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Fig. 2. Cell-to-cell variability in the source or target affects the gradient fluctuations differently. (A) Idealized situation with fluctuating production rate in the source (different colors), but identical target cells. Morphogen concentration c along a slice (dashed line) in the y-direction close to the source (bottom left), and at a larger distance from the source (bottom right). (B) Theoretical (x) for the situation in A based on the model in Fig. 1C in two dimensions. Here, j fluctuates, while D and k are constant. (x) decreases with increasing distance x from the source, as in A. (C) The opposite situation to A: different target cells, identical source. (D) Calculation corresponding to C based on the model in Fig. 1C in two dimensions. D and k fluctuate, j is constant. Following an abrupt decrease very close to the source, (x) increases with increasing x. (E) (x) when cell-to-cell variability affects both the source and the target, i.e. with fluctuating j, D and k. The effects in A and C are superimposed. A pronounced minimum of (x) at a finite distance from the source occurs. Whereas its location and the magnitude of (x) depend on parameter choice, the qualitative behavior of the curve is independent of these parameters for different noise intensities of the same order of magnitude. Parameters in B,D,E are _D/a=7, _D/D₀=1, _k/k₀=1, _j/j₀=0.37 (for details, see continuum limit and Fig. S2 in the supplementary material).

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