Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2003 Jul 7;223(1):1-18.
doi: 10.1016/s0022-5193(03)00035-3.

The Topology of the Regulatory Interactions Predicts the Expression Pattern of the Segment Polarity Genes in Drosophila Melanogaster

Affiliations
Free PMC article

The Topology of the Regulatory Interactions Predicts the Expression Pattern of the Segment Polarity Genes in Drosophila Melanogaster

Réka Albert et al. J Theor Biol. .
Free PMC article

Abstract

Expression of the Drosophila segment polarity genes is initiated by a pre-pattern of pair-rule gene products and maintained by a network of regulatory interactions throughout several stages of embryonic development. Analysis of a model of gene interactions based on differential equations showed that wild-type expression patterns of these genes can be obtained for a wide range of kinetic parameters, which suggests that the steady states are determined by the topology of the network and the type of regulatory interactions between components, not the detailed form of the rate laws. To investigate this, we propose and analyse a Boolean model of this network which is based on a binary ON/OFF representation of mRNA and protein levels, and in which the interactions are formulated as logical functions. In this model the spatial and temporal patterns of gene expression are determined by the topology of the network and whether components are present or absent, rather than the absolute levels of the mRNAs and proteins and the functional details of their interactions. The model is able to reproduce the wild-type gene expression patterns, as well as the ectopic expression patterns observed in overexpression experiments and various mutants. Furthermore, we compute explicitly all steady states of the network and identify the basin of attraction of each steady state. The model gives important insights into the functioning of the segment polarity gene network, such as the crucial role of the wingless and sloppy paired genes, and the network's ability to correct errors in the pre-pattern.

Figures

Fig. 1.
Fig. 1.
The network of interactions between the segment polarity genes. The shape of the nodes indicates whether the corresponding substances are mRNAs (ellipses), proteins (rectangles) or protein complexes (octagons). The edges of the network signify either biochemical reactions (e.g. translation) or regulatory interactions (e.g. transcriptional activation). The edges are distinguished by their signatures, i.e. whether they are activating or inhibiting. Terminating arrows (→) indicate translation, post-translational modifications (in the case of CI), transcriptional activation or the promotion of a post-translational modification reaction (e.g. SMO determining the activation of CI). Terminating segments (⊣) indicate transcriptional inhibition or in the case of SMO, the inhibition of the post-translational modification reaction CI→CIR.
Fig. 2.
Fig. 2.
Illustration of the network expansion process used to construct the functional topology. To express the logical rule governing the transcription of hh graphically, we introduce the complementary node CIR¯ and the composite node ECR¯. The expanded network contains real nodes (filled circles) and pseudo-nodes (open circles), an interdependence relation between CIR and CIR¯ (dotted line), edges corresponding to the activation of ECR¯ (dash-dotted lines) and a single edge expressing the activation of hh transcription.
Fig. 3.
Fig. 3.
Functional topology of the network affecting the second cell of the parasegment. Filled circles represent real nodes, open circles represent pseudo-nodes, denoted according to Table 2. Pseudo-nodes with multiple indexes correspond to intercellular interactions and either receive some of their inputs from the neighboring cells, or contribute to the expression of the nodes in the neighboring cells (not shown). Symmetrical edges between nodes and their complementaries are drawn with dotted lines; edges determining the expression of composite nodes are drawn with dash-dotted lines; edges determining the expression of real nodes in the next time step are continuous. Double arrows denote a pair of oppositely directed edges.
Fig. 4.
Fig. 4.
Wild-type expression patterns of the segment polarity genes. Here and hereafter left corresponds to anterior and right to posterior in each parasegment. Horizontal rows correspond to the pattern of individual nodes—specified at the left side of the row—over two full and two partial parasegments. Each parasegment is assumed to be four cells wide. A black (gray) box denotes a node that is ON (OFF). (a) The experimentally observed initial state before stage 8. en, wg and hh are expressed in one-cell-wide stripes, while the broad ptc and ci stripes are complementary to en. (b) The steady state of the model when initialized with the pattern in (a). This pattern is in agreement with the observed gene expression patterns during stages 9–11 (see text).
Fig. 5.
Fig. 5.
Ectopic expression patterns of the segment polarity genes obtained from the model by varying the initial conditions or inactivating certain nodes. (a) Broad-type expression pattern. The stripes of en, wg, ptc and hh are broader than normal, while the ci stripe narrows and CIR is not expressed. The anterior broadening of the en stripe together with the posterior broadening of the wg stripe induces an ectopic “border” in the middle of the parasegment. This state arises if wg, en or hh is initiated in broader stripes than wild type. This pattern is in perfect agreement with the experimentally observed gene expression after heat shock experiments on en and hh (see text). A similar pattern, only without ptc, PTC and PH expression, is obtained from the model when the expression of ptc is kept OFF, in agreement with observations on ptc mutants (see text). (b) Stable pattern with no stripes for wg, en, hh and ptc. This pattern arises if any of wg, en or hh is kept OFF in the model, when wg initiation is substantially delayed, or when intercellular interactions are disrupted.
Fig. 6.
Fig. 6.
Patterns of wg and PTC obtained as solutions of Eq. (4). (a) Solution leading to the non-segmented pattern of Fig. 5(b). (b) Solution corresponding to the wild-type pattern of Fig. 4(b). (c) Solution leading to a variant of the wild-type pattern of Fig. 4(b) differing from it only in the expression of PTC that in this case becomes ubiquitous. (d), (e) Ectopic solutions that lead to patterns with no parasegment borders. The only difference between the two patterns is in the width of the PTC stripe (three- and four-cells-wide, respectively). (f) Solution leading to the broad type pattern of Fig. 5(a). (g), (h) Almost wild-type solutions with two wg stripes. The two patterns differ only in the width of the PTC stripe. (i), (j) Ectopic solutions similar to (d) and (e), but with two wg stripes.
Fig. 7.
Fig. 7.
Various stable patterns of the segment polarity genes obtained from Eq. (3). (a) Almost wild-type expression pattern with two wg stripes. This state corresponds to the solution of Eq. (3) presented in Fig. 6(g). (b) Ectopic pattern with displaced wg, en and hh stripes. This state arises from the solution on Fig. 6(d). (c) Variant of the ectopic pattern shown in (b) with two wg stripes. This state is determined from the solution 6(h).
Fig. 8.
Fig. 8.
Stable expression pattern of the segment polarity genes after a round of cell division, as obtained from our model. We assume that at this stage WG and HH can be transported through the neighboring cells. This pattern is in good agreement with experimental observations of stage 11 embryos.
Fig. 9.
Fig. 9.
The pattern obtained from our model when we start from wild-type initial conditions, but SLP is not functional. Note that en is expressed in two stripes, on both sides of the wg stripe.

Similar articles

See all similar articles

Cited by 222 articles

See all "Cited by" articles

Publication types

LinkOut - more resources

Feedback