Spatial molecular model

We implemented our optimized molecular model on a simplified template of a seedling. The template consisted of approximately 800 cells, classified into cotyledon, hypocotyl, root, and root tip regions (Fig 1B). Each cell contained an implementation of the revised compact model. To simulate growth of the seedlings, we added a row of cells to the root tip every 24 h. During this growth, we kept the root tip region of the template fixed in size. To do this, after the addition of new cells, the previously uppermost root tip cells became root cells instead.

We set the light sensitivity of the cell, L_sens , to vary depending on the position within the template. In doing so, we found that modest differences in L_sens were sufficient to generate period differences between regions. To approximate the period differences that we observed between regions in experiments (Fig 2A) we set L_sens  = 1.6 for cotyledon cells, L_sens  = 1.0 for hypocotyl cells, L_sens  = 0.65 for root cells, and L_sens  = 0.95 for root tip cells. As the template grows, the uppermost root tip cells become root cells, so the light sensitivity of these cells decreases so that they have a sensitivity characteristic of root cells, L_sens  = 0.65. This caused the clock period of these cells to slow.

As the coupling agents have yet to be clearly identified by experimental studies, we initially assumed individual cells to be coupled through CL. Our model for coupled plant cells is described as follows:

As in the revised single‐cell model, cαm and cαp represent the concentration of the α‐th mRNA and protein (or protein complex) respectively for α = CL, P97, P51, and EL, in the i‐th cell (i=1,2,…,N). P again represents activity of the dark accumulated protein P. To generate cell‐to‐cell variability in periods, we multiply the derivative with respect to the time of each molecular species by the time scaling parameter τ. τ is a real number randomly selected from the normal distribution N(1, 0.059), N(1, 0.028), N(1, 0.073), N(1, 0.089) for cells from the cotyledon, hypocotyl, root, or root tip respectively, as informed by the analysis of single‐cell experimental data (see “Characterizing clock periods from experiments”).

In the first equation, the CL gene is locally coupled to its neighboring cells, where J_local is the coupling strength and c¯CL,im=14∑j∈NicCL,jm represents averaged expression level over 4 neighboring cells (left, right, above, and below). In the case of local coupling between 8 neighboring cells (left, right, above, below, left above, left below, right above, and right below) or global coupling, the averaged expression becomes c¯CL,im=18∑j∈NicCL,jm or c¯CL,im=1N∑j=1NcCL,j(m) respectively. In Fig EV2 we varied the identity of the local coupling component. Here, the averaged expression becomes c¯α,im=14∑j∈Nicα,jm or c¯α,ip=14∑j∈Nicα,jp for coupling through mRNA or protein respectively, for α = CL, P97, P51, EL. The coupling term is appended to the equation of the corresponding molecular species. We set the local coupling strength as J_local  = 0, 0.01, 0.1, 1, 2, or 4.

In Fig ​Fig4,4, we simulated long‐distance coupling between the hypocotyl and root tip cells through the movement of ELF4. To implement this, a long‐distance coupling term is appended to the equations describing EL protein in root tip cells, where J_long is the long‐distance coupling strength and c¯EL,longp=1NR∑j∈RcEL,jp represents the averaged expression level over cells in the hypocotyl, R. We set the long‐distance coupling strength as J_long  = 0, 0.01, 0.1, 1, 2, or 4.