Martin Krzywinski / Genome Sciences Center / Martin Krzywinski / Genome Sciences Center / - contact me Martin Krzywinski / Genome Sciences Center / on Twitter Martin Krzywinski / Genome Sciences Center / - Lumondo Photography Martin Krzywinski / Genome Sciences Center / - Pi Art Martin Krzywinski / Genome Sciences Center / - Hilbertonians - Creatures on the Hilbert Curve
Poetry is just the evidence of life. If your life is burning well, poetry is just the ashLeonard Cohenburn somethingmore quotes

EMBO Practical Course: Bioinformatics and Genome Analysis, 5–17 June 2017.

visualization + design

Like paths? Got your lines twisted in a bunch?
Take a look at my 2014 Pi Day art that folds Pi.

Hilbert Curve Art, Hilbertonians and Monkeys

I collaborated with Scientific American to create a data graphic for the September 2014 issue. The graphic compared the genomes of the Denisovan, bonobo, chimp and gorilla, showing how our own genomes are almost identical to the Denisovan and closer to that of the bonobo and chimp than the gorilla.

Martin Krzywinski @MKrzywinski

Here you'll find Hilbert curve art, a introduction to Hilbertonians, the creatures that live on the curve, an explanation of the Scientific American graphic and downloadable SVG/EPS Hilbert curve files.

The graphic won a Bronze medal at Malofiej 23. Art direction by Jen Christiansen. Text by Kate Wong. Spot illustrations by Portia Sloan Rollings.
Scientific American Hilbert Curve genome graphic of human, denisovan, chimp, bonobo and gorilla genomes by Martin Krzywinski. / Martin Krzywinski @MKrzywinski
Scientific American | Tiny genetic differences between humans and other primates pervade the genome. Art direction by Jen Christiansen. Text by Kate Wong. Spot illustrations by Portia Sloan Rollings.

monkey genomes

This page accompanies my blog post at Scientific American, which itself accompanies the figure in the magazine.

In the blog post I argue that the genome is not a blueprint—a common metaphor that doesn't leave room for appreciating the complexity of the genome—and talk about the process of creating the figure.

the graphic


The graphic shows the differences between the genome sequence of human and each of Denisovan, chimp, bonobo and gorilla. Differences are measured by the fraction of bases in the gene regions of human sequence that do not align to the other genome.

The approximately 1 Gb of sequence of gene regions (most introns are included) is divided into 2,047 bins which are mapped onto the Hilbert curve as circles.

The color of the circle, which represents about 500 kb of sequence, encodes the fraction of unaligned bases.

The original color scheme submitted for production was derived from the yellow-orange-red Brewer palette.

measuring differences

There's more than one way to do it.

The approach taken by the graphic is one of the simplest—this is why it was chosen. It's easy to understand and easy to explain. On the other hand, the answer depends on the state of the sequence resources for each species (especially bonobo, whose sequence assembly is in version 1) and completely overlooks the functional implications of these differences.

The real goal of identifying differences, a relatively superficial problem, is to find the subset of differences that make a difference, which is a deep problem.

Spitting images are identical within spitting error.

For example, if someone told you that Vancouver, Canada and Sydney, Australia were 85% similar, you would likely assume that (a) this metric isn't that useful to you unless it aligns to your priorities in how city similarities should be judged, (b) other metrics would give different answers, and (c) some parts of Sydney are nothing like Vancouver while others might be identical. This goes the same for genomes, except that cities are easier to figure out since we built them ourselves.

The differences will be scattered throughout the genome and will take many forms: single base changes, small insertions or deletions, inversions, copy number changes, and so on. In parts critical to basic cell function we expect no differences (e.g. insulin gene exons) while in genes that are rapidly evolving we expect to see some differences.

A comparison of protein coding genes reveals approximately 500 genes showing accelerated evolution on each of the gorilla, human and chimpanzee lineages, and evidence for parallel acceleration, particularly of genes involved in hearing.
Insights into hominid evolution from the gorilla genome sequence by Scally et al.

Parts of the genome that don't impact function are going to accumulate differences at a background rate of mutation.

uncertainty in life sciences

Any single-number statistic that compares two genomes is necessarily going to be a gross approximation. Such numerical measures should be taken as a starting point and at best as some kind of average that hides all of the texture in the data.

Statements like "the 1% difference" are incomplete because they do not incorporate an uncertainty. If you see four separate reports claiming a 1%, 2%, 5% and 7% difference, this does not necessarily mean that we cannot agree. It means that the error in our measurement is large. You might venture a guess that the answer is somewhere in the range 1–7% (at the very least).

While confidence intervals and error bars are a sine qua non in physical sciences, assessing uncertainty in life sciences is a lot more difficult. To assess the extent of biological variation, which will add to the uncertainty in our result, we need to collecting data from independent biological samples. Often this is too expensive or not practical.

To provide a sober and practical guide to statistics for the busy biologist, Naomi Altman and myself write the Points of Significance column in Nature Methods. These kinds of resources are needed as long as errors persist in the translation between statistical analysis and conclusions (e.g. `5 sigma` and P values).

Two compatible estimates can easily and wrongly be interpreted as incompatible facts.

We don't yet have a full handle on individual levels of genomic variation, especially for non-human primates for which we have a single and incomplete genome. Even for humans, although we have resources like dbSNP, which catalogue individual variation, it is common to use the canonical human reference sequence for analysis. This reference sequence is only a single instance of a human genome (in fact, parts of it are derived from different individuals).

As a result, many of the reported values (and certainly almost all that make it to popular media) are without any confidence limits and thus are likely to be interpreted as fact rather than as an estimate. This causes all sorts of problems—two compatible estimates can easily (but wrongly) be interpreted as incompatible facts.

As an example, look at the phylogenetic trees in the figure below. Without incorporating uncertainty, the top tree presents a fixed and deceptive state of what we know about the uncertainty in what we know.

Phylogenetic tree / Martin Krzywinski @MKrzywinski
Without incorporating uncertainty into results and data graphics we cannot tell how precise our observations and calculations are. (zoom)

Recent work has shed some light on the uncertainty in determining population split times. The two trees in the figure above are generated from the data in the table below, from Langergraber KE, Prufer K, Rowney C et al. 2012 Generation times in wild chimpanzees and gorillas suggest earlier divergence times in great ape and human evolution Proc Natl Acad Sci U S A 109 (39) 15716-15721.

Phylogenetic tree / Martin Krzywinski @MKrzywinski
Original and recalibrated population split times from several recent studies. (zoom)

Notice that the human/chimp/gorilla split time uncertainty overlaps the human/chimp split.

The addition of uncertainty is the inevitable consequence of making multiple measurements and upgraded analytical models. It is a blessing not a curse.

when we measure, we estimate

That our genome is "similar" to that of the chimp, bonobo and gorilla is not in dispute. How to classify and quantify the differences is an active field of research, a process that often looks like a dispute.

We do science so that our minds are changed.

We have been sequencing quickly and cheaply for less than 10 years. It's amazing how much we've been able to understand in such a short period of time. Genome sequencing (or some kind of genotyping) is now routinely done in the treatment of cancer. It is not long before a medical diagnosis will include an assessment of the full genome sequence.

As we sequence more and reflect more, we expect to change our minds. In fact, this is why we do science: so that our minds are changed.

Scientists engage the public in the process of scientific inquiry, testing and observation by way of reports in popular science media and newspapers. Understanding these reports requires that one holds as a core value to process of science and its outcomes. Groups with different agendas and a fundamentally different epistemology hijaack observations such as "In 30% of the genome, gorilla is closer to human or chimpanzee than the latter are to each other." (from the gorilla sequence paper) in an attempt to argue that our evolutionary models are sinfully wrong. They don't understand the implications of the uncertainty in our measurements (e.g. phylogenetic tree figure above) and have world outlooks that are impervious to the impact of observation.

It is certain that these genomes hold more surprises for us, but not in the way these groups claim.

Is our science incomplete? Absolutely. How do we address this? We do more science.

genome is not a blueprint

The genome is not blueprint. It's also absolutely not a recipe, which is promulgated by people who agree that it is not a blueprint. I explain my view of this here and why I think these analogies have disasterous effects on the public understanding of how their genomes (i.e. their bodies) work.

Sometimes metaphors are wonderful and they help expand our mind.

I, a universe of atoms, an atom in the universe.
—Richard Feynman

Other times they are like jailors, keeping us from having productive thoughts.

Genomics: the big blueprint

You might argue that "blueprint" is one of the closest words in meaning, so its use is justified. The trouble is that its actually very far in meaning.

Consider the following figure.

Genome is not a blueprint / Martin Krzywinski @MKrzywinski
The genome is not a blueprint and you should never say that it is. You shouldn't even say that it's like one, because it's nothing like one.

A blueprint shows you "what". A genome doesn’t encode "what". It doesn’t even encode “how”. Nor does it encode "from what". It encodes "with what", which is several degrees removed from "what". I promise that this will make sense shortly.

The reason why the blueprint analogy is pernicious is that it makes it sound like once the genome sequence is known, the rest easily follows. The reality is that these days the genome sequence is easily determined and the rest follows with great effort (or never) (see The $1,000 genome, the $100,000 analysis? by Elaine Mardis).

I'm going to try to motivate you that the analogy is false by an example. Suppose that you wanted to build a house but instead of getting blueprints from the architect, you received this strange drawing.

Genome is not a blueprint. / Martin Krzywinski @MKrzywinski
If your home had a genome, it might look like this. (zoom)

You’d be right to be confused—welcome to genome science. This house’s genome looks a lot like a set of tools and bears no resemblance to the house itself. The genome tells you nothing about (a) what the function of each tool is, (b) the effect of the tools form to its function (e.g. what are the many ways in which a hammer can diverge from its original shape before it ceases to be useful), (c) what the tools act on (this is why above I said "with what" rather than "from what"), (d) how the tools act together, and importantly (e) what the tools are used to build.

This is more of a way a genome works. It encodes the protein enzymes that make biochemical reactions possible at room temperature. In the house example, the tools encoded by the genome (e.g. saw, hammer) can be thought of automatically doing their job when they’re in the presence of the correct material (wood, nail). This is in analogy to enzymes, which mediate reactions when in physical proximity of chemical substrates.

The genome is not a code of life. It is a code of tools.

Neither wood nor nails—both essential materials for construction—appear anywhere in your home's genome. This directly translates into a biochemical example. We use sugar as a source of energy but the genome hints nothing at this—it only encodes the enzymes that act on sugar. Things are made more complex by the fact that the function of an enzyme is essentially impossible to predict without additional information, such as knowledge of functions of enzymes with similar characteristics.

You can probably imagine that the effect of changes in the home's genome is extraordinary difficult to predict. The figure below extends our example to that of your neighbour, which was recently observed to have collapsed. I’ll leave you to work out the mystery yourself.

Genome is not a blueprint. / Martin Krzywinski @MKrzywinski
Why exactly did your neighbour's home fall down? You suspect the root cause lies in its genome.

So next time someone says that the genome is a blueprint, or that it is the "code of life", point out that it is merely the "code of tools" for life, which is the emerging property of a set of chemicals confined within a physical space.

hilbert curve in genomics

The use of the Hilbert curve in genomics is not new. It appeared on the cover of Science in 2009 in connection to the 3-dimensional packing of the genome. It is an order 5 curve and just a flip of the curve I use in the Scientific American graphic. Here the corners of the curve have been smoothed out to give it a more organic and gooey feel.

Hilbert curve on cover of Science. / Martin Krzywinski @MKrzywinski
(left) Hilbert curve on cover of Science (Oct 2009) (right) Portion of Figure 2 from accompanying article Comprehensive Mapping of Long-Range Interactions Reveals Folding Principles of the Human Genome.

At least one tool exists (HilbertVis) that allows you to wrap genomic data onto the curve.

Anders S 2009 Visualization of genomic data with the Hilbert curve Bioinformatics 25 (10) 1231-1235.

I've used the Hilbert curve before to show the organization of genes in the genome. This figure shows the chromosome at a much higher resolution than would be possible if an ordinary line was used.

Chromosome 1 gene position and size on a Hilbert curve. / Martin Krzywinski @MKrzywinski
The size and position of genes on human chromosome 1. Genes implicated in cancer and generally in disease are highlighted. (zoom)

Because the Hilbert curve stretches the line into a square, it increases our ability to see details in data at higher resolution. In the figure below you can see distinct clumpiness in the organization of genes on the chromsome that is not representative of a purely random sampling.

Chromosome 1 gene position and size on a Hilbert curve. / Martin Krzywinski @MKrzywinski
Gene distribution is not random. This can be effectively demonstrated at high resolution using a Hilbert curve. (zoom)

data sources

Except for the Denisovan, the net alignments (e.g. human vs chimp net) from UCSC Genome browser were used for the analysis.

Gaps were intersected with human gene regions. For each gene, the region between the start of the first coding region and end of the last coding region was used.

human (Homo sapiens sapiens)

The RefSeq gene annotation from the UCSC Genome table browser was used. The union of all 51,010 RefSeq gene records was used.

The gene region was taken as the extent of the gene's coding sequence (CDS), not just the exons within it.

For example, for the BRCA2 gene, the RefSeq entry is

                        tx                cds               
BRCA2 NM_000059 chr13 + 32889616-32973809 32890597-32972907 

                        exons exonstart            exonend
                        27    32889616,32890558... 32889804,32890664... 

This record's contribution was the region 32890597-32972907, shown in bold above.

The total size of the union of tx regions is 1.28 Gb (20,722 coverage elements), of cds regions as defined above is 0.99 Gb (24,931 coverage elements) and of exons is 74.5 Mb (225,404 coverage elements).

Assembly version: Feb 2009 (CRCh37/hg19)

International Human Genome Sequencing Consortium 2004 Finishing the euchromatic sequence of the human genome Nature 431 (7011) 931-945.


30x sequence was aligned to the human genome at Max Planck (data portal).

Meyer M, Kircher M, Gansauge MT et al. 2012 A high-coverage genome sequence from an archaic Denisovan individual Science 338 (6104) 222-226.

chimp (Pan troglodytes)

Assembly version: Feb 2011 (panTro4)

Chimpanzee Sequencing and Analysis Consortium 2005 Initial sequence of the chimpanzee genome and comparison with the human genome Nature 437 (7055) 69-87.

bonobo (Pan paniscus)

Assembly version: May 2012 (panPan1).

Prufer K, Munch K, Hellmann I et al. 2012 The bonobo genome compared with the chimpanzee and human genomes Nature 486 (7404) 527-531.

At the moment this genome is available only on the test version of the browser.

Assembly version: Feb 2009 (CRCh37/hg19)

gorilla (Gorilla gorilla gorilla)

Assembly version: May 2011 (gorGor3.1/gorGor3)

Scally A, Dutheil JY, Hillier LW et al. 2012 Insights into hominid evolution from the gorilla genome sequence Nature 483 (7388) 169-175.

news + thoughts

Classification and regression trees

Fri 28-07-2017
Decision trees are a powerful but simple prediction method.

Decision trees classify data by splitting it along the predictor axes into partitions with homogeneous values of the dependent variable. Unlike logistic or linear regression, CART does not develop a prediction equation. Instead, data are predicted by a series of binary decisions based on the boundaries of the splits. Decision trees are very effective and the resulting rules are readily interpreted.

Trees can be built using different metrics that measure how well the splits divide up the data classes: Gini index, entropy or misclassification error.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Classification and decision trees. (read)

When the predictor variable is quantitative and not categorical, regression trees are used. Here, the data are still split but now the predictor variable is estimated by the average within the split boundaries. Tree growth can be controlled using the complexity parameter, a measure of the relative improvement of each new split.

Individual trees can be very sensitive to minor changes in the data and even better prediction can be achieved by exploiting this variability. Using ensemble methods, we can grow multiple trees from the same data.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. Nature Methods 14:757–758.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. Nature Methods 13:803-804.

...more about the Points of Significance column

Personal Oncogenomics Program 5 Year Anniversary Art

Wed 26-07-2017

The artwork was created in collaboration with my colleagues at the Genome Sciences Center to celebrate the 5 year anniversary of the Personalized Oncogenomics Program (POG).

Martin Krzywinski @MKrzywinski
5 Years of Personalized Oncogenomics Program at Canada's Michael Smith Genome Sciences Centre. The poster shows 545 cancer cases. (left) Cases ordered chronologically by case number. (right) Cases grouped by diagnosis (tissue type) and then by similarity within group.

The Personal Oncogenomics Program (POG) is a collaborative research study including many BC Cancer Agency oncologists, pathologists and other clinicians along with Canada's Michael Smith Genome Sciences Centre with support from BC Cancer Foundation.

The aim of the program is to sequence, analyze and compare the genome of each patient's cancer—the entire DNA and RNA inside tumor cells— in order to understand what is enabling it to identify less toxic and more effective treatment options.

Principal component analysis

Thu 06-07-2017
PCA helps you interpret your data, but it will not always find the important patterns.

Principal component analysis (PCA) simplifies the complexity in high-dimensional data by reducing its number of dimensions.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Principal component analysis. (read)

To retain trend and patterns in the reduced representation, PCA finds linear combinations of canonical dimensions that maximize the variance of the projection of the data.

PCA is helpful in visualizing high-dimensional data and scatter plots based on 2-dimensional PCA can reveal clusters.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Principal component analysis. Nature Methods 14:641–642.

Background reading

Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.

...more about the Points of Significance column

`k` index: a weightlighting and Crossfit performance measure

Wed 07-06-2017

Similar to the `h` index in publishing, the `k` index is a measure of fitness performance.

To achieve a `k` index for a movement you must perform `k` unbroken reps at `k`% 1RM.

The expected value for the `k` index is probably somewhere in the range of `k = 26` to `k=35`, with higher values progressively more difficult to achieve.

In my `k` index introduction article I provide detailed explanation, rep scheme table and WOD example.

Dark Matter of the English Language—the unwords

Wed 07-06-2017

I've applied the char-rnn recurrent neural network to generate new words, names of drugs and countries.

The effect is intriguing and facetious—yes, those are real words.

But these are not: necronology, abobionalism, gabdologist, and nonerify.

These places only exist in the mind: Conchar and Pobacia, Hzuuland, New Kain, Rabibus and Megee Islands, Sentip and Sitina, Sinistan and Urzenia.

And these are the imaginary afflictions of the imagination: ictophobia, myconomascophobia, and talmatomania.

And these, of the body: ophalosis, icabulosis, mediatopathy and bellotalgia.

Want to name your baby? Or someone else's baby? Try Ginavietta Xilly Anganelel or Ferandulde Hommanloco Kictortick.

When taking new therapeutics, never mix salivac and labromine. And don't forget that abadarone is best taken on an empty stomach.

And nothing increases the chance of getting that grant funded than proposing the study of a new –ome! We really need someone to looking into the femome and manome.

Dark Matter of the Genome—the nullomers

Wed 31-05-2017

An exploration of things that are missing in the human genome. The nullomers.

Julia Herold, Stefan Kurtz and Robert Giegerich. Efficient computation of absent words in genomic sequences. BMC Bioinformatics (2008) 9:167


Sat 01-07-2017
Clustering finds patterns in data—whether they are there or not.

We've already seen how data can be grouped into classes in our series on classifiers. In this column, we look at how data can be grouped by similarity in an unsupervised way.

Martin Krzywinski @MKrzywinski
Nature Methods Points of Significance column: Clustering. (read)

We look at two common clustering approaches: `k`-means and hierarchical clustering. All clustering methods share the same approach: they first calculate similarity and then use it to group objects into clusters. The details of the methods, and outputs, vary widely.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.

Background reading

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

...more about the Points of Significance column

What's wrong with pie charts?

Thu 25-05-2017

In this redesign of a pie chart figure from a Nature Medicine article [1], I look at how to organize and present a large number of categories.

I first discuss some of the benefits of a pie chart—there are few and specific—and its shortcomings—there are few but fundamental.

I then walk through the redesign process by showing how the tumor categories can be shown more clearly if they are first aggregated into a small number groups.

(bottom left) Figure 2b from Zehir et al. Mutational landscape of metastatic cancer revealed from prospective clinical sequencing of 10,000 patients. (2017) Nature Medicine doi:10.1038/nm.4333

Tabular Data

Tue 11-04-2017
Tabulating the number of objects in categories of interest dates back to the earliest records of commerce and population censuses.

After 30 columns, this is our first one without a single figure. Sometimes a table is all you need.

In this column, we discuss nominal categorical data, in which data points are assigned to categories in which there is no implied order. We introduce one-way and two-way tables and the `\chi^2` and Fisher's exact tests.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Tabular data. Nature Methods 14:329–330.

...more about the Points of Significance column

Happy 2017 `\pi` Day—Star Charts, Creatures Once Living and a Poem

Tue 14-03-2017

on a brim of echo,

capsized chamber
drawn into our constellation, and cooling.
—Paolo Marcazzan

Celebrate `\pi` Day (March 14th) with star chart of the digits. The charts draw 40,000 stars generated from the first 12 million digits.

Martin Krzywinski @MKrzywinski
12,000,000 digits of `\pi` interpreted as a star catalogue. (details)

The 80 constellations are extinct animals and plants. Here you'll find old friends and new stories. Read about how Desmodus is always trying to escape or how Megalodon terrorizes the poor Tecopa! Most constellations have a story.

Martin Krzywinski @MKrzywinski
Find friends and stories among the 80 constellations of extinct animals and plants. Oh look, a Dodo guardings his eggs! (details)

This year I collaborate with Paolo Marcazzan, a Canadian poet, who contributes a poem, Of Black Body, about space and things we might find and lose there.

Check out art from previous years: 2013 `\pi` Day and 2014 `\pi` Day, 2015 `\pi` Day and and 2016 `\pi` Day.