Modeling homeoprotein intercellular transfer unveils a parsimonious mechanism for gradient and boundary formation in early brain development

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows

Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.

Homeoprotein signaling in the developing and adult nervous system

Signaling classically involves the secretion of diverse molecules that bind specific cell-surface receptors and engage intracellular transduction cascades. Some exceptions-namely, lipophilic agents-can cross plasma membranes to bind intracellular receptors and be carried to the nucleus to regulate transcription. Homeoprotein transcription factors are among the few proteins with such a capacity. Here, we review the signaling activities of homeoproteins in the developing and adult nervous system, with particular emphasis on axon/cell migration and postnatal critical periods of cerebral cortex plasticity. We also describe homeoprotein non-cell-autonomous mechanisms and explore how this "novel" signaling pathway impacts emerging research in brain development and physiology. In this context, we explore hypotheses on the evolution of signaling, the role of homeoproteins as early morphogens, and their therapeutic potential for neurological and psychiatric diseases.

Local homeoprotein diffusion can stabilize boundaries generated by graded positional cues

Boundary formation in the developing neuroepithelium decides on the position and size of compartments in the adult nervous system. In this study, we start from the French Flag model proposed by Lewis Wolpert, in which boundaries are formed through the combination of morphogen diffusion and of thresholds in cell responses. In contemporary terms, a response is characterized by the expression of cell-autonomous transcription factors, very often of the homeoprotein family. Theoretical studies suggest that this sole mechanism results in the formation of boundaries of imprecise shapes and positions. Alan Turing, on the other hand, proposed a model whereby two morphogens that exhibit self-activation and reciprocal inhibition, and are uniformly distributed and diffuse at different rates lead to the formation of territories of unpredictable shapes and positions but with sharp boundaries (the 'leopard spots'). Here, we have combined the two models and compared the stability of boundaries when the hypothesis of local homeoprotein intercellular diffusion is, or is not, introduced in the equations. We find that the addition of homeoprotein local diffusion leads to a dramatic stabilization of the positioning of the boundary, even when other parameters are significantly modified. This novel Turing/Wolpert combined model has thus important theoretical consequences for our understanding of the role of the intercellular diffusion of homeoproteins in the developmental robustness of and the changes that take place in the course of evolution.

Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting

Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.

Dissection of a Krox20 positive feedback loop driving cell fate choices in hindbrain patterning

A positive autoregulatory loop required for the expression of the transcription factor Krox20 was dissected using in vivo quantitative data and biophysical modelling to demonstrate how Krox20 controls cell fate decision and rhombomere size in the hindbrain.

Positive autoregulation of Krox20 underpins a bistable switch that turns a transient input signal into cell fate commitment, as demonstrated in single cell analyses.

The duration and strength of the input signal control the size of the hindbrain segments by modulating the distribution between two cell fates.

The progressive extinction of Krox20 expression involves a destabilization of the loop by repressor molecules.

Although feedback loops are essential in development, their molecular implementation and precise functions remain elusive. Using enhancer knockout in mice, we demonstrate that a direct, positive autoregulatory loop amplifies and maintains the expression of Krox20, a transcription factor governing vertebrate hindbrain segmentation. By combining quantitative data collected in the zebrafish with biophysical modelling that accounts for the intrinsic stochastic molecular dynamics, we dissect the loop at the molecular level. We find that it underpins a bistable switch that turns a transient input signal into cell fate commitment, as we observe in single cell analyses. The stochasticity of the activation process leads to a graded input–output response until saturation is reached. Consequently, the duration and strength of the input signal controls the size of the hindbrain segments by modulating the distribution between the two cell fates. Moreover, segment formation is buffered from severe variations in input level. Finally, the progressive extinction of Krox20 expression involves a destabilization of the loop by repressor molecules. These mechanisms are of general significance for cell type specification and tissue patterning.

Signaling with homeoprotein transcription factors in development and throughout adulthood

The concept of homeoprotein transduction as a novel signaling pathway has dramatically evolved since it was first proposed in 1991. It is now well established in several biological systems from plants to mammals. In this review, the different steps that have led to this unexpected observation are recalled and the developmental and physiological models that have allowed us (and a few others) to consolidate the original hypothesis are described. Because homeoprotein signaling is active in plants and animals it is proposed that it has predated the separation between animals and plants and is thus very ancient. This may explain why the basic phenomenon of homeoprotein transduction is so minimalist, requiring no specific receptors or transduction pathways beside those offered by mitochondria, organelles present in all eukaryotic cells. Indeed complexity has been added in the course of evolution and the conservation of homeoprotein transduction is discussed in the context of its synergy with bona fide signaling mechanism that may have added robustness to this primitive cell communication device. The same synergy possibly explains why homeoprotein signaling is important both in embryonic development and in adult functions fulfilled by signaling entities (e.g. growth factors) themselves active throughout development and in the adult. The cell biological mechanism of homeoprotein transfer is also discussed. Although it is clear that many questions are still in want of precise answers, it appears that the sequences responsible both for secretion and internalization are in the DNA-binding domain and very highly conserved among most homeoproteins. On this basis, it is proposed that this signaling pathway is likely to imply as many as 200 proteins that participate in a myriad of developmental and physiological pathways.

Homeoprotein signaling in development, health, and disease: a shaking of dogmas offers challenges and promises from bench to bed

Homeoproteins constitute a major class of transcription factors active throughout development and in adulthood. Their membrane transduction properties were discovered over 20 years ago, opening an original field of research in the domain of vector peptides and signal transduction. In early development, homeoprotein transfer participates in tissue patterning, cell/axon guidance, and migration. In the axon guidance model, homeoproteins exert their non-cell autonomous activity through the regulation of translation, in particular, that of nuclear-transcribed mitochondrial mRNAs. An important aspect of these studies on patterning and migration is that homeoproteins sensitize the cells to the action of other growth factors, thus cooperating with established signaling pathways. The role of homeoprotein signaling at later developmental stages is also of interest. In particular, the transfer of homeoprotein Otx2 into parvalbumin-expressing inhibitory neurons (PV-cells) in the visual cortex regulates cortical plasticity. The molecular deciphering of the interaction of Otx2 with binding sites at the surface of PV-cells has allowed the development of a specific Otx2 antagonist that reopens plasticity in the adult cortex and cures mice from experimental amblyopia, a neurodevelopmental disease. Finally, the use of homeoproteins as therapeutic proteins in mouse models of glaucoma and Parkinson disease is reviewed. In the latter case, engrailed homeoproteins protect mesencephalic dopaminergic neurons by increasing the local translation of complex I mitochondrial mRNAs. In conclusion, this review synthesizes 20 years of work on the fundamental and potentially translational aspects of homeoprotein signaling.

Engrailed homeoprotein recruits the adenosine A1 receptor to potentiate ephrin A5 function in retinal growth cones

Engrailed 1 and engrailed 2 homeoprotein transcription factors (collectively Engrailed) display graded expression in the chick optic tectum where they participate in retino-tectal patterning. In vitro, extracellular Engrailed guides retinal ganglion cell (RGC) axons and synergises with ephrin A5 to provoke the collapse of temporal growth cones. In vivo disruption of endogenous extracellular Engrailed leads to misrouting of RGC axons. Here we characterise the signalling pathway of extracellular Engrailed. Our results show that Engrailed/ephrin A5 synergy in growth cone collapse involves adenosine A1 receptor activation after Engrailed-dependent ATP synthesis, followed by ATP secretion and hydrolysis to adenosine. This is, to our knowledge, the first evidence for a role of the adenosine A1 receptor in axon guidance. Based on these results, together with higher expression of the adenosine A1 receptor in temporal than nasal growth cones, we propose a computational model that illustrates how the interaction between Engrailed, ephrin A5 and adenosine could increase the precision of the retinal projection map.

Homeoprotein intercellular transfer, the hidden face of cell-penetrating peptides

Cell-Penetrating Peptides (CPPs) are small peptides internalized by live cells, gaining access to their cytoplasm and intracellular organelles (i.e., mitochondria, nucleus) and are used as pharmacological tools. This is indeed a very important issue, fully justifying the efforts of several groups to better understand the mechanisms of peptide transduction and to verify if and how this strategy can be translated into therapeutic improvements. However, the discovery of peptide transduction is a consequence of that of a novel signaling mechanism based on the intercellular transfer of homeoprotein transcription factors. Indeed, the first and probably most popular CPPs (Tat and Penetratin) correspond to domains that drive TAT (HIV) and homeoprotein transcription factors into the cells. These findings have fostered several studies on transduction and allowed the design of "nonnatural" CPPs. As useful as they are, these lines of research have, in general, neglected the fact that protein transduction is a signaling mechanism, in its own right, with important physiological functions. In this chapter, I describe some of these functions and propose that this class of signaling molecules, in particular homeoproteins, may also be used as therapeutic agents.

Extracellular Engrailed participates in the topographic guidance of retinal axons in vivo

Engrailed transcription factors regulate the expression of guidance cues that pattern retinal axon terminals in the dorsal midbrain. They also act directly to guide axon growth in vitro. We show here that an extracellular En gradient exists in the tectum along the anterior-posterior axis. Neutralizing extracellular Engrailed in vivo with antibodies expressed in the tectum causes temporal axons to map aberrantly to the posterior tectum in chick and Xenopus. Furthermore, posterior membranes from wild-type tecta incubated with anti-Engrailed antibodies or posterior membranes from Engrailed-1 knockout mice exhibit diminished repulsive activity for temporal axons. Since EphrinAs play a major role in anterior-posterior mapping, we tested whether Engrailed cooperates with EphrinA5 in vitro. We find that Engrailed restores full repulsion to axons given subthreshold doses of EphrinA5. Collectively, our results indicate that extracellular Engrailed contributes to retinotectal mapping in vivo by modulating the sensitivity of growth cones to EphrinA.

Morphogenesis by coupled regulatory networks: reliable control of positional information and proportion regulation

Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing multicellular organism. As an example we study the developmental problems of domain formation and proportion regulation in the presence of noise, as well as in the presence of cell flow. We find that networks that solve this task exhibit a hierarchical structure of information processing and are of similar complexity as developmental circuits of living cells. Proportion regulation is scalable with system size and leads to sharp, precisely localized boundaries of gene expression domains, even for large numbers of cells. A detailed analysis of noise-induced dynamics, using a mean-field approximation, shows that noise in gene expression states stabilizes (rather than disrupts) the spatial pattern in the presence of cell movements, both for stationary as well as growing systems. Finally, we discuss how this mechanism could be realized in the highly dynamic environment of growing tissues in multicellular organisms.

Homeoproteins as natural Penetratin cargoes with signaling properties

Most of this volume is dedicated to a very important and pragmatic issue which is to design ways of internalizing active pharmacological compounds into cells. In fact, many vectors have now been developed and the improvement in the technology can be seen on two main fronts. A first one is the identification of extremely efficient cargoes, for example siRNAs, which can enter the cells once attached to the vectors. A second one is the development of chemical vectors designed after the properties of the peptides and of tags allowing in vivo addressing to specific organs, for example the brain, cell types or sub-cellular compartments. This chapter is of a different nature, as it is devoted to the physiological significance of protein transduction and to the comparative analysis of the Penetratin PTD with its parental proteins, the homeoproteins. Although very academic, these two issues are of practical interest for the rational design of new vectors and the identification of unforeseen pathological mechanisms and pharmacological targets.