A biophysical mechanism may control the collinearity of Hoxdgenes during the early phase of limb development

Abstract

A biophysical model has been proposed which deals with the observed collinearity of Hox gene expressions in developing vertebrate limbs. It is assumed that physical forces gradually dislocate the genes of the Hoxd cluster from inside the chromosome territory into the interchromosome domain, where the genes are activated. In particular, the action of Coulomb electric forces has been estimated in detail. Genetic engineering experiments (deletions, duplications and transpositions) were recently reported for Hoxd expression during limb development. Here, we analyse these results and show that the biophysical model explains them successfully.

Introduction

The collinearity of Hox gene expressions is a surprising feature observed during animal development along the primary and secondary body axes [1, 2]. These gene expressions follow in space and time the sequence of gene ordering from 3' to 5' in the Hox cluster [2, 3]. In the Hoxd cluster, the genes are lined up in the 3' to 5' direction and their expression domains (Hoxd1, Hoxd2, Hoxd3, ...) along the anteroposterior axis follow a peculiar pattern: the anterior border of expression for each gene is shifted in the anterior-posterior direction -- for example, the anterior border of Hoxd1 expression is more anterior than the anterior border of Hoxd2 expression etc. Thus, a pattern of partially overlapping expression domains along the head to tail axis is formed ('spatial collinearity') [2]. Furthermore, the genes of the Hoxd cluster are activated one after the other in the same 3' to 5' order ('temporal collinearity') [2, 3]. Tarchini and Duboule [4] have put forward a model in which, during early limb budding (first wave), two regulatory influences control the activation of Hoxd genes: one mechanism is located at the telomeric (3')side of the cluster (early limb control regulation; ELCR) and the other relies on sequences centromeric to the cluster (POST). Thus, in order to describe the data in terms of biomolecular processes only, two opposing collinearity mechanisms have to be introduced [4].

The biophysical model -- Comparison with experiments

An alternative biophysical model was introduced, dealing with the initial stages of limb development [5]. According to this model, the inactive Hox cluster is anchored inside the chromosome territory (CT), where the gene regulatory regions are inaccessible for transcription. Physical forces may pull the Hox fibre towards the interchromosome domain (ICD). Just outside the CT, the genes co-localise both in cis and in trans with local concentrations of transcription factories, and gene transcription is initiated (Figure 1). The intensity of a Hox gene transcription decreases when the gene moves in the ICD away from the CT boundary. Since the nature of the physical forces is unknown, we consider the electric Coulomb forces as plausible candidates [5]. Normally, the Hox cluster is negatively charged, and positive polar molecules are deposited at some distance from the cluster, as shown schematically in Figure 1. The positive charges, P, in every cell nucleus correspond to an extracellular morphogen, which forms a gradient along the anteroposterior axis;[5]P is high in the posterior cells and decreases gradually towards the anterior cells. A Coulomb force is created that pulls the Hox cluster; it decondenses the gene fibre and translocates the Hox genes in the ICD, following the 3' to 5' order (Figure 1).

Figure 1

Hoxd extrusions. When no positive charges are deposited opposite the 5' Hoxd subcluster, the subcluster remains inside the chromosome territory (CT). (a) For a low distribution of positive charges P (++), a small Coulomb force FI is created and one gene (Hoxd9) is extruded in the interchromosome domain (ICD). This occurs in domain D9 for cells in which the morphogen concentration is above the corresponding threshold T9. (b) For increased positive charges P (+ + + +), the force F2 is stronger and two consecutive genes (Hoxd9 and Hoxd10) are extruded. This occurs in domain D10, where the morphogen is above threshold T10.

The biophysical model does not merely describe Hox gene collinearity. Its aim is to explain it and to provide the mechanism that causes the modes of Hox gene expression by integrating and coordinat-ing actions at both the multicellular and subcellular levels. Of course, the control regions, such as ELCR and any other regulatory elements that have yet to be discovered, are essential tools of the biochemical machinery that participate in the realisation of Hox gene expression. We believe, however, that this essential biomolecular pathway is triggered and controlled by a more fundamental, single and unidirectional mechanism, such as the one presented here. The biophysical model reproduces spatial, temporal and quantitative collinearities well [5].

Gene deletions, duplications and transpositions

Duboule and collaborators [4, 6, 7] have performed detailed and extensive experiments of Hoxd gene deletions and duplications in order to explore the features of collinearity during vertebrate limb development. Their findings for the early phase of limb development [4] are highly illuminating, and it is worth comparing them with the biophysical model predictions.

Suppose the subcluster of the 5' Hoxd genes has an evenly distributed negative charge N (N = 10 in arbitrary units) and that every gene region (Hoxd 9, ... Hoxd13) carries a charge N/5 = 2. Before activation of the 5' Hoxd subcluster, all genes are embedded inside the CT. In this case, we can set P = 0 and the Coulomb force is 0. For activation of the first gene (Hoxd 9), we set P = 2 (in arbitrary units) and P = 10 when all genes (Hoxd9, ..., Hoxd13) are extruded in the ICD.

The measure of the Coulomb force F acting on the subcluster is proportional to the positive and negative charges. For our rough comparative estimates, we can assume:

$$F=P\times N$$

In this truncated Coulomb equation, we neglect the dependence of F on the distance between positive and negative charges, and the Coulomb's constant is set at 1 (in appropriate units). The Coulomb force causes gene fibre decondensation and extrusion of length L. We assume, in a first approximation, that this extrusion length L is proportional to F in the spirit of Hooke's law of elastic spring expansion. Deletion of one Hoxd gene region causes a reduction in the negative charge of the cluster; therefore, the Coulomb force will decrease and consequently the extrusion length of the Hoxd fibre will be shortened. The opposite will occur with a duplication of one Hoxd gene region in the cluster: the larger the duplication, the longer the gene fibre extrusion. In the supplementary material, we present some indicative experiments of gene deletions, duplications and transpositions [8] and compare them with the biophysical model predictions. The agreement is astonishing.

Discussion

In an analysis of the Hoxd locus in mouse development, activation along the primary anteroposterior axis is accompanied by fibre extrusion from the CT [9]. In the limb bud, at the same stage (E 9.5), however, no looping out is detected, even though the locus is still decondensed. A further confirmation of this difference is needed, taking into account that at that stage Hoxd expressions (eg Hoxd4) in the mouse limb bud are much weaker than in the tailbud [9].

The biophysical model explains how collinearity phenomena occur during the early stages of limb development. At later stages, when all Hoxd genes are expressed, secondary regulations and gene interactions modulate their expressions and the complex landscape of digits starts emerging. Recently, Montavon et al. [7] analysed experimentally and theoretically the features of quantitative collinearity in developing digits. They used some of their essential findings to formulate a model for the differential importance of gene rank -- the relative position of Hoxd genes with respect to the 5' extremity of the cluster. For instance, they observed that when Hoxd13 (the most strongly expressed gene) was deleted, the gene that substituted for it in the last 5' position was expressed with an increased intensity. It is instructive to view this result in the framework of the biophysical model: as soon as Hoxd13 is activated, the whole gene fibre is extruded and Hoxd13 is located closest to the surface of the CT, and its expression is therefore strongest. (This occurs in the posterior domain of the limb bud.) When Hoxd13 is deleted, the extruding Coulomb force F decreases and the extruded fibre retreats toward the interior of the CT. The consecutive gene (eg Hoxd12) is dislocated towards the CT surface and consequently its expression is strengthened. This is the essence of the observation by Montavon et al. [7] and it indicates, on the one hand, that this observation constitutes additional evidence in favour of the biophysical model. On the other hand, it shows that our interpretation of quantitative collinearity can be extended to all stages of limb development. Finally, the above authors have managed to establish a quasi-linear relationship between the total transcriptional activity at the locus and the number of transcription units -- e.g. active genes in developing digits (Figure 4b in reference [7]). This remarkable correlation supports our hypothesis of Coulomb force variations and the corresponding proportional changes in the extruded fibre lengths (reminiscent of Hooke's linear law of elastic expansions).