Undifferentiated cells are identical at many different scales, they share not only the same DNA, but also the same genes and the same overall gene regulatory networks (GRN), that in turn underlie heterogeneous expression patterns for each gene in space and time during development. Hence, multi-gene configurations are established during development, and cells attain specific fates at particular sites and times, in response to signals that are dependent on their position, and/or their cell lineage. Experimental results suggest that in plants cell differentiation strongly depends upon positional information 
, but it is likely that cell fate is the result of a dynamic interplay between positional information and intracellular GRN dynamics 
. Nonetheless, understanding how positional information is generated and maintained, as well as how such information is coupled to intracellular GRN dynamics, are key to understanding pattern formation during development.
Cell fate can be determined by a single GRN if it presents multiple attractors, each determining the expression profile (expression state of all the genes within the GRN), that is characteristic of each cell type. Recently, it has become possible to postulate GRN models grounded on experimental data. Such models have been successful at discovering developmental modules or sub-networks able to recover and predict multi-gene expression profiles observed in cell types, thus providing a dynamical mechanism to understand how different cell types are attained, given a fixed GRN topology that should be present within all the cells 
. However, multicellular models that explicitly incorporate cell-cell coupling mechanisms to generate a meta-GRN model, in which the spatial and temporal dynamics of cell-fate attainment can be followed are only starting to appear. For example, Benítez and collaborators 
were able to recover spatial cell patterns observed in Arabidopsis thaliana
epidermis by coupling intracellular GRN via diffusion of some of the network components according to available experimental data.
Undoubtedly, cell differentiation is a complicated choreography that should involve intricate interactions between intercellular communication mechanisms and intracellular processes that regulate gene expression, without a central controller or principal choreographer. Instead, cell differentiation and morphogenesis take place in structures with specific physical characteristics that establish fields that, at least, should reinforce positional information also emerging from molecular mechanisms that couple and feedback from the dynamics of intracellular GRNs during cell differentiation. The importance of such physical fields and mechanisms has recently received special attention providing a new approach to developmental biology. For example, a recent study 
has demonstrated that alterations of the stress distribution, that determines the patterns of microtubule orientations in Arabidopsis thaliana
shoot apical growing cells, modifies morphogenesis in a predictable way. However, this and similar papers have not explicitly coupled such physical fields to the dynamics of the GRN underlying cell-fate determination.
In this paper, we focus on a previously characterised GRN that underlies floral organ primordial cell specification during early stages of flower development 
. We use this example in order to illustrate a more general approach to couple GRN dynamics across tissues with a single physical field that provides positional information. The studied GRN has been shown to recover the multigenic expression profiles observed in the four main types of primordial cells established during early stages of flower development (see for instance, 
In contrast to animals, plant morphogenesis takes place during the entire life cycle from groups of undifferentiated cells called meristems. Two main meristems remain active during the whole life-cycle of plants: the shoot apical meristem (SAM) and the root apical meristem (RAM). From the former, the inflorescence meristem arises upon the transition to flowering and in its flanks flower primordia are formed.
During early floral development, the floral meristem is subdivided into four concentric regions of primordial cells that will eventually form the floral organs that from the outside to the centre are: sepals, petals, stamens and carpels 
. The spatial pattern of flower morphogenesis is widely conserved among the
flowering plant species and thus a robust and generic underlying mechanism is expected, but not well understood up to now. The only exception is Lacandonia schismatica
, whose flower presents a homeotic inversion with central carpels surrounded by stamens.
The now classical ABC model of flower development 
establishes the necessary combinatorial gene functions for sepal, petal, stamen and carpel specification 
. The ABC model proposes that class A genes alone are responsible for the development of sepals, but act together with class B genes to specify petal development. Class C genes alone are responsible for specifying carpel development, but act together with class B genes to determine stamen development. However, this model does not explain how such combinatorial gene functions are spatio-temporally established during flower development.
Cell differentiation thus involves at least two aspects. First, a physical field is required to break the symmetry of the spatial domain into different regions in which distinct sets of transcription factors are expressed and exert their function. Therefore, a phase-field model of the kind used in the physics of free boundary problems 
could be used to model physical fields in any developmental system. Second, a GRN responding to the physical field, and consequently able to reach different attractors (fixed gene configurations) depending on the cell position in space. In this paper we aim to showing that such interplay between a physical field and the dynamics of the GRN is sufficient to recover a morphogenetic pattern that resembles that observed during early flower development. The first component involves a macroscopic field, while the second aspect implies modelling the GRN dynamics that occurs at a microscopic scale. Physical fields may be of various types and they could be sensed by morphogens, such as auxins in plants. In fact meristems and primordia of lateral organs are formed in places where there is a peak of auxin concentration 
, which seems to trigger the production of undifferentiated cells. Other chemicals, as cytokinins, have been proposed to start the formation of the meristem, which paradoxically are substances that inhibit cell proliferation.
This paper is organised as follows: In the next section we describe in detail the physical field model that is used to generate the spatio-temporal information. Then, we postulate a simplified version of the flower organ identity GRN and the mechanism by which the GRN is coupled to the macroscopic physical field. In the third section we present results from numerical calculations from the model that couples the GRN dynamics and the physical field. Our results suggest that such coupled dynamics is sufficient to recover a geometrical distribution of the flower organ primordia that resembles that observed during early flower development. In order to validate the model we analyse all possible mutations predicted by this model and compare results with patterns of previously studied mutants, or provide predictions for those which have not been studied and for the effects of altering the physical field or the shape of the meristem.