Bulletin of Mathematical Biology (2006) 68: 1073–1094 DOI 10.1007/s11538-006-9124-6 ORIGINAL ARTICLE Feedback Loops, Reversals and Nonlinearities in Lymphocyte Development Ramit Mehr The Mina & Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan 52900, Israel Received: 3 October 2005 / Accepted: 13 February 2006 / Published online: 23 June 2006 C  Society for Mathematical Biology 2006 Abstract Systems of differentiating cells are often regarded by experimental biol- ogists as unidirectional processes, in which cells spend a fixed time at each succes- sive developmental stage. However, mathematical modeling has in several cases revealed that differentiating cell systems are more complex than previously be- lieved. For example, non-linear transitions, feedback effects, and even apparent reversals have been suggested by our studies on models for the development of lymphocytes and their receptor repertoires, and are reviewed in this paper. These studies have shown that cell population growth in developing lymphocyte subsets is usually nonlinear, as it depends on the density of cells in each compartment. Additionally, T cell development has been shown to be subject to feedback regu- lation by mature T cell subsets, and B cell development has been shown to include a phenotypic reflux from an advanced to an earlier developmental stage. The chal- lenges we face in our efforts to understand how the repertoires of these cells are generated and regulated are also discussed here. Keywords B and T lymphocytes · Natural killer cells · Cellular proliferation · Cellular differentiation · Repertoire development · Computational modeling · Simulations Abbreviations BCR, B cell receptor; BM, bone marrow; DN, double-negative; DP, double-positive; FTOC, fetal thymus organ culture; MHC, major histocompatibil- ity complex; NK, natural killer; TCR, T cell receptor. 1. Introduction Systems of cell differentiation are usually regarded, or at least depicted by biol- ogists, as simple “decision trees,” in which successive cellular choices restrict the Corresponding author. E-mail addresses: mehrra@mail.biu.ac.il, URL: http://repertoire.os.biu.ac.il (Ramit Mehr).