Modelling Cell Signalling and Pattern Formation

1. Modelling Cell Signalling and Pattern Formation Nick Monk Department of Computer Science Erik Plahte & Siren Veflingstad Agricultural University of Norway, Ås Collaboration: WTEC Systems Biology Study Group, 8 July 2004

2. Delta-Notch Signalling: the Neurogenic Network Meir et al., Current Biology 12, 778-786 (2002).

3. Intercellular Signalling Networks • Model as a regular lattice of cells (epithelial sheet) • Intercellular signalling couples gene-protein interaction networks within each cell • May be diffusive or juxtacrine signalling

4. Questions and Issues • What limitations and possibilities result from patterning on cellular arrays? • At what level of detail do we have to model the internal dynamics of cells in order to understand patterning in tissues? Cells are not well-stirred bags of chemicals; internal structure is important. • How important are transient dynamics? • In development, patterning is hierarchical. Patterns are not formed from homogeneity, but from earlier patterns. Can we incorporate this in our models? • What features of intercellular signalling networks ensure that robustness and regulative capacity emerge at the tissue/organism level?

5. Stochastic fate assignment Loss of key genes (e.g. Dl and N) leads to over-assignment of bristles Dl and N expressed uniformly during assignment Uniform unregulated overexpression of Dl or N has little effect Delta, Notch,… Lateral Inhibition: Bristle Spacing Renaud & Simpson, Dev. Biol. 240, 361–376 (2001).

6. Delta-Notch–mediated cell competition Dl activates N on neighbouring cells (signalling) N activity represses Dl “activity” (within the same cell) N activity determines cell fate (via regulated transcription) D1 N2 N1 D2 Di = average of D in cells neighbouring cell i f and g are increasing and decreasing, resp.  and  are 1st order degradation rates

7. Typical Behaviour: Lateral Inhibition Collier et al., J. theor. Biol. 183, 429–446(1996).

8. The neurogenic network: Drosophila

9. Eukaryotic transcription and time delays • There is an irreducible delay of ~15–20 min from initiation of a transcript to appearance of functionalmRNA in the cytoplasm • The delay can be much longer (>16 hrs for human dystrophin) • Delay equations should be used to model transcription

10. (or distributed delay equivalents) Delayed Delta-Notch cell competition To account for the three transcriptional steps in the neurogenic network, a delay (of around an hour) should be incorporated in the competition model (Delta alone takes ~20 min to transcribe). Deal first with the simple model to assess the effect of the delay. D1 N2   N1 D2

11. Discrete vs. distributed delay Fixed:  = 100 Distributed:  = 100 +/– 32  = 3.5 Oscillations and spatial patterns

12. Bad news for the neurogenic network model “best case” scenario: growth of pattern from homogeneous steady state (hss). One cell on each side of hss. If non-delayed model takes 2 hours to pattern, the model with a 1 hour delay takes ca. 14 hours. More generally, the time taken to pattern grows rapidly with the delay.

13. The neurogenic network: Drosophila

14. The neurogenic network: C. elegans

15. Phase locking and spatial patterning Spatially inhomogeneous initial conditions can lead to blocks of phase-locked cells, separated by sharp boundaries (which can act as centres of spatial pattern formation) [c.f. somitogenesis]

16. Hes1 oscillates in cultured mouse cells hes1 Hes1 mRNA – Hes1 protein Half–lives: mRNA: ~24 min protein: ~22 min … but a non-delayed (ODE) model can’t oscillate… Hirata et al. predicted extra components in the feedback loop. (c.f. physics/engineering) Hirata et al., Science 298, 840–843(2002).

17.  = 18.5 min Delay model for the Hes1 feedback loop x hes1 Hes1 mRNA  y Hes1 protein The transcriptional delay has been observed directly for Hes7 Bessho et al.Genes & Dev. 17, 1451 (2003).

18. P53–mdm2 feedback loop x p53 z Mdm2  y mdm2 mdm2 Bar-Or et al., PNAS 97, 11250–11255(2000). [predicted “factor X” in loop using ODE model]

19. Hoffmann et al., Science 298, 1241–1245(2002) Nuclear NF-B – IB feedback loop Signal (e.g. TNF) NF-B IB IB nucleus IB IB note that the constitutive inhibitors (IB and IB) damp the oscillations

20. Conclusions • It is important to treat cells seriously in models of pattern formation. • Time delays and spatial heterogeneity can be critical. • Transcription networks involve significant delays: these affect parameter fitting, dynamics and network prediction. • The N  Dl interaction is unlikely to be mediated by transcription (during competition). Post-translational protein–protein interaction? Suggest that (de novo) pattern formation is a 2–step process: 1. labile patterning by protein–protein interaction 2. fixation by regulation of gene expression.