Molecular Framework of a Regulatory Circuit Initiating Two-Dimensional Spatial Patterning of Stomatal Lineage

Stomata, valves on the plant epidermis, are critical for plant growth and survival, and the presence of stomata impacts the global water and carbon cycle. Although transcription factors and cell-cell signaling components regulating stomatal development have been identified, it remains unclear as to how their regulatory interactions are translated into two-dimensional patterns of stomatal initial cells. Using molecular genetics, imaging, and mathematical simulation, we report a regulatory circuit that initiates the stomatal cell-lineage. The circuit includes a positive feedback loop constituting self-activation of SCREAMs that requires SPEECHLESS. This transcription factor module directly binds to the promoters and activates a secreted signal, EPIDERMAL PATTERNING FACTOR2, and the receptor modifier TOO MANY MOUTHS, while the receptor ERECTA lies outside of this module. This in turn inhibits SPCH, and hence SCRMs, thus constituting a negative feedback loop. Our mathematical model accurately predicts all known stomatal phenotypes with the inclusion of two additional components to the circuit: an EPF2-independent negative-feedback loop and a signal that lies outside of the SPCH•SCRM module. Our work reveals the intricate molecular framework governing self-organizing two-dimensional patterning in the plant epidermis.

SPCH + SCRM ! SPCH SCRM . (1) In this reaction, the increasing rate of u 3 concentration (equivalent to the decreasing rate of u 1 or u concentration) is described by where k + and k − are the association and dissociation rate constants, respectively.
(ii) SPCH (u 1 ) is constitutively synthesized, reacts according to reaction (1), is degraded depending on MAPK signaling (m), and diffuses between cell i and neighboring cell j: where A 1 is the synthesis rate, B 1 is the background decay rate, B 1m is the coefficient of MAPK-dependent degradation, K m is the half-saturation coefficient of m, and d u1 is the coupling rate between neighboring cells.
(iii) SCRM (u ) is synthesized in response to u 3 ), reacts according to reaction (1), is degraded depending on the MAPK signaling (m), and diffuses between cell i and neighboring cell j: where A 0 is the background synthesis rate, A is the synthesis coefficient, K 0 is the half-saturation coefficient of u 3 , B is the background decay rate, B m is the coefficient of MAPK-dependent degradation, K m is the half-saturation coefficient of m, and d u is the coupling rate between neighboring cells.
likely have limited diffusion. We introduced 1/100 of the coupling rates to u 1 and u .
It has been shown experimentally that enhanced diffusion in SPCH affect stomatal patterning[55], while the underlying mechanism is beyond the scope of this study.
(iv) u 3 ) reacts according to reaction (1) and is degraded at a constant rate: where B 3 is the decay rate.
v 1 ) is synthesized in response to u 3 ), is degraded at a constant rate, and diffuses between cell i and neighboring cell j: where G is the reaction rate coefficient of negative feedback loop, C 1 is the synthesis coefficient, K 1 is the half-saturation coefficient of u 3 , D 1 is the decay rate, and d v1 is the coupling rate between neighboring cells. C 0 indicates the concentration of peptide (S3 Fig D and S5 Fig A). For simplicity our model does not include peptide-processing steps, such COpeptide cleavage reported very recently [37], as a function of activity.
(vi) TMM (w) is synthesized in response to u 3 ) and is degraded at a constant rate: where C 3 is the synthesis coefficient, K 3 is the half-saturation coefficient of u 3 , and D 3 is the decay rate.
We found that protein accumulation and hence the epidermis lacking stomatal-lineage cells ( Fig   D). Together with previous reports 6], the following can be proposed. The regulatory framework described in the above includes two feedback loops: a positive one by SPCH/ roles in patterning of stomatal differentiation. In fact, this regulatory relationship is equivalent to that of the activator-inhibitor system, one of well-known theoretical (vii) An assumed molecule (v ) is synthesized in response to u 3 ), is degraded at a constant rate, and diffuses between cell i and neighboring cell j: where C is the synthesis coefficient, K is the half-saturation coefficient of u 3 , D is the decay rate, and d v is the coupling rate between neighboring cells.
(viii) Expression level of reporter SPCHpro::GFP (g u ) is activated in the same manner as SPCH (u 1 , Eq. (3)) and is degraded at a constant rate: where B g is the decay rate.
(ix) Expression level of reporter EPF2pro::GFP (g v ) is activated in the same manner v 1 , Eq. (6)) and is degraded at a constant rate: where D g is the decay rate.

III. Regulation of MAPK signaling activity
We now consider the MAPK signaling activity (m) that is induced by two v 1 )-dependent and v -dependent: where m 1 indicates the effect of the -dependent pathway, which involves two S, which is most likely Stomagen) and two receptor dimers where k 1 , k , k 3 , k 4 , k 5 , and k 6 are equilibrium constants.
where K w and K v are the half-saturation coefficients of w and v 1 , respectively (S7 Fig   E  -can be described by where C EE , C ES , C TE , and C TS are constants.
In tmm mutant, we have In er erl1 erl2 triple mutant, because the receptor dimers are absent (i.e. C EE = C ES = C TE = C TS = 0), we have