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.

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...

We present the Pareto task inference method (ParTI; http://www.weizmann.ac.il/mcb/UriAlon/download/ParTI) for inferring biological tasks from high-dimensional biological data. Data are described as a polytope, and features maximally enriched closest to the vertices (or archetypes) allow identification of the tasks the vertices represent. We demonstrate that human breast tumors and mouse tissues are well described by tetrahedrons in gene expression space, with specific tumor types and biological functions enriched at each of the vertices, suggesting four key tasks.

A recurring theme in biological circuits is the existence of components that are antagonistically bifunctional, in the sense that they simultaneously have two opposing effects on the same target or biological process. Examples include bifunctional enzymes that carry out two opposing reactions such as phosphorylating and dephosphorylating the same target, regulators that activate and also repress a gene in circuits called incoherent feedforward loops, and cytokines that signal immune cells to both proliferate and die. Such components are termed "paradoxical", and in this review we discuss how they can provide useful features to cell circuits that are otherwise difficult to achieve. In particular, we summarize how paradoxical components can provide robustness, generate temporal pulses, and provide fold-change detection, in which circuits respond to relative rather than absolute changes in signals.

Actors, dancers and musicians that improvise together report special moments of togetherness: high performance and synchrony, seemingly without a leader and a follower. Togetherness seems to conflict with individuality- the idiosyncratic character of each person's performance. To understand the relation of individuality and togetherness, we employed the mirror game paradigm in which two players are asked to mirror each other and create interesting synchronized motion, with and without a designated leader. The mirror game enables quantitative characterization of moments of togetherness in which complex motion is generated with high synchrony. We find that each person as a leader does basic strokes of motion with a characteristic signature, in terms of the shape of their velocity profile between two stopping events. In moments of togetherness both players change their signature to a universal stroke shape. This universal velocity profile resembles a half-period of a sine wave, and is therefore symmetric and maximally smooth. Thus, instead of converging to an intermediate motion signature, or having one player dominate, players seem to shift their basic motion signatures to a shape that is altogether different from their individually preferred shapes; the resulting motion may be easier to predict and to agree on. The players then build complex motion by using such smooth elementary strokes.