dimensional representation of the data to reconstruct the original data as output. Autoencoders are highly
scalable. However, it can be difficult to interpret the embeddings with respect to the original features.
Cell Systems 14, 844–859, October 18, 2023 849

ll
OPEN ACCESSA

Synthesis
Figure 2. DNA-global positioning system(DNA-GPS)B(A) Conceptual diagram of applying DNA-GPS tolocate spatial positions of Slide-seq barcoded
beads. DNA-GPS infers the spatial coordinates ofbeads having unique bead barcodes (BCs). Satellite
barcodes (BCs) released from satellite devices areconcatenate to bead BCs. The satellite BC counts
fused to each bead BC reflect proximities between
the bead and satellite devices and can be used toinfer the locations of bead BCs. Poly(A)ed RNAs
released from a tissue section are also captured,
reverse transcribed and concatenated to bead BCs
so that the transcription profiles can be mapped
onto the reconstructed space.
(B) Hypothetical design to fuse satellite BCs to beadBCs together with poly(A)ed RNAs (a close-up viewof A). The poly(T) primers encoding bead BCs capture both poly(A)ed RNAs from nearby cells andpoly(A)-tailed satellite (sBC) from nearby satellite
devices. Reverse transcription and polymerase
extension fuse RNA and satellite BC sequences tothe bead BCs.
(C) Proposed workflow to obtain spatial transcriptomics image using only sequencing data.
Each bead BC is associated with two count profiles:
a gene expression profile by RNA sequence counts
and a satellite BC count profile. The gene expression
profiles are stored as rows of a gene expression
matrix (top) and the satellite BC count profiles are
stored as rows of a satellite BC count matrix (bottom). Because bead BCs that are nearby in physicalspace collect similar counts of satellite BCs, we canuse the similarities between satellite BC profiles toreconstruct locations of bead BCs with manifold
learning. Gene expression profiles of bead BCs arethen mapped to the spatial positions.

C

Figure S1). The method is not limited to 2D reconstructions: if amethod were devised to distribute beads and satellites in 3D,then manifold learning could be applied to reconstruct the 3D
positions. In summary, DNA-GPS uses manifold learning to learn
the low-dimensional embedding corresponding to the original
bead positions from the high-dimensional vectors of satellite
barcode counts.
Manifold learning methods aim to find a low-dimensional surface, or manifold, embedded in a high-dimensional space. They
can be thought of as a subset of dimensionality reduction
methods, with the stronger assumption of an underlying lowdimensional structure. For example, t-distributed stochastic
neighbor embedding (t-SNE)84,85 and uniform manifold approximation and projection (UMAP)86 are frequently used in scRNAseq to create visualizations of high-dimensional transcription
profiles88 (Figure 2C). In these visualizations, the low-dimensional structure is an abstract ‘‘manifold of cell states.’’ Manifold
learning has great potential to recover the very concrete manifolds of underlying 2D or 3D positions of cells or molecules inspace from higher dimensional data, such as molecular interactions. In the Slide-seq example, the goal is to recover the
positions of bead barcodes on a 2D surface from the satellite
barcode counts. A large number of manifold learning algorithms
exist that vary in their assumptions, limiting what structures they
can recover, and their computational complexity (Box 3). In DNAGPS, we use local distances between positional barcodes to
850 Cell Systems 14, 844–859, October 18, 2023

reconstruct their positions because distances plateau for points
that share no reads from a common satellite. This results in a
non-linear manifold structure. As we require the method to scale
to hundreds of thousands or millions of beads, we focused onforce-based methods over spectral approaches.
RESULTS
Simulation design
We performed extensive simulations to test the feasibility of
DNA-GPS and to guide the design of satellite barcode systems.
For our initial simulations, we modeled satellite barcodes asdiffusing from point-sources, producing Gaussian profiles (Figure 3A). In subsequent simulations, we tested other nonGaussian satellite profiles, motivated by possible experimental
implementations of satellite barcodes. We modeled positional
barcodes with Slide-seq beads on which satellite barcodes arecaptured. We simulated bead positions using (1) ground-truth
positions from the Slide-seq datasets20 as well as (2) regulargrids of hundreds of thousands of densely packed 10-mm beads
to test scalability. Each bead captures reads from nearby satellite barcodes, where the number of reads is proportional to theintensity of the satellite barcode’s Gaussian profile at the bead’s
position. We tested the robustness of image reconstruction tomultiple parameters including sequencing depth and diffusionlevel of satellite barcodes.

llOPEN ACCESS

Synthesis
A

C

B

Figure 3. Simulation of spatial transcriptomics by DNA-GPS(A) Simulation of satellite devices (filled dots) distributed over barcoded beads (white open circles; 10 mm diameter) based on the density observed in a Slide-seq
dataset. Arbitrarily selected satellites are colored with the Gaussian diffusion of their satellite BCs (blurred pattern) with a standard deviation s of 50 mm represented by radius circles of the corresponding colors. Scale bars: 50 mm.
(B) Correlation between ground-truth distance and Euclidean distance between normalized satellite BC count profiles for 105 randomly selected pairs of beads
from a synthetic square dataset (C). While the distances are initially correlated, the sBC profile distance plateaus once the two beads share no satellites incommon. This motivates the use of a manifold learning method that preserves local distances.
(C) DNA-GPS reconstructions on a simulated dataset with 105 densely packed beads and three sets of ground-truth bead positions from the Slide-seq dataset.
The top row shows ground-truth positions artificially colored for the simulated data and colored by cell states for the Slide-seq datasets. The middle row shows
the DNA-GPS reconstruction using the same coloring as the top row. The bottom row shows the DNA-GPS reconstruction where each bead is colored by the
distance between the ground truth and reconstructed position after alignment through a simple linear transformation. All reconstructions achieve a medianreconstruction distance below 20 mm using 100,000 satellites/cm2, 50 mm diffusion, and 130 UMIs per bead (556 total reads per bead).

In practice, beads can vary in quality, with higher quality beads
capturing more reads and vice versa. To mimic an experimental
distribution of bead qualities, we used the distribution of read per
bead counts from the Slide-seq kidney dataset, downsamplingto achieve lower sequencing depths (Figures S2A and S2B).
Further, multiple satellites may share the same barcode, due tofinite satellite barcode complexity and the non-uniform distribution of barcodes, and reads from satellites sharing the same barcode are indistinguishable (Figure S2C). We accounted for this in
our simulations by randomly selecting a barcode for each satellite device from a pool of possible barcodes according to an
experimental distribution of barcode frequencies (Figure S2C).
This corresponds mathematically to a random projection in satellite barcode space. However, random projections are known topreserve pairwise distances in high dimensions.89 Indeed, when
we examined the Euclidean distance between beads in ‘‘projected’’ satellite barcode count space, we found that beads
that are spatially close together share similar satellite barcode
vectors and were close together in high-dimensional space (Figure 3B). This correlation understandably dropped off at largescale distances because satellite barcodes only diffuse to alimited extent and any pair of beads that share no satellites incommon are roughly the same distance apart in the satellite barcode count space.
We found that the UMAP algorithm86 can leverage local distances in satellite barcode count space to reconstruct the positions of positional barcodes at 10–30 mm resolution (Figure 3C).
Although UMAP is known to not exactly preserve structures,90
we demonstrate in simulations that it could effectively reconstruct bead barcode positions at the near-single-cell resolution.
We used a linear transformation to align the output of UMAP to
the ground truth for quantitative comparison, as the output of
UMAP may be scaled, rotated, or flipped relative to the original
embedding, and computed the distance of each reconstructed
position to the ground truth. However, in practice the reconstructions would not need to be aligned. For both the Slide-seq beadpositions and grids of densely packed beads, we performed agrid of simulations testing all combinations of 6 diffusion levels,
4 satellite barcode densities, 11 sequencing depths, and
4 UMAP hyperparameter settings (STAR Methods).
Simulation results
In our simulations on densely packed beads, DNA-GPS
achieved reconstructions with as high as 10-mm resolution,
Cell Systems 14, 844–859, October 18, 2023 851

ll
OPEN ACCESSA

Synthesis
Figure 4. Single-cell resolution is possible
over a range of physical parameters(A) The best reconstruction across satellite densities
and UMAP parameters on the synthetic dataset foreach combination of sequencing depth and diffusion level. Images show the distance to the groundtruth for each bead with the median distance inset.
DNA-GPS can achieve reconstructions with as highas 10 mm resolution, with the flexibility to trade asmall decrease in resolution for a large decrease in
sequencing depth. The reconstructions were successful over a wide range of sequencing depths anddiffusion levels.
(B) Complement of the cumulative distribution ofbead distances to ground truth for each of the four
reconstructions (i–iv) indicated in (A). Dashed lines
indicate the 50th and 90th percentiles of beads.
These distributions showed that, while we reported
median values for reconstruction resolution, there
were not many outlier beads that the method could
not place, with >90% of beads within twice themedian distance.
See also Figures S2–S7.

B

measured as median distance of a bead in the aligned reconstruction to the ground truth, with >90% of beads within 20 mm(Figures 4A and 4B). For the Slide-seq simulations, the best reconstructions achieved a resolution of 15 mm at as low as
130 UMI (556 reads per bead [rpb]) (Figure S9). As our model depends on UMI counts, while sequencing cost depends on reads,
we provide both values in our results (Figures S5, S6, and S9).
On the dense grids of beads, DNA-GPS achieved a resolutionof 10 mm at as low as 180 UMI (1,110 rpb). However, sequencing
depth can be significantly reduced with only a moderatedecrease in resolution, with DNA-GPS achieving reconstructions
under 20 mm at as few as 40 UMI (90 rpb) and 30 mm resolution
with as few as 15 UMIs per bead (30 rpb).
Further, the reconstructions are robust to variation in physicalparameters and non-Gaussian diffusion (Figures S4–S9). DNAGPS achieved reconstructions under 20 mm for all but one
combination of parameters with diffusion R30 mm and all satellite barcode densities, requiring no more than 180 UMI(1,110 rpb) (Figure S4). Similarly, 30 mm resolution could beachieved for all but one combination of parameters at no
more than 85 UMI (280 rpb). For the Slide-seq positions,
DNA-GPS achieved near-single-cell resolution (<30 mm) at all
852 Cell Systems 14, 844–859, October 18, 2023

diffusion levels R30 mm and all satellite
barcode density levels at read depths as
low as 25 UMI (50 rpb). Further, simulating
diffusion from bacterial colonies (STAR
Methods), we found that the simulations
were robust to non-Gaussian diffusion,achieving peak resolution of 13 and30 mm resolution at as low as 25 UMI(50 rpb) (Figure S8).
Our simulations suggest DNA-GPS
could achieve resolutions as high as
10 mm, with the flexibility to trade a moderate decrease in resolution for a significant
decrease in required sequencing depth.
Using experimental values for ground-truth bead positions, satellite barcode redundancy, and bead quality, we found that our
method can achieve near-single-cell resolution over satellite
densities from 25,000to 250,000 satellite barcodes per cm2,and diffusion levels from 30 to 100 mm, with the best performance occurring with 50 mm diffusion. These results can guidethe development of experimental systems of satellite barcodesand demonstrate the method is easily scalable to hundreds ofthousands of beads.
Comparison to other spatial genomics technologies
We next sought to compare the potential resolution and scalability of DNA-GPS to other state-of-the-art spatial transcriptomics
technologies. Using our simulation results and an exponential
model, we modeled the performance of DNA-GPS as a functionof how deeply we sequence satellite barcodes, as we are able tolocalize beads more precisely as barcodes are sequenced moredeeply (Figure 5A). Using this model, we estimated the resolution(mm) and field-of-view (image width of a square in mm) achievedby DNA-GPS for different sequencing depths (of satellite barcodes) and compared them with seven leading methods (Figure 5B). Intuitively, the number of rpb varies along each curve.

llOPEN ACCESS

Synthesis
A

B

Figure 5. Comparison of DNA-GPS applied to Slide-seq with other spatial transcriptomics technologies(A) Best median reconstruction resolution versus mean reads per bead (rpb) obtained from the simulated data sweep with an exponential line of best fit.
(B) Performance of DNA-GPS and current spatial transcriptomics technologies. Lines indicate interpolated DNA-GPS performance estimated for different readdepths for sequencing satellite BCs using the curve fit in (A) and assuming densely packed 10 mm beads. For DNA-GPS, resolution is given by the median distanceto the ground truth. For the other technologies (103 Visium,15 DBiT-seq,16 HDST,19 Slide-seq,20 Seq-Scope,21 Pixel-seq,22 Stereo-seq,23 XYZeq,17 and sciSpace18), resolution is given by the distance between adjacent pixels (or beads) to capture transcriptomes and values are shown based on the largest experimental demonstration in their respective publications. The background color represents read count per pixel (or bead) to readout transcriptome (when a totalread count of 1010 is given). Cellular sizes were estimated as spherical diameters of their volumes collected from BioNumbers.76

With 10 billion reads (one NovaSeq run), DNA-GPS can localize
108 beads to generate a 10 cm by 10 cm image at the resolutionof individual cells (17 mm).
Current large-scale RNA-seq studies often profile 106 cells at
depths of 5,000 reads per cell.46 Sequencing an additional 500
reads per cell, our simulations suggest that DNA-GPS could
reconstruct cell positions as accurately as 10 mm resolution.
More generally, the cost of DNA-GPS can be thought of as apercent increase in the original sequencing budget that depends
on the desired sequencing depth for the transcriptome anddesired resolution, where near-single-cell resolution reconstructions can be achieved by increasing the budget by <10%. As
sequencing costs drop and studies are able to profile larger
cell populations, DNA-GPS could continue to scale as a small
overhead on the original sequencing budget.
Toward an experimental implementation of DNA-GPS
An experimental implementation of DNA-GPS could be achievedby multiple approaches, where the key components are thefollowing.
Satellite formation: a large number of satellite barcodesshould be densely distributed to cover the target space, inwhich satellite barcodes of a unique sequence are produced
in a single point source. Our simulations suggest there can besome level of barcode redundancy, consistent with experimentally observed levels (STAR Methods).
Satellite transmission: When transmitting satellite barcodes
to the tissue sample, some diffusion is beneficial so thatspatial beads (or pixels) receive satellite barcodes from multiple neighboring satellites. Our simulations suggest the
optimal diffusion level is 50 mm for densely packed 10 mmbeads (Figure 4A).
Information anchoring: Satellite barcodes must be captured
together with genomic material from cells, and both are
fused to positional barcodes. This information anchoring al-lows a spatial genomics image to be formed after satellite
barcodes are used to localize positional barcodes.
There are multiple potential implementations for each of thesecomponents, which are based on existing methods (Figure 6A).
For example, the satellite formation step could be achieved byculturing engineered bacterial colonies expressing unique satellite barcodes or by forming ‘‘polonies’’ of satellite barcodes
through in-gel PCR (Box 4). Satellite barcodes could then betransmitted to the surface of positional barcodes or tissue byeither free diffusion or electrophoresis blotting, where diffusionlevel could be tuned during this step. Finally, spatially distributed
satellite barcodes and genomic materials could be anchored toeither positional barcodes of pixel-based spatial genomics, or
single-cell barcodes of single-cell genomics.
Thus, one potential end-to-end implementation could stamp
E. coli colonies expressing unique, poly(A)ed satellite RNA barcodes onto a surface of Slide-seq barcoded beads of unidentified
locations, followed by the deposition of tissue sample (Figure 6B). Satellite barcodes and local transcriptomes would
then be captured by positional barcodes on the beads andsequenced together with the positional barcode sequences.
Spatial transcriptome profiles would then be associated withbarcoded beads’ positions (which are identified using satellite
barcode profiles by DNA-GPS).
To highlight the flexibility of DNA-GPS, we present a second
potential implementation. Instead of using beads, satellite barcodes could be directly deposited onto tissue, potentially by using
electrophoresis to improve transfer (Figure 6C).The tissue is thenapplied to the paper, where single-stranded satellite barcode
molecules stick to cells (and nuclei).18 After dissociation of thesatellite-attached tissue into single cells, any cellular indexing
single-cell genomics methods (e.g., split-and-pooling anddroplet encapsulation) can conjugate single-cell RNAs (orDNAs) and their associated satellite barcode profiles to the single-cell barcodes, enabling scalable spatial genomics with
Cell Systems 14, 844–859, October 18, 2023 853

ll
OPEN ACCESS

Synthesis

A

B

C

Figure 6. Possible implementations of DNA-GPS for diverse modalities of spatial genomics(A) The potential implementations of DNA-GPS. Any DNA-GPS implementation requires three components: (1) satellite formation, (2) satellite transmission and (3)information anchoring. We envision that satellite formation could be implemented by either engineering bacterial colonies each expressing unique satellite BCs orseeding a gel with unique satellite BC DNA molecules to form polonies (see Box 4). Satellite transmission could be achieved by either free diffusion or electrophoresis blotting. Finally, information anchoring could be implemented by either capturing RNA on positional ID clusters such as barcoded beads or withstandard single-cell genomics methods.
(B) Example 1. E. coli colonies serve as satellite devices and barcoded beads of unidentified bead BCs serve as image pixels. The colonies and then the tissue
sample are stamped onto the beads.
(C) Example 2. Diffused satellite barcodes can be directly deposited to a target tissue section, where single-stranded satellite BCs stick to cells (or nuclei). Afterdissociation of the satellite-attached tissue into single cells, any of the single-cell genomics platforms can conjugate single-cell genomic materials and theirsatellite BCs to the single-cell identifiers (cell BCs), enabling scalable spatial transcriptomics at the resolution of individual cells.

single-cell resolution. Theoretically, any modality of highcoverage single-cell genomics could be transformed into spatial
genomics with this strategy, as long as satellite barcodes can be
captured by single-cell identifiers together with genomic materialof interest.
DISCUSSION
The past decade has witnessed the development of numerous
spatial genomics technologies that can be broadly divided into
854 Cell Systems 14, 844–859, October 18, 2023

optical imaging, positional indexing, and mathematical cartography methods. Optical imaging technologies can profile the
3D distribution of molecules across cells or tissues, but the useof optics introduces fundamental trade-offs between field-ofview, resolution, and the number of molecular species to be profiled. Positional indexing technologies have scaled 2D spatial
genomics to the level of whole organs and bodies. However, apriori approaches are limited in scale, and a posteriori approaches require optical in situ sequencing to retrospectively
identify positional barcodes. Both strategies limit the specimens

ll
OPEN ACCESS

Synthesis
Box 4. Potential implementations to realize satellite barcodes

Satellite E. coli device
poly(A)A)
poly(A)
EGFP

Satellite BC AAAAA

Paper disc in
E. coli culture

Culture place paper discon a LB agar plate
200 µmE. coli culture
LB+agarose

Spread and culture
on a LB agar plate
200 µmRandom DNA
template in PAA gel

In-gel PCR
200 µmBACTERIAL COLONIES
Sparsely spread bacterial cells form clonal colonies on an agar gel surface. This phenomenon has widely been adopted in molecular cloning to isolate clonal DNA plasmid products. We propose the use of spatially distributed Escherichia coli colonies as an
option to produce many locally distributed satellite barcodes, where each E. coli cell serves as a satellite device to producepoly(A)ed satellite RNA barcodes from its plasmid DNA. Upon cell lysis, the unique satellite RNA barcode signals are diffusedfrom the positions of their source colonies. The challenge is making uniform sizes of colonies as small and dense as possible.
We found that such colonies could be generated by placing a filter paper soaked with a barcoded cell culture on an agar media
and culturing overnight. We also found that cells embedded in a soft agarose with culture media yielded spatially segregated, tinycolonies.
POLONIES
PCR amplification of sparsely distributed DNA molecules embedded in polyacrylamide gel confers polymerase colonies (polonies).
Clonal DNA amplicons are produced at proximal but not identical positions to their templates and therefore form diffused patterns
from the original positions along with PCR cycles. Since each polony can consist of unique clonal DNA barcode molecules, polonies can also be used as satellite devices. Overall size and density of polonies are controllable by with gel concentrations, PCR
conditions and the number of template molecules.
Cell Systems 14, 844–859, October 18, 2023 855

ll
OPEN ACCESS

to 2D tissue slices because there has been no efficient approachto acquire z sections by stamping tissue slices on a surface of
positional barcodes. 3D spatial transcriptomics has beenachieved by in situ sequencing of a small tissue block. However,this approach is time consuming. Indeed, ExSeq takes 10 h to
localize spatial barcodes over 1 field of view (around0.01 mm2) across 150 z sections.14 In addition, all the in situsequencing-based approaches cannot take advantage ofadvances in non-optical sequencing technologies. While
computational cartography technologies offer the possibility of
localizing positions from sequencing data alone, they have yet
to achieve large-scale demonstrations. DNA-GPS is a theoreticalframework for optics-free mathematical cartography, which allows computational localization of positional barcodes byapplying manifold learning to satellite barcodes.
One of the biggest challenges to implementing DNA-GPS
would be controlling the satellite barcode diffusion pattern. While
we only found small decreases in resolution for non-Gaussian
diffusion, we found these reconstructions were more sensitive
to physical parameters such as satellite device density and diffusion distance (Figure S8). Further, it is possible that chaotic liquid
flows could be induced by stamping satellite barcodes onto a tissue or onto positional barcodes. These chaotic flows could makereconstruction impossible because satellite barcodes would be
distributed incoherently across positional barcodes. It is worth
noting that chaotic flow could potentially affect other spatial
omics technologies that stamp a tissue slice on an array of pixels
because they also capture mRNA molecules in a buffer. Althoughseveral studies investigated the effect of molecular diffusion,
most of them have only assessed local diffusion profiles by the
distance between observed and expected locations, and thepotential perturbation by the chaotic liquid flow remains to beaddressed.20,23 Thus, understanding the nature of the diffusion
and optimizing the transfer protocol for better reconstruction
by DNA-GPS would also benefit spatial omics technology
development.
While we have presented DNA-GPS as applied to transcriptomic sequencing, the core framework could also be applied toother modalities. As seen in the recent extensions of spatial technologies to various genomic modalities,6–8,16,24,55 the satellite
barcode approach of DNA-GPS should be adaptable to mostomics modalities at scale with proper experimental design. For
example, an ATAC-seq extension would be possible by treating
tissue genomic DNA with Tn5 transposases so that the genomic
fragments from open chromatin regions are captured by the anchor barcodes. Further, while positional indexing approaches are
restricted to profiling flat, 2D slices of tissues, DNA-GPS could in
principle profile 3D volumes in an unbiased way, if one could
distribute satellite barcodes uniformly over the volume. A somewhat easier starting point might be curved 2D surfaces, which
could be achieved by flowing satellite barcodes over the surface
an organ or through the interior of the network of blood vessels or
lymph ducts could provide a window into full organisms by flowing satellite barcodes through these natural conduits.
STAR+METHODS
Detailed methods are provided in the online version of this paper
and include the following:
856 Cell Systems 14, 844–859, October 18, 2023

Synthesis
d KEY RESOURCES TABLE
d RESOURCE AVAILABILITY

B Lead contact
B Materials Availability
B Data and code availabilityd METHOD DETAILSB Data generation
B Bead quality and barcode overlap
B Forming the sBC count matrix
B Reconstructions
B Hyperparameter selection
B Aligning reconstructions
B Robustness to physical parameters
B Robustness to bead quality
B Robustness to alternate diffusion schemes
B Slide-seq reconstructions
SUPPLEMENTAL INFORMATION
Supplemental information can be found online at https://doi.org/10.1016/j.
cels.2023.08.005.
ACKNOWLEDGMENTS
We thank members of the Schiebinger lab and Yachie lab for valuable discussions and critical assessment of the work, especially Rebecca Bonham-Carterfor the help with the theorem proof. This study was supported by the Pilot Innovation Fund program (PIF003) of the Genome British Columbia (Genome BC)(to N.Y. and G.S.), the Canada Research Chair program by the Canadian Institutes for Health Research (CIHR) (to N.Y.), the Canada Foundation for Innovation (CFI) (to N.Y.), the Multiscale Human Program of the Canadian Institute forAdvanced Research (CIFAR) (to N.Y.), the Allen Distinguished InvestigatorAward (to N.Y.), and the Career Award at the Scientific Interface from the Burroughs Wellcome Fund (to G.S.). Y.K. and S.I. were supported by the Japan
Society for the Promotion of Science (JSPS) Research Fellowships. The
high-throughput sequencing data analysis was partly performed with the
SHIROKANE Supercomputer at the University of Tokyo Human Genome
Center.
AUTHOR CONTRIBUTIONS
N.Y. and Y.K. conceived the high-level concept of DNA-GPS. G.S., L.G., A.A.,
Y.K., and M.H. conceived the implementation. G.S. and N.Y. designed thestudy. L.G., A.A., Y.K., and M.H. performed the analyses. S.I. and S.K. supported and performed the generation satellite barcodes. L.G., A.A., Y.K.,
N.Y., and G.S. wrote the manuscript.
DECLARATION OF INTERESTS
L.G., A.A., Y.K., M.H., N.Y., and G.H. have filed a provisional patent related to
DNA-GPS.
INCLUSION AND DIVERSITY
We support inclusive, diverse, and equitable conduct of research.
Received: April 27, 2022
Revised: April 19, 2023
Accepted: August 25, 2023
Published: September 25, 2023
REFERENCES
1. Svensson, V., Vento-Tormo, R., and Teichmann, S.A. (2018). Exponential
scaling of single-cell RNA-seq in the past decade. Nat. Protoc. 13,
599–604.

ll
Synthesis
2. Stoeckius, M., Hafemeister, C., Stephenson, W., Houck-Loomis, B.,
Chattopadhyay, P.K., Swerdlow, H., Satija, R., and Smibert, P. (2017).
Simultaneous epitope and transcriptome measurement in single cells.
Nat. Methods 14, 865–868. https://doi.org/10.1038/nmeth.4380.
3. Gawad, C., Koh, W., and Quake, S.R. (2016). Single-cell genome
sequencing: current state of the science. Nat. Rev. Genet. 17, 175–188.
https://doi.org/10.1038/nrg.2015.16.
4. Cusanovich, D.A., Daza, R., Adey, A., Pliner, H.A., Christiansen, L.,
Gunderson, K.L., Steemers, F.J., Trapnell, C., and Shendure, J. (2015).
Multiplex single cell profiling of chromatin accessibility by combinatorial
cellular indexing. Science 348, 910–914. https://doi.org/10.1126/science.aab1601.
5. Rao, A., Barkley, D., França, G.S., and Yanai, I. (2021). Exploring tissue architecture using spatial transcriptomics. Nature 596, 211–220. https://doi.
org/10.1038/s41586-021-03634-9.
6. Deng, Y., Bartosovic, M., Ma, S., Zhang, D., Kukanja, P., Xiao, Y., Su, G.,
Liu, Y., Qin, X., Rosoklija, G.B., et al. (2022). Spatial profiling of chromatin
accessibility in mouse and human tissues. Nature 609, 375–383. https://doi.org/10.1038/s41586-022-05094-1.
7. Liu, Y., DiStasio, M., Su, G., Asashima, H., Enninful, A., Qin, X., Deng, Y.,
Nam, J., Gao, F., Bordignon, P., et al. (2023). High-plex protein and wholetranscriptome co-mapping at cellular resolution with spatial CITE-seq.
Nat. Biotechnol. https://doi.org/10.1038/s41587-023-01676-0.
8. Deng, Y., Bartosovic, M., Kukanja, P., Zhang, D., Liu, Y., Su, G., Enninful,
A., Bai, Z., Castelo-Branco, G., and Fan, R. (2022). Spatial-CUT&Tag:
spatially resolved chromatin modification profiling at the cellular level.
Science 375, 681–686. https://doi.org/10.1126/science.abg7216.
9. Chen, K.H., Boettiger, A.N., Moffitt, J.R., Wang, S., and Zhuang, X. (2015).
RNA imaging. Spatially resolved, highly multiplexed RNA profiling in single
cells. Science 348, aaa6090. https://doi.org/10.1126/science.aaa6090.
10. Eng, C.L., Lawson, M., Zhu, Q., Dries, R., Koulena, N., Takei, Y., Yun, J.,
Cronin, C., Karp, C., Yuan, G.C., et al. (2019). Transcriptome-scale super-resolved imaging in tissues by RNA seqFISH. Nature 568, 235–239.
https://doi.org/10.1038/s41586-019-1049-y.
€n,
11. Borm, L.E., Mossi Albiach, A., Mannens, C.C.A., Janusauskas, J., Özgu
C., Fernández-Garcı́a, D., Hodge, R., Castillo, F., Hedin, C.R.H.,
Villablanca, E.J., et al. (2023). Scalable in situ single-cell profiling by electrophoretic capture of mRNA using EEL FISH. Nat. Biotechnol. 41,
222–231. https://doi.org/10.1038/s41587-022-01455-3.
12. Lee, J.H., Daugharthy, E.R., Scheiman, J., Kalhor, R., Yang, J.L., Ferrante,
T.C., Terry, R., Jeanty, S.S., Li, C., Amamoto, R., et al. (2014). Highly multiplexed subcellular RNA sequencing in situ. Science 343, 1360–1363.
https://doi.org/10.1126/science.1250212.
13. Wang, X., Allen, W.E., Wright, M.A., Sylwestrak, E.L., Samusik, N., Vesuna,S., Evans, K., Liu, C., Ramakrishnan, C., Liu, J., et al. (2018). Three-dimensional intact-tissue sequencing of single-cell transcriptional states.
Science 361. https://doi.org/10.1126/science.aat5691.
14. Alon, S., Goodwin, D.R., Sinha, A., Wassie, A.T., Chen, F., Daugharthy,
E.R., Bando, Y., Kajita, A., Xue, A.G., Marrett, K., et al. (2021).
Expansion sequencing: spatially precise in situ transcriptomics in intact
biological systems. Science 371. https://doi.org/10.1126/science.
aax2656.
15. Ståhl, P.L., Salmén, F., Vickovic, S., Lundmark, A., Navarro, J.F.,
Magnusson, J., Giacomello, S., Asp, M., Westholm, J.O., Huss, M., et al.
(2016). Visualization and analysis of gene expression in tissue sections
by spatial transcriptomics. Science 353, 78–82. https://doi.org/10.1126/
science.aaf2403.
16. Liu, Y., Yang, M., Deng, Y., Su, G., Enninful, A., Guo, C.C., Tebaldi, T.,
Zhang, D., Kim, D., Bai, Z., et al. (2020). High-spatial-resolution multiomics sequencing via deterministic barcoding in tissue. Cell 183, 1665–
1681.e18. https://doi.org/10.1016/j.cell.2020.10.026.
17. Lee, Y., Bogdanoff, D., Wang, Y., Hartoularos, G.C., Woo, J.M., Mowery,
C.T., Nisonoff, H.M., Lee, D.S., Sun, Y., Lee, J., et al. (2021). XYZeq:
spatially resolved single-cell RNA sequencing reveals expression hetero-

OPEN ACCESS

geneity in the tumor microenvironment. Sci. Adv. 7. https://doi.org/10.
1126/sciadv.abg4755.
18. Srivatsan, S.R., Regier, M.C., Barkan, E., Franks, J.M., Packer, J.S.,
Grosjean, P., Duran, M., Saxton, S., Ladd, J.J., Spielmann, M., et al.
(2021). Embryo-scale, single-cell spatial transcriptomics. Science 373,
111–117. https://doi.org/10.1126/science.abb9536.
19. Vickovic, S., Eraslan, G., Salmén, F., Klughammer, J., Stenbeck, L.,
Schapiro, D., Äijö, T., Bonneau, R., Bergenstråhle, L., Navarro, J.F.,
et al. (2019). High-definition spatial transcriptomics for in situ tissue
profiling. Nat. Methods 16, 987–990. https://doi.org/10.1038/s41592019-0548-y.
20. Rodriques, S.G., Stickels, R.R., Goeva, A., Martin, C.A., Murray, E.,
Vanderburg, C.R., Welch, J., Chen, L.M., Chen, F., and Macosko, E.Z.
(2019). Slide-seq: A scalable technology for measuring genome-wide
expression at high spatial resolution. Science 363, 1463–1467. https://doi.org/10.1126/science.aaw1219.
21. Cho, C.S., Xi, J., Si, Y., Park, S.R., Hsu, J.E., Kim, M., Jun, G., Kang, H.M.,
and Lee, J.H. (2021). Microscopic examination of spatial transcriptome using Seq-Scope. Cell 184, 3559–3572.e22. https://doi.org/10.1016/j.cell.
2021.05.010.
22. Fu, X., Sun, L., Dong, R., Chen, J.Y., Silakit, R., Condon, L.F., Lin, Y., Lin,S., Palmiter, R.D., and Gu, L. (2022). Polony gels enable amplifiable DNA
stamping and spatial transcriptomics of chronic pain. Cell 185, 4621–
4633.e17. https://doi.org/10.1016/j.cell.2022.10.021.
23. Chen, A., Liao, S., Cheng, M., Ma, K., Wu, L., Lai, Y., Qiu, X., Yang, J., Xu,
J., Hao, S., et al. (2022). Spatiotemporal transcriptomic atlas of mouseorganogenesis using DNA nanoball-patterned arrays. Cell 185, 1777–
1792.e21. https://doi.org/10.1016/j.cell.2022.04.003.
24. Zhao, T., Chiang, Z.D., Morriss, J.W., LaFave, L.M., Murray, E.M., Del
Priore, I., Meli, K., Lareau, C.A., Nadaf, N.M., Li, J., et al. (2022). Spatial genomics enables multi-modal study of clonal heterogeneity in tissues.
Nature 601, 85–91. https://doi.org/10.1038/s41586-021-04217-4.
25. Weinstein, J.A., Regev, A., and Zhang, F. (2019). DNA microscopy: opticsfree spatio-genetic imaging by a stand-alone chemical reaction. Cell 178,
229–241.e16. https://doi.org/10.1016/j.cell.2019.05.019.
26. Hoffecker, I.T., Yang, Y., Bernardinelli, G., Orponen, P., and Högberg, B.
(2019). A computational framework for DNA sequencing microscopy.
Proc. Natl. Acad. Sci. USA 116, 19282–19287. https://doi.org/10.1073/
pnas.1821178116.
27. Boulgakov, A.A., Xiong, E., Bhadra, S., Ellington, A.D., and Marcotte, E.M.
(2018). From space to sequence and back again: iterative DNA proximity
ligation and its applications to DNA-based imaging. Preprint at bioRxiv.
https://doi.org/10.1101/470211.
28. Nitzan, M., Karaiskos, N., Friedman, N., and Rajewsky, N. (2019). Gene
expression cartography. Nature 576, 132–137. https://doi.org/10.1038/
s41586-019-1773-3.
29. Jensen, E. (2014). Technical review: in situ hybridization. Anat. Rec.
(Hoboken) 297, 1349–1353. https://doi.org/10.1002/ar.22944.
30. Cui, C., Shu, W., and Li, P. (2016). Fluorescence in situ hybridization: cellbased genetic diagnostic and research applications. Front. Cell Dev. Biol.
4, 89. https://doi.org/10.3389/fcell.2016.00089.
31. Chen, F., Tillberg, P.W., and Boyden, E.S. (2015). Optical imaging.
Expansion microscopy. Science 347, 543–548. https://doi.org/10.1126/
science.1260088.
32. Gao, R., Asano, S.M., and Boyden, E.S. (2017). Q&A: expansion microscopy. BMC Biol. 15, 50. https://doi.org/10.1186/s12915-017-0393-3.
33. Takei, Y., Zheng, S., Yun, J., Shah, S., Pierson, N., White, J., Schindler, S.,
Tischbirek, C.H., Yuan, G.C., and Cai, L. (2021). Single-cell nuclear architecture across cell types in the mouse brain. Science 374, 586–594.
https://doi.org/10.1126/science.abj1966.
34. Takei, Y., Yun, J., Zheng, S., Ollikainen, N., Pierson, N., White, J., Shah, S.,
Thomassie, J., Suo, S., Eng, C.L., et al. (2021). Integrated spatial genomics
reveals global architecture of single nuclei. Nature 590, 344–350. https://doi.org/10.1038/s41586-020-03126-2.

Cell Systems 14, 844–859, October 18, 2023 857

ll
OPEN ACCESS

35. Payne, A.C., Chiang, Z.D., Reginato, P.L., Mangiameli, S.M., Murray, E.M.,
Yao, C.C., Markoulaki, S., Earl, A.S., Labade, A.S., Jaenisch, R., et al.
(2021). In situ genome sequencing resolves DNA sequence and structure
in intact biological samples. Science 371. https://doi.org/10.1126/science.aay3446.
36. Tainaka, K., Kubota, S.I., Suyama, T.Q., Susaki, E.A., Perrin, D., UkaiTadenuma, M., Ukai, H., and Ueda, H.R. (2014). Whole-body imaging
with single-cell resolution by tissue decolorization. Cell 159, 911–924.
https://doi.org/10.1016/j.cell.2014.10.034.
37. Tang, F., Barbacioru, C., Wang, Y., Nordman, E., Lee, C., Xu, N., Wang, X.,
Bodeau, J., Tuch, B.B., Siddiqui, A., et al. (2009). mRNA-seq whole-transcriptome analysis of a single cell. Nat. Methods 6, 377–382. https://doi.
org/10.1038/nmeth.1315.
38. Ramsköld, D., Luo, S., Wang, Y.C., Li, R., Deng, Q., Faridani, O.R.,
Daniels, G.A., Khrebtukova, I., Loring, J.F., Laurent, L.C., et al. (2012).
Full-length mRNA-seq from single-cell levels of RNA and individual circulating tumor cells. Nat. Biotechnol. 30, 777–782. https://doi.org/10.1038/
nbt.2282.
39. Picelli, S., Björklund, Å.K., Faridani, O.R., Sagasser, S., Winberg, G., andSandberg, R. (2013). Smart-seq2 for sensitive full-length transcriptome
profiling in single cells. Nat. Methods 10, 1096–1098. https://doi.org/10.
1038/nmeth.2639.
40. Macosko, E.Z., Basu, A., Satija, R., Nemesh, J., Shekhar, K., Goldman, M.,
Tirosh, I., Bialas, A.R., Kamitaki, N., Martersteck, E.M., et al. (2015). Highly
parallel genome-wide expression profiling of individual cells using nanoliter droplets. Cell 161, 1202–1214. https://doi.org/10.1016/j.cell.2015.
05.002.
41. Klein, A.M., Mazutis, L., Akartuna, I., Tallapragada, N., Veres, A., Li, V.,
Peshkin, L., Weitz, D.A., and Kirschner, M.W. (2015). Droplet barcoding
for single-cell transcriptomics applied to embryonic stem cells. Cell 161,
1187–1201. https://doi.org/10.1016/j.cell.2015.04.044.
42. Zheng, G.X., Terry, J.M., Belgrader, P., Ryvkin, P., Bent, Z.W., Wilson, R.,
Ziraldo, S.B., Wheeler, T.D., McDermott, G.P., Zhu, J., et al. (2017).
Massively parallel digital transcriptional profiling of single cells. Nat.
Commun. 8, 14049. https://doi.org/10.1038/ncomms14049.
43. Datlinger, P., Rendeiro, A.F., Boenke, T., Senekowitsch, M., Krausgruber,T., Barreca, D., and Bock, C. (2021). Ultra-high-throughput single-cell RNA
sequencing and perturbation screening with combinatorial fluidic indexing. Nat. Methods 18, 635–642. https://doi.org/10.1038/s41592-02101153-z.
44. De Rop, F.V., Ismail, J.N., Bravo González-Blas, C., Hulselmans, G.J.,
Flerin, C.C., Janssens, J., Theunis, K., Christiaens, V.M., Wouters, J.,
Marcassa, G., et al. (2022). Hydrop enables droplet-based single-cell
ATAC-seq and single-cell RNA-seq using dissolvable hydrogel beads.
eLife 11. https://doi.org/10.7554/eLife.73971.
45. Clark, I.C., Fontanez, K.M., Meltzer, R.H., Xue, Y., Hayford, C., MayZhang, A., D’Amato, C., Osman, A., Zhang, J.Q., Hettige, P., et al.
(2023). Microfluidics-free single-cell genomics with templated emulsification. Nat. Biotechnol. https://doi.org/10.1038/s41587-023-01685-z.
46. Cao, J., Spielmann, M., Qiu, X., Huang, X., Ibrahim, D.M., Hill, A.J., Zhang,F., Mundlos, S., Christiansen, L., Steemers, F.J., et al. (2019). The singlecell transcriptional landscape of mammalian organogenesis. Nature 566,
496–502. https://doi.org/10.1038/s41586-019-0969-x.
47. Cao, J., Packer, J.S., Ramani, V., Cusanovich, D.A., Huynh, C., Daza, R.,
Qiu, X., Lee, C., Furlan, S.N., Steemers, F.J., et al. (2017). Comprehensive
single-cell transcriptional profiling of a multicellular organism. Science
357, 661–667. https://doi.org/10.1126/science.aam8940.
48. Rosenberg, A.B., Roco, C.M., Muscat, R.A., Kuchina, A., Sample, P., Yao,Z., Graybuck, L.T., Peeler, D.J., Mukherjee, S., Chen, W., et al. (2018).
Single-cell profiling of the developing mouse brain and spinal cord withsplit-pool barcoding. Science 360, 176–182. https://doi.org/10.1126/science.aam8999.
49. Cao, J., O’Day, D.R., Pliner, H.A., Kingsley, P.D., Deng, M., Daza, R.M.,
Zager, M.A., Aldinger, K.A., Blecher-Gonen, R., Zhang, F., et al. (2020).

858 Cell Systems 14, 844–859, October 18, 2023

Synthesis
A human cell atlas of fetal gene expression. Science 370. https://doi.
org/10.1126/science.aba7721.
50. Wu, S.J., Furlan, S.N., Mihalas, A.B., Kaya-Okur, H.S., Feroze, A.H.,
Emerson, S.N., Zheng, Y., Carson, K., Cimino, P.J., Keene, C.D., et al.
(2021). Single-cell CUT&Tag analysis of chromatin modifications in differentiation and tumor progression. Nat. Biotechnol. 39, 819–824. https://doi.
org/10.1038/s41587-021-00865-z.
51. Bartosovic, M., Kabbe, M., and Castelo-Branco, G. (2021). Single-cell
CUT&Tag profiles histone modifications and transcription factors in complex tissues. Nat. Biotechnol. 39, 825–835. https://doi.org/10.1038/
s41587-021-00869-9.
52. Nagano, T., Lubling, Y., Stevens, T.J., Schoenfelder, S., Yaffe, E., Dean,
W., Laue, E.D., Tanay, A., and Fraser, P. (2013). Single-cell Hi-C reveals
cell-to-cell variability in chromosome structure. Nature 502, 59–64.
https://doi.org/10.1038/nature12593.
53. Stickels, R.R., Murray, E., Kumar, P., Li, J., Marshall, J.L., Di Bella, D.J.,
Arlotta, P., Macosko, E.Z., and Chen, F. (2021). Highly sensitive spatialtranscriptomics at near-cellular resolution with Slide-seqV2. Nat.
Biotechnol. 39, 313–319. https://doi.org/10.1038/s41587-020-0739-1.
54. Drmanac, R., Sparks, A.B., Callow, M.J., Halpern, A.L., Burns, N.L.,
Kermani, B.G., Carnevali, P., Nazarenko, I., Nilsen, G.B., Yeung, G.,
et al. (2010). Human genome sequencing using unchained base reads
on self-assembling DNA nanoarrays. Science 327, 78–81. https://doi.
org/10.1126/science.1181498.
55. Zhang, D., Deng, Y., Kukanja, P., Agirre, E., Bartosovic, M., Dong, M., Ma,
C., Ma, S., Su, G., Bao, S., et al. (2023). Spatial epigenome-transcriptome
co-profiling of mammalian tissues. Nature 616, 113–122. https://doi.org/
10.1038/s41586-023-05795-1.
56. Boulgakov, A.A., Ellington, A.D., and Marcotte, E.M. (2020). Bringing microscopy-by-sequencing into view. Trends Biotechnol. 38, 154–162.
https://doi.org/10.1016/j.tibtech.2019.06.001.
57. Satija, R., Farrell, J.A., Gennert, D., Schier, A.F., and Regev, A. (2015).
Spatial reconstruction of single-cell gene expression data. Nat.
Biotechnol. 33, 495–502. https://doi.org/10.1038/nbt.3192.
58. Ginzberg, M.B., Kafri, R., and Kirschner, M. (2015). Cell biology. On being
the right (cell) size. Science 348, 1245075. https://doi.org/10.1126/science.1245075.
59. Ocqueteau, C., Cury, M., Becker, L., Morgado, E., González, U., Muxica,
L., and Gunther, B. (1989). Three-dimensional morphometry of mammalian cells. I. Diameters. Arch. Biol. Med. Exp. 22, 89–95.
60. Mitsui, Y., and Schneider, E.L. (1976). Relationship between cell replication and volume in senescent human diploid fibroblasts. Mech. Ageing
Dev. 5, 45–56. https://doi.org/10.1016/0047-6374(76)90007-5.
61. Finegood, D.T., Scaglia, L., and Bonner-Weir, S. (1995). Dynamics of betacell mass in the growing rat pancreas. Estimation with a simple mathematical model. Diabetes 44, 249–256. https://doi.org/10.2337/diab.44.3.249.
ska, D.F., Gnad, F., and
62. Wisniewski, J.R., Ostasiewicz, P., Dus, K., Zielin
Mann, M. (2012). Extensive quantitative remodeling of the proteome between normal colon tissue and adenocarcinoma. Mol. Syst. Biol. 8, 611.
https://doi.org/10.1038/msb.2012.44.
63. Beck, M., Schmidt, A., Malmstroem, J., Claassen, M., Ori, A.,
Szymborska, A., Herzog, F., Rinner, O., Ellenberg, J., and Aebersold, R.
(2011). The quantitative proteome of a human cell line. Mol. Syst. Biol. 7,549. https://doi.org/10.1038/msb.2011.82.
64. Zhao, L., Kroenke, C.D., Song, J., Piwnica-Worms, D., Ackerman, J.J.,
and Neil, J.J. (2008). Intracellular water-specific MR of microbeadadherent cells: the HeLa cell intracellular water exchange lifetime. NMR
Biomed. 21, 159–164. https://doi.org/10.1002/nbm.1173.
65. Géléoc, G.S., Casalotti, S.O., Forge, A., and Ashmore, J.F. (1999). A sugartransporter as a candidate for the outer hair cell motor. Nat. Neurosci. 2,
713–719. https://doi.org/10.1038/11174.
66. Calvillo, L., Latini, R., Kajstura, J., Leri, A., Anversa, P., Ghezzi, P., Salio,
M., Cerami, A., and Brines, M. (2003). Recombinant human erythropoietin
protects the myocardium from ischemia-reperfusion injury and promotes

llSynthesis
beneficial remodeling. Proc. Natl. Acad. Sci. USA 100, 4802–4806. https://doi.org/10.1073/pnas.0630444100.
67. Harker, L.A., Roskos, L.K., Marzec, U.M., Carter, R.A., Cherry, J.K.,
Sundell, B., Cheung, E.N., Terry, D., and Sheridan, W. (2000). Effects ofmegakaryocyte growth and development factor on platelet production,platelet life span, and platelet function in healthy human volunteers.
Blood 95, 2514–2522.
€nzing, S., Allmeling, A.M., Gerlach, J.T., Behr, J., and
68. Krombach, F., Mu
Dörger, M. (1997). Cell size of alveolar macrophages: an interspecies comparison. Environ. Health Perspect. 105 (Suppl 5 ), 1261–1263. https://doi.
org/10.1289/ehp.97105s51261.
69. Goyanes, V.J., Ron-Corzo, A., Costas, E., and Maneiro, E. (1990).
Morphometric categorization of the human oocyte and early conceptus.
Hum. Reprod. 5, 613–618. https://doi.org/10.1093/oxfordjournals.humrep.a137155.
70. Livingston, J.N., Lerea, K.M., Bolinder, J., Kager, L., Backman, L., andArner, P. (1984). Binding and molecular weight properties of the insulin receptor from omental and subcutaneous adipocytes in human obesity.
Diabetologia 27, 447–453. https://doi.org/10.1007/BF00273909.
71. Diez-Silva, M., Dao, M., Han, J., Lim, C.T., and Suresh, S. (2010). Shapeand biomechanical characteristics of human red blood cells in health anddisease. MRS Bull. 35, 382–388. https://doi.org/10.1557/mrs2010.571.
72. Gilmore, J.A., McGann, L.E., Liu, J., Gao, D.Y., Peter, A.T., Kleinhans,
F.W., and Critser, J.K. (1995). Effect of cryoprotectant solutes on water
permeability of human spermatozoa. Biol. Reprod. 53, 985–995. https://doi.org/10.1095/biolreprod53.5.985.
73. Schmid-Schönbein, G.W., Shih, Y.Y., and Chien, S. (1980). Morphometryof human leukocytes. Blood 56, 866–875.
74. Ballas, S.K. (1987). Erythrocyte concentration and volume are inversely
related. Clin. Chim. Acta 164, 243–244. https://doi.org/10.1016/00098981(87)90078-7.
75. Rosengren, S., Henson, P.M., and Worthen, G.S. (1994). Migration-associated volume changes in neutrophils facilitate the migratory process
in vitro. Am. J. Physiol. 267, C1623–C1632. https://doi.org/10.1152/ajpcell.1994.267.6.C1623.

OPEN ACCESS

82. Belkin, M.a.N.P., and Niyogi, P. (2003). Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput. 15, 1373–
1396. https://doi.org/10.1162/089976603321780317.
83. Donoho, D.L., and Grimes, C. (2003). Hessian eigenmaps: locally linear
embedding techniques for high-dimensional data. Proc. Natl. Acad. Sci.
USA 100, 5591–5596.
84. Van Der Maaten, L. (2014). Accelerating t-SNE using tree-based algorithms. J. Mach. Learn. Res. 15, 3221–3245.
85. Van der Maaten, L., and Hinton, G. (2008). Visualizing data using t-SNE.
J. Mach. Learn. Res. 9, 2579–2605.
86. McInnes, L., Healy, J., and Melville, J. (2018). Umap: uniform manifold
approximation and projection for dimension reduction. Preprint at arXiv.
https://doi.org/10.48550/arXiv.1802.03426.
87. Tschannen, M., Bachem, O., and Lucic, M. (2018). Recent advances in autoencoder-based representation learning. Preprint at arXiv. https://doi.
org/10.48550/arXiv.1812.05069.
88. Becht, E., McInnes, L., Healy, J., Dutertre, C.A., Kwok, I.W.H., Ng, L.G.,
Ginhoux, F., and Newell, E.W. (2018). Dimensionality reduction for visualizing single-cell data using UMAP. Published online December 3, 2018.
Nat. Biotechnol. https://doi.org/10.1038/nbt.4314.
89. Cleary, B., Cong, L., Cheung, A., Lander, E.S., and Regev, A. (2017).
Efficient generation of transcriptomic profiles by random composite measurements. Cell 171, 1424–1436.e18. https://doi.org/10.1016/j.cell.2017.
10.023.
90. Damrich, S., and Hamprecht, F.A. (2021). On UMAP’s true loss function.
Adv. Neural Inf. Process. Syst. 34, 5798–5809.
91. Nishimasu, H., Shi, X., Ishiguro, S., Gao, L., Hirano, S., Okazaki, S., Noda,
T., Abudayyeh, O.O., Gootenberg, J.S., Mori, H., et al. (2018). Engineered
CRISPR-Cas9 nuclease with expanded targeting space. Science 361,
1259–1262. https://doi.org/10.1126/science.aas9129.
92. Shen, W., Le, S., Li, Y., and Hu, F. (2016). SeqKit: a cross-platform and ultrafast toolkit for FASTA/Q file manipulation. PLoS One 11, e0163962.
https://doi.org/10.1371/journal.pone.0163962.

76. Milo, R., Jorgensen, P., Moran, U., Weber, G., and Springer, M. (2010).
BioNumbers–the database of key numbers in molecular and cell biology.
Nucleic Acids Res. 38, D750–D753. https://doi.org/10.1093/nar/gkp889.

93. Kijima, Y., Evans-Yamamoto, D., Toyoshima, H., and Yachie, N. (2023). A
universal sequencing read interpreter. Sci. Adv. 9, eadd2793. https://doi.
org/10.1126/sciadv.add2793.

77. Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24, 417–441.

94. Danecek, P., Bonfield, J.K., Liddle, J., Marshall, J., Ohan, V., Pollard, M.O.,
Whitwham, A., Keane, T., McCarthy, S.A., Davies, R.M., et al. (2021).
Twelve years of SAMtools and BCFtools. GigaScience 10. https://doi.
org/10.1093/gigascience/giab008.

78. Torgerson, W.S. (1952). Multidimensional scaling: I. Theory and method.
Psychometrika 17, 401–419.
79. Izenman, A.J. (2012). Introduction to manifold learning. Wiley Interdiscip.
Rev. Comput. Stat. 4, 439–446.
80. Roweis, S.T., and Saul, L.K. (2000). Nonlinear dimensionality reduction by
locally linear embedding. Science 290, 2323–2326.

95. Camacho, C., Coulouris, G., Avagyan, V., Ma, N., Papadopoulos, J.,
Bealer, K., and Madden, T.L. (2009). BLAST+: architecture and applications. BMC Bioinformatics 10, 421. https://doi.org/10.1186/1471-210510-421.

81. Tenenbaum, J.B., de Silva, V., and Langford, J.C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–
2323. https://doi.org/10.1126/science.290.5500.2319.

96. Umeyama, S. (1991). Least-squares estimation of transformation parameters between two point patterns. IEEE Trans. Pattern Anal. Mach. Intell. 13,
376–380.

Cell Systems 14, 844–859, October 18, 2023 859

ll
OPEN ACCESS

Synthesis

STAR+METHODSKEY RESOURCES TABLEREAGENT or RESOURCESOURCEIDENTIFIER

Chemicals, peptides, and recombinant proteins
Phusion High-fidelity DNA polymerase

NEB

NEB M0530

KAPA Library Quantification Kit Illumina

KAPA Bioscience

KK48245x Phusion HF Buffer

NEB

B0518S

dNTP

NEB

N0447

Nippon Genetics

FG-91302

Slide-seq positions

Rodriques et al.20

Single Cell Portal: https://singlecell.broadinstitute.org/
single_cell/study/SCP354/slideseq-study

Raw amplicon sequencing data
for estimating barcode overlap

This study

NCBI BioProject: PRJNA 993711

SI#1275 PS1.0-PAMlib-180720-FW
TAACTTACGGAGTCGCTCTACGGC
CTGCAGGTCGACTCTAGAGGAThis study

N/A

SI#1274 PS2.0-PAMlib-180720-RV
GGATGGGATTCTTTAGGTCCTGG
TTGTAAAACGACGGCCAGTGAAThis study

N/A

Nishimasu et al.91

N/A

Samtools v.1.9.74-gf69e678

Genome Research Limited

http://www.htslib.org/

Seqkit v0.10.1

Shen et al.92

https://bioinf.shenwei.me/seqkit/
download/

NCBI Blast+ v.2.6.0

NIH National Laboratory of Medicine

https://ftp.ncbi.nlm.nih.gov/blast/
executables/blast+/LATEST/INTERSTELLAR v.1.0.0

Kijima et al.93

https://github.com/yachielab/Interstellar

CellRanger v3.0.1

10x Genomics

https://support.10xgenomics.com/
single-cell-gene-expression/software/
downloads/latest

R v. 4.1.1

R Projecthttps://cran.r-project.org/

Python v.3.6.10

Python Software Foundation

https://www.python.org/downloads/

UMAP v.0.4.2

Anaconda Org

https://anaconda.org/conda-forge/umap-learn

Critical commercial assays
FastGene PCR/Gel Extraction Kit
Deposited data

Oligonucleotides

Recombinant DNA
Barcoded plasmid library
Software and algorithms

Other
Illumina HiSeq 2000 sequencer

Illumina

N/A

PhiX Control v3

Illumina

FC-110-3001

Simulation codes and resources

This manuscript

GitHub: https://github.com/
schiebingerlab/DNA-GPS(version of record deposited at Zenodo:
https://doi.org/10.5281/zenodo.8088532)

RESOURCE AVAILABILITY
Lead contact
Further information and requests for resources should be directed to and will be fulfilled by the Lead Contact, Geoffrey Schiebinger(geoff@math.ubc.ca).
e1 Cell Systems 14, 844–859.e1–e4, October 18, 2023

ll
Synthesis

OPEN ACCESS

Materials Availability
This study did not generate new materials.
Data and code availabilityd Sequencing data for the barcode count distribution has been deposited to NCBI BioProject (NCBI BioProject: PRJNA993711).
d This paper analyzes existing, publicly available data. The access links to the datasets are listed in the key resources table.
d All original code has been deposited at https://github.com/schiebingerlab/DNA-GPS and is publicly available as of the date of
publication. DOIs are listed in the key resources table.
d Barcode distribution data is available at https://github.com/schiebingerlab/DNA-GPS/data.
d Any additional information required to reanalyze the data reported in this paper is available from the lead contacts upon request.
METHOD DETAILS
Data generation
To generate data, we chose ground truth positions for beads and randomly generated satellite positions extending slightly beyond
the beads to ensure uniform reads. We used ground truth positions from the Slide-seq kidney, hippocampus, and cerebellum 2 datasets as well as dense grids of 100,000 beads to test scalability. For most simulations, we modelled the reads from each satellite as
following a Gaussian distribution where the width of the Gaussian determined the level of diffusion (See also Method S1). However,
we also performed simulations exploring non-Gaussian diffusion from simulated bacterial colonies (See Robustness to alternate
diffusion schemes). In addition to sBC diffusion, the density of satellite devices was a hyperparameter for data generation.
Bead quality and barcode overlap
To sample an sBC read matrix, C, we needed to define the distributions of satellite barcode redundancy and bead quality. To accountfor varying bead qualities, we utilized the distribution present in the Slide-seq kidney dataset (See Figure S2B). Slide-seq datasets
were downloaded from Single Cell Portal. cDNA sequences were extracted from the BAM file and stored as FASTQ format using
samtools.94 The reads were converted into 10x Chromium V3 format using INTERSTELLAR v1.0.0,93 and the formatted FASTQ
file was downsampled using seqkit.92 Each downsampled file was mapped to the reference genome version of mm10 using
CellRanger v3.0.1 to obtain a UMI count matrix. This resulted in the mean rpb to UMI curves shown in Figure S2. We found thatthe read to UMI curve differed between different Slide-seq samples. As our model depends on UMI while sequencing cost depends
on reads, we provide both values in our results.
Barcodes do not occur uniformly in practice leading to some satellites sharing common barcodes. We quantified the extent of thisoverlap by conducting the following experiment. We used a barcoded plasmid library that has been previously generated.91 To
generate the high-throughput sequencing library, the plasmid pUC19 encoding eight randomized nucleotides (48 possible barcode
combinations) was subjected to PCR amplification. The 1st PCR was performed with 20 mL reaction volume, composed of 1 mL ofplasmid library, 0.5 mL each of 20 mM forward (SI#1275) and 20 mM reverse (SI#1274) primers, 0.2 mL of Phusion High-fidelity DNA
Polymerase (NEB M0530), 4 mL of 5x Phusion HF Buffer (NEB #B0518S), and 2 mL of 2 mM dNTPs (NEB #N0447) with the following
thermal cycle condition: 98 C for 30 s, 30 cycles of 98 C for 10 s, 60 C for 10 s, and 72 C for 60 s, and then 72 C for 5 min for the final
extension. The 1st PCR product was then purified using FastGene PCR/Gel Extraction Kit (Nippon Genetics #FG-91302). For index
PCR to attach Illumina P5 and P7 index sequences, the 2nd PCR was performed with 20 mL reaction volume, composed of 1 mL ofplasmid library, 1 mL each of 10 mM P5 and 10 mM P7 primers, 0.2 mL of Phusion High-fidelity DNA Polymerase (NEB M0530), 4 mL of
5x Phusion HF Buffer (NEB #B0518S), and 2 mL of 2 mM dNTPs (NEB #N0447) with the following thermal cycle condition: 98 C for 30s, 15 cycles of 98 C for 10 s, 60 C for 10 s, and 72 C for 60 s, and then 72 C for 5 min for the final extension. The 2nd PCR product wasthen purified using FastGene PCR/Gel Extraction Kit (Nippon Genetics #FG-91302) and pooled. The pooled sequencing sample wasquantified using a KAPA Library Quantification Kit Illumina (KAPA BIOSYSTEMS #KK4824) and analyzed by paired-end sequencing
using Illumina HiSeq2000 with 20% PhiX spike-in control (Illumina #FC-110-3001). The sequencing reads were demultiplexed
according to the sample indices and constant sequences using NCBI Blast+ (version 2.6.0)95 with the blast-short option. Using
read alignment information, 8-mer barcodes were extracted to count each barcode abundance. The resulting barcode occurrence
distribution is shown in Figure S2C. We sampled satellite barcodes from this distribution for our simulations.
Forming the sBC count matrix
To create the sBC count matrix, we first form a matrix with no barcode redundancy where for each bead we sample a bead quality
from the Slide-seq kidney distribution and then sample the specified number of reads from the sBC distribution determined by thebead’s position. We then generate a barcode for each satellite, following the experimental distribution, and combine columns of theinitial matrix sharing a barcode. Our data generation process has three hyperparameters: (1) density of satellites, (2) diffusion level,and (3) sequencing depth. We tested a grid of four satellite densities, sBCs/cm2 ˛ [25000, 50000, 100000, 250000], six diffusionlevels, s ˛ [10, 20, 25, 30, 50, 75, 100] mm, and 11 downsampling levels, mean rpb ˛ [10, 30, 50, 70, 90, 140, 280, 555, 1100,
2225, 4445].

Cell Systems 14, 844–859.e1–e4, October 18, 2023 e2

ll
OPEN ACCESS

Synthesis

Reconstructions
UMAP is a dimensionality reduction technique that is frequently used with single-cell data to reduce a gene expression matrix to twodimensions for visualization. However, by applying it to our sBC matrix we can recover the underlying two-dimensional manifold. As
UMAP allows an arbitrary distance function, we tested Euclidean distance and cosine similarity on raw counts, row-normalized, andlog-tpm normalized data and found the row-normalized Euclidean distance resulted in the best reconstructions.
Hyperparameter selection
UMAP introduces two hyperparameters: (1) the number of neighbors to consider for each bead, n_neighbors, and (2) the minimum
distance between points in the low-dimensional space, min_dist. We tested a grid of four values for each hyperparameter, min_dist ˛[0.25, 0.5, 0.75, 1] and n_neighbors ˛ [25, 50, 75, 100], for every combination of hyperparameters from our data simulation. As we
consistently achieved good reconstructions using 60 neighbors, we fixed n_neighbors to 60 for the figures and values reported in the
text. We found the best value of min_dist to vary with diffusion level and sequencing depth, with a value of 0.25 performing best for
30 mm diffusion and a value of 1 performing better for diffusion R50 mm. Setting these two value for min_dist based only on diffusion,
we achieved reconstructions are within 5 mm of best reconstruction in more than 80% of cases (See Figure S6).
Aligning reconstructions
As distances passed to UMAP are relative, the embedding may be a rotation, reflection, scaling, or translation of the ground truth. Wealigned each embedding to the ground truth using the Kabsch-Umeyama algorithm,96 which finds the rigid transformation (rotation,reflection, scaling, and translation) that minimizes the sum of distances between corresponding points in the embedding and theground truth.
Robustness to physical parameters
We achieved mean alignment distances as low as 10 mm and could achieve 20 mm alignment distances for all but one combination ofsBC density and diffusion level from 30-100 mm (see Figure S4). In these ranges, physical parameters do not limit whether a reconstruction is possible. Rather, some combinations result in higher resolution reconstructions for the same sequencing cost. While weachieved successful reconstructions down to 20 mm of diffusion, they had high alignment errors even at the highest sequencing depth(see Figure S7). We did not achieve successful reconstructions for diffusion below 20 mm. As preliminary experiments had alreadygenerated 20,000 bacterial colonies/cm2, we did not test lower sBC densities.
While the median alignment distance is a convenient statistic to compare between reconstructions, it is also important that there
are not large number of outliers with high alignment distances, corresponding to beads that cannot be accurately placed. Figure S5
shows that in most cases >90% of beads are no more than twice the median alignment distance.
Robustness to bead quality
We repeated the simulations assuming uniform bead quality. As expected, the reconstructions improved compared to the experimental bead quality distribution. However, the improvements were moderate, with the best reconstruction only improving from 10
to 7 mm and the best alignment error per UMI curves closely tracking (see Figure S9A). This suggests the method is robust to changes
in the distribution of bead qualities. Further, we believe the experimentally obtained bead quality distribution is a conservative
estimate of what could be achieved in practice. For example, the 10x protocol achieves a less extreme distribution than Slideseq and Drop-seq which employ similar library preparation protocols (See Figure S9B).
Robustness to alternate diffusion schemes
As one potential implementation of satellite devices is through E. coli colonies, we wanted to understand the potential impact of nonuniform diffusion from non-point source satellite devices on reconstruction quality. To simulate bacterial colonies, we generated a
10 mm grid and randomly assigned a subset of pixels barcodes from the experimental barcode distribution, where the size of the subset determined the satellite device density and was a hyperparameter for the simulation. We then simulated the colonies by defining
the probability of each pixel spreading to an adjacent empty pixel at a single step, and then repeatedly simulating steps until wereached a target density of pixels with assigned barcodes. We simulated Gaussian diffusion from each point in the final grid, resulting
in irregular diffusion patterns due to the irregular colony shapes. For our simulations, we used a final density of 90%, so 10% of anchors relied solely on diffusion to receive sBC reads (See Figure S8A). As a colony must consist of multiple E. coli cells and colonies
cannot overlap, we tested lower sBC densities of 5000, 10000, 20000, and 30000 sBCs/cm2. For all other parameters, we tested thesame values used in the sweep with uniform Gaussian diffusion.
With such irregular colonies, DNA-GPS is able to achieve a resolution of 13 mm, only a 3 mm degradation from the uniform Gaussian
simulations and was still able to achieve under 30 mm resolution at as low as 25 UMI (50 rpb) (See Figure S8B). However, the robustness to physical parameters decreased, with the method only being able to achieve 20 mm resolution at 7/16 diffusion andsBC density parameter combinations and 30 mm resolution at 12/16 combinations, compared to 15/16 with uniform Gaussian
diffusion.

e3 Cell Systems 14, 844–859.e1–e4, October 18, 2023

ll
Synthesis

OPEN ACCESS

Slide-seq reconstructions
Using bead positions from the Slide-seq kidney, cerebellum 2, and hippocampus datasets we were able to achieve alignment distances as low as 15 mm and could achieve 30 mm alignment distances for all but one combination of number of satellites and diffusionlevels from 30-100 mm (See Figures S3 and S7). We believe that the reconstructions were slightly worse for the Slide-seq bead positions because only beads positioned over the tissue were included in the dataset, leading to regions without beads. UMAP assumes
that sampled points are uniformly distributed, so our reconstructions perform best when beads have close to uniform density. In
practice, all beads would be sequenced leading to roughly uniform density and making these tests a conservative estimate ofreconstruction quality. Despite this limitation, the reconstructions with the Slide-seq positions were still at the low end of thesingle-cell size range.

Cell Systems 14, 844–859.e1–e4, October 18, 2023 e4