The Measure of Success: Constraints, Objectives, and Tradeoffs in Morphogen-mediated Patterning

A large, diverse, and growing number of strategies have been proposed to explain how morphogen gradients achieve robustness and precision. We argue that, to be useful, the evaluation of such strategies must take into account the constraints imposed by competing objectives and performance tradeoffs. This point is illustrated through a mathematical and computational analysis of the strategy of self-enhanced morphogen clearance. The results suggest that the usefulness of this strategy comes less from its ability to increase robustness to morphogen source fluctuations per se, than from its ability to overcome specific kinds of noise, and to increase the fraction of a morphogen gradient within which robust threshold positions may be established. This work also provides new insights into the longstanding question of why morphogen gradients show a maximum range in vivo.In recent years, much research on morphogen gradients has shifted from purely mechanistic questions—how gradients form and how morphogens signal—to strategic ones—how gradients perform well in the face of various kinds of constraints and perturbations. Forty years ago, Francis Crick was among the first to call attention to constraints that morphogens face, noting that the time required to spread a signal by random transport through a tissue varies with the square of distance (Crick 1970). Using order-of-magnitude calculations, he argued that observed biological maxima for morphogen-mediated patterning were just about where they should be if morphogen signals spread by aqueous diffusion.Although the idea that diffusion time is what limits the sizes of morphogen gradients remains untested, Crick''s work established a precedent of seeking explanations for developmental processes in terms of constraints imposed by the physical world. In the area of biological pattern formation, continued interest in how real-world limits constrain mechanisms has led many current investigators to focus on matters of robustness, the engineering term that describes the relative insensitivity of a system''s behavior to perturbations it may be expected to encounter. With respect to morphogen gradients, most work has focused on parametric robustness, i.e., insensitivity to parameter values (e.g., the dosage of genes, levels, or rate constants of enzymes Eldar et al. 2002; Eldar et al. 2003; Eldar et al. 2004; Bollenbach et al. 2005; Shimmi et al. 2005; White et al. 2007]). Some investigators have also focused on the “precision” of morphogen gradients, which may be understood as robustness to the causes and effects of natural variation among individuals in a population (Houchmandzadeh et al. 2002; Gregor et al. 2007; Tostevin et al. 2007; Bollenbach et al. 2008; Emberly 2008).Remarkably, after hardly a decade of intensive study of such questions, we find ourselves awash in a sea of diverse and intriguing mechanisms for conferring one or another type of robustness on morphogen-mediated patterning. Mechanisms that operate at the level of gradient formation include self-enhanced morphogen degradation (Eldar et al. 2003), facilitated transport (Eldar et al. 2002; Shimmi et al. 2005), serial transcytosis (Bollenbach et al. 2005), presteady state patterning (Bergmann et al. 2007), and competition between morphogens for binding to inhibitors (Ben-Zvi et al. 2008). Mechanisms that operate at the level of morphogen detection and interpretation include morphogenetic apoptosis (Adachi-Yamada and O''Connor 2002), cell rearrangement (Ashe and Briscoe 2006), integration of signals from multiple morphogens (McHale et al. 2006; Morishita and Iwasa 2008), and various types of local cell-to-cell signaling (e.g., Amonlirdviman et al. 2005).Why so many strategies? Biologists are often quick to ascribe multiplicity to redundancy, but the perspective of engineering suggests a different view. Most engineers accept the “no free lunch” principle (also referred to as “conservation of fragility”), which states that any mechanism that increases robustness in one setting (i.e., to one type of perturbation, or with respect to one type of output) always compromises it in another. The fact that every strategy comes at a price has been offered as an explanation for the seemingly inescapable fragility of highly engineered, modern technology (Carlson and Doyle 2002). By building complex machines that resist everything we think of, we inevitably create susceptibilities to the things we neglected. Although biology is not the result of human engineering, we have no reason to believe that natural selection can circumvent the limits that engineers confront.In a world of no free lunch, one must evaluate a strategy not just by what it is good for, but the “price” of using it. With regard to morphogen-mediated patterning, it is reasonable to suggest that diverse strategies exist because each comes at a different price. If so, achieving meaningful biological understanding requires that we engage in a sort of cost-benefit analysis, in which each strategy is evaluated in the context of the performance objectives of the organism and constraints of the physical world. This is a tall order, as there is a great deal we still do not know about the performance needs of developing organisms (for example, for all the work performed so far on morphogen gradient robustness, we still know little about the magnitudes of the perturbations that need to be withstood). Nevertheless, there is no reason not to get started, as even through the early investigation of hard questions, one commonly learns useful things.