Contact-mediated cellular communication supplements positional information to regulate spatial patterning during development

Chandrashekar Kuyyamudi, Shakti N. Menon, and Sitabhra Sinha

Phys. Rev. E 103, 062409 – Published 21 June 2021

Abstract

Development in multicellular organisms is marked by a high degree of spatial organization of the cells attaining distinct fates in the embryo. Recent experiments showing that suppression of intercellular interactions can alter the spatial patterns arising during development suggest that cell fates cannot be determined by the exclusive regulation of differential gene expression by morphogen gradients (the conventional view encapsulated in the French flag model). Using a mathematical model that describes the receptor-ligand interaction between cells in close physical proximity, we show that such intercellular signaling can regulate the process of selective gene expression within each cell, allowing information from the cellular neighborhood to influence the process by which the thresholds of morphogen concentration that dictate cell fates adaptively emerge. This results in local modulations of the positional cues provided by the global field set up by the morphogen, allowing interaction-mediated self-organized pattern formation to complement boundary-organized mechanisms in the context of development.

Received 11 February 2021
Revised 21 May 2021
Accepted 2 June 2021

DOI:https://doi.org/10.1103/PhysRevE.103.062409

Physics Subject Headings (PhySH)

Biological self-organization Cell communication Developmental pattern formation Emergence of patterns

Gene regulatory networks

Pattern formation

Nonlinear DynamicsInterdisciplinary PhysicsStatistical Physics & ThermodynamicsPhysics of Living SystemsNetworks

Authors & Affiliations

Chandrashekar Kuyyamudi ^1,2, Shakti N. Menon ¹, and Sitabhra Sinha ^1,2

¹The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
²Homi Bhabha National Institute, Anushaktinagar, Mumbai 400 094, India

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Vol. 103, Iss. 6 — June 2021

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Images

Figure 1
Contact-mediated signaling regulates the differential expression of cell fates dictated by morphogen concentration profiles. (a) Schematic diagrams illustrating the French Flag problem, namely, how positional information provided by spatial gradients of morphogen concentration specify patterns of cell fates in embryonic tissue. Equally sized domains of cells exhibiting one of three different fates, viz., blue, white, and red, characterize the idealized situation (left), shown for the case of patterning in the ventral region ( $V$ ) of the vertebrate neural tube by a gradient of Sonic hedgehog morphogen (whose concentration profile is displayed). Under different conditions, variations preserving the chromatic order and number of fate boundaries of the idealized situation can arise (a: right, top row); however, other variations may violate these (a: right, bottom row). (b) Schematic diagram of a pair of cells coupled via Notch signaling in the presence of an external morphogen. Each cell contains a morphogen interpretation module comprising a regulatory circuit of fate-inducing genes $B, W$ , and $R$ . Notch intracellular domains (NICD), released upon successful binding of Notch receptors to ligands from the neighboring cell, affect expression of $B, W$ , and $R$ with strengths $θ_{1, 2, 3}$ , respectively. This in turn regulates the production of Notch ligand with strengths $θ_{4, 5, 6}$ . (c) Spatial variation of the response to the morphogen $S_{M}$ across a one-dimensional domain comprising 30 cells. The three insets display the time evolution of gene expression levels $Y$ ( $= B, W$ , or $R$ , in arbitrary units) for cells that are subject to low, intermediate, and high morphogen concentrations, respectively. (d) The resulting final expression levels $Y$ of the patterning genes. The maximally expressed gene at each cell determines its fate, as shown in the schematic representation of the $1 D$ domain displayed at the bottom.
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Figure 2
The diversity in the spatial patterns of cell fates is controlled by the nature of interactions underlying Notch-mediated intercellular coupling. The intercellular interactions can be classified into four types, determined by whether NICD up or downregulates the patterning genes, and in turn, the genes up or downregulate ligand production, represented by the four motifs in the upper left corners in (a)–(d) [arrows representing up/downregulation are as indicated in Fig. 1]. For each type, the frequency distributions of different flags, i.e., patterns representing the sequential arrangement of distinct cell fates, are obtained by randomly sampling $θ_{1, ..., 6}$ , are shown in (a)–(d) for a $1 D$ domain comprising 30 cells subject to the morphogen gradient shown in Fig. 1. In the absence of intercellular coupling, the domain is divided into three equal segments of cells having different fates [as in Fig. 1]. The flags obtained upon coupling the cells are characterized by the number of fate boundaries $n_{B}$ and the difference $d_{H}$ with the pattern in the uncoupled system (which has equal chromatic divisions). For types I, II (where NICD downregulates $B, W$ , and $R$ ) almost all flags have the same chromatic order and $n_{B}$ as the idealized flag shown in Fig. 1 (a, left), with $d_{H}$ limited to very low values [(a) and (b), cf. Fig. 1 (a, right, top row)]. In contrast, the flags seen for types III, IV (where NICD upregulates $B, W$ , and $R$ ) exhibit large variation from the uncoupled case in terms of both $d_{H}$ and $n_{B}$ [(c) and (d), cf. Fig. 1 (a, right, bottom row)]. For each type, sample flags are displayed in ascending order of $d_{H}$ along the corresponding axis.
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Figure 3
Sensitivity of the flags to intercellular coupling parameters. (a)–(d) Dependence of the variation in cell fates on the spatial location $i$ of each cell in a $1 D$ domain, as well as, the differential contributions of the coupling parameters $Θ$ to the variation, for the four types of Notch-mediated interactions. The top half of each panel shows the variance $σ^{2}$ of the discrete variable representing the three possible fates (blue, white, red) that a cell can attain. The bottom halves display the fraction of the variance that can be accounted for by independently varying each of the parameters (colored according to the legend), as quantified by the first order sensitivity index $S 1$ . (a, b) When NICD downregulates the patterning genes, most of the variation is localized around the two fate boundaries of the uncoupled case and is sensitive to changes in $θ_{2}$ and $θ_{3}$ . In contrast, (c, d) variation is seen across the domain when NICD upregulates the genes, with most of the contribution from $θ_{1}, θ_{2}$ , and $θ_{3}$ . (e, f) Focusing on types I, II for which chromatic order and $n_{B}$ of the flags are invariant, we observe that the lengths of the red and white segments ( $l_{R}$ and $l_{W}$ , respectively) are narrowly distributed around those in the uncoupled case ( $l_{R}^{*} = 10, l_{W}^{*} = 10$ ). The sensitivity of the segment lengths to the parameters $Θ$ are shown in the concentric piecharts (outer: $l_{R}$ , middle: $l_{W}$ , inner: $l_{B}$ ). (g, h) The dependence of the location $i_{b}$ of the two fate boundaries (shown in blue and red, respectively) on the parameters $θ_{2}$ and $θ_{3}$ , with contour lines shown at the top.
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