Models of Biological Development

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Models of Development

How does structure emerge from a structureless state without an externalorganising force?We all start out as an undifferentiated clump of cells, all withthe same genetic code ?

Dr.S.S.D.PandeyGlobal Synergetic Foundationssd@globalsynergetic.org 15th June 2008

©Global Synergetic Foundation

Dr.S.S.D.PandeyGlobal Synergetic Foundation

Self Organisation

Complex patterns can be produced by application of simple rules to

simple initial states.

In biological systems chemical signals combined with nonlinear localinteraction are able to produce very complex patterns.

Symmetry breaking: the initial undifferentiated state isunstable. Feedback amplifies deviations, turning noise intopattern.

How to Make a Brain

Grow a large number of similar cellsAllow them to differentiate into different types depending on

the neighborhood.Diffuse long range chemical signalsLet neurons send out connections towards their favoritechemical(s).Connect, and possibly remove failed cells and connections.Repeat, add other kinds of plasticity.

Reaction-Diffusion Systems

An important class of pattern forming systems consists ofchemicals diffusing and reacting with each other.

If the interactions are nonlinear and the diffusion coefficientsdifferent, interesting instabilities result.

Can be modelled with partial differential equations or cellularautomata.

Turing Patterns

Alan Turing 1952: Spontaneous symmetry breaking inreaction-diffusion systems.

Diffusion of morphogens among identical cells ordered in aRing

Turing showed that when individually stable cells areconnected, diffusion can cause instability and patternformation

Analysis of linear system

A basic example with two morphogens. Let x and y be theirdeviations from equilibrium in each cell:

In order to get stability of isolated cells (no diffusion terms

The signs of the constant matrix are forced into one of these forms

Activator and depleted substrate

Activator and inhibitor

The normal mode trick

The behavior of x and y can be analysed by expressing themas normal modes

ξ and η can now be used instead; this is usually simplerbecause different Fourier modes are decoupled

Doing the stability analysis for ξ and η gives:

As long as μ and ν are small the steady state x=y=0 is stable.Beyond a certain point, one of the modes will become unstable, andsmall disturbances will create an exponentially growing periodicpattern.Diffusion produces patterns instead of dissolving them!This requires that μ is not equal to ν; lateral inhibition

Meinhardt: Hydra Development

Model head development as activator-inhibitor pair with characteristiclength of the same order as body length.

Regeneration after division.

Symmetry breaking during growth

Effect of cutting

Diffusion works only over short scales.

Embryonic fields in which developmental decisions take place are smaller 1mm and less than 100 cells across

The early local state is translated into a permanent cell state by changes ingene expression

A hierarchy of genes that activate each other in turn

Meinhardt: Segmentation

Several morphogens dependent on main gradient.Location information important

Segmentation as gene activation

Reparation of a gap

Reversal

Hamahashi and Kitano: DrosophilaEmbryogenesis

Reaction diffusion of gene products regulating gene expression

Hierarchical arrangement of maternal, early and late genes

Based on known genes

Meinhardt: Snail Shells

1D reaction diffusion system.Complex shell patterning involves several

morphogens.

2D Reaction-Diffusion Systems

Wide variety of patternsLeaf primordia, fur patterns, vasculature, retinotopic maps

Barrio et. al.: Fish Patterns

Spots and leaf primordia

Vascular networks

Cells differentiate when a signal reaches a thresholdSignal production is dependent on a substrate that isremoved by differentiated cells

Hentschel & Fine:

Activity Dependent Dendritic Morphogenesis

Calcium as a morphogen.Sub membrane calcium concentration controls the local growthvelocity.Excitable membrane. Positive feedback for calcium influx.Calcium catalytic growth produces branching patterns

Hely, Graham and van Ooyen:

Dendrite branching

Elongation and branching due to MAP2 bound to microtubuli

AxogenesisAxons seek out their target using growth cones sensing

chemical gradients.

How far can a gradient guide?

Three constraints:Too low concentration: almost no receptors will be boundToo high concentration: all receptors will be boundConcentration difference across cone must be larger than noise

Relative difference:

Absolute difference:

Results in a maximum distance of 1mm for a diffusing signal,1cm for an optimally distributed substrate-bound signal.

Fleischer: Axons following chemical gradients

Bundling Model of Hentschel and van Ooyen(Model I)

Chemoattractant towards target cells

Chemoattractant from growth cones causes bundling

Chemorepellant from growth cones, dependent on target cell

chemoattractant, causes dispersion near target

Cone growth towards chemical gradient.

Model II

Instead of chemical signals from growth cones, physicalattachment when they get close enough.

Attachment strength depends on chemo attractant fromtarget.

Random axon movement.

Results

Model I produces nice fasciculation and unbundling near target.Topological Organisation.

Model II does not bundle globally, does not unbundle. Pathfinder cells.

Phenomenological Development Modeling

Cellular AutomataDiffusion Limited AggregationLindenmeyer-systems

Conclusion

Complex patterns and Organisation can beachieved by simple rules.

Diffusion of chemo attractants or morphogens caninducelong-range order.

More and more morphogens and genetic

networks have been identified.

A lot of data is waiting for modeling.

Thank You very much

Dr.S.S.D.Pandey ssd@globalsynergetic.org

Centre for Studies in Complexity

Global Synergetic Foundation

www.globalsynergetic.org

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