A morphogen gradient model for pattern regulation. I. Formation of non-repetitive and repetitive structures

A model for pattern formation is proposed based on two concentration gradients S and Sigma. S is a local morphogen generated by a reaction-diffusion mechanism while Sigma is a by-product of the S-decomposition. Under certain conditions S is well approximated by S(x,L) = alpha(L)f(x L ), where alpha(L) is a scaling function of the length L and f(x L ) is a monotonie function of the relative distance x L from the origin. Sigma degradates and diffuses in the field, reaching a stable L-dependent homogeneous distribution. An allosteric protein P with several active sites reacts with S and Sigma and separates the field into segments. To every segment a corresponding active state of P is dominant. Pattern regulation is automatically achieved since the compartmerttal separation depends explicitly only on x L . For the case of repetitive patterns, a supplementary Gierer-Meinhardt mechanism is introduced for activator X and inhibitor Y. The level of Sigma can affect the decomposition rate of X or Y, e.g. via a second order degradation reaction, hence making the chemical wavelength lambda size-dependent. For a particular decay scheme of Y, a variation of L induces a change of lambda so that finally the number of repetitive structures becomes independent of the field size.     

Genetics of morphogen gradients

The organization of cells and tissues is controlled by the action of 'form-giving' signalling molecules, or morphogens, which pattern a developmental field in a concentration-dependent manner. As the fate of each cell in the field depends on the level of the morphogen signal, the concentration gradient of the morphogen prefigures the pattern of development. In recent years, molecular genetic studies in Drosophila melanogaster have allowed tremendous progress in understanding how morphogen gradients are formed and maintained, and the mechanism by which receiving cells respond to the gradient.     

Mechanisms of morphogen movement

Morphogens are defined as signaling molecules that are produced locally, yet act directly at a distance to pattern the surrounding field of cells in a concentration-dependent manner. In recent years many laboratories have devoted their attention to how morphogens actually reach distant cells. Several models have been proposed, including diffusion in the extracellular space and planar transcytosis. A combination of genetic, developmental, and cell-biological approaches have been taken to tackle this issue. I will present the models and discuss the types of experiments that have been designed to test them. It stands out that most of the work has been carried out in Drosophila. Morphogens contribute to patterning of the vertebrate nervous system, and the same signaling molecules have recently been shown to play important, possibly instructive, roles in axon guidance. Little, if anything, is known about the movement of morphogens in the context of nervous system development. The long-standing tradition of biophysical studies on diffusion in the brain extracellular space, along with the sophisticated in vitro culture systems developed in neurobiology laboratories, may provide new tools and ideas to test these models in a new context.     

A Dictyostelium morphogen that is essential for stalk cell formation is generated by a subpopulation of prestalk cells

The stalk cell differentiation inducing factor (DIF) has the properties required of a morphogen responsible for pattern regulation during the pseudoplasmodial stage of Dictyostelium development. It induces prestalk cell formation and inhibits prespore cell formation, but there is as yet no strong evidence for a morphogenetic gradient of DIF. We have measured DIF accumulation by monolayers of isolated prestalk and prespore cells in an attempt to provide evidence for such a gradient. DIF is accumulated in the largest quantities by a subpopulation of prestalk cells that specifically express the DIF-inducible genes pDd56 and pDd26. Since it has been shown recently that cells that express pDd56 are localized in the central core of the prestalk cell region of the pseudoplasmodia, our current results suggest a morphogenetic gradient generated by this region.     

Systems control of BMP morphogen flow in vertebrate embryos

Embryonic morphogenetic programs coordinate cell behavior to ensure robust pattern formation. Having identified components of those programs by molecular genetics, developmental biology is now borrowing concepts and tools from systems biology to decode their regulatory logic. Dorsal-ventral (D-V) patterning of the frog gastrula by Bone Morphogenetic Proteins (BMPs) is one of the best studied examples of a self-regulating embryonic patterning system. Embryological analyses and mathematical modeling are revealing that the BMP activity gradient is maintained by a directed flow of BMP ligands towards the ventral side. Pattern robustness is ensured through feedback control of the levels of extracellular BMP pathway modulators that adjust the flow to the dimensions of the embryonic field.     

Scaling of morphogen gradients

Individuals of the same or closely related species can vary substantially in size. Still, the proportions within and between tissues are precisely kept. This adaptation of pattern with size termed scaling, is receiving a growing attention. We review experimental evidence for scaling, and describe theoretical models for mechanisms that scale morphogen gradients. We particularly note the Expansion-Repression mechanism, in which a diffusible molecule that positively regulates the morphogen gradient width is repressed by morphogen signaling. The Expansion-Repression circuit provides scaling in a robust manner and is readily implemented by a host of molecular mechanisms. We suggest means for identifying such a circuit in a system of interest.     

A reaction-diffusion theory of morphogenesis with inherent pattern invariance under scale variations

In the framework of reaction-diffusion theory we deal with the problem of pattern regulation in morphogenesis. A generic model is proposed where the kinetic terms follow constraints imposed by scale invariance considerations. These constraints allow a class of kinetic schemes to be formulated so that, starting with an initially homogeneous morphogen distribution in the field, a stable gradient is established of the form: S(chi,L) = Lpf(chi/L). Here L is the length of the morphogenetic field, chi is the position variable and f(chi/L) is some monotonic function of the relative distance. With this distribution a scale invariant gradient can be constructed which leads to pattern regulation. A linear stability analysis of the model permits the definition of the parameter values enabling the system to abandon the homogeneous state spontaneously. Simulations of the evolution of the system towards its final stable state result in approximate pattern invariance for different field lengths. The accuracy of this invariance is in agreement with some recent quantitative experimental findings in both developing and regenerating systems.     

Regulation of the ammonia assimilatory enzymes in Salmonella typhimurium.

The regulation of glutamate dehydrogenase (EC 1.4.1.4), glutamine synthetase (EC 6.3.1.2), and glutamate synthase (EC 2.6.1.53) was examined for cultures of Salmonella typhimurium grown with various nitrogen and amino acid sources. In contrast to the regulatory pattern observed in Klebsiella aerogenes, the glutamate dehydrogenase levels of S. typhimurium do not decrease when glutamine synthetase is derepressed during growth with limiting ammonia. Thus, it appears that the S. typhimurium glutamine synthetase does not regulate the synthesis of glutamate dehydrogenase as reported for K. aerogenes. The glutamate dehydrogenase activity does increase, however, during growth of a glutamate auxotroph with glutamate as a limiting amino acid source. The regulation of glutamate synthase levels is complex with the enzyme activity decreasing during growth with glutamate as a nitrogen source, and during growth of auxotrophs with either glutamine or glutamate as limiting amino acids.     

On surface geometry coupled to morphogen

An expression is derived for both the Gauss and the Mean curvature of a surface, in terms of three simple cell parameters. The surface is thought of as composed of a single-cell thick sheet of cells joined laterally. The three cellular parameters involved are the ratios of (linear) basal to apical dimension in two orthogonal directions, S1 and S2, and the cell thickness "h". These three parameters may be envisioned as functions of a morphogen or morphogens which vary from point to point over the (middle) surface. As an example, the "reaction-diffusion" equations which are often used to describe pattern-formation in early development can be seen as possible candidates for these morphogens, when the resultant surface deformations are given when the dependence of the three cellular parameters are specified as a function of morphogen concentration. The coupling back of the surface deformations to the set of reaction-diffusion equations is simply given, and is through the dependence on geometry of the Laplacian operator which enters these equations.     

14-3-3σ (sigma) regulates proliferation and differentiation of multipotent p63-positive cells isolated from human breastmilk

The mammary gland is a dynamic organ that only undergoes complete differentiation during pregnancy. Differentiation is fuelled by asymmetric division of stem cells that reside in normally quiescent niches in the resting gland in response to pregnancy-associated hormones. Loss of regulation of stem cells is believed to underlie some breast cancers. This process is poorly understood in humans since it is difficult to extract stem cells from the lactating gland. We have identified a p63-positive population in breastmilk that proliferates and differentiates into at least two separate mammary lineages in culture. Nuclear translocation of p63 coincides with expression of the cell-cycle arrest protein 14-3-3σ (Sigma) and precedes differentiation. Transient down-regulation of Sigma promotes maintenance of the p63-positive population without affecting normal differentiation. We propose that p63-postive cells from breastmilk represent a novel source of cells to model regulation of mammary gland development and tumorigenesis.     

cactus, a maternal gene required for proper formation of the dorsoventral morphogen gradient in Drosophila embryos.

The dorsoventral pattern of the Drosophila embryo is mediated by a gradient of nuclear localization of the dorsal protein which acts as a morphogen. Establishment of the nuclear concentration gradient of dorsal protein requires the activities of the 10 maternal 'dorsal group' genes whose function results in the positive regulation of the nuclear uptake of the dorsal protein. Here we show that in contrast to the dorsal group genes, the maternal gene cactus acts as a negative regulator of the nuclear localization of the dorsal protein. While loss of function mutations of any of the dorsal group genes lead to dorsalized embryos, loss of cactus function results in a ventralization of the body pattern. Progressive loss of maternal cactus activity causes progressive loss of dorsal pattern elements accompanied by the expansion of ventrolateral and ventral anlagen. However, embryos still retain dorsoventral polarity, even if derived from germline clones using the strongest available, zygotic lethal cactus alleles. In contrast to the loss-of-function alleles, gain-of-function alleles of cactus cause a dorsalization of the embryonic pattern. Genetic studies indicate that they are not overproducers of normal activity, but rather synthesize products with altered function. Epistatic relationships of cactus with dorsal group genes were investigated by double mutant analysis. The dorsalized phenotype of the dorsal mutation is unchanged upon loss of cactus activity. This result implies that cactus acts via dorsal and has no independent morphogen function. In all other dorsal group mutant backgrounds, reduction of cactus function leads to embryos that express ventrolateral pattern elements and have increased nuclear uptake of the dorsal protein at all positions along the dorsoventral axis. Thus, the cactus gene product can prevent nuclear transport of dorsal protein in the absence of function of the dorsal group genes. Genetic and cytoplasmic transplantation studies suggest that the cactus product is evenly distributed along the dorsoventral axis. Thus the inhibitory function that cactus product exerts on the nuclear transport of the dorsal protein appears to be antagonized on the ventral side. We discuss models of how the action of the dorsal group genes might counteract the cactus function ventrally.     

Physical-chemical properties of the estrogen receptor released by deoxyribonuclease I

The physical-chemical properties of the nuclear estrogen receptor released by DNase I were characterized. Nuclei were isolated from MCF-7 cells previously exposed to 10-nM-[3H]estradiol. The parameters determined were: sedimentation coefficients (S) on a sucrose gradient, Stokes radii (Rs) by gel filtration on a Sephadex G-200 column and the binding ability to a DNA-cellulose column. The molecular weights (Mr) and frictional ratios (f/fo) were calculated from the S and Rs values. The properties of the receptor released by DNase I obtained from Worthington were compared to the properties of the receptor released by DNase I obtained from Sigma. Digestion with DNase I (Worthington) excised a receptor form which could be solubilized from nuclei by EDTA. This form sedimented at 5.2S with a Rs = 7.08 nm and a calculated Mr = 152.000. About 40% of this receptor form bound to a DNA-cellulose column. 0.4 M KCl dissociated this receptor form into a smaller form sedimenting at 4.2S with Rs = 4.64 nm and a calculated Mr = 80.000. The properties of the receptor solubilized by micrococcal nuclease followed by DNase I (Worthington) digestion were identical to the properties of the DNase I (Worthington) released receptor. Digestion with DNase I (Sigma) released a 3.2S receptor form, which diffused through the nuclear membrane and a 4-5S form which could be extracted from nuclei by EDTA. The 3.2S receptor had a Rs = 2.41 nm, a calculated Mr = 32.000 and less than 5% of it bound to a DNA-cellulose column. Digestion with micrococcal nuclease followed by DNase I (Sigma) solubilized a receptor form with identical properties to the 3.2S receptor. These results suggest that DNase I (Worthington) released a receptor form still associated with some molecules, probably chromatin proteins, which complexed it to DNA, while DNase I (Sigma) released the estradiol binding fragment of the receptor (meroreceptor) as a result of a proteolytic activity present in this preparation.     

Perturbations in morphogen gradients induce budding in hydra.

Lateral grafting of small pieces of midregion tissue into different levels of the hydra body column was done to assess the influence of the host hypostome and basal disc (or, of the underlying morphogenetic gradients) in inducing secondary structures in the transplanted tissue; and also to identify the role, if any, of the induced secondary structures (or, perturbed morphogen gradients) on the pattern of the host. The same midpiece tissue differentiated to a basal disc when grafted near the host hypostome, and to a small hypostome with tentacles when grafted near the host basal disc. Chimeras with induced secondary basal discs showed a phenomenal increase in budding compared to the controls and to the chimeras having induced hypostomes. These results indicate a positive cross-reaction between both organizing regions during patterning in hydra.     

Theoretical and experimental approaches to understand morphogen gradients

Morphogen gradients, which specify different fates for cells in a direct concentration‐dependent manner, are a highly influential framework in which pattern formation processes in developmental biology can be characterized. A common analysis approach is combining experimental and theoretical strategies, thereby fostering relevant data on the dynamics and transduction of gradients. The mechanisms of morphogen transport and conversion from graded information to binary responses are some of the topics on which these combined strategies have shed light. Herein, we review these data, emphasizing, on the one hand, how theoretical approaches have been helpful and, on the other hand, how these have been combined with experimental strategies. In addition, we discuss those cases in which gradient formation and gradient interpretation at the molecular and/or cellular level may influence each other within a mutual feedback loop. To understand this interplay and the features it yields, it becomes essential to take system‐level approaches that combine experimental and theoretical strategies.