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Figure 2

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ZDB-FIG-210927-32

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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 2

Cost-precision trade-off associated with the point measurement.

(a) Schematic of the model. (b) The position-dependent lower bound of the trade-off product $π_{o, \min} (x_{b})$ $π_{o, \min} (x_{b})$ , obtained numerically. The gray hashed area represent the inaccessible regions. The trade-off product of the morphogen profiles of Bcd, Wg, Hh, and Dpp are shown in the respective insets. (c) The black line denotes the optimal characteristic decay length ( $λ_{\min}$ $λ_{\min}$ ) with respect to the position $x_{b} / L$ $x_{b} / L$ . The color scale indicates the trade-off product $π_{o} (x_{b})$ $π_{o} (x_{b})$ computed for each pair of $λ / L$ $λ / L$ and $x_{b} / L$ $x_{b} / L$ values. The grea dotted line depicts the linear approximation of $λ_{\min}$ $λ_{\min}$ at large $L$ $L$ . In (b) and (c), the depicted trade-off product is normalized by $α_{o} L / l_{cell}$ $α_{o} L / l_{cell}$ . The parameters for the naturally occurring morphogen profiles are further described in Appendix 3, Length scales of Bcd, Wg, Hh, and Dpp, and Appendix 3—table 1.

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