Optimal placement of multiple morphogen sources

Y. Morishita, Y. Iwasa

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


During development, cells grow, differentiate, divide, and die according to their spatial positions, yet the positional information given to cells by morphogens (diffusive chemicals) includes considerable noises from various origins. In this paper, we examine a relationship between fluctuations in morphogen concentrations that the cells receive and the precision of positional specification by the morphogens in multidimensional space. As a method to quantify the precision, we introduce a measure of "ambiguity of positional information," based on the information entropy. We discover that the location of morphogen sources crucially affects the ambiguity, and that the ambiguity becomes minimum when the angle made by gradient vectors of different morphogens cross at a right angle in a target region under a given organ geometry (orthogonality principle). We conjecture that morphogen sources in development might be placed at the nearly optimal position that minimizes the ambiguity of positional information. This is supported by experimental data on the configurations of two major sources of spatial patterning, the apical ectodermal ridge (AER) and the zone of polarizing activity (ZPA), in vertebrate limb development. Indeed, their predicted configuration agrees very well with the one observed in experiments. We believe that the placement of morphogen sources to minimize the ambiguity of positional information is a basic principle in development of multicellular organisms beyond this particular example.

Original languageEnglish
Article number041909
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
Publication statusPublished - Apr 16 2008

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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