Lec 13 Teaching Prep: Part 2 — RD math + master regulators + three knobs
2026-05-11 18:00:09 • 17:00
Lecture 13 Teaching Prep. Part 2. The Math, the Master Regulators, and the Three Nobsynthesis.
Hey Michael! Welcome to Part 2 of your Lecture 13 prep.
You are picking up at the halfway mark about 35 minutes into the lecture.
The first half landed the pattern blending story.
The pufferfish punchline, that pattern blending created what taxonomists thought were distinct species,
is your strongest moment of the lecture.
Carry that energy into Part 2. The second half has three jobs.
Make the touring math concrete enough that students don't glaze.
Land the regulatory toolkit.
Tie it all up with the three nobsynthesis.
One pacing reminder before we start.
You have about 40 minutes left for 15 or 16 slides.
That is two and a half minutes per slide on average.
Some slides are 60 seconds, some are four minutes.
Watch your phone clock at the ALX3 slide.
If you are past 65 minutes by ALX3 you need to compress plants and bridge.
Slide 21 is the reaction diffusion in 30 seconds slide.
Don't try to teach the math.
The slide makes the point in one move.
Two diffusing chemicals.
One activates itself and the other.
The other inhibits the first.
The inhibitor diffuses faster.
That is the entire mechanism in three sentences.
Then the result.
Local activator pockets stabilize,
separated by long range inhibition.
Periodic pattern emerges with a characteristic wavelength.
The knob is the diffusion ratio.
Larger ratio means stripes.
Closer ratio means spots than uniform.
Geometry interacts with the ratio to give labyrinths and rosettes.
The Miyazawa figure on the right shows the parameter sweep.
You already walked the spots to labyrinth to inverse spots logic
during the labyrinth reveal slide.
So this slide is a math callback, not a math introduction.
90 seconds.
The verbal model to deliver if a student looks lost.
Activator is short range auto catalytic.
Wherever there is some, more shows up.
Inhibitor is a long range diffusing break.
Suppresses the activator everywhere except where it is already concentrated.
Periodic pattern emerges because activator pockets are spaced by long range inhibition.
Slide 22 is the watch the instability form video slide.
About three minutes total.
62% of the slide is a reaction diffusion video.
The same kind of simulation that ran on the Miyazawa sphere.
Let the video run for 30 to 45 seconds.
Then pause.
Ask students to name the first thing they see.
Local differences amplify from noise.
Then spacing stabilizes.
The core intuition.
The system does not draw a stripe.
It amplifies small differences until a stable wavelength emerges.
Then the TPS.
45 seconds.
If you changed one parameter, would you expect the pattern to change first in color,
wavelength orientation or boundary sharpness?
The answer you are looking for is wavelength.
That is the primary thing the diffusion ratio controls.
Color is downstream.
Orientation is geometry dependent.
Boundary sharpness is a different parameter.
Don't grade hard.
Just take two answers.
Validate wavelength.
Then advance.
Slide 23 is Murray's scaling rule.
The mouse cheat-alepered tiger elephant slide.
This is one of the cleanest visuals in the lecture.
Five photos in a row.
Each with a one line pattern category and a one line explanation.
Mouse uniform body too small.
Cheetah spots medium body short wavelength.
Lepard rosettes larger body, more complex output.
Tiger stripes longer body single wavelength fits.
Elephant uniform body too large instability damps.
Murray modeled an embryonic body as a tube.
Ran a single reaction diffusion equation.
Varied only the body length to width ratio.
Got this entire sequence.
Same touring equation.
Body size is the boundary condition.
That is the bumper sticker.
The side note worth mentioning.
Spotted cats can have striped tails.
Striped cats never have spotted tails.
Cheetahs have stripes on the tail tip.
Tigers don't get spots.
The model predicts this.
At the small diameter of a tail,
the same activator inhibitor dynamics
produce stripes by default.
Tigers bodies are already past the tube striper gene.
Their tails return to it.
Cheetahs go from spots to stripes
as you move down the body to the narrow tail.
This is a great moment of biological prediction
from a one parameter model.
Two minutes.
Slide 24 is the geometry slide.
Curved surfaces and effective diffusion.
Three minutes.
The teaching line.
Once a touring system has a preferred wavelength,
the body tells the system where that wavelength
fits most easily.
Curved surfaces change effective diffusion.
Local curvature can favor one striped direction.
A 2D touring rule on a 3D animal-like surface
can produce naturally oriented stripes.
The zebra photo on the right is the visual anchor.
A stripe is a wavelength plus an orientation.
Murray's rule sets the wavelength.
The newer curvature dependent models set the orientation.
Don't get into the math.
The conceptual point is that the body is not just a canvas.
It is part of the patterning system.
This is the slide to drop if you're running long.
The Murray slide alone carries the scaling argument.
Slide 25 is the Cheetah Cubs video slide.
90 seconds.
Cheetah Cubs are born with a dorsal mantle of long silvery hair
that obscures their spots.
The mantle fades over the first three months
and the adult spotted phenotype emerges.
The teaching move.
Pattern is not a fixed image.
It is a developmental trajectory.
Two hypotheses for the mantle.
Cripsis looks like a honey badger, deeter's predators.
Thermaragulation.
Silver mantle for solar reflection and dents.
Either way the pattern changes as the animal grows.
Single-turing parameter sets cannot explain this.
There must be temporal modulation.
Same point for taper babies, lion cubs, wild boar piglets,
all of stripes or spots that vanish in adults.
Slide 26 is the juvenile pattern slide.
Three minutes.
Big taper juvenile photo on the left.
High contrast stripes and spots.
Ontojeny is part of the phenotype.
Juvenile Cripsis may be selected in a different habitat.
Pattern can fade as body size, behavior, and predation risk change.
The same genotype can encode a time series, not one image.
The project implication.
Ask when the photo was taken in the animal's life.
If you only have one photo,
you're inferring from one snapshot.
A juvenile pattern and an adult pattern
can imply different developmental mechanisms,
different receivers and different functions.
Ask the room.
If this were the only photo you had,
what would you infer about the adult?
That answer is wrong for tapers.
And that is the point.
You are now pivoting from mechanism to gene level evolution.
This is the second major chapter of Part 2.
Slide 27 is the evodivo of butterfly wing slide.
The nymphilid ground plan.
The big idea is that despite extraordinary diversity,
all nymphilid butterfly wing patterns
can be parsed into a small set of homologous elements
that vary in size, color, and presence.
Central symmetry system, border SLI, marginal bands,
discol-spot.
Each element is independently tunable.
Modular evodivo.
Change one element, leave the rest.
This is what made butterfly patterns so explosively diverse.
The heliconious photos on the right
are the perfect illustration.
H, melpomony and H,
eroto are not sister species separated
by about 10 million years.
But where they co-occur,
they have evolved nearly identical wing patterns,
malerian mimicry.
The convergence happened by tweaking
the same regulatory genes.
Optics for red.
W and TA for the central symmetry system.
This is evodivo in its strongest form.
Same toolkit, parallel evolution.
Two minutes.
Slide 28 is the master regulators table.
The big payoff slide of this block.
Seven genes in a table.
W and TA.
Optics, cortex, double sex,
agudy, ALX3,
connection 41.8.
Each gene gets an effect and a lineage.
The bumper sticker line at the bottom.
A handful of genes deployed differently
generate most vertebrate and butterfly pattern diversity.
Highlights worth calling out.
W and TA.
Mazavargus 2017.
Knockout in Heliconius abolishes
the entire central symmetry system.
One gene, entire pattern element gone.
Cortex, Nato 2016.
The gene behind the famous bis-done peppered moth
industrial malinism story.
And a major axis of Heliconius variation.
Two textbook stories.
One gene.
Double sex.
Conte 2014.
In Papilio Polytes,
D-sexyleals control which females mimic toxic models.
Sex limited mimicry from a single switch.
ALX3, Malarino 2016.
Striped grass, mouse dorsal stripes.
Coming up in detail on the next two slides.
The teaching frame.
Evo-Divo is real and it is tractable.
These are not mysterious.
We know the genes, the proteins,
often the regulatory elements.
Three minutes on this slide.
Slide 29 is the single gene flip slide.
Three columns.
Mouse with a goody.
Striped grass, mouse with ALX3.
Zebrafish with Connection 41.8 leopard.
The unifying point across mammals and fish.
Single gene perturbations cause category level pattern changes.
Uniform to striped.
Striped to spotted.
Spotted to uniform.
Selection has lots of accessible levers.
A point mutation in a regulatory element
can move an animal across pattern category space in one step.
That is why pattern evolution looks so fast in clades
like sicklids, heliconious, big cats.
The closing line.
One locus.
Category change.
Pattern is available.
Two minutes.
Slide 30 is the ALX3 deep dive.
About four minutes.
This is the gene level deep dive that makes the single gene flip
slide less abstract.
Two figures stacked on the left.
The development panel and the ALX3 in situ panel.
Walk students from embryo to expression to adult stripe.
First the stripe develops as a spatial domain
during embryonic development.
Then ALX3 expression marks that domain before the adult pattern is obvious.
Then the mechanism.
ALX3 represses melanocyte differentiation through myth.
Less melanin in one dorsal band means a blonde stripe.
The key contrast you want to land.
This is not a free running Turing stripe field.
It is closer to positional information.
A prepotterned regulatory domain tells pigments cells what to do.
This reinforces the mechanism map from slide seven.
ALX3 is a regulatory switch deployed in a specific spatial domain.
Not Turing.
Slide 31 is the plant slide.
Mimulus positional information.
Two minutes.
The teaching move.
Plant petal patterns are essentially walt-bert.
Cells don't migrate.
Anthosign in pigmentation is a local biosynthesis decision.
Position is decided by transcription factor gradients,
the NYB, BCHLH, WD40 complex.
Nectar guides direct pollinators.
Mimulus's bumblebee attracting bull's eye is positional information pure.
The contrast you want to draw.
Animals have cells that migrate neural crust,
chromato-4 precursors.
That migration enables self-organization.
Plants have cells that stay put.
Pattern is decided by which cells turn on which biosynthesis pathway,
which is decided by morphogen-like gradients.
Walt-bert all the way.
The LEC-6 callback.
B-C-U-V.
Mimulus has UV-absorbing center versus UV-reflecting periphery.
A bull's eye invisible to humans.
Slide 32 is the nectar guide deep dive.
Pattern receiver gene.
This is the slide to drop if you are running long.
Three minutes if you keep it.
The slide makes the plant story feel less like a side quest.
Three levels.
Mechanism.
Positional information.
Development gene.
Guideless.
A mixed-like NYB gene.
Function.
Pollinator guidance.
The slide bridges to next week's function unit,
where pollinator vision determines what the pattern is.
Slide 33 is the three knobs of pattern evolution.
The synthesis slide.
The big payoff.
Three knobs.
One.
The cell palette which chromata-four types are available.
Two.
The patterning rule.
Turing parameters and Walt-bert gradients.
Three.
The master regulators.
Which genes deploy which rule where and when.
Connect each knob back to the lecture.
Nob-1 is LEC-11 plus today's Irid-4 crystallotype slide.
Palette dimensionality.
Nob-2 is today's RD-math plus Murray scaling.
Rule parameters.
Nob-3 is today's master regulator table.
Gene level deployment.
Big picture takeaway.
Pattern is high-dimensional,
but each dimension is independently mutable.
Selection can move an animal through pattern space
rapidly without compromising other functions.
That is why pattern explodes in radiating clades.
Land the line.
Each knob is a mutational target.
Selection turns them.
Two minutes.
Slide 34 is the bridge to function.
Three patterns.
Three jobs.
Three photos and three columns.
Zebra, Heliconius, Peacock.
Does the zebra hide confuse predators?
Cool the body.
Does Heliconius warn predators mimic?
Does the Peacock signal sexually?
Don't answer any of these.
Pose the questions.
The unifying point.
Same patterning logic.
Three different selection pressures.
This is the teaser for next week's unit.
Tell students to bring their best guest Tuesday
for the zebra question.
Mention caro's striped skin work
egress biting fly experiments.
The thermoregulation hypothesis.
Two minutes.
Slide 35 is the exit ticket.
Pick one species.
Three sentences.
Cell palette, which chromata four types.
Patterning rule.
Turing or pre-pattern.
Why?
One target gene.
What gene would you knock out to disrupt the pattern?
Submit on Bruin Learn before midnight.
The exit ticket maps directly to the project.
Every fish image they analyze will need cell palette
inferred from color and reflectance.
Patterning rule inferred from spatial geometry.
Candidate gene from the literature.
The project is now a structured exercise
rather than open-ended.
Land it.
The exit ticket is the spine of your project
pattern analysis right up.
60 seconds.
A note on energy through the second half.
The lecture pivots three times.
Our demurrie math to ontogeny trajectory
to evodevo regulators.
Each pivot is a moment where the room can lose you.
The two transitions to watch are the Murray-Tuchida Cubs pivot,
mechanism to ontogeny, and the ALX3
to plants pivot animals to plants.
In both cases, you need an explicit verbal bridge.
Don't just advance.
Say something like, so the math sets
where pattern goes, but pattern also moves through time.
Watch this Chida Cubs.
And later, that was animals.
Now watch what happens when cells can't migrate.
Plants make pattern entirely differently.
Then advance.
One closing image to carry into the room.
The three-nob synthesis is the punchline
you are working toward for 75 minutes.
Treat the ALX3 and master regulator slides
as the foundation under that synthesis.
If you skip them or rush them,
the three-nob synthesis lands as a list.
If you spend two extra minutes on ALX3
doing the embryo expression adult walk through,
the three-nob synthesis lands as a payoff.
End of part two.
End of prep.
Go give the lecture.