An evolutionary model for the origin of non-randomness, long-range order and fractality in the genome.

We present a model for genome evolution, comprising biologically plausible events such as transpositions inside the genome and insertions of exogenous sequences. This model attempts to formulate a minimal proposition accounting for key statistical properties of genomes, avoiding, as far as possible, unsupportable hypotheses for the remote evolutionary past. The statistical properties that are observed in genomic sequences and are reproduced by the proposed model are: (i) deviations from randomness at different length scales, measured by suitable algorithms, (ii) a special form of size distribution (power law distribution) characterising different levels of genome organisation in the non-coding, and (iii) extensive resemblance in the alternation of coding and non-coding regions at several length scales (self-similarity) in long genomic sequences of higher eukaryotes.

Pattern formation in a Turing's type model with minimal reactional complexity

Turing's original reaction network is systematically studied, particularly in what concerns: (a) Its ability to produce patterns in a predictable way. (b) The feasibility of its concentration-independent sink term. Despite the widely accepted view that Turing's original model presents some inherent inability to produce regular structures, the pattern formation properties of this model are found to obey the predictions of the corresponding Linear Stability Analysis in the one-dimension and in 'small' two-dimensional systems. An 'Enzymatic' variation of the original Turing's Model is introduced, where the unrealistic sink term is substituted by an enzymatic degradation. It seems that reaction networks of this type can inspire a promising search for chemical or biochemical experimental systems with pattern formation properties, even in the absence of high non-linearities. It is pointed out that temporal oscillations, impossible for the original Turing's Model, are stable and persistent in its Enzymatic variation.

Modes of morphogen cooperation for limb formation in vertebrates and insects.

Diffusing morphogens in cooperation can control gene expression in developing limbs. Additive cooperation corresponds to the Boolean operator OR and implies the equivalent action of the (suitably scaled) concentrations of two morphogens, either by their alternative binding to the same receptor or by another way of convergence of their effects during the signal transduction procedure. This cooperation can explain the spatial and temporal collinearities of the expression of hoxd genes in the vertebrate limb bud. A multiplicative cooperation of morphogens (corresponding to the Boolean operator AND), produced at the DPP and WG domains in the Drosophila leg imaginal disc, may account for the expression domains observed for Dll and dac. A molecular interpretation of the multiplicative morphogen cooperation is proposed. Some experiments are suggested for further testing of the model.

A standard deviation based quantification differentiates coding from non-coding DNA sequences and gives insight to their evolutionary history.

A method quantifying the randomness of nucleotide sequences is developed, based on the introduction of a standard deviation type of quantity involving locally computed means and a length scale around which is assessed the clustering of nucleotides. It is pointed out that the value taken by this modified standard deviation may distinguish between coding rich and non-coding rich sequences. Moreover, the approach described herein allows the determination of some minimal characteristics of an evolutionary scenario which can account for the origin of the clustering in the nucleotide distribution of the different parts of the genome.

The "clustered structure" of the purines/pyrimidines distribution in DNA distinguishes systematically between coding and non-coding sequences.

A method allowing to measure the inhomogeneous distribution of purines/pyrimidines in nucleotide sequences is developed. We show that this measure relates to the coding or non-coding character of the considered sequence. Coding sequences present a near to the random Pu or Py distribution. This property is shared by both protein-coding DNA and functional RNA-coding DNA. Non-coding sequences present a highly clustered inhomogeneity. We propose the hypothesis, corroborated with appropriate computer simulations, that this is due to the action of various transposition events accumulated for long time periods.

Gradient model describes the spatial-temporal expression pattern of Hoxa genes in the developing vertebrate limb.

Pattern formation of the developing vertebrate limb is mainly controlled by the zone of polarizing activity (ZPA) and the apical ectodermal ridge (AER) which may act as sources of diffusing morphogens. These sources are tightly interconnected and maintained by positive feedback and, together with the established role of Wnt7 a on the dorsal side of the bud, they constitute a cartesian reference frame for the processes of patterning and growth of the limb bud. As an input to our model we have used the local extent and temporal activity of the AER source as it is reflected by Fgf-4 expression in the ridge. We have assumed that this source produces a morphogen which diffuses in the three-dimensional limb field and degradates by first-order kinetics. When in a cell the morphogen concentration exceeds a particular threshold value, a gene is switched on. To every threshold corresponds a specific gene. In the following we introduce an order of increasing concentration thresholds corresponding to the sequence of Hoxa-10, 11, and 13 genes (threshold collinearity). With this simple rule of correspondence we can reproduce both spatial and temporal collinearities of Hoxa gene expression. This outcome may be the first direct observable effect of a putative morphogen in the developing limb. The expression patterns are essentially transient, and they are followed by sequential refinements which lead to the final limb structures. Furthermore, the continuous flow of the morphogen through the progress zone guarantees the coherent course of patterning and limb growth. Several experiments are proposed for additional tests of the validity of the model and the eventual reversibility of Hoxa gene expression.

Small angle dislocations of the newt limb axes can test the validity of several regeneration models.

We describe two experiments on the regenerating forelimbs of the urodele Triturus cristatus. In the first, a contralateral grafting is performed where the anteroposterior axis of the regenerating blastema coincides with the dorsoventral axis of the host stump. In the second, the regenerating blastema is ipsilaterally rotated on the stump at angles 90 degrees or 270 degrees. For these experimental setups several regeneration models, each based on different reference frames (cartesian versus polar coordinates), have diverging predictions for the resulting supernumerary outgrowths. We have analyzed these outgrowths morphologically and histologically and we conclude that both experiments are well described by a hierarchical extension of the Polar Coordinate Model.

Left-right asymmetry in vertebrates.

A mechanism for the generation of the morphological left-right asymmetry in higher organisms is proposed, based on the idea that chirality at the molecular level is the primordial source for macroscopic asymmetry. This mechanism accounts for a variety of experimental results on artificial production of situs inversus and fits well with mutations in mice causing visceral transposition.

Diffusion or autocatalysis of retinoic acid cannot explain pattern formation in the chick wing bud.

We have collected several experimental data of pattern duplications due to the ZPA transplantation or application of retinoic acid on the developing chick limb bud. We have compared these data with the predictions of models based on diffusion or autocatalysis of retinoids. It turns out that these models cannot comprehensively explain the data. More specifically, retinoic acid cannot be either diffusing from a ZPA source or participate in an autocatalytic gradient formation.