Pattern, growth, and control

Abstract

Systems biology seeks not only to discover the machinery of life but to understand how such machinery is used for control, i.e., for regulation that achieves or maintains a desired, useful end. This sort of goal-directed, engineering-centered approach also has deep historical roots in developmental biology. Not surprisingly, developmental biology is currently enjoying an influx of ideas and methods from systems biology. This Review highlights current efforts to elucidate design principles underlying the engineering objectives of robustness, precision, and scaling as they relate to the developmental control of growth and pattern formation. Examples from vertebrate and invertebrate development are used to illustrate general lessons, including the value of integral feedback in achieving set-point control; the usefulness of self-organizing behavior; the importance of recognizing and appropriately handling noise; and the absence of "free lunch." By illuminating such principles, systems biology is helping to create a functional framework within which to make sense of the mechanistic complexity of organismal development.

Figure 1

Control objectives in morphogenesis. The figure compares some of the experimental systems, discussed in this review, that are being used to study developmental regulation, canalization, robustness, and precision. The Drosophila wing imaginable disc (A) is an excellent model for both growth control and pattern formation (through the action of long-range morphogens, such as Hedgehog, Decaptentaplegic [Dpp], and Wingless). The wing disc demonstrates both scaling of pattern to size and scaling of size to pattern. The early Xenopus embryo (B) provides an excellent system for studying pattern formation in the absence of growth, as well as the scaling of pattern to size. Pattern formation has been extensively studied along the anteroposterior axis (C) and the dorsoventral axis (D) of the Drosophila embryo. Anteroposterior patterning is initiated by the transcription factor Bicoid, which acts as a long-range morphogen within the cytoplasm of the syncytial early embryo, controling a cascade of long-range and self-organizing events that segment the embryo into specific regions (stripes). Dorsoventral patterning utilizes the long-range morphogen Dpp to trigger, among other things, a self-organizing process at the dorsal midline. Self-organization also characterizes the mechanism by which narrow, straight veins are positioned on the Drosophila wing (E) during the pupal stage. The development of pigment stripes in teleost fish, such as the zebrafish (F), provides another opportunity to investigate self-organizing patterns, especially in the context of regeneration, which has shed new light on mechanism. Mammalian brain (G) and muscle (H) are good models of organ size control; in the case of muscle, genetic studies have revealed a critical role for feedback from chalones. Feedback regulation of growth has long been known about through studies on regeneration of the mammalian liver (I). More recently, studies in the mouse olfactory epithelium (J) have shed light on mechanisms underlying feedback control of both size and regenerative speed. Analogous mechanisms appear to be at work in mammalian hematopoiesis (K). Other excellent experimental systems, not shown here, include the early vertebrate spinal cord and hindbrain (pattern formation); vertebrate limb buds (pattern formation, growth control); vertebrate and invertebrate retinas (growth control); and plant shoot apical meristems (pattern formation). Figure 1J courtesy of Kim Gokoffski and Anne Calof.

Figure 2

Two modes of organization in the control of pattern. The performance objectives of patterning systems include both controlling the locations of events relative to each other, and controlling them relative to pre-specified landmarks. Turing patterns are one example of self-organizing pattern (A). Repeated patterns form spontaneously, and exhibit spacings that depend primarily upon the details of local signal activation, inhibition and spread, with relatively little influence from events outside the system. In contrast, long-range morphogen gradients typify boundary-driven organization (B). They inform cells of their location relative to fixed landmarks. In both cases, morphogens establish a characteristic “length scale” or “wavelength”. In the first case (A), pattern is a direct reflection of that scale, such that elements (rows of spots) occur once per length scale. In the second case (B), the length scale simply determines how gradually “positional information” decays over space; where pattern elements occur (blue, red, green blocks) depends upon how cells interpret the positional information they receive.

Figure 3

Versatility of integral feedback control. Integral feedback is particularly useful for achieving set-point control, in which a system achieves a pre-specified steady-state behavior independent of external (and often many internal) perturbations. The essence of integral control is to relay a signal that reflects the time integral of error (the difference between the actual and desired state of the system). Biological systems often use this type of control to achieve robust, perfect adaptation, i.e. to return to a zero-activity state even after sustained perturbations. For example, in bacterial chemotaxis (A) integral feedback adaptively modulates signaling to maximize sensitivity to changes in chemoattractant levels (Alon et al., 1999; Yi et al., 2000). Integral feedback in the control of cell growth has been described for two distinct systems. Production of chalones, such as GDF11, by differentiated cells in the olfactory epithelium inhibits progenitor self-renewal (B), providing a feedback signal that increases (decreases) in time as long as the probability of progenitor cell renewal is greater (lesser) than 50% (Lander et al., 2009a). Mechanical compression within the Drosophila wing disc increases with disc size (C), potentially providing a growth inhibitory signal that increases in time as long as cells are proliferating (Shraiman, 2005). Integral feedback can also be used to make a morphogen gradient scale to fit the territory between its source of production and a distant boundary (D). In this case, the morphogen inhibits the production of a molecule that acts at long range to expand the range (length scale) of the morphogen (Ben-Zvi and Barkai, 2010). In such a scenario, buildup of the expander over time provides a time- integrated error signal, which only vanishes when the morphogen gradient expands all the way to the distant boundary.

Figure 4

Reducing noise in pattern formation. In boundary-organized pattern formation, the ability of cells to form organized patterns depends upon the accuracy with which they can measure their positions within a morphogen gradient. Under idealized conditions (A), cells that autonomously adopt a new behavior at a particular threshold value of morphogen concentration will produce a sharp spatial border. In reality, reading a morphogen gradient is fraught with noise: Variability in morphogen level, in gene expression, in cell size, and the stochastic nature of biochemical processes, will cause autonomously acting cells to produce “salt-and-pepper” borders (B). Many sources of noise lead to fluctuations on a time scale too slow for cells to compensate simply by integrating signals over time. In principle, processes that enable cells to collaborate with their neighbors can also reduce the noisiness in morphogen gradient interpretation, producing smoother borders. Such collaboration can take many forms. For example, in (C), the noisy signal in panel B was used to drive the production of an activator in a Turing process (the activator induces its own longer-range inhibitor), the level of which was used as a source of positional information. Note the improved border sharpness. Analyses such as this suggest that the combined use of different modes of pattern organization (boundary- vs. self-organized) can be useful in achieving robust patterning.

Figure 5

Performance tradeoffs and morphogen gradients. A. For simple morphogen gradients formed by diffusion with constant receptor-mediated uptake, the ability to achieve performance objectives (e.g., robustness to uncertainty in morphogen production rate; positional precision; and patterning range) is constrained by unintended side effects of performance enhancing-strategies, such as altering levels of morphogen and receptor expression or function. B. These tradeoffs may be analyzed quantitatively, by calculating robustness and precision as a function of distance and gradient range. S_x,v is the sensitivity of position to the rate of morphogen production; w is the size the window of imprecision due to ligand- binding noise. The filled box shows the “useful fractions” where performance constraints on both S_x,_v and w are met. C. Parameter space exploration suggests that there is some distance beyond which a simple morphogen gradient cannot simultaneously achieve robustness to morphogen synthesis rate, and positional precision, at any location. Useful fractions are plotted as a function of patterning range, for various values of gradient length scale. Panels B and C are adapted from (Lander et al., 2009b).