The Growing Canvas of Biological Development

Transcription

1 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

2 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 August 2006 Doursat, R. - The Growing Canvas of Biological Development 2

3 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 Doursat, R. - The Growing Canvas of Biological Development 3

4 1. The Problem of the Form Free vs. guided forms Forms everywhere: physical, biological, social, artificial thermal convection sand dunes, city Baltimore, animal gecko, plant pomegranate, by Köhler chemical reaction BZ, by A. Winfree, University of Arizona building Architecture Program, animal spots August 2006 Doursat, R. - The Growing Canvas of Biological Development 4

5 1. The Problem of the Form Free vs. guided forms Different types and taxonomies of pattern formation forms can be inert vs. living, natural vs. human-made, organism vs. collectivity, small vs. large scale, emergent vs. designed, etc. 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 texturegarden.com/java/rd fruit fly embryo Sean Caroll, U of Wisconsin larval axolotl limb Gerd B. Müller August 2006 Doursat, R. - The Growing Canvas of Biological Development 5

6 1. The Problem of the Form Free vs. guided forms Biological forms are a combination of free and guided domains of free pattern embedded in a guided morphology spots, stripes in skin angelfish, ommatidia in eye dragonfly, repeated copies of a guided form, distributed as a free pattern flowers in tree cherry tree, segments in insect centipede, images.encarta.msn.com August 2006 Doursat, R. - The Growing Canvas of Biological Development 6

7 1. The Problem of the Form Free vs. guided forms Development: the missing link of the Modern Synthesis Darwin discovered the evolution of the phenotype Mendel guessed, then Watson & Crick revealed the genotype 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 August 2006 Doursat, R. - The Growing Canvas of Biological Development 7

8 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 Doursat, R. - The Growing Canvas of Biological Development 8

9 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? August 2006 Doursat, R. - The Growing Canvas of Biological Development 9

10 1. The Problem of the Form Engineered vs. self-organized forms Biological development is autonomous guided order organisms are not designed or assembled externally; they grow the spontaneous making of an organism from a single cell is the epitome of a self-organizing, decentralized complex system August 2006 Doursat, R. - The Growing Canvas of Biological Development 10

11 1. The Problem of the Form Engineered vs. self-organized forms Human construction is heteronomous guided order 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? challenge: guided robotic self-assembly (virtual, then physical)? August 2006 Doursat, R. - The Growing Canvas of Biological Development 11

12 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 August 2006 Doursat, R. - The Growing Canvas of Biological Development 12

13 2. Stained-Glass Patterning a. Background: genetic switches Reminder: the standard pathway of molecular biology DNA segment (gene) is transcribed into messenger RNA 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 Doursat, R. - The Growing Canvas of Biological Development 13

14 2. Stained-Glass Patterning a. Background: genetic switches Genetic expression is controlled by genetic switches example: E. coli grown on glucose does not normally produce β-galactosidase, an enzyme breaking down lactose Lac repr β-gal GENE when lactose is present, however, β-gal gene is expressed lactose Lac repr 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 Doursat, R. - The Growing Canvas of Biological Development 14

15 2. Stained-Glass Patterning a. Background: genetic switches Genetic switches are controlled by genetic expression switch = regulatory site on DNA ( lock ) near a gene + protein that binds to this site ( key ), promoting or repressing the gene GENE A GENE B GENE C PROT A PROT B key PROT C lock GENE I 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 Doursat, R. - The Growing Canvas of Biological Development 15

16 2. Stained-Glass Patterning a. Background: genetic switches Developmental genes are expressed in spatial domains thus combinations of switches can create patterns by union and intersection, for example: I = (not A) and B and C GENE A GENE A GENE B GENE B GENE CC GENE I Drosophila embryo GENE I after Carroll, S. B. (2005) Endless Forms Most Beautiful, p117 August 2006 Doursat, R. - The Growing Canvas of Biological Development 16

17 2. Stained-Glass Patterning a. Background: genetic switches Striping in the Drosophila embryo anteroposterior (A/P) axis is segmented into periodic band patterns this striping process is controlled by a 5-tier gene regulatory hierarchy a few lateral signaling interactions also refine and sharpen boundaries from Carroll, S. B., et al. (2001) From DNA to Diversity, p63 August 2006 Doursat, R. - The Growing Canvas of Biological Development 17

18 2. Stained-Glass Patterning a. Background: genetic switches Identity domains in Drosophila embryo the dorsoventral (D/V) and proximodistal (P/D) axes are also segmented their intersection with A/P segments create the organ primordia and imaginal discs these domains specify the identity of the future appendages (leg, wing, antenna, etc.) from Carroll, S. B., et al. (2001) From DNA to Diversity, p74 August 2006 Doursat, R. - The Growing Canvas of Biological Development 18

19 2. Stained-Glass Patterning b. A feedforward model of gene regulatory network Two-tier GRN model: combinatorial patterning for example: gene A promotes, but gene B represses, gene I I +1-1 y A > 0 A B A B I = A and (not B) A B x y B > 0 x I I x I x 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 Doursat, R. - The Growing Canvas of Biological Development 19

20 2. Stained-Glass Patterning b. A feedforward model of gene regulatory network Three-tier GRN model: integrating positional gradients A and B are themselves triggered by proteins X and Y X Y A I B I +1-1 a A X a' b Y B b' I = A and (not B) A = σ(ax + a'y +a") B = σ(bx + b'y +b") X x Y y X I A B x x x y y I A > 0 B > 0 x x 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 Doursat, R. - The Growing Canvas of Biological Development 20

21 2. Stained-Glass Patterning b. A feedforward model of gene regulatory network A simple Positional-Boundary-Identity GRN model top layer m identity nodes I k= 1 m I k (t)=σ( i w' ki B i θ' k ) or middle layer I k (t)= i sign(w' ki ) B i I 1 I 2 I 3 w' 11 w' 34 B 1 B 2 B 3 B 4 n boundary nodes B i = 1 n B i = σ(w ix X+w iy Y θ i ) with σ(z) =(1 e λz ) / (1 + e λz ) bottom layer 2 positional nodes X and Y w 1x X Y w 4y similar to the good old perceptron August 2006 Doursat, R. - The Growing Canvas of Biological Development 21

22 2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs A lattice of Positional-Boundary-Identity (PBI) GRNs network of networks: each GRN is contained in a cell, coupled to neighboring cells via the positional nodes (for diffusion) a pattern of gene expression is created on the lattice I 1 I 2 I 3 B 1 B 2 B 2 B 4 X Y B 2 I 1 August 2006 Doursat, R. - The Growing Canvas of Biological Development 22

23 2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs Example of numerical simulation with random weights the embryo s partitioning into territories is similar to the colorful compartments between lead cames in stained-glass works I 1 I 2 I 3 I 1 (x, y) I 2 (x, y) I 3 (x, y) B 1 B 3 B 4 B 1 (x, y) B 2 (x, y) B 3 (x, y) B 4 (x, y) X(x, y) Y(x, y) X Y August 2006 Doursat, R. - The Growing Canvas of Biological Development 23

24 2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs Summary: simple feedforward hypothesis developmental genes are broadly organized in tiers, or generations : earlier genes map the way for later genes gene expression propagates in a directed fashion: first, positional morphogens create domains, then domains intersect switch combo August 2006 Doursat, R. - The Growing Canvas of Biological Development 24

25 2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs Toolkit genes are often multivalent exception to the feedforward paradigm: toolkit genes that are reused at different stages and different places in the organism 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 Doursat, R. - The Growing Canvas of Biological Development 25

26 2. Stained-Glass Patterning c. Pattern formation on a lattice of GRNs More realistic variants of GRNs add recurrent links within tiers domains are not established independently but influence and sharpen each other subdivide tiers into subnetworks this creates modules that can be reused and starts a hierarchical architecture switch combo 2 switch combo August 2006 Doursat, R. - The Growing Canvas of Biological Development 26

27 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 August 2006 Doursat, R. - The Growing Canvas of Biological Development 27

28 3. The Growing Canvas a. Gene economics Problem: how many boundary nodes? this simplistic perceptron-like PBI architecture can theoretically reproduce any segmentation motif, given enough B nodes broad identity domains can be circumscribed by a few B nodes y B 1 y B 1 I 1 I 3 B 2 I 1 I 3 B 1 B 2 X Y B 1 X Y B n B n x x... however, more numerous (and finer) morphological details would require many more boundary nodes August 2006 Doursat, R. - The Growing Canvas of Biological Development 28

29 3. The Growing Canvas a. Gene economics Morphological refinement by iterative growth details are not created in one shot, but gradually added while, at the same time, the canvas grows from Coen, E. (2000) The Art of Genes, pp August 2006 Doursat, R. - The Growing Canvas of Biological Development 29

30 3. The Growing Canvas b. Fractal patterning Iterative refinement using a hierarchical GRN instead of one flat tier of B nodes, use a pyramid of PBI modules the activation of an I node controls the onset of a new P layer in the first stage, a base PBI network creates broad domains I 1,1 B 1,4 I 3,m y B 1 B 2 y B 2 B 1,4 I 1 I 3 X 1, Y 1 I 2 B 1 B 3 X 3, Y 3 I 1,1 I 3,m B 3 B 1 X Y B n B n X Y I 2 x x in the next stage, another set of PBI networks subdivide these domains into compartments at a finer scale, etc. August 2006 Doursat, R. - The Growing Canvas of Biological Development 30

31 3. The Growing Canvas b. Fractal patterning Example of numerical simulation with preset weights small stained glass embedded into bigger stained glass 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 Doursat, R. - The Growing Canvas of Biological Development 31

32 General idea 3. The Growing Canvas b. Fractal patterning possibility of image generation based on a generic hierarchical GRN (here: illustration, not actual simulation) X 2,3, Y 2,3 X 2 Y 2 X 1, Y 1 X 3, Y 3 X Y August 2006 Doursat, R. - The Growing Canvas of Biological Development 32

33 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 August 2006 Doursat, R. - The Growing Canvas of Biological Development 33

34 4. Discussion and Future Work Originality Are developmental GRNs really complex? 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 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 Doursat, R. - The Growing Canvas of Biological Development 34

35 4. Discussion and Future Work Additional morphogenetic mechanisms Differential growth and geometrical folding differential growth guided patterning GRN-controlled expression maps 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 guided patterning cell death August 2006 Doursat, R. - The Growing Canvas of Biological Development 35

36 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 Doursat, R. - The Growing Canvas of Biological Development 36

37 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 August 2006 Doursat, R. - The Growing Canvas of Biological Development 37