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\textbf{Text S2}}
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\section*{Auxin transport model}
We make the following two extensions to the model of Merks et al. \cite{merks}. First, after a cell has reached a certain threshold concentration of auxin, it is assumed that the initiation of a primordium leads to the start of an auxin flow into the underlying pro-vascular tissue and thus to a lowering of the local peak concentration \cite{reinhardt}. Second, we incorporate auxin induced cell growth \cite{woodward}.
The auxin and PIN dynamics in 2D cells are then given by
\begin{eqnarray}\label{eq:jonsson}
\frac{dA_i}{dt}&=&T\sum _{j\in N_i}\frac{A_jP_{ji}}{k_a+A_j}-\frac{A_iP_{ij}}{k_a+A_i})+D\sum_{j\in N_i}L_{ij}(A_j-A_i)+p-(d_{dec}+d_{dep,i})A_i+\phi_bL_{ij} \nn \\
\frac{dP_{i}}{dt}&=&\sum_{j\in N_i}(-k_1\frac{P_if(A_j)}{k_m+P_i}+k_2P_{ij})\nn\\
\frac{dP_{ij}}{dt}&=& k_1\frac{P_if(A_j)}{k_m+P_i}-k_2P_{ij}.
\end{eqnarray}
%% 1 auxin, 2+3 pin cycling
The variables $A$ and $P$ are scaled into dimensionless form.
$A_i$ is the concentration of auxin in cell $i$, $P_{ij}$ the PIN concentration in cell $i$ at the wall facing neighbor $j$, $j \in N_i$ is the set of cells $j$ adjacent to cell $i$, $D$ diffusive transport coefficient ($m^{-1}s^{-1}$), $L_{ij}$ the length of a cell wall between cell $i$ and $j$ ($m$), $T$ active transport parameter ($s^{-1}$), $p$ a uniform constant production ($s^{-1}$), $d_{dec}$ decay ($s^{-1}$), $d_{dep}$ auxin depletion after a primordium has initiated ($s^{-1}$), $\phi_b$ the auxin inflow from the meristem boundary ($m^{-1}s^{-1}$), $P_i$ the amount of PIN in the endosome of cell $i$ and $\theta$ the threshold value for primordium activation (dimensionless). Further, $k_1$ and $k_2$ ($s^{-1}$) are the parameters that characterize the PIN cycling between endosome and cell membrane, and $k_a$, $k_m$ and $k_r$ are Michaelis-Menten constants.
The first equation describes the auxin concentration per cell, the second and the third describe the cycling of the PIN's between the endosome and the cell walls.
Additional notations and conditions are
\begin{eqnarray}\label{eq:jonsson2}
d_{dep,i}&=& d_{dep} \mbox{ after } A_i\ge \theta \mbox{ and 0 otherwise }\nn \\
f(A_j)&=& \frac{A_j}{k_r+A_j}\nn\\
P_i+\sum_{j\in N_i}P_{ij} &=&k_3\nn\\
\phi_b&=&\phi_b \mbox{ in boundary cells, for } n_{c1}\le n_c \le n_{c2}, \mbox{ and 0 elsewhere}.
\end{eqnarray}
The first equation states that after the auxin threshold concentration $\theta$ has been reached the cell differentiates and starts to pump auxin into the pro-vascular tissue underneath it, with a rate $d_{dep,i}A_j$. The second equation is a saturation function. The third equation expresses that the total amount of PIN in a cell ($k_3$) is conserved. The fourth expression represents the boundary condition that an auxin influx $\phi_b$ takes place via the outer membrane of the boundary cells. The influx takes place whenever the total amount of meristem cells is in the range [$n_{c1}, n_{c2}$]. \add{The cell surface increases with}
\begin{equation}\label{eq:growth}
\frac{ds_i}{dt}=(1+\frac{k_4A_i}{k_5+A_i})\gamma,
\end{equation}
with $s$ the surface area ($m^2$), $k_4$ and $k_5$ dimensionless parameters, and $\gamma$ the growth rate constant ($m^2s^{-1}$). \add{The growth of the cell depends on the resulting turgor pressure, the strain of the cell walls, and the pressure from surrounding cells. The cell growth is} determined by solving the minimal energy problem
\begin{equation}\label{eq:H}
H=\lambda_A\sum_i(s(i)-S_T(i))^2+\lambda_m\sum_j(l(j)-L_T(j))^2,
\end{equation}
with $H$ the generalized potential energy, $\lambda_A$ describes turgor pressure resistance, $\lambda_m$ is a spring constant, $s(i)$ and $S_T(i)$ the actual cell area and predefined resting area respectively, and $l(j)$ and $L_T(j)$ the actual wall length and predefined resting length, respectively. Indices $i$ and $j$ sum over all cells and cell walls, respectively.
The algorithm is described in more detail in \cite{merks2}. After a cell has undergone a division, the daughter cells start with the auxin level of the parent. Differentiated cells produce differentiated daughter cells. Each simulation starts with 4 cells, and $A_i=0$ for all 4 cells. For the auxin and PIN dynamics in equation (\ref{eq:jonsson}) a fifth order Runge-Kutta algorithm was used \cite{merks2}.
\subsection*{Simulation results for wild type}
Comparing the positions of the auxin maxima with the positions of organs on a real \textit{Arabidopsis} meristem, we conclude that on average our simulations yield slightly more auxin maxima on petal positions and less on reproductive organ positions. This is at least partly due to the 2D approximation of the upper hemisphere of the meristem.
As is well-known from the Mercator projection of the earth globe onto a 2D map, projecting the meristem surface onto a plane through the equator creates a deformation of the cells that is non-uniform in space. Since we did not incorporate this deformation, our approximation results in extra cells in the outer region, and less in the center.
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