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Monday, July 16, 2018

Seashell Simulation

(Book image from large online vendor.)
I've decided it's about time I did a book review. The book is probably not going to already be on your reading list. You are likely to have never heard of it and if you brought it up at a party, I don't expect you'd see a glimmer of recognition among your conversational targets. That said, I think it is a important book because it approaches an interesting topic in biology in a different way than most biology books and in doing so may reach an audience which normally wouldn't connect with biology books.

The book is: "The Algorithmic Beauty of Sea Shells", by Hans Meinhardt (ISBN 3-540-44010-0). I own a copy of the third edition in English. The first version was printed in 1995 in Germany.

At first glance, the book appears to be about how the patterns on sea shells are formed. The book talks very little about molluscs, however. In the first chapter, Meinhardt introduces us to the idea of dynamical systems and how they're involved everywhere in the origin of patterns in the world we live in. From sand dunes to fern leaves, everything we see is a snapshot of a dynamical system. He then goes on to introduce seashell patterns as the history of a complicated dynamic system that played out over the life of the animal.

Chapters 2-9 develop an increasingly detailed mathematical model describing more and more complex patterns found on seashells. You don't have to be able to follow the math to follow the discussion. There are lovely photos and images from the author's computer simulations at every turn. However, if you are interested in the math, the essentials are laid out for you to explore. This detailed mathematical description of the biology is what is often lacking in biology books and what may attract the interest of people who normally would shy away from the "soft-science" that biology is often perceived to be.

Chapter 10 discusses efforts to mathematically model the shapes of seashells. Again, the math is only written out lightly and there are numerous figures illustrating the efforts that have come out of the research into the subject.

Chapter 11 introduces a computer program the author wrote to generate the many simulations illustrated throughout the book. The software comes with the book in the form of a CD-ROM and can can be run on any modern computer using DOSBox, an emulator of the DOS operating system on an x86 computer. This chapter can be entirely ignored if you're not interested in the software.

Chapter 12 takes the lessons learned in chapters 2-9 and applies them in a simplified way to the more complicated biology that is responsible for how plants, animals, and other organisms develop. If you're interested in how the bones of chicken wings (or our arms) are laid out, this is the chapter that might gain your interest. The topics discussed here are much less worked out than the detailed analysis of how seashell patterns are formed.

When I first came upon this book, I was already a biology student at university who also did extensive computer programming. and math. The book spoke to me in a way that no biology book had done before. If you are interested in math as applied to biology, or in how you can convince computers to do complex math, this book will probably be of great interest to you. If you are interested in the complexities of biology and how we can approach the beginnings of an understanding about them, this book will probably be of great interest to you. If you have no interest in math or biology, then this book will probably not be for you. (Also. What are you doing here at this blog?)

I found the software included with the book to be clunky and slow. It is written in basic and run through a slow interpreter. I decided it would be fun and educational to re-implement the software in a faster language. I was using Turbo Pascal and so began writing. After several years, during which many other things took up most of my time, I had written a program which replicated much of the original software.

The figure at right is from my own software. It takes about 1% of the time to compute as it did in the original program, so it is much easier to play around with generating many different versions. Unfortunately, my program isn't yet complete. There are numerous simulations where my output doesn't quite match the author's. Whenever I am able to dedicate some time to working on this project, I find I am able to resolve more issues, but it will still take some time yet before I am "done".

Eventually, I'd like to write up a detailed description of what I learned while re-implementing the software. If I found the time, I'd like to extend the software in new directions. I've done some initial work towards simulating more realistic 2d clusters of cells, but without any of the complicated math needed for pattern generation. I'd like to explore the evolutionary dynamics that can lead to complex pattern formation. (Things like the various forms of mimicry and what not.) For now, I've put up the various figures I've generated at my Flickr account.


Monday, July 9, 2018

In Miniature

My unnamed micro-tomato variety.
I've been growing miniature-sized tomato plants for several years. They first got my attention because I could grow them in a balcony-railing planter right outside my kitchen. Soon after I decided I wanted to breed new varieties that could grow in the same tiny spaces. A few years in, I'm stabilizing one new micro-tomato variety that produces larger fruit than any of the varieties I started with. (Later on in the growing season, I'll be able to illustrate the size difference in the fruit.)

Breeding a plant to be shorter can allow it to direct more of its resources into producing the fruit or seeds we're interested in rather than the stems we find less useful. This reallocation comes at the cost of the plant being overgrown by weeds much easier, so the plants require our assistance to do well.

Efforts in the 1930s-1960s to breed wheat, barley, rice, and maize into shorter, more productive versions is part of what we now refer to as the Green Revolution. Though changes in crop production systems and agricultural inputs also were also developed during this period, the alteration of plant structure through breeding efforts is considered to have been a major factor responsible for increasing grain production during that time period.

There are efforts to produce dwarfed tomato varieties for field production, such as the Ground-Dew and Ground-Jewel varieties from the University of Minnesota. These are a size up from the micro varieties I've been working with.
Right now I have eleven plants of my micro-tomato variety growing in a two square foot planter. A single normal sized plant will occupy a much larger space. It will be interesting to compare the production of my micro plants vs. an individual normal sized plant in my garden by the end of the growing season.

Even if the micros can produce more mass of tomatoes for a given area than a normal sized variety, it doesn't necessarily mean such a small variety would be useful for field-scale production. In a small planter, I can keep ahead of weeds to a degree that would be cost-prohibitive in a field situation.

Until recently, I hadn't thought about growing miniature versions of other crops. A few days ago I learned of a corn variety called, "Mini-Maize". It, like the first micro-tomatoes was bred for use as a research plant. The smaller size and shorter life-cycle allows more plants and more generations to be grown in the limited spaces available in a research biology lab. A plant biology researcher I interact with occasionally on Twitter has offered to send me some seeds for this corn, so maybe I'll be adding this crop to my balcony garden.

Unknown dwarfed sunflower mutant.
A few years ago I found this photo of a mutant sunflower that came out of some research program. I haven't been able to find any detailed description of it, nor can I currently find where the photo came from. Like the other dwarfed crops I've mentioned, I can imagine this plant might be more efficient at seed production with respect to area. I can also imagine how any weed pressure at all might negate those gains. I'd really love to have seeds from such a plant, as I can easily imagine growing them on a windowsill.

What is it that makes a plant dwarfed? The classical story is of hormone production or response. Gibberellins are one group of plant hormones that , among other roles, are responsible for stem elongation. If a plant produces lower levels of these gibberellins, or the receptors that allow cells to respond to them, then the plant will have shorter stems than usual.

This can potentially happen without reducing the size of other plant parts, resulting in short plants with normal sized leaves and fruit. This ideal reallocation of energy resources in the plant to our goals doesn't always happen. In the real world, the fruit or seed cluster size is often reduced somewhat along with the overall size reduction because of a link between gibberellins and meristem size. A smaller floral meristem results in a smaller flower and then fruit. Recent research suggests stem elongation and fruit size are regulated by gibberellins via different pathways, so we may be able to resolve the issue in the future and thus further increase crop productivity.


Thursday, April 5, 2018

The Naming of Things

If you've been following me here for a bit, you've probably noticed I'm interested in plant breeding (especially garden veggies). My main goals are to have healthy plants that grow and produce well for me with minimal inputs in my short-season climate. The measure of, "tasty" I go by is what tastes good to me and my family, with what other people consider tasty (when I occasionally do taste-tests) held to a lesser significance.

Two large cherry sized, blocky, white tomatoes. They're sitting on a notebook with a sketched map of the garden, showing where all the plants are and which plants were grown from the same batches of seed. There is a blue pen pointing at the specific plant which produced the fruit.
From 2017, with garden notes.
I've been working with tomatoes for several years and have developed some more fine-tuned ideas about what I want the plants to become. One of my lines, seen at right, is approaching stability. That is to say, most plants from one year to the next produce very similar fruit. The fruit are blocky, large-cherry sized, white (well, paler than yellow) in color, and have a very thick outer fruit-wall (not the skin). They've tested well with people in and outside my immediate family, so I've been thinking about the possibility of distributing their seed in the future.

A few dozen of the large white cherry tomatoes sitting on a white plastic cutting board.
From 2016.
In my personal notes, I've been using the rather uncreative name of, "Abbey White" for these tomatoes. It is sufficiently descriptive to let me know what I'm talking about in my notes, but it isn't a name I expect to attach to the variety when/if I start distributing it. I could easily adjust it to, "Abbey's White", but I'm not sure I want to go with that either.

In the forground is a ceramic bowl filled with diced white tomatoes. In the background is a large wooden cutting board covered in white, yellow, and orange tomatoes (as well as a few green tomatilloes).
From 2016.
"Wait. Tomatoes are red, right!?" A white tomato might seem kinda unusual, but it's just one of a very wide spectrum of colors that tomatoes can be found in. (Check out these companies I have no affiliation with: Artisan Seeds, Baker Creek Heriloom Seeds, TomatoEden, and SeedSavers Exchange. There's so much more diversity in color and taste available if you're willing to grow tomatoes from seed.) My tomatoes tend to be any color but red. Red fruit that have turned up in my garden have tended to have a taste I didn't favor, so over a few years I stopped growing as many red tomatoes. I expect I'll need to bring in some new genetics before I can grow red tomatoes that will taste good to me.

While I was thinking about how to go about naming this variety (and others in the future), I came across twitter user @JanelleCShane. She's been playing with Recurrent Neural Networks (basically a type of AI (specifically a type of machine learning)) trained on diverse datasets, like fruit names (or knitting patterns (or Irish melodies)), so I tweeted:

(I only later noticed my garbled grammar.) I was somewhat surprised when she responded back, asking if I had a list of tomato variety names she could train her AI with. I didn't, but I was pretty sure I could pull one together pretty quickly from online resources. After some looking, I found several sources ([1], [2], [3], [4], [5], [6]) with large lists of tomato variety names. To avoid spending too much time gathering the names, I wrote web scrapers to process each source and output text files with lists of names. In total, across the six sources, I collected 11,719 distinct tomato variety name strings. Some may represent extinct varieties. Some are in other languages. Some are numerical codes. There's also capitalization and spelling variations. I threw them all into a file that Janelle could use to train her AI.

Have a look at her blog post on the tomato name trained AI at: http://aiweirdness.com/post/172622965862/tomatonames

So. What did the trained AI come up with? Well, at first the AI got overly fascinated with the numerical code names in the training dataset. It produced lots of new "names" that would be quite not useful for naming a new variety. Janelle stripped out most of the code names from the list and trained the AI again.

This time there were some really good results, some really wrong results, and all sorts of weirdness in between. I've highlighted some of my favorites from each category.

The Good,the Weird,and the Wrong.
  • Floranta
  • Sweet Lightning
  • Speckled Boy
  • Flavelle
  • Market Days
  • Fancy Bell
  • Pinkery Plum
  • Mountain Gem
  • Garden Sunrise
  • Honey Basket
  • Cold Brandy
  • Sun Heart
  • Flaminga
  • Sunberry
  • Special Baby
  • Golden Pow
  • Birdabee
  • Sandwoot
  • Bear Plum
  • The Bango
  • Grannywine
  • Sun Burger
  • Bungersine
  • First No.4
  • Smoll Pineapple
  • The Ball
  • Golden Cherry Striped Rock
  • Eggs
  • Old German Baby
  • Frankster Black
  • Bumbertime
  • Adoly Pepp Of The Wonder
  • Cherry, End Students
  • Small Of The Elf
  • Champ German Ponder
  • Pearly Pemper
  • Green Zebra Pleaser
  • Flute First
  • Speckled Garfech
  • Green Dork
  • Cluster Gall
  • Shirve’s Gigant Bullburk
  • Giant Ballsteak
  • Black Crape
  • Brandywine, True Grub
  • Caraball
  • Ranny Blue Ribber
  • Roma Wasting Star
  • Scar Giant
  • Bug Beauty
  • Banana Placente
  • Bananana
  • Stoner
  • Speckled Bake
  • Ruck
  • Green Boor
  • Wonder Bagg
  • Sun Bung
  • Bellende
  • Shart Delight
  • Solad Piss

There were also a collection that would fit perfectly among the real tomato names, though they'd be kinda strange in other contexts.
  • Matt's Sandwich
  • Indigo Tree
  • Striped Hollow Potato Leaf
  • Lelly's Yellow Stuffers
  • Terra Pink Strain
  • Greek Boar
  • Ton's Oxheart
  • Babla's German Paste
  • Mortgage Lifter, Honey Blues

I really like when the AI tried to name a tomato after a person. It didn't have enough examples for real human names, but it gave it a good solid try.
  • Matt's Sandwich
  • Lelly's Yellow Stuffers
  • Ton's Oxheart
  • Babla's German Paste
  • Shirve’s Gigant Bullburk

Amusingly, the AI came up with an existing name that wasn't in the training dataset. "Sunberry" is the name of another fruit. It's a close relative of the tomato, so I think I'll call that a positive score for the AI.

Do any of these names fit my tomato? I'm not sure. I do rather like, "Flavelle" and, "Mountain Gem". I'll probably have to let the ideas ferment a while before I come to a decision.

I have recently seen a tomato that the name, "Speckled Garfech" would be perfect for. It came out of someone else's breeding program, so I won't share a photo. Imagine a yellow/orange striped tomato covered in green spots.
Two photos combined. The top half is a photo of a large yellow ceramic bowl filled with small cherry tomatoes. The cherry tomatoes area a mix of white and pale orange with a pink blush on one end. The bottom half is a photo of a closeup of a single larger tomato that is white with pale dark stripes. There are smaller red tomatoes and other items in the background.
From 2017.

I've got a couple more tomato lines that I'd like to stabilize (photographs at right). The upper photo shows a mix of small, very sweet cherries in pale-yellow/white with a pink blush on the bottom end of some. I'll be growing seeds from the ones with the blush. I expect the same phenotype will turn up next year, but I'm also sure there are lots of recessive alleles still hiding in them (for larger fruit, other tastes, and not having the blush).

The lower photo is of a larger, meaty white with pale stripes. This one is a bit further along already thanks to some lucky genetics, even though this phenotype only appeared in the last year. The fruit color, size, and shape are all due to recessive alleles, so those traits should already be stable. The stripes, flavor, and plant growth details probably won't be stable yet. I'll be growing several seeds from this fruit this year to find out.


Tuesday, March 20, 2018

Genetics of Male-Sterile Plants

Male sterile plants are an incredibly important piece of classical biotechnology. (To be clear, they're not the result of "genetic engineering".) They allow the efficient production of hybrid varieties, which dominate the corn, rice, sunflowers, etc. markets because of their high productivity (due to heterosis, hybrid vigor) and consistency (due to genetic uniformity).

Without male-sterile genetics a seed producer has to prevent pollen from one parent from being transferred to the other parent, somehow. This is time-consuming and arduous work (like detasseling corn), or was simply impossible (like with wheat). With male-sterile genetics there is no pollen to worry about in one parent, so there is no need for intensive efforts to prevent pollen transfer. All a seed producer has to do is grow the male-sterile plant inter-cropped with the intended pollen-donor, then collect seeds only from the male-sterile plant. Every seed will be a hybrid. It's as simple as that!

Most male-sterile mutations can be found in cytoplasmic DNA. The mutations can be found sporadically or generated by various experimental methods. With cytoplasmic-male-sterile mutants, all progeny of the plant will also be male-sterile. Once they have been found, they can be introduced into any variety (with some effort) by traditional breeding methods.

At the top are two circles. Yellow at left, with a female symbol beside it; pink at right, with a male & female symbol beside it. Immediately below them, halfway betwen, is another circle representing a hybrid of the above circles. This one is half yellow and half pink, to illustrate the genetic contribution from the parents in the top row. There is only a female symbol beside this circle. There are eleven further circles below. Each is placed horizontally halfway between the previous hybrid and the original pink circle. In each subsequent hybrid circle, the proportion of yellow (as a pie diagram slice) is reduced by half. All the subsequent hybrid circles only have the female symbol beside them. The very bottom circle is filled entirely in pink, representing a male-sterile version of the original [pink] variety.
Fig 1.
We start with a target variety (pink in diagram at left) that produces normal pollen and a source variety with a cytoplasmic-male-sterile trait (yellow in diagram at right). We cross the two varieties, with the first variety as the pollen-donor. The resulting seeds all carry the male-sterile trait, but only 50% of their genetics are like the target variety.

We cross the resulting plants back to the target variety and the new seeds will share 75% of their genetics with the target variety. If we do this backcross again, the next generation will be 87.5% identical to the target variety. (Then 93.75%, then 96.875%, then 98.4375%.) Each generation brings our male-sterile plants closer and closer (by 50% of remaining difference) to our target variety. Eventually the only difference between our target variety and the male-sterile plants is the male-sterility trait itself.

At this point, we've made a male-sterile version of our initial target variety. It can then be used in making large numbers of F1 hybrid seed. As long as the original target variety is maintained, the male-sterile version of that variety can also be maintained by continuing to cross with it.

The figure was drawn from a vague memory of a similar figure illustrating conversion of a sunflower variety into a male-sterile version. I saw the figure years ago and I think it was associated with some USDA research. I wasn't able to find it while writing this, but I'll add a note here with the citation/link if I come across it later. The original author/artist deserves the credit for the method of visualizing the illustrated concept.

(The figure also illustrates the process of introducing any single dominant trait into a target variety via recurrent back-crossing, with dominant-carrying individuals chosen at each generation. With recessive traits, it is more complicated.)

Similar to previous figure, but after every two generations two rows (2 and 3, respecitvely) of circles are added in to represent the selfing and screening for double-recessives that must be done. In total, this figure is much longer and appears much more complicated.
Fig 2.
Less commonly, a male-sterile mutation can be found in nuclear DNA. These are also called genetic-male-sterility and are harder to work with because they're usually recessive. With recessive traits (male-sterile or otherwise), you have to do test selfings every two generations in order to be sure you can re-capture the double-recessive individuals for the next back-cross generation.

In the figure at right, I have each circle labeled with their genotype with respect to the recessive male-sterile trait. ("msms" is the genotype corresponding to the male-sterile phenotype.) Each circle is filled in yellow and pink to represent the contribution from the genomes of the initial strains, as in the previous figure.

As a result of the additional complexity of maintaining and using male-sterile traits caused by nuclear mutations, very few varieties have been developed using them. (A couple are mentioned in [link].) As soon as a cytoplasmic-male-sterile trait is found or made for a species, it would become the trait of choice by seed producers.

The utility of any male-sterile trait is limited to those who are trying to produce large numbers of consistent F1 hybrid seed. These traits would be neutral or positive for home gardeners who don't save seed from year to year. (Positive because they're cheaper to produce than regular F1 seed.) Anyone who saves seed from year to year, from home-gardeners to amateur plant breeders like myself, would probably find the traits annoying and want to avoid them.

With the small number of plants in each generation that I have space to grow for most of my projects, I really don't want a few (or most (or all)) of them to be partly sterile. Fortunately, like any other negative trait, you can select against it if it does turn up in your plant breeding projects and it will soon cease to be a significant issue for you.


Wednesday, March 7, 2018

Potato Onion and Gene Networks

I've been growing onions in my garden for a couple years. Like most of my garden veggies, they're not exactly the typical sort. A few years back I received a large sample of "potato onion" true seed derived from work by Kelly Winterton. Potato onions are an old-fashioned perennial form of the typical garden onion (Allium cepa). The "potato" in their name is because they're grown by planting some of the previous year's crop, like as is done with potatoes.

Kelly's introduction into potato onion breeding came from a lucky break, when he planted some of his onions in the fall to see if they could overwinter in the ground at his northerly location. The next season, all of those bulbs flowered prolifically. The important thing he did was to save all those seeds an then try growing them the next year, next to his pre-existing potato onion clones. The high diversity and robust growth of his seedlings caught his attention and started a bit of a movement. (For more details of his work, read through his site.)

Seedling onions, next to seedling Siberian irises.
I'd read about Kelly's work, so when I had the chance to get a batch of seeds from one of his lines, I jumped at the chance. My first year working with them, I just tossed a scattering of seeds into a 4"x4" pot and let the seedlings fight amongst themselves for the rest of that year. (I wanted to select for aggressive growers.) At the end of the year, I separated the survivors and planted them in the main garden to overwinter. (I wanted to select for those that were very cold-hardy too.) In the end, I had six plants from that first batch.

Two had lots of luxuriant leafy growth, while the other four seemed to grow a little while and then stall out. I was kinda sad most of the plants didn't seem to do anything, but I left them alone until the first frosty night. As I was pulling up the plants, I got some surprises. All four of the poorly growing plants had grown bulbs, with three of them perfectly formed (though small). The two that grew dramatically produced lots of divisions, but no bulbs.

One of the rapid-growing plants flowered twice over the season, so I was able to collect a next generation of seed. Since the plant didn't bulb up the way I wanted, I found myself with a puzzle. I had no idea if those new seeds would all grow into plants with the same growth habit and no bulbs, or if the nice bulb shape could be produced by some hidden recessive alleles. I really liked the aggressive and early growth shown by this plant, so I didn't want to discard its seeds either.

It took a while of searching before I stumbled on to some useful search queries to get what I was looking for. The first useful paper I found (Lee et al., 2013) goes into detail examining a set of six genes in A. cepa that are related to those associated with the control of flowering in the model plant Arabidopsis thaliana. These "Flowering Locus" genes are transcription factors that regulate how plants develop. The paper has a great deal of interesting information about these genes, but the parts I found most interesting were the experiments showing the interactions between the genes. In this sort of case, I like constructing an interaction network to help me understand what is going on.

Basic model from Lee et al.
The basic model they came up with encompasses three specific genes (AcFT1, AcFT2, & AcFT4). AcFT2 is induced by sufficient winter cold and then induces flowering. AcFT1 induces bulbing and AcFT4 inhibits AcFT1. Sufficiently long days inhibit AcFT4. All together, we get the network at right.

The two larger inferences we can make from this network are drawn dashed and in color. AcFT4 inhibits bulbing (by inhibiting AcFT1). Sufficient daylight hours stimulates AcFT1 (by inhibiting AcFT4) and thus promote bulbing.

There are a couple more interactions in the biology, so we'll add them. When the flowering pathway is activated in typical onions, the bulbing pathway is suppressed. We'll represent this as a negative influence from AcFT2 to AcFT1, though logically the inhibition could manifest further along the bulbing pathway. The Lee et al. paper doesn't mention this, but I feel this is justifiable from my experience growing onions through to flowering. An interesting point mentioned in the paper, but not discussed in detail was that AcFT4 over-expression plants showed no senescence of leaves in the fall (in addition to no bulbing), instead growing vegetatively until being stopped by winter.

Expanded model for onion.
The Lee et al. paper describes how vernalization regulates flowering in a few other species. They don't examine in detail how it is happens in onions, but their review of how it is regulated in Arabidopsis thaliana gives us a good model for how it might work. The variations in the system in different species does highlight how transcription factor networks can easily be rewired to impact development.

The model doesn't clearly indicate the default activities of the genes. AcFT1, AcFT2, AcFT4, and AtFLC are all active by default. Because AcFT1 and AcFT2 are negatively regulated by AcFT4 and AtFLC, they (and the flowering or bulbing downstream development) are initially inactive.

The authors in Lee et al. describe how flowering is regulated in a few other model plants for comparison. In short, the same genes are used, but they the comparable interaction network between them has different links. Though the genes are highly conserved, how they work together to drive development is not. The upshot of this is that studies of these genes in other plants is of limited utility to understanding the onions that led me down this path.
Mutations to expanded model for onion.

Even in onions there is evidence for significant diversity in how this regulatory network is put together. In Lee et al., the authors hypothesize that leaks may have an overactive FT4 homolog (shown at left as "X1" on the interaction between daylight hours and AcFT4), resulting in the lack of bulbing and leaf senescence seen in the plant.

Some onions have different vernalization requirements to start flowering. An onion could be entirely resistant to cold as an influence in its blooming, as in "X2" of this figure. Blooming in these onions would be triggered by other influences not described in my figures, such as plant size or age.

The third mutation I have in this figure ("X3") breaks the interaction between AcFT2 and AcFT1. This would prevent flowering from interfering with bulb formation and is what seems to be going on in potato onions. When a potato onion blooms, it will form a bulb from a different growth point that is almost as large as if it hadn't bloomed. This is much different than for regular onions, where flowering results in a tiny inedible bulb.

Though there are as of yet no genetic studies illustrating this hypothetical mutation in potato onions, it would be relatively easy to undertake. Potato onions and regular onions are the same species and easily cross (if both are flowering at the same time). Sequencing a large number of F2 progeny would help make a connection between variations in genetic sequence and the phenotype of flowering inhibition of bulbing. It might even be faster to sequentially modify one onion type with mutations to match the FT genes (and surrounding regulatory regions) of the other onion type.

The second technique would at the very least be helpful in validating any findings from the first technique, since what I have indicated as a single interaction could actually involve several other genes. The consequence of this could be that the two FT genes might show now sequence differences at all between the two onion types.

What inspired me to start digging into the biology of bulbing/flowing was the hope that I could make some predictions about the genetics of the potato onions I'm growing.

My robustly growing, but non-bulbing, potato onion seedlings appear to mimic what would be expected if the "X2" mutation described above was involved. I collected seeds from the best of these plants in hopes that they might contain a recessive bulbing trait that would appear in segregations in the next generation. Unfortunately, I still don't know. The phenotype could be due to either a dominant or recessive mutation. I'll just have to grow out as many of these seeds as I have room for and find out. Answering this question will take another two years, so stay tuned.

I'll also be growing a large number of seeds from the batch I originally received. I wasn't expecting so much diversity to appear in them, so now I'm really interested in what other trait combinations will turn up.


Monday, February 19, 2018

A Bird's View of Color

Figure from [link].
Most birds have much better color vision than mammals. In general, they have four distinct types of color-sensing cones in their eyes, compared to the usual three for us and two for most other mammals. The fourth cone that birds have is sensitive to ultraviolet (UV), letting them perceive colors we can only imagine. The other three cones don't precisely match up with our three, but they cover basically the same range of frequencies.

To get an idea of what things look like to birds, we have to incorporate that UV information we can't see. Taking photographs of the UV world can take some special equipment, but even consumer grade cameras can be altered to better capture UV light. I've been interested in photography for a while and I've been interested in UV photography, but I haven't yet invested in the equipment I'd need to take UV photos. For now I have to rely on people posting occasional UV photos to get an idea what things look like. (For a good selection of photos in UV and other frequency bands, go take a look at: photographyoftheinvisibleworld.blogspot.com)

You can look at UV light photos next to visual light photos to get an idea of what things look like to birds, but I decided to see if I could do one step better. I wrote a script which takes four image channels (Red, Green, Blue, Ultraviolet) and compresses them into the three we can see (RGB). The math for this is pretty simple and so doesn't match what really happens in detail, but it might help us get an idea of what things look like to birds.

\(R_h = R_b + \frac{G_b}{3}\)
\(G_h = \frac{2(G_b+B_b)}{3}\)
\(B_h = \frac{B_b}{3} + U_b\)

RGBU (bird vision) -> RGB (human vision).
This math is represented visually in the diagram at right. At the top are the four image channels that birds can see and at bottom are the three we can see. All the information that birds can see in their red channel goes into our red channel, along with a third of what birds see in their green channel. The other channels of a bird's vision are similarly apportioned into the channels we can see by moving from top to bottom in the figure.

Conceptually, this is similar to drawing a 3D cube on a 2D sheet of paper. Some information is lost in the transformation, but much of it comes through the process and allows us to visualize something that otherwise can't be done (in 2D). In this case, we're transforming a 4D data structure into a 3D one, that just happens to be presentable as a color photo.

To show what this math means for a photo, I found a nice example paired set of visual and UV images from photographyoftheinvisiblew... to work with.

RGBU image channels along top; RGB and compressed RGBU images at bottom.
Original photos from [link].

In UV this flower of the Marsh Marigold (Caltha palustris) is dramatically marked, but in our composite RGBU image it really doesn't stand out that much. Flowers rarely utilize birds for their pollination, so it shouldn't be any surprise that they might not look too dramatic to birds. (Bees can't see red, but can see UV, so they'd have no problem seeing the marks on this flower.)

Can we find some nice UV imagery of something that birds would care about? Well, it's a bit harder to make paired visual and UV photos of a creature which is suspicious of your intentions. Recently, I came across a post by twitter user @JamieDunning illustrating some dramatic fluorescence on the beak of a Puffin specimen he was examining. It occurred to me that something strongly fluorescent should also be UV-dark, since the UV energy is being absorbed and released at visual frequencies instead of reflected. I realized from this I could construct a simulated UV-channel by inverting the fluorescence image (and mapping the images together to correct for the different camera position (and using a bit of artistry to clean up the fluorescence image)). Performing the same image channel compression as I did earlier, we get the lower-right portion of the next figure.

RGBU image channels along top; RGB and compressed RGBU images at bottom.
Original photos from [link].

It would be nice to have a comparable real UV-photo for doing this comparison, but that the simulated bird-vision of the Puffin's beak shows a much greater color contrast than we saw with the Marsh Marigold (and that both results align with the evolutionarily expected results) suggests this might be a useful approach.

My wish-list, money-is-no-option, sort of data for doing this kind of image analysis would be that produced from hyper-spectral imaging. A hyper-spectral camera takes images at a large range of narrow frequency bands. We could map that data (vs. the color sensitivity spectra illustrated in the figure at the top of this post) to what either birds or humans can see, as well as something like the transformation I've described here to illustrate in human vision what a bird could see.

I'm not sure anyone would provide sufficient funding for me to explore this, however.

@JamieDunning recently submitted a paper comparing the original photo with spectrophotometer examination of regions of the bill. I'm looking forward to their paper to see how the results compare to the predictions from my playing around with the math.


Monday, February 12, 2018

Chromosome Painting

The figure at left shows the metaphase chromosomes of a pepper root-tip, in all their squiggly false-color glory. In it you can count the number of chromosomes and (with some little background research) determine the overall ploidy of the source plant. (It has 24 chromosomes, so is a diploid.)

The original image had all the same information, but it was much harder to look at and learn from. This is a fundamental lesson of, and reason for, data visualization.

Step 0.
The original image comes from Twitter user @ChaoticGenetics. They're studying chile genetics and routinely post cool photos derived from their work. The question paired with this image was, "How many chromosomes does everyone see?" I figured I'd take a stab at it.

Lets dive into the details of how I made my figure. I use GIMP for essentially all my image editing needs. With each step figure I'll include the menu options for each command I use in brackets, so others can repeat the procedure.

0) Load the image with GIMP. Open "Tool Options" [Control-B] and "Layers" [Control-L] windows.

Step 1.
Step 3.
1) Select a rectangular region around the interesting looking chromosomes, then crop [Image > Crop to Selection] the image.

Step 2.
2) Select the "Eraser Tool" and erase all the background color and spots that don't appear as chromosomes.

3) Right-click on the image in the layer window. Select, "Add Alpha Channel". Discard the color information in the image [Colors > Desaturate]. Remove the background color [Colors > Color to Alpha (Set "From:" color to white.)].

Step 4.
4) From the layer window, make a new image layer filled in white. Move this layer beneath the image layer. Select the image layer.

Step 5.
5) Using the "Free Select Tool", draw around a visually distinct chromosome. Invert the color of the selection [Colors > Invert]. Change the color of the selection [Colors > Components > Channel Mixer... (red=50,0,0; green=0,0,0; blue=0,0,50)].

Step 6.
6) Many of the chromosomes in this example are adjacent or overlapping with another. For these, we have to use some knowledge about chromosomes and some artistry. Lets have a look at the cluster here highlighted in green.

Step 7.
7) At this scale, chromosomes are essentially linear structures. They don't branch and they don't loop. From this we can tell the green feature in step 6 is actually three chromosomes. I cut each chromosome out of the image and pasted into a new layer. From there I could clean up their shape a little before changing the colors and recombining them.
Step 8.

8) Going progressively through the image, isolating and coloring the most apparent chromosomes at each stage, we come to 16 chromosomes that we can be confident about. (So, our cell isn't a haploid with 12 chromosomes.)

We're left with the region at left I've highlighted in pink. This region would need to account for a further 8 chromosomes to reach the expected diploid count of 14 in total. Though there are probably a few chromosomes in this region that we can confidently separate, much of it is down to guesswork.

It is possible for this specific pepper plant to have fewer chromosomes. Though it is unlikely for a chromosome pair to be lost, since each has been conserved over a long time period and likely contains critical genes, it is common enough evolutionarily for chromosomes to fuse. That pink mess could hypothetically be 6 or 4 chromosomes, though this one image isn't sufficient evidence to make me think it is likely. If the same pattern is shown in a few more images from the same plant, especially if the chromosomes are better spread, then I'd start to consider that as increasingly likely.

For now, the balance of the evidence leads me to think there are 24 chromosomes and they're just not perfectly isolated. So, I divided the uncertain pile of chromosomes into the number that I expect are remaining. Any figure you make will invariably include your assumptions. The key is to try and make those assumptions reasonable or at least apparent to the reader (though this may require some nice caption-writing).

Interestingly, there's a protocol which can experimentally produce the sorts of painted chromosomes we're simulating here. Fluorescent In-Situ Hybridization (FISH) relies on making DNA probes which are stained a unique color for each chromosome. When the probes are applied to a chromosome spread, the result helps visualize chromosome crossovers, deletions, and other large scale alterations that can be important in diagnosing cancer and other disorders. The setup work for this is pretty intense, so it's probably not going to be used for the simple task of seeing how many chromosomes a plant has.

While I was in grad school, I routinely modified figures from papers I was reviewing for in-class (or in-lab) presentations. Usually highlighting different components of the figure in different colors (like here), to make them stand out more when displayed. I was doing the hard work of figuring out the important parts of the figures so students watching my presentation didn't have to. My goal was for them to focus on what I was saying about the figures and see what wanted them to see at a glance.

Using colors to present different partitions of a larger dataset ended up being central to my last large graduate project (YMAP) as well as an important part of my current [non-academic] job. While using colors for data presentation, it is important to keep in mind that not everyone has the same ability to see color. The most common forms of color-blindness are often called Red-Green-colorblindness. From this, it is a good idea to try and avoid the commonly used Red-Green color scheme seen so often in biology research figures. (Blue-Yellow is a good alternative, but there are subtleties I'll have to go into later.) Being conscious of the issues means they will inform your decisions, even if you're not fully aware of the topic.

This post was inspired by a conversation over on Twitter. (You can follow me there as @thebiologistisn.)

The original picture of the chromosome spread was made by @ChaoticGenetics, who gave permission for me to use it in this post.