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When the internal box size r tends to the lattice size R, both clustered and segregated configurations converge to the uniform configuration.
When the box size r converges toward the lattice size R, the clustered and segregated configurations are closing to the uniform one.
With the uniform or segregated configurations however, the dynamics exhibit a qualitative change as D decreases below 2×10−2, switching from an oscillatory regime to a stationary one where all species fluctuate around a constant steady state.
In the uniform configuration, the 15 gene copies are positioned at independent randomly-chosen lattice sites, whereas in the clustered and segregated configurations, we start by positioning internal boxes of linear size r at random positions in the lattice, and place the gene copies inside the boxes.
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As a comparison, the segregation of gas and liquid phases was studied under microgravity resulting in similar segregated configuration determined by surface tension (Figure 3).
The clustered configuration corresponds to a first case of demixing: G T gene triplets composed of one G 0, one G 1 and one G 2 gene are restricted inside non-overlapping subregions of space The segregated configuration illustrates a different case of demixing: the 3 gene types i ∈{0,1,2} are segregated into 3 subregions of space, each subregion containing all the G T copies of a given type.
By definition, with a unique copy of each gene (G T =1), the uniform and segregated spatial configurations are identical.
The results of the 2D individual-based stochastic simulations for the segregated gene configuration with large demixing however show a strikingly different behavior.
The segregated and clustered configurations illustrated in Figure 3 above correspond to high demixing (i.e. r/ R<0.010).
Selected probes segregating 1 1 (pseudo-testcross) and 3 1 (dominant markers in F2) received the acronym of BC and F2 reflecting their segregation configurations.
The spatial configuration of the genes corresponded to the (a") uniform, (b") clustered (r =3) or (c") segregated (r =3) configuration, corresponding to the FZCA points labelled (a"), (b") and (c"), respectively in Figure 5 B. Here, G T =1, while all other parameters were according to the standard set defined in the Methods section.
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