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BackgroundHistone H1 is involved in the formation and maintenance of chromatin higher order structure. H1 has multiple isoforms; the subtypes differ in timing of expression, extent of phosphorylation and turnover rate. In vertebrates, the amino acid substitution rates differ among subtypes by almost one order of magnitude, suggesting that each subtype might have acquired a unique function. We have devised a competitive assay to estimate the relative binding affinities of histone H1 mammalian somatic subtypes H1a-e and H1° for long chromatin fragments (30–35 nucleosomes) in physiological salt (0.14 M NaCl) at constant stoichiometry.ResultsThe H1 complement of native chromatin was perturbed by adding an additional amount of one of the subtypes. A certain amount of SAR (scaffold-associated region) DNA was present in the mixture to avoid precipitation of chromatin by excess H1. SAR DNA also provided a set of reference relative affinities, which were needed to estimate the relative affinities of the subtypes for chromatin from the distribution of the subtypes between the SAR and the chromatin. The amounts of chromatin, SAR and additional H1 were adjusted so as to keep the stoichiometry of perturbed chromatin similar to that of native chromatin. H1 molecules freely exchanged between the chromatin and SAR binding sites. In conditions of free exchange, H1a was the subtype of lowest affinity, H1b and H1c had intermediate affinities and H1d, H1e and H1° the highest affinities. Subtype affinities for chromatin differed by up to 19-fold. The relative affinities of the subtypes for chromatin were equivalent to those estimated for a SAR DNA fragment and a pUC19 fragment of similar length. Avian H5 had an affinity ~12-fold higher than H1e for both DNA and chromatin.ConclusionH1 subtypes freely exchange in vitro between chromatin binding sites in physiological salt (0.14 M NaCl). The large differences in relative affinity of the H1 subtypes for chromatin suggest that differential affinity could be functionally relevant and thus contribute to the functional differentiation of the subtypes. The conservation of the relative affinities for SAR and non-SAR DNA, in spite of a strong preference for SAR sequences, indicates that differential affinity alone cannot be responsible for the heterogeneous distribution of some subtypes in cell nuclei.

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A method is given for quantitatively rating the social acceptance of different options which are the matter of a complete preferential vote. Completeness means that every voter expresses a comparison (a preference or a tie) about each pair of options. The proposed method is proved to have certain desirable properties, which include: the continuity of the rates with respect to the data, a decomposition property that characterizes certain situations opposite to a tie, the Condorcet-Smith principle, and clone consistency. One can view this rating method as a complement for the ranking method introduced in 1997 by Markus Schulze. It is also related to certain methods of cluster analysis and one-dimensional scaling.The outcome of a vote is commonly expected to specify not only a winner and an ordering of the candidates, but also a quantitative estimate of the social acceptance of each of them. Such a quantification is expected even when the individual votes give only qualitative information.The simplest voting methods are clearly based upon such a quantification. This is indeed the case of the plurality count as well as that of the Borda count. However, it is well known that these methods do not comply with basic majority principles nor with other desirable conditions. In order to satisfy certain combinations of such principles and conditions, one must resort to other more elaborate methods, such as the celebrated rule of Condorcet, Kemény and Young (see Monjardet 1990 and Tideman 2006, pp. 182-190), the method of ranked pairs (Tideman 1987;Zavist and Tideman 1989; Tideman 2006, pp. 219-223), or what we will refer to as the method of paths, which was introduced by Schulze in 1997 (posted in a mailing list about election methods; R. Camps · X. Mora (B) · L. Saumell

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