Science Advances Cover
6 January 2023, Issue 9, Volume 1
contents
The cover design accompanies the publication of INTERSTELLAR — Kijima, Y. et al. A universal sequencing read interpreter (2023) Science Advances 9. — a kind of universal sequencing read interpreter. Its role is to convert sequencing reads from one sequencing platform to another.
The need for this arises because each platform has a different format for its barcodes that store single cell, spatial and molecular identifiers.
Given that INTERSTELLAR is a kind of “Rosetta Stone” for reads, I thought it would be interesting to try to create something that looked like a puzzle, while encoding barcode sequences from various platforms.
For example, here are some sets of barcodes that all store the same information but vary only by their format.
# 10X, quartz and drop-seq barcodes ATGAAAGAGCGGGTATCCTTAGTCTTCA TACTACGGTTACGGTGTCTTTT AAAAGGTGTAAATTAACCAC CCGTGAGAGTTCTGGCCCAGACTTTATT TTACCGTGGCCTCTTTGCTAGG AAAGTGCCACAACTGCGGAA GCATGATGTCAAGCAGTGCAGGTCCTTG TCTCACTTCACTCCGCTCGCGG AAAATCAGTACGCGGAGTGA GAGAGGTTCCCAATAGCTCTGCTATGGC ACTTCAATTCTGCCGTATATAT AAATCCATAGAGGGCCACGA GTGTCCTCAGACAGCATGGTTTATTCGC GCGCAATAGTCTCCAGGGGCGG AAATGGGGTCAGCCAGTTCG ...
Barcode bases are encoded onto the 2-dimensional faces of hypercubes by oriented triangles.
Bases are assigned to faces by traversing the faces in order of the coordinates that correspond to the face's plane.
For example, suppose we want to encode ATGAAA onto a 3-dimensional cube. The cube has 6 faces, which we enumerate as follows
[0] xy x,y,0 A [1] xy x,y,1 T [2] xz x,0,z G [3] xz x,1,z A [4] yz 0,y,z A [5] yz 1,y,z A
The first is the face in the `xy` plane at `z=0`, the second in the `xy` plane at `z=1`. We then advance to the next dimension for the second component of the plane coordinate — bringing us to the `xz` plane at `y=0` and `y=1`.
When we go to higher dimensions, the sample process applies. Except now, we have more faces — `2^d` for `d` dimensions. For example, a `d=5` cube has 80 faces to which we can encode 80 bases as follows.
[0]xy000A [1]xy001T [2]xy010G [3]xy011A [4]xy100A [5]xy101A [6]xy110G [7]xy111A [8]x0z00G [9]x0z01C [10]x0z10G [11]x0z11G [12]x1z00G [13]x1z01T [14]x1z10A [15]x1z11T [16]x00u0C [17]x00u1C [18]x01u0T [19]x01u1T [20]x10u0A [21]x10u1G [22]x11u0T [23]x11u1C [24]x000vT [25]x001vT [26]x010vC [27]x011vA [28]x100vC [29]x101vC [30]x110vG [31]x111vT [32]0yz00G [33]0yz01A [34]0yz10G [35]0yz11A [36]1yz00G [37]1yz01T [38]1yz10T [39]1yz11C [40]0y0u0T [41]0y0u1G [42]0y1u0G [43]0y1u1C [44]1y0u0C [45]1y0u1C [46]1y1u0A [47]1y1u1G [48]0y00vA [49]0y01vC [50]0y10vT [51]0y11vT [52]1y00vT [53]1y01vA [54]1y10vT [55]1y11vT [56]00zu0G [57]00zu1C [58]01zu0A [59]01zu1T [60]10zu0G [61]10zu1A [62]11zu0T [63]11zu1G [64]00z0vT [65]00z1vC [66]01z0vA [67]01z1vA [68]10z0vG [69]10z1vC [70]11z0vA [71]11z1vG [72]000uvT [73]001uvG [74]010uvC [75]011uvA [76]100uvG [77]101uvG [78]110uvT [79]111uvC
Here, I've shortened how a face is described. For example xy011A is the face in the `xy` plane at `z=0, u=1, v=1` on which we encode an A.
Given a hypercube whose faces encode a sequence, to decode the sequence we need to know the orientation of unit axes in space. This allows us to figure out the coordinates of each vertex.
Once we have the coordinates, we traverse the faces in the order described above and look at its triangle. If the triangle has a corner at `[0,0]` of the face plane, then the base is an A. If the triangle has a corner at [0,1]`, it's a C. And so on.
For example, a face x0z11 will be a square in the `xz` plane. If we see a tringle corner at `(x,z) = (0,0)`, then we have an A.
You can't easily decode the sequence from a 2-dimensional image of a cube — even if the coordinate axes were shown, some faces would be hidden by others in the image (especially as the number of dimensions is increased).
The code that creates the images is based on the work I did for Max Cooper's Ascent video from his Unspoken Words album.
Below, I'll walk through some early prototypes of the design. Each shows an array of 4 × 4 cubes encoding random sequence. Each cube is randomly rotated.
Even with only black and white, if I use a difference blend (e.g. white on white makes black, and vice versa), interesting patterns emerge.
If I start to shrink the triangles towards their corners (here by 50%), the design gains space and the arrangements of triangles becomes even more interesting.
Shrinking the triangles even more (by 75%), we start to see even more room — perfect to accomodate more dimensions.
When we go to `d=6` dimensions, our cubes now have 192 faces. In this image, edges are also drawn. You can see how diverse the 2-dimensional projections are. These images are very similar to the scene at 1:44 in the Ascent video, with the only difference being that Ascent uses `d=5` and (at this point in the video) the cube corners have not yet appeared.
Once we hide the edges, the corners, how by themselves, give a sense of a flock of birds.
Rich complexity in the patterns arise when we enlarge the triangles ‐ here shrunk by only 50%.
Time for some color. I took the viridis color maps and filled the triangles with a gradient that mapped their z coordinate.
Below are takes that use the viridis color map with half- and full-sized triangles.
While I found the viridis scheme to be a little too cold, the inferno palette feld just the right amount of warmth.
I also experimented with blending two color maps together when the full face was drawn. These don't encode any sequence, but have a very pretty look to them.
These all look like jewels and at `d=6`, a blend of three cubes, each with a different color map, looks very intriguing. Hhere, I blend three cubes that use viridis, inferno and magma color maps. Magma is very similar to inferno, except it tends more towards the purple at its centre.
Below, I show all individual images from which I made selections for a given version of the final design. There were 6 designs.
For each of the 3 sequence platforms, I tried inferno, plasma, magma, turbo, viridis, mako and white color maps. The inferno, magma and plasma maps are practically identical. For subsequent designs, I won't show images that use the magma or plasma maps.
The final designs all show three superimposed cubes, each with its own rotation. Two cubes use a color map and one is drawn with white triangles — blended together with various Photoshop blend modes.
The first design is a close crop of the cubes. Below I show all the images by color map and platform.
The design used the inferno color maps for 10X and Quartz layers and the white map for the Drop-seq layers. Below, I show how these were blended together.
Blending two inferno cubes creates a lot of saturated colors, without a strong sense of depth. The third layer (white, hue blend) very nicely creates a tapering off effect.
Although this design only uses `d=4` dimensions, it's one of my favourites. It's the only one that shows an array of cubes. In each cell of the array, you see the same set of three cubes (for each of the sequencing platforms) — the only thing that is different is the rotation.
The simplest of all designs — and my favourite. The magic sauce in this design is the soft light blend mode for the second cube.
At `d=8` dimensions, each cube has 1,792 faces. In total, there is about 5.3 kb of sequence encoded here.
The last design pushes to `d=9` dimensions, where now a cube has 4,608 faces.
Symmetric alternatives to the ordinary least squares regression
What immortal hand or eye, could frame thy fearful symmetry? — William Blake, "The Tyger"
This month, we look at symmetric regression, which, unlike simple linear regression, it is reversible — remaining unaltered when the variables are swapped.
Simple linear regression can summarize the linear relationship between two variables `X` and `Y` — for example, when `Y` is considered the response (dependent) and `X` the predictor (independent) variable.
However, there are times when we are not interested (or able) to distinguish between dependent and independent variables — either because they have the same importance or the same role. This is where symmetric regression can help.
Luca Greco, George Luta, Martin Krzywinski & Naomi Altman (2025) Points of significance: Symmetric alternatives to the ordinary least squares regression. Nat. Methods 22:1610–1612.
Beyond Belief Campaign BRCA Art
Fuelled by philanthropy, findings into the workings of BRCA1 and BRCA2 genes have led to groundbreaking research and lifesaving innovations to care for families facing cancer.
This set of 100 one-of-a-kind prints explore the structure of these genes. Each artwork is unique — if you put them all together, you get the full sequence of the BRCA1 and BRCA2 proteins.
Propensity score weighting
The needs of the many outweigh the needs of the few. —Mr. Spock (Star Trek II)
This month, we explore a related and powerful technique to address bias: propensity score weighting (PSW), which applies weights to each subject instead of matching (or discarding) them.
Kurz, C.F., Krzywinski, M. & Altman, N. (2025) Points of significance: Propensity score weighting. Nat. Methods 22:638–640.
Happy 2025 π Day—
TTCAGT: a sequence of digits
Celebrate π Day (March 14th) and sequence digits like its 1999. Let's call some peaks.
Crafting 10 Years of Statistics Explanations: Points of Significance
I don’t have good luck in the match points. —Rafael Nadal, Spanish tennis player
Points of Significance is an ongoing series of short articles about statistics in Nature Methods that started in 2013. Its aim is to provide clear explanations of essential concepts in statistics for a nonspecialist audience. The articles favor heuristic explanations and make extensive use of simulated examples and graphical explanations, while maintaining mathematical rigor.
Topics range from basic, but often misunderstood, such as uncertainty and P-values, to relatively advanced, but often neglected, such as the error-in-variables problem and the curse of dimensionality. More recent articles have focused on timely topics such as modeling of epidemics, machine learning, and neural networks.
In this article, we discuss the evolution of topics and details behind some of the story arcs, our approach to crafting statistical explanations and narratives, and our use of figures and numerical simulations as props for building understanding.
Altman, N. & Krzywinski, M. (2025) Crafting 10 Years of Statistics Explanations: Points of Significance. Annual Review of Statistics and Its Application 12:69–87.