Biological systems that perform multiple tasks face a fundamental trade-off: A given phenotype cannot be optimal at all tasks. Here we ask how trade-offs affect the range of phenotypes found in nature. Using the Pareto front concept from economics and engineering, we find that best-trade-off phenotypes are weighted averages of archetypes--phenotypes specialized for single tasks. For two tasks, phenotypes fall on the line connecting the two archetypes, which could explain linear trait correlations, allometric relationships, as well as bacterial gene-expression patterns. For three tasks, phenotypes fall within a triangle in phenotype space, whose vertices are the archetypes, as evident in morphological studies, including on Darwin's finches. Tasks can be inferred from measured phenotypes based on the behavior of organisms nearest the archetypes.

SUMMARY Many sensory systems, such as vision and hearing, show a response that is proportional to the fold-change in the stimulus relative to the background, a feature related to Weber’s law. Recent experiments suggest such a fold-change detection feature in signaling systems in cells: a response that depends on the fold-change in the input signal, and not on its absolute level (Cohen-Saidon et al., in press; Goentoro and Kirschner, submitted; both in this volume). It is therefore of interest to find molecular mechanisms of gene regulation that can provide such fold-change detection. Here we demonstrate theoretically that fold-change detection can be generated by one of the most common network motifs in transcription networks, the incoherent feedforward loop (I1-FFL), in which an activator regulates both a gene and a repressor of the gene.The fold-change detection feature of the I1-FFL applies to the entire shape of the response, including its amplitude and duration, and is valid for a wide range of biochemical parameters.

Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold changes in input and not on absolute levels. Thus, a step change in input from, for example, level 1 to 2 gives precisely the same dynamical output as a step from level 2 to 4, because the steps have the same fold change. We ask what the benefit of FCD is and show that FCD is necessary and sufficient for sensory search to be independent of multiplying the input field by a scalar. Thus, the FCD search pattern depends only on the spatial profile of the input and not on its amplitude. Such scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing/convecting chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. Furthermore, we show that FCD entails two features found across sensory systems, exact adaptation and Weber's law, but that these two features are not sufficient for FCD. Finally, we present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feed-forward loops. We find that bacterial chemotaxis displays feedback within the present class and hence, is expected to show FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study, thus, suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields.adaptation | sensory response | spatial search O rganisms and cells sense their environment using sensory systems. Certain sensory systems have been extensively studied, and their input-output relations are well-characterized, including human senses, such as vision (1, 2), touch, and hearing, and unicellular senses, such as bacterial chemotaxis (3). Many sensory systems have common features. One such feature is exact adaptation in which the output to a change in input to a new constant level gradually returns to a level independent of the input. A second common feature, called Weber's law, states that the maximal response to a change in signal is inversely proportional to the background signal (4): Δy = kΔu/u 0 , where k is a constant, y is the output, and Δu is the signal change over the background u 0 . Weber's law in vision, chemotaxis, and other sensory systems applies over a range of several orders of magnitude of background input levels. Note that this definition stems from current practice that generalizes Weber's original measurements on psychophysical threshold sensitivity (4-7).Recent studies of the input-output properties of certain cellular signaling systems (8, 9) suggest that these systems show a feature called fold-change detection (FCD): a response whose entire shape, including its amplitude and duration, depends only on fold changes in input and not on absolute levels (10) (Fig. 1 A and...

Evolutionary theory has long argued that the entrenched rules of development constrain the range of variations in a given form, but few empirical examples are known. Here we provide evidence for a very deeply conserved skeletal module constraining the morphology of the phalanges within a digit. We measured the sizes of phalanges within populations of two bird species and found that successive phalanges within a digit exhibit predictable relative proportions, whether those phalanges are nearly equal in size or exhibit a more striking gradient in size from large to small. Experimental perturbations during early stages of digit formation demonstrate that the sizes of the phalanges within a digit are regulated as a system rather than individually. However, the sizes of the phalanges are independent of the metatarsals. Temporal studies indicate that the relative sizes of the phalanges are established at the time of initial cell condensation. Measurements of phalanges across species from six major taxonomic lineages showed that the same predictable range of variants is conserved across vast taxonomic diversity and evolutionary time, starting with the very origins of tetrapods. Although in general phalangeal variations fall within a range of nearly equal-sized phalanges to those following a steep large-to-small gradient, a novel derived condition of excessive elongation of the distal-most phalanges has evolved convergently in multiple lineages, for example under selection for grasping rather than walking or swimming. Even in the context of this exception, phalangeal variations observed in nature are a small subset of potential morphospace.developmental module | developmental constraint | phalanx

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