The Growing Canvas of Biological Development Multiscale Pattern Generation on an Expanding Lattice of Gene Regulatory Networks
René Doursat Brain Computation Laboratory, Department of Computer Science and Engineering University of Nevada, Reno
The Growing Canvas of Biological Development 1. Introduction: The Problem of the “Form” 2. Genetic Principles of Stained-Glass Patterning 3. Multiscale Segmentation: The Growing Canvas 4. Discussion and Future Work
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The Growing Canvas of Biological Development 1. Introduction: The Problem of the “Form” a. Free vs. guided forms b. Engineered vs. self-organized forms
2. Genetic Principles of Stained-Glass Patterning 3. Multiscale Segmentation: The Growing Canvas 4. Discussion and Future Work
August 2006
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1. The Problem of the “Form” Free vs. guided forms
¾ Forms everywhere: physical, biological, social, artificial
thermal convection sand dunes, www.scottcamazine.com
city
animal
Baltimore, www.dnr.state.md.us
gecko, www.cepolina.com
plant pomegranate, by Köhler www.plant-pictures.de
chemical reaction
building
animal spots
BZ, by A. Winfree, University of Arizona
Architecture Program, www.pvamu.edu
www.scottcamazine.com
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1. The Problem of the “Form” Free vs. guided forms
¾ Different types and taxonomies of pattern formation 9 forms can be inert vs. living, natural vs. human-made, organism vs. collectivity, small vs. large scale, emergent vs. designed, etc. 9 distinction among natural emergent forms: free vs. guided
free: e.g., Turing morphogenesis randomly amplified fluctuations unpredictable: 4, 5 or 6 spots? statistically homogeneous
guided: e.g., organism development deterministic genetic control reproducible: 4 limbs, 5 digits heterogeneous, rich in information
convection cells
reaction-diffusion
fruit fly embryo
larval axolotl limb
www.chabotspace.org
texturegarden.com/java/rd
Sean Caroll, U of Wisconsin
Gerd B. Müller
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1. The Problem of the “Form” Free vs. guided forms
¾ Biological forms are a combination of free and guided 9 domains of free pattern embedded in a guided morphology
ommatidia in eye
spots, stripes in skin
dragonfly, www.phy.duke.edu/~hsg/54
angelfish, www.sheddaquarium.org
9 repeated copies of a guided form, distributed as a free pattern
flowers in tree
segments in insect
cherry tree, www.phy.duke.edu/~fortney
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centipede, images.encarta.msn.com
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1. The Problem of the “Form” Free vs. guided forms
¾ Development: the missing link of the Modern Synthesis 9 Darwin discovered the evolution of the phenotype 9 Mendel guessed, then Watson & Crick revealed the genotype 9 although the genotype-phenotype correlation is well established, the (epi)genetic mechanisms of development are still unclear
mutation
??
evolution
?? Purves et al., Life: The Science of Biology
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1. The Problem of the “Form” Free vs. guided forms
“When Charles Darwin proposed his theory of evolution by variation and selection, explaining selection was his great achievement. He could not explain variation. That was Darwin’s dilemma.” “To understand novelty in evolution, we need to understand organisms down to their individual building blocks, down to their deepest components, for these are what undergo change.” —Marc W. Kirschner and John C. Gerhart (2005) The Plausibility of Life, p. ix August 2006
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1. The Problem of the “Form” Free vs. guided forms
How does a static, nonspatial genetic code dynamically unfold in time and 3-D space? How are morphological changes correlated with genetic changes?
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1. The Problem of the “Form” Engineered vs. self-organized forms
¾ Biological development is autonomous guided order 9 organisms are not designed or assembled externally; they grow 9 the spontaneous making of an organism from a single cell is the epitome of a self-organizing, decentralized complex system
www.infovisual.info
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1. The Problem of the “Form” Engineered vs. self-organized forms
¾ Human construction is heteronomous guided order 9 buildings and devices do not grow, they are assembled → can we shift the paradigm, with inspiration from biology? can we design or, better, evolve the genetic code of a house? 9 challenge: guided robotic self-assembly (virtual, then physical)
? www.tpub.com
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The Growing Canvas of Biological Development 1. Introduction: The Problem of the “Form” 2. Genetic Principles of Stained-Glass Patterning a. Background: genetic switches b. A feedforward model of gene regulatory network c. Pattern formation on a lattice of GRNs
3. Multiscale Segmentation: The Growing Canvas 4. Discussion and Future Work
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2. Stained-Glass Patterning a. Background: genetic switches
¾ Reminder: the standard pathway of molecular biology 9 DNA segment (gene) is transcribed into messenger RNA 9 mRNA is translated into a protein (by ribosomes and tRNA) GENE
DNA mRNA
protein
→ simplified 1-to-1 view, ignoring post-transcriptional (splicing) and post-translational effects, etc. August 2006
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2. Stained-Glass Patterning a. Background: genetic switches
¾ Genetic expression is controlled by genetic “switches” 9 example: E. coli grown on glucose does not normally produce β-galactosidase, an enzyme breaking down lactose Lac repr
β-gal GENE
9 when lactose is present, however, β-gal gene is expressed lactose
La cr ep r
β-gal GENE
→ the cause is a DNA-binding protein “lac repressor” that blocks β-gal gene expression, but falls off when lactose is present August 2006
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2. Stained-Glass Patterning a. Background: genetic switches
¾ Genetic switches are controlled by genetic expression 9 switch = regulatory site on DNA (“lock”) near a gene + protein that binds to this site (“key”), promoting or repressing the gene GENE B GENE C
GENE A “key” PROT A
PROT B
PROT C GENE I “lock”
9 switches can combine to form complex regulatory functions → since switch proteins are themselves produced by genes, a cell can be modeled as a gene-to-gene regulatory network (GRN) August 2006
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2. Stained-Glass Patterning a. Background: genetic switches
¾ Developmental genes are expressed in spatial domains 9 thus combinations of switches can create patterns by union and intersection, for example: I = (not A) and B and C GENE B GENE B GENE GENECC
GENE AGENE A
GENE I
Drosophila embryo
GENE I
after Carroll, S. B. (2005) Endless Forms Most Beautiful, p117 August 2006
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2. Stained-Glass Patterning a. Background: genetic switches
¾ Striping in the Drosophila embryo 9 anteroposterior (A/P) axis is segmented into periodic band patterns 9 this striping process is controlled by a 5-tier gene regulatory hierarchy 9 a few “lateral” signaling interactions also refine and sharpen boundaries August 2006
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from Carroll, S. B., et al. (2001) From DNA to Diversity, p63 17
2. Stained-Glass Patterning a. Background: genetic switches
¾ Identity domains in Drosophila embryo 9 the dorsoventral (D/V) and proximodistal (P/D) axes are also segmented 9 their intersection with A/P segments create the organ primordia and imaginal discs 9 these domains specify the identity of the future appendages (leg, wing, antenna, etc.) August 2006
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from Carroll, S. B., et al. (2001) From DNA to Diversity, p74 18
2. Stained-Glass Patterning b. A feedforward model of gene regulatory network
¾ Two-tier GRN model: combinatorial patterning 9 for example: gene A promotes, but gene B represses, gene I y
I +1
-1
A
B
A>0 B>0
A
A
B x
B
x
y
I = A and (not B) I x
I
I
x
9 therefore, gene I is expressed where A is high but B is low → the domain of gene I is at the intersection of A and not-B August 2006
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2. Stained-Glass Patterning b. A feedforward model of gene regulatory network
¾ Three-tier GRN model: integrating positional gradients 9 A and B are themselves triggered by proteins X and Y Y
X
+1
-1
B
I
I = A and (not B) A = σ(aX + a'Y +a") B = σ(bX + b'Y +b") X≈x Y≈y
A>0
x
A B a' b a b' X Y
A
y
X
I
B>0 A
B x
x
y
I x
I
x
9 X and Y diffuse along two axes and form concentration gradients → different thresholds of lock-key sensitivity create different territories of gene expression in the geography of the embryo August 2006
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2. Stained-Glass Patterning b. A feedforward model of gene regulatory network
¾ A simple Positional-Boundary-Identity GRN model 9 top layer m identity nodes Ik = 1…m Ik(t) = σ(∑i w'ki Bi − θ'k) or Ik(t) = ∏i sign(w'ki) Bi 9 middle layer n boundary nodes Bi = 1…n
I1
I2
I3
w'11 B1
w'34 B2
w1x
B3
B4 w4y
X Y Bi = σ(wix X + wiy Y − θi) with σ(z) = (1 − e−λz) / (1 + e−λz) 9 bottom layer → similar to the good old “perceptron” 2 positional nodes X and Y August 2006
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2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs
¾ A lattice of Positional-Boundary-Identity (PBI) GRNs 9 network of networks: each GRN is contained in a cell, coupled to neighboring cells via the positional nodes (for diffusion) 9 a pattern of gene expression is created on the lattice
I1
B1
I2
I3
B2
B2
X
Y
B4
B2 I1 August 2006
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2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs
¾ Example of numerical simulation with random weights 9 the embryo’s partitioning into territories is similar to the colorful compartments between lead cames in stained-glass works I1 I2 I3 I1(x, y)
I2(x, y)
I3(x, y) B1 B3 B4
B1(x, y) X(x, y)
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B2(x, y)
B3(x, y)
B4(x, y) Y(x, y)
Doursat, R. - The Growing Canvas of Biological Development
X Y 23
2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs
¾ Summary: simple feedforward hypothesis 9 developmental genes are broadly organized in tiers, or “generations”: earlier genes map the way for later genes 9 gene expression propagates in a directed fashion: first, positional morphogens create domains, then domains intersect
switch combo
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2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs
¾ Toolkit genes are often multivalent 9 exception to the feedforward paradigm: “toolkit” genes that are reused at different stages and different places in the organism 9 however, a toolkit gene is triggered by different switch combos, which can be represented by duplicate nodes in different tiers
switch combo 2 switch combo
after David Kingsley, in Carroll, S. B. (2005) Endless Forms Most Beautiful, p125 August 2006
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2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs
¾ More realistic variants of GRNs 9 add recurrent links within tiers → domains are not established independently but influence and sharpen each other 9 subdivide tiers into subnetworks → this creates modules that can be reused and starts a hierarchical architecture
switch combo 2 switch combo
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The Growing Canvas of Biological Development 1. Introduction: The Problem of the “Form” 2. Genetic Principles of Stained-Glass Patterning 3. Multiscale Segmentation: The Growing Canvas a. Gene economics b. Fractal patterning
4. Discussion and Future Work
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3. The Growing Canvas a. Gene economics
¾ Problem: how many boundary nodes? 9 this simplistic perceptron-like PBI architecture can theoretically reproduce any segmentation motif, given enough B nodes 9 broad identity domains can be circumscribed by a few B nodes B1
B1
y I1
y
I3 B1
B2
X
Y
I1
B2 B1
I3
X
Y
Bn
Bn
x
x
9 . . . however, more numerous (and finer) morphological details would require many more boundary nodes August 2006
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3. The Growing Canvas a. Gene economics
¾ Morphological refinement by iterative growth 9 details are not created in one shot, but gradually added. . .
9 . . . while, at the same time, the canvas grows
from Coen, E. (2000) The Art of Genes, pp131-135 August 2006
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3. The Growing Canvas b. Fractal patterning
¾ Iterative refinement using a hierarchical GRN 9 instead of one flat tier of B nodes, use a pyramid of PBI modules 9 the activation of an I node controls the onset of a new P layer 9 in the first stage, a base PBI network creates broad domains I1,1
B2
B1 B2
I3,m
y
B1,4
y I1
B1,4 I2 X1, Y1
X3, Y3 B1
X
I1,1
I3,m B3
B3
Y
I3
B1
X
Y
Bn
Bn
I2
x
x
9 in the next stage, another set of PBI networks subdivide these domains into compartments at a finer scale, etc. August 2006
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3. The Growing Canvas b. Fractal patterning
¾ Example of numerical simulation with preset weights 9 small stained glass embedded into bigger stained glass 9 here, a 2-layer architecture of GRNs: 5 boundary nodes, 12 rectangular domains, 2 of which become further subdivided
2 “rectangular” domains become further subdivided 2 “horizontal” + 3 “vertical” boundary nodes August 2006
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3. The Growing Canvas b. Fractal patterning
¾ General idea 9 possibility of image generation based on a generic hierarchical GRN 9 (here: illustration, not actual simulation) X2,3, Y2,3
X2
Y2
X1, Y1
X3, Y3
X
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Y
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The Growing Canvas of Biological Development 1. Introduction: The Problem of the “Form” 2. Genetic Principles of Stained-Glass Patterning 3. Multiscale Segmentation: The Growing Canvas 4. Discussion and Future Work a. Originality b. Additional morphogenetic mechanisms c. Evolution
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4. Discussion and Future Work Originality
¾ Are developmental GRNs really “complex”? 9 previous studies have modeled GRNs as complex networks, for example random, scale-free or biologically detailed Salazar, Sole, Kauffman: aposteriori statistical analysis, identifying correlations between GRN connectivity modules and patterns Molsjness (“Cellerator”), von Dassow (“Ingeneue”): biologically faithful simulations
9 this work adopts a more controlled, heuristic (and artificial) approach a GRN is roughly a hierarchical directed acyclic graph makes it easier to see the causal link from genotype to phenotype no pretention to biological realism; only exploiting some aspects of development August 2006
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4. Discussion and Future Work Additional morphogenetic mechanisms
¾ Differential growth and geometrical folding 9 guided patterning — GRN-controlled expression maps 9 9 9 9 differential growth
differential growth — domain-specific proliferation rates free patterning — Turing-like epigenetic pattern formation elastic folding — deformation from cellular mechanistic forces cell death — detail-sculpting from removal guided patterning
differential growth
free patterning
elastic folding
cell death guided patterning August 2006
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4. Discussion and Future Work Evolution
Given a GRN, what shape is created? Given a desired shape, what GRN will create it? Evolutionary algorithm based on shape “fitness”: literally equivalent to evolution & natural selection final shape
initial GRN cell August 2006
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The Growing Canvas of Biological Development 1. Introduction: The Problem of the “Form” 2. Genetic Principles of Stained-Glass Patterning 3. Multiscale Segmentation: The Growing Canvas 4. Discussion and Future Work
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