Some physical aspects of embryogenesis Ana Hočevar Department of Theoretical Physics (F-1) “Jožef Stefan” Institute Adviser: doc. dr. Primož Ziherl January 2009

Outline Introduction Gastrulation = invagination and elongation Physical models of invagination Model of convergent extension Cell pattern formation Conclusions

living systems with many interacting components and a goal-directed behaviour → reproduction seeks general principles limited to defined classes (animals vs. plants) “laws” rarely in mathematical terms (e.g.,promotion of evolution by natural selection) “laws” less exact than in physics DNA is the carrier of genetic information, the sequence of bases is of central importance Biology vs. Physics nonliving world → goal-directed behaviour irrelevant idealists seeking for universal laws, valid everywhere in time and space, expressed in a mathematical form model the system in terms of minimal number of relevant features DNA is a long polyelectrolyte with interesting elastic properties – sequence of bases is irrelevant Biological systems are also physical systems! We expect the role of physics to be particularly obvious in early animal development → embryogenesis. “The obvious inability of present-day physics and chemistry to account for such events is no reason at all for doubting that they can be accounted for by those sciences.” Schrödinger

THE DEVELOPING EMBRYO AND HEAD-TO-TAIL BODY AXIS FORMATION a period when the role of physics is evident 1 cellcells divideblastula = a spheregastrulationgastrula invagination, elongationcell pattern formation an important process during which the main body axis is formed accompanied by gastrulation GASTRULATION

Physical description of infolding Drasdo-Forgacs model embryo is an aggregate of cells assign energy to each cell: Interaction energy Bending energy Rotational energy Monte Carlo simulation reproduces invagination.

Simulation works in three stages: Cells divide, volume of daughter cells equal to the volume of the first cell, spontaneous curvature = 0 Blastula is formed, proliferation is arrested, non-uniform curvature is introduced Whole region simultaneously folds inwards D. Drasdo and G. Forgacs (2000)

Invagination is described as a pathway in the v-c diagram. B. Božič et al. (2006) Svetina model blastula = a vesicular object shape governed by elastic energy minimum reduced volume: integrated vesicle curvature:

Model of convergent extension Tissue narows along a given axis and elongates in the perpendicular direction due to cell intercalation Important in a variety of processes, not only gastrulation (e.g., Drosophila germband elongation) K. Irvine and E. Wieschaus (1994)

Zajac-Jones-Glazier model Differential adhesion hypothesis (DAH) Cell-cell adhesive energy has a certain anisotropy J ll, J ss, J ls... dissimilar energy densities L ll, L ss, L ls... total cell-cell contact lengths of each type l, s... average long and short side lengths of each cell S l, S s... total contact length between long/short cell sides and the surrounding N... number of cells Disordered aggregate: Three types of cell contacts Ordered aggregate: Free of mixed contacts

Total energy: Ordered elongated aggregates have lower energy! Simulations reproduce tissue extension. real Xenopus embryo simulation (Zajac et al. 2003)

Convergent extension is not important only in gastrulation: Ascidian notochord formation chordates vertebrates ascidians urochordates

Early embryonic pattern formation All cells have equal DNA – how do they “know” whether to develop into a tail or into a head? DNA represents a genetic code for protein manufacturing – but not all encoded proteins are produced in all cells! → GENE EXPRESSION Gene expression is governed by certain proteins – transcriptor factors.

The mother attaches mRNA for Bicoid protein to the end of the egg! Bicoid protein concentration gradientHunchback protein concentration Cell pattern formation and differentiation is driven by diffusion. Pattern formation in Drosophila embryo T. Gregor et al. (2005)

Conclusions Processes in simple animal embryos can be described by biomechanical models – Drasdo-Forgacs: curvature anisotropy – Svetina: integrated vesicle curvature change – Zajac-Jones-Glazier: differential adhesion – Diffusion driven pattern formation Much room for improvement – More general laws – A single model that would account for all stages of gastrulation Gastrulation in Drosophila embryo