Size-Regulated Symmetry Breaking in Reaction-Diffusion Models of Developmental Transitions

Abstract

<jats:p>The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organisation. Many of these transitions are achieved by spontaneous symmetry breaking mechanisms, allowing cells and tissues to acquire pattern and polarity by virtue of local interactions without an upstream supply of information. The combined work of theory and experiment has elucidated how these systems break symmetry during developmental transitions. Given that such transitions are multiple and their temporal ordering is crucial, an equally important question is how these developmental transitions are coordinated in time. Using a minimal mass-conserved substrate-depletion model for symmetry breaking as our case study, we elucidate mechanisms by which cells and tissues can couple reaction–diffusion-driven symmetry breaking to the timing of developmental transitions, arguing that the dependence of patterning mode on system size may be a generic principle by which developing organisms measure time. By analysing different regimes of our model, simulated on growing domains, we elaborate three distinct behaviours, allowing for clock-, timer- or switch-like dynamics. Relating these behaviours to experimentally documented case studies of developmental timing, we provide a minimal conceptual framework to interrogate how developing organisms coordinate developmental transitions.</jats:p>

How cells determine the number of polarity sites

“…Classical (not mass-conserved) Turing models exhibit a characteristic length scale, such that local peaks of an activator form spontaneously at spatial intervals corresponding to this length scale. Cells develop one or more peaks depending on how large the cell is compared to the characteristic length scale (Cornwall Scoones, Banerjee, & Banerjee, 2020;Meinhardt, 2008).…”

“…Moreover, recent advances have provided insight into how such systems can be tuned to produce unipolar or multipolar outcomes (Chiou et al, 2018;Goryachev & Leda, 2020;Halatek et al, 2018). One property that can effectively control the number of polarity sites that form is cell size (Cornwall Scoones et al, 2020). For example, there is a minimum size below which MCAS circuits are unable to polarize at all, and recent work indicates that the decrease in cell size that occurs during worm embryogenesis causes a switch from asymmetric cell division of polarized large cells to symmetric division of unpolarized small cells (Hubatsch et al, 2019).…”

Size regulation of multiple organelles competing for a limiting subunit pool

“…Furthermore, an increase in system size (i.e., increase in total pool size as the total subunit concentration is kept constant) can drive a transition from multiple coexisting structures to the growth of a single structure ( S10 Fig ). This size-dependent transition is a feature of stochastic dynamics, and can coordinate size-dependent symmetry breaking and pattern formation in developmental systems that follow similar feedback motifs [ 63 ].…”

Symmetry Breaking as an Interdisciplinary Concept Unifying Cell and Developmental Biology

“…Goryachev and Leda discuss recent theoretical work exploring this question in the minimal mass-conserved activator–substrate models and conclude that the choice between competition and coexistence of structures is determined by the complex interplay of multiple system parameters, rather than by the type of the molecular mechanism [ 33 ]. Developing this theme further, Banerjee and colleagues consider induction of multiple structures in dynamically growing systems [ 34 ]. Finally, Beta, Gov, and Yochelis discuss a dynamic pattern, representative of intracellular actin waves, in a minimal activator–inhibitor model with mass conservation [ 35 ].…”