Modeling homeoprotein intercellular transfer unveils a parsimonious mechanism for gradient and boundary formation in early brain development
Section snippets
Background
In pluricellular organisms, positional information is necessary to all developmental processes. In the neuroepithelium, positional information regulates the fate of territories, the place of borders between these territories, axonal guidance and synapse formation. It is not clear, as yet, how positional information is generated and how cells respond to this information. Within the proposed models, distinction should be made between syncitial (i.e. fly embryos or muscle fibers) and pluricellular
Mathematical models of gradient formation
We will reason on one row of cells. However, if there is a property of invariance in one direction, the conclusions can be extended to two-dimensional epithelia. The scenario is based on unidirectional morphogen fluxes across a territory not expanding trough cell division. Gradient initiation requires that an inducing step (inducer XA) triggers in a first cell the synthesis of homeoprotein A. Since A is a transcription factor with auto-catalytic activity, this synthesis labels the cell. The
Generating and maintaining gradients
We present in Fig. 2 various types of gradients generated for different values of parameter α, which measures the rate of decay from cell to cell. When α<1, gradients decay almost exponentially and after a few cells, homeoprotein concentration is already a few percent of its initial value. Interestingly, for α=1, the decay is linear, while for α>1, the gradient concentration does not decrease to zero, rather after a few cell, it converges exponentially to the asymptotic value .
In the
Messenger protein concept
The model presented here is based on the messenger protein concept (Prochiantz, 2000; Prochiantz and Joliot, 2003). This concept has been proposed following the observation that homeoprotein transcription factors signal between cells due to their unique intercellular transfer properties (Maizel et al., 2002; Joliot and Prochiantz, 2004). Taking Pax6 as an example, it was shown that blocking its extracellular activity hampers the extension of the eye territory (Lesaffre et al., 2007). In that
Conclusions
We have shown that morphogenetic gradients can be generated by local homeoprotein transfer in absence of long range diffusion. This model is parsimonious and allows us to explain the formation of boundaries and to evaluate its robustness. Although derived under very different considerations, our model lead to equations that share similarities with standard reaction–diffusion models.
Gradient and boundary formation has various consequences in the field of development and evolution. We think that
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Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows
2018, Journal of Computational PhysicsCitation Excerpt :Recovering the source location from incomplete information about the emitting signal is a generic problem in several fields of science, such as finding an emitter in signal processing, the food source by smelling a few molecules and many more. In the context of cell biology, the question of how a cell can sample its environment and decide its final destination remains open, but it starts with the detection of an external gradient concentration that the cell must use to transform cell positional information into its genetic specialization and differentiation [30,12]. During axonal growth and guidance, the growth cone (which is the tip of a neuronal cell) uses external concentration gradients [10,25] to decide whether to continue moving or to stop, to turn right or left.
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2014, Seminars in Cell and Developmental BiologyCitation Excerpt :These additional effects create a decreasing concentration and/or production of morphogens [23]. In an asymmetric propagation model (propagating from the left to the right in one dimensional domain)[23], an intracellular endocytozed morphogen A (which can also be a secondary messenger pathway due to binding of receptors) needs to be distinguished from an external morphogens A and the model formulation along a finite number of cells for k ≥ 1 is Long range gradients can be obtained when α > 1 [23]: the rich variety of solutions of reaction–diffusion equations allows generating very different types of gradients [4], for example, short or long range, stable or unstable.
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2011, Journal of Theoretical BiologyCitation Excerpt :When we apply our model to the regulation of hunchback by the bicoid morphogenic gradient, we focus on the sharp boundary in the hb density at the middle of the embryo. Several mechanisms accounting for the formation of sharp boundaries have been proposed: Some mechanisms (Burz et al., 1998; Lebrecht et al., 2005; Ptashne and Gann, 2002; Gregor et al., 2007) result from cooperative binding while others include a bistable gene (Lopes et al., 2008) or the antagonistic action of a repressor and activator gradient (Lohr et al., 2009; Wu et al., 1998; Kasatkin et al., 2008; Holcman et al., 2007). Here, we use neither the repression of hb in the posterior half nor the cooperative binding of bcd, but we show that, in the absence of these two mechanisms, a smooth morphogenetic gradient can trigger a sharp boundary for an autoregulated gene.
Morphogenesis by coupled regulatory networks: Reliable control of positional information and proportion regulation
2009, Journal of Theoretical BiologyCitation Excerpt :The emergence of sharp spatial expression boundaries of many genes in development, besides other genes that exhibit more graded profiles, is notoriously hard to explain in reaction–diffusion-based models. Recently it was shown in models of homeoprotein intercellular transfer (Kasatkin et al., 2007; Holcman et al., 2007) that restricted local diffusion of a morphogen regulating its own expression can generate a morphogenetic gradient. When two of these gradients meet, for certain parameter values a sharp boundary is created (Kasatkin et al., 2007).
Extracellular Engrailed Participates in the Topographic Guidance of Retinal Axons In Vivo
2009, NeuronCitation Excerpt :These results further confirm the specificity of the Engrailed signaling mechanism. The exuberance of guidance molecules already identified could mask redundancy, true physiological and mandatory interactions, or interactions not absolutely necessary but bringing robustness to the system (Brunet et al., 2007; Holcman et al., 2007). Redundancy is well illustrated by a recent study on triple EphrinA (A2/A3/A5) and double EphrinA (A2/A5) plus β2 subunit of the nicotinic acetylcholine receptor (A2/5/β) mutants (Pfeiffenberger et al., 2006).
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D. Holcman is supported by the program “Chaire d’Excellence”. D. Holcman incumbent to the Madeleine Haas Russell Career Development Chair.