(430p) Robustness and Optimality in Developing Organisms

In Nature, a developing organism must overcome significant variations in both environmental conditions (such as temperature, humidity, nutrition) as well as genetic backgrounds [1]. Despite these variations, embryos in the wild display a high degree of robustness. Experiments designed to probe the limits of developmental robustness often impose even harsher conditions on embryogenesis: from loss-of-funciton mutations to exposure to steep temerpature gradients [2,3]. Remarkably, development proceeds normally under many of these conditions. Molecular studies have ascribed this robustness to the underlying regulatory networks [4]. In particular, experimental and theoretical studies have demonstrated robustness at the level of the receptor-mediated tissue patterning network [5-7]. Here, we discuss a study regarding the optimality of the shape of common receptor-mediated signaling gradients, as related to the robustness of downstream targets. In a developing organism, cell-cell communication, through a ligand/receptor pair, is responsible for tissue patterning. In the paradigm of the morphogen gradient model, a locally secreted ligand spreads through the extracellular space, invoking differential, concentration-dependent responses in the neighboring cells. However, despite the prevalence of morphogen gradients in the development of all animal species, the shapes of such gradients remain a relative mystery. Remarkably, theoretical studies of the formation of morphogen gradients, when taking into account the known biophysical processes, have shown that the shape of the gradient is largely dependent on a single dimensionless parameter: the Thiele modulus [7-9]. Using scaling arguments, we expect the value of the Thiele modulus, in biological contexts, to be ?order one [7].? A very small Thiele modulus will result in a flat gradient, incapable of differentially patterning the tissue, while the sharp gradient resulting from a large Thiele modulus will prove similarly incapable. This suggests there may be an optimal value of the Thiele modulus, which leads to the ?best? gradient shape. Indeed, in the analysis of the simplest cases, this optimal value is related to the spatial location of the most robust gene expression with respect to perturbations in receptor concentration. We illustrate these simple cases and show more realistic examples as well [7,10]. [1] Houchmandzadeh, B.; Wieschaus, E. & Leibler, S., Nature, 2002 , 415, 798-802. [2] Golembo, M.; Yarnitzky, T.; Volk, T. & Shilo, B., Genes Dev., 1999 , 13, 158-162. [3] Lucchetta, E.M.; Lee, J.H.; Fu, L.A.; Patel, N.H. & Ismagilov, R.F., Nature, 2005, 434, 1134-1138. [4] Eldar, A.; Shilo, B-Z.. & Barkai, N., Curr. Opin. Genet. Dev., 2004 , 14, 435-439. [5] Eldar, A.; Dorfman, R.; Weiss, D.; Ashe, H.; Shilo, B-Z.. & Barkai, N., Nature, 2002, 419, 304-308. [6] Eldar, A.; Rosin, D.; Shilo, B-Z.. & Barkai, N., Dev. Cell, 2003, 5, 635-646. [7] Goentoro, L.; Kowal, C.P.; Martinelli, L.; Schupbach T.; & Shvartsman, S.Y., submitted for publication. [8] Gregor, T.; Bialek, W.; Steveninck, R.R.d.R.v.; Tank, D.W. & Wieschaus, E.F. Proc. Natl. Acad. Sci. USA, 2005, 102, 18403-18407. [9] Lander, A.D.; Nie, Q. & Wan, F.Y., Dev. Cell, 2002, 2, 785-796. [10] Reeves, G.T.; Kalifa, R.; Klein, D.E.; Lemmon, M.A. & Shvartsman, S.Y., Dev. Biol., 2005, 284, 523-535.