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Figure 3.

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ZDB-FIG-210927-57

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Song et al., 2021 - Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation

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Figure 3.

Cost-precision trade-off associated with the space-time-averaged measurement.

(a) Schematic of the model. (b) The optimal trade-off product $π_{T} (x_{b})$ $π_{T} (x_{b})$ obtained numerically with respect to the location of the target boundary position normalized by the sensor size ( $x_{b} / a$ $x_{b} / a$ ). The gray hashed area represent the inaccessible regions. Shown are the trade-off products of the morphogens profiles of Bcd, Wg, Hh, and Dpp. (c) The black line denotes the optimal characteristic decay length ( $λ_{\min}$ $λ_{\min}$ ) with respect to the position $x_{b} / a$ $x_{b} / a$ . The color scale indicates the trade-off product $π_{T} (x_{b})$ $π_{T} (x_{b})$ computed for each pair of $λ / a$ $λ / a$ and $x_{b} / a$ $x_{b} / a$ values. The gray dotted line depicts the linear approximation of $λ_{\min}$ $λ_{\min}$ . The white dotted line depicts the linear approximation of $λ_{\min}$ $λ_{\min}$ for the point measurement model. In (b) and (c), the depicted trade-off product is normalized by $α_{o}$ $α_{o}$ . The parameters for the naturally occurring morphogen profiles are further described in the Appendix 3, Length scales of Bcd, Wg, Hh, and Dpp, and Appendix 3—table 1.

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