Cinquin Lab

Cinquin O. PLoS Computational Biology 3(2) e32 (2007)

Abstract

The oscillations of the somitogenesis clock are linked to the fundamental process of vertebrate embryo segmentation, yet little is known about their generation. In zebrafish, it has been proposed that Her proteins repress the transcription of their own mRNA. However, in its simplest form, this model is incompatible with the fact that morpholino knockdown of Her proteins can impair expression of their mRNA. Simple self-repression models also do not account for the spatiotemporal pattern of gene expression, with waves of gene expression shrinking as they propagate. Here we study computationally the networks generated by the wealth of dimerization possibilities amongst transcriptional repressors in the zebrafish somitogenesis clock. These networks can reproduce knockdown phenotypes, and strongly suggest the existence of a Her1-Her7 heterodimer, so far untested experimentally. The networks are the first reported to reproduce the spatiotemporal pattern of the zebrafish somitogenesis clock; they shed new light on the role of Her13.2, the only known link between the somitogenesis clock and positional information in the paraxial mesoderm. The networks can also account for perturbations of the clock by manipulation of FGF signaling. Achieving an understanding of the interplay between clock oscillations and positional information is a crucial first step in the investigation of the segmentation mechanism.

Cinquin O., Page K.M. Bull. Math. Biol. 69(2), pp483-494 (2007)

Abstract

High-dimensional switches have been proposed as a way to model cellular differentiation, particularly in the context of basic Helix-Loop-Helix (bHLH) competitive heterodimerization networks. A previous study derived a simple rule showing how many elements can be co-expressed, depending on the rate of competition within the network. A limitation to that rule, however, is that many biochemical parameters were considered to be identical. Here we derive a generalized rule. This in turns allows one to study more ways in which these networks could be regulated, linking intrinsic cellular differentiation determinants to extracellular cues.

Cinquin O., J. Theor. Biol. 238(3), pp532-540 (2006)

Abstract

The readout of morphogen concentrations has been proposed to be an essential mechanism allowing embryos to specify cell identities (Wolpert Trends Genet 12 (1996) 359), but theoretical and experimental results have led to conflicting ideas as to how useful concentration gradients can be established. In particular, it has been pointed out that some models of passive extracellular diffusion exhibit traveling waves of receptor saturation, inadequate for the establishment of positional information. Two alternative (but not mutually exclusive) models are proposed here, which are based on recent experimental results highlighting the roles of extracellular glycoproteins and morphogen oligomerization. In the first model, inspired from the interactions of Dally and Dally-like with Wingless and Decapentaplegic in the third-instar Drosophila wing disc, two morphogen populations are considered: one in a cell-membrane phase, and another one in an extracellular-matrix phase, which does not interact with receptors; in the second model, inspired from biochemical studies of Sonic Hedgehog, morphogen oligomers are considered to diffuse freely without interacting with receptors. The existence of a dynamic sub-population of freely-diffusing morphogen allows the system to establish a gradient of bound receptor, which is suitable for the specification of positional information. Recent experimental results are discussed within the framework of these models, as well as further possible experiments. The role of Notum in the setup of the Wingless gradient is also shown to be likely not to involve a gradient in Notum distribution, even though Notum is only expressed close to the source of Wingless synthesis.

Cinquin O., Demongeot J., J. Theor. Biol. 233(3), pp391-411 (2005)

Abstract

Many genes have been identified as driving cellular differentiation, but because of their complex interactions, the understanding of their collective behaviour requires mathematical modelling. Intriguingly, it has been observed in numerous developmental contexts, and particularly hematopoiesis, that genes regulating differentiation are initially co-expressed in progenitors despite their antagonism, before one is upregulated and others downregulated. We characterise conditions under which 3 classes of generic “master regulatory networks”, modelled at the molecular level after experimentally-observed interactions (including bHLH protein dimerisation), and including an arbitrary number of antagonistic components, can behave as a “multi-switch”, directing differentiation in an all-or-none fashion to a specific cell-type chosen among more than 2 possible outcomes. bHLH dimerisation networks can readily display coexistence of many antagonistic factors when competition is low (a simple characterisation is derived). Decision-making can be forced by a transient increase in competition, which could correspond to some unexplained experimental observations related to Id proteins; the speed of response varies with the initial conditions the network is subjected to, which could explain some aspects of cell behaviour upon reprogramming. The coexistence of antagonistic factors at low levels, early in the differentiation process or in pluripotent stem cells, could be an intrinsic property of the interaction between those factors, not requiring a specific regulatory system.

Cinquin O., J. Theor. Biol. 222(4), pp459-468 (2003)

Abstract

A striking pattern of oscillatory gene expression, related to the segmentation process (somitogenesis), has been identified in chick, mouse, and zebrafish embryos. Somitogenesis displays great autonomy, and it is generally assumed in the literature that somitogenesis-related oscillations are cell-autonomous in chick and mouse. We point out in this article that there would be many biological reasons to expect some mechanism of coupling between cellular oscillators, and we present a model with such coupling, but which also has autonomous properties. Previous experiments can be re-interpreted in light of this model, showing that it is possible to reconcile both autonomous and non-autonomous aspects. We also show that experimental data, previously interpreted as supporting a purely negative-feedback model for the mechanism of the oscillations, is in fact more compatible with this new model, which relies essentially on positive feedback.

Cinquin O., Demongeot J., C.R. Biol. 325(11), pp1085-1095 (2002)

Abstract

We discuss the influence of positive and negative feedback on the stability of a system, which is not clear-cut, and involves complex, mathematical problems. We show in particular that positive feedback can have a stabilising effect on some systems. We also point out the role that positive feedback plays in the digital treatment of signals required by cellular signalling, drawing on analogies from electronics, and the role that negative feedback plays in making a system robust against alteration of its parameters. Both positive and negative feedback can be seen as important enhancers of the properties of biological systems.

Cinquin O., Demongeot J., J. Theor. Biol. 216(2), pp229-241 (2002)

Abstract

Most biological regulation systems comprise feedback circuits as crucial components. Negative feedback circuits have been well understood for a very long time; indeed, their understanding has been the basis for the engineering of cybernetic machines exhibiting stable behaviour. The importance of positive feedback circuits, considered as “vicious circles”, has however been underestimated. In this article we give a demonstration based on degree theory for vector fields of the conjecture, made by Rene Thomas, that the presence of positive feedback circuits is a necessary condition for autonomous differential systems, covering a wide class of biologically relevant systems, to possess multiple steady states. We also show ways to derive constraints on the weights of positive and negative feedback circuits. These qualitative and quantitative results provide respectively structural constraints (i.e. related to the interaction graph) and numerical constraints (i.e. related to the magnitudes of the interactions) on systems exhibiting complex behaviours, and should make it easier to reverse-engineer the interaction networks animating those systems on the basis of partial, sometimes unreliable, experimental data. We illustrate these concepts on a model multistable switch, in the context of cellular differentiation, showing a requirement for sufficient cooperativity. Further developments are expected in the discovery and modelling of regulatory networks in general, and in the interpretation of bio-array hybridisation and proteomics experiments in particular. Keywords: positive feedback, multistationarity, multistability, stability, regulation, interaction networks, switch, cellular differentiation