The Périgord black truffle (Tuber melanosporum Vittad.) and the Piedmont white truffle dominate today's truffle market. The hypogeous fruiting body of T. melanosporum is a gastronomic delicacy produced by an ectomycorrhizal symbiont endemic to calcareous soils in southern Europe. The worldwide demand for this truffle has fuelled intense efforts at cultivation. Identification of processes that condition and trigger fruit body and symbiosis formation, ultimately leading to efficient crop production, will be facilitated by a thorough analysis of truffle genomic traits. In the ectomycorrhizal Laccaria bicolor, the expansion of gene families may have acted as a 'symbiosis toolbox'. This feature may however reflect evolution of this particular taxon and not a general trait shared by all ectomycorrhizal species. To get a better understanding of the biology and evolution of the ectomycorrhizal symbiosis, we report here the sequence of the haploid genome of T. melanosporum, which at approximately 125 megabases is the largest and most complex fungal genome sequenced so far. This expansion results from a proliferation of transposable elements accounting for approximately 58% of the genome. In contrast, this genome only contains approximately 7,500 protein-coding genes with very rare multigene families. It lacks large sets of carbohydrate cleaving enzymes, but a few of them involved in degradation of plant cell walls are induced in symbiotic tissues. The latter feature and the upregulation of genes encoding for lipases and multicopper oxidases suggest that T. melanosporum degrades its host cell walls during colonization. Symbiosis induces an increased expression of carbohydrate and amino acid transporters in both L. bicolor and T. melanosporum, but the comparison of genomic traits in the two ectomycorrhizal fungi showed that genetic predispositions for symbiosis-'the symbiosis toolbox'-evolved along different ways in ascomycetes and basidiomycetes.

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Functions of bounded variation in an abstract Wiener space, i.e., an infinite-dimensional Banach space endowed with a Gaussian measure and a related differential structure, have been introduced by M. Fukushima and M. Hino using Dirichlet forms, and their properties have been studied with tools from analysis and stochastics. In this paper we reformulate, in an integral-geometric vein and with purely analytical tools, the definition and the main properties of BV functions, and investigate further properties.

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