Fig 1.
SAM (shoot apical meristem) location and morphology.
(A) The SAM is located at the apex of the plant shoot (arrow). (B) Longitudinal section of the SAM. The SAM consists of three layers: L1 (epidermal cell layer), L2 (subepidermal cell layer) and L3 (corpus cell layer). (C) SAM view from the top. CZ: central zone, location of stem cells, PZ: peripheral zone, location of transit amplifying cells. OC: organizing center, location of cells producing signals that induce stem cell fate. L1, L2, L3: layers of the SAM. (D) Spatial expression patterns of key signals.
Fig 2.
Overview of SAM geometry and regulatory feedbacks.
(A) The SAM is modelled as a disc of radius R. The domain where WUS is produced is modelled as a concentric disc of radius r. (B) Regulatory signals: activating feedbacks are indicated in green, inhibiting feedbacks are indicated in red. The depicted interaction network functions at each position of the meristem. The expression domains of the respective factors evolve dynamically as a result of the interaction network, the initial condition and the diffusion of the factors. The number of OC cells determines the radius r. The OC is located below the SAM. The numbers in brackets correspond to the references on which the respective interaction is based.
Fig 3.
Signal concentrations in over-expression and loss-of-function experiments.
Signal concentrations along the diameter of the meristem, position 0 corresponds to the center: WUS (solid red), CLV3 (dashed blue), CK (dotted green) and HEC (dashdotted purple). (A) Unperturbed steady-state of the wild-type meristem. (B) Ubiquitous over-expression of WUS: The system converges to a state with CLV3 expression in the whole meristem. The equilibrium concentration of WUS in the wild-type is shown for comparison (densely dotted black). (C) WUS loss of function: The system converges to a steady-state with negligible CLV3 concentrations, which corresponds to the experimentally observed loss of stem cells. Breakdown of the negative feedback between WUS and CLV3 leads to high concentrations of WUS molecules that are not functional. (D) CLV3 over-expression: The system converges to a state with higher CLV3 and slightly reduced WUS concentrations. (E) CLV3 loss of function: Due to the missing negative feedback the OC expands and the CZ spreads over the whole meristem. (F) Reduced degradation of CK: The system converges to a state with constant in space signal concentrations. For comparison the CLV3 profile of the wild-type steady-state is depicted (loosely dotted olive). (G) CK loss of function does not lead to significant changes in the simulations. (H) HEC over-expression in stem cells: The central zone expands until it reaches the boundary of the meristem. (I) HEC loss of function (so called HEC triple mutant): The system converges to a state with lower WUS and CLV3 concentrations and a smaller meristem. HEC concentration (dashdotted purple) is equal to zero. For comparison, the CLV3 (loosely dotted olive) and WUS (densely dotted black) profiles of the wild-type steady-state are depicted.
Table 1.
Parameter values corresponding to the wild type (unperturbed) scenario.
Fig 4.
Numerical calculation of the steady-state.
(A) For the depicted initial condition the system approaches the equilibrium depicted in Fig 3(A). The corresponding evolution of R and r is depicted in (B) and (C) respectively. Calculations have been performed for different mesh sizes N and time steps △t: N = 25 and △t = 0.2 (22704 degrees of freedom), N = 50 and △t = 0.05 (90404 df), N = 100 and △t = 0.0125 (360804) and N = 200 and △t = 0.003125 (1441604 df).
Fig 5.
The blue curve describes the zero level-set of function G. The points (R1, 0) and (R2, R2) correspond to the intersection of the zero level-set of function G with the lines r = 0 and r = R. The value of the function F in these points is negative. For r = 0 and r = R we are able to solve (1) explicitly. Moreover, we know that there exists at least one point for which function F is positive. The latter is a consequence of the parameter choice. Thus there exists at least one point (R*, r*) such that: G(R*, r*) = 0, F(R*, r*) = 0 and in the neighborhood of this point for R > R* it holds F(R, r*) ≥ 0 and for R < R* it holds F(R, r*) < 0. Further on, we will consider the stability of the steady state solution (R*, r*).
Fig 6.
Local stability of the steady state.
Both plots present values of the function F(R, r). In (A) we set R = R*, in (B) we set r = r*. The dashed red lines correspond to F(R*, r*) = 0. All calculations were done for mesh size N = 50 (90404 degrees of freedom). Also the value F(R*, r*) is calculated using the value of pdbasic corresponding to the mesh size N = 50.
Fig 7.
Time dynamics of CLV3 over-expression.
Numerical calculation of CLV3 concentration for different time points after induction of ubiquitous WUS over-expression with c = 2.9: red solid for time t = 0.2, dashed blue for time t = 0.4, dotted green for time t = 0.6, dashdotted purple for time t = 0.8 and densely dotted olive time t = 1. As observed in experiments [41] the zone of high CLV3 expression extends in radial direction.
Fig 8.
Direct effect of HEC on OC cells.
Simulation of HEC over-expression with (A-B) and without (C-D) a direct effect of HEC on OC cell differentiation. (A-B) Time evolution of meristem and OC radius during HEC over-expression in stem cells. The simulations assume a direct effect of HEC on OC cells. (C-D) Time evolution of meristem and OC radius during HEC over-expression in stem cells. The simulations assume no direct effect of HEC on OC cells. Unlike in the experiments the WUS expressing domain does not extend over the whole meristem. For all depicted simulation we set c = 0.05.