Invertases are ubiquitous enzymes that irreversibly cleave sucrose into the reducing sugars fructose and glucose. Plant invertases not only play an important role in the partitioning of carbon between source tissue (photosynthetic leaves) and heterotrophic sink tissues such as seeds, tubers and fruits, they also function in plant development and in responses to biotic and abiotic stress. Three types of invertase isoenzymes, which are encoded by small gene families, are regularly found in plants. Cell wall-bound acidic invertases cleave sucrose in the apoplastic space (apoplastic invertases). Soluble acid invertases are located in the vacuole (vacuolar invertases), whereas soluble neutral invertases are located in the cytoplasm [1, 2].

In the potato (Solanum tuberosum), carbon is stored as starch polymers in tubers. Besides starch, tubers also contain small amounts of sucrose, glucose and fructose. The amounts of starch and sugars present in tubers depend on the genotype and on environmental factors. Storage at low temperature (e.g. 4°C) for several weeks leads to conversion of a small fraction of starch into sugars in tubers, with consequent accumulation of glucose and fructose, in particular [3, 4]. This phenomenon of 'cold-induced sweetening' is an adaptive response to cold stress, as sugars have long been known to have an osmoprotective function in plants [5]. Invertases, together with other proteins, play a role in determining the tuber sugar content before and during cold storage. Invertase activity is present in tubers and increases during cold storage [6–8]. Transcripts of vacuolar invertase accumulate in the tubers upon cold storage [9–11] and invertase antisense inhibition changes the hexose to sucrose ratio in the tubers [10]. The content of the reducing sugars glucose and fructose in tubers is an important criterion of quality for the potato processing industry. During deep frying at high temperatures, reducing sugars and amino acids undergo a non-enzymatic Maillard reaction, which results in a dark brown color and inferior taste of potato chips or French fries due to polyphenol formation [12, 13]. With increasing tuber sugar content, the chip color changes from light yellow to brown or even black. Although the enzymatic and biochemical steps in the interconversion between starch and sugars are well known in plants in general and potato in particular, the triggering and the regulation of cold-induced sweetening in potato is not fully understood [3, 4, 14]. In addition, the impact of natural variation in potato genes involved in carbohydrate metabolism on the quantitative variation of tuber starch and sugar content among different genotypes is completely unknown.

Genetic mapping of quantitative trait loci (QTL) for tuber starch and sugar content on the one hand [15, 16] and localization of genes that function in carbohydrate metabolism and transport on the other [17] have pointed to a number of candidate genes, which roughly colocalize with QTL for tuber starch and sugar content [18]. Among these are three independent loci encoding invertase genes. Potato cDNAs encoding apoplastic and vacuolar invertases have been cloned and characterized previously [10, 11, 19, 20]. Using invertase cDNA sequences as molecular markers, these three potato invertase loci have been mapped [17]. The Pain-1 locus on chromosome III encodes a vacuolar invertase, whereas the loci Inv _ap -a and Inv _ap -b on chromosomes X and IX, respectively, encode apoplastic invertases [17]. Two tandemly duplicated genes, InvGE and InvGF, encoding apoplastic invertases have been identified in one genomic fragment of 9 kb [21]. InvGE and InvGF are orthologous to the closely related tomato invertase genes LIN5 and LIN7, respectively, which are also tandemly duplicated and located on tomato chromosome 9 [22]. The Inv _ap -b locus maps to the orthologous position on potato chromosome IX. In view of the colinearity of the genomes of potato and tomato [23], InvGE/InvGF can both be assigned to the Inv _ap -b locus. The locus Inv _ap -a on chromosome X was mapped with the same cDNA probe 'pCD141' [20] as Inv _ap -b, and is orthologous to a tomato locus on chromosome 10 encoding the tandemly duplicated invertase genes LIN6 and LIN8 [22]. Genomic sequences of the potato Inv _ap -a and Pain-1 loci have not been reported.

Association mapping in populations of tetraploid potato varieties and breeding clones has revealed 'single-strand conformation polymorphisms' (SSCPs) [24] in invertase genes at all three loci, which were associated with tuber starch content, and/or chip color [25, 26]. Most significant were associations with SSCP markers derived from the Pain-1 gene on chromosome III [25]. These marker-trait associations are either direct (i.e. allelic variants of the invertase gene itself are causal for the phenotypic variation) or indirect (genes that are physically linked but unrelated to the invertase gene are responsible for the QTL) in effect. In the latter case, the association observed at an invertase locus is the result of linkage disequilibrium between the invertase gene and other, unknown genes in the same haplotype block [27]. Unfortunately, neither QTL linkage mapping down to single-gene resolution [28] nor high-resolution association mapping using thousands of individuals for complex traits such as tuber starch content and chip color is practicable in the cultivated potato. An alternative approach is the direct functional analysis of invertase allelic variants to elucidate their roles in determining variation in tuber starch and sugar content. This requires the cloning and characterization of full-length invertase cDNA alleles from representative potato genotypes, and the identification of cDNA alleles that correspond to the associated SSCP markers. Here we report the results of such a study.

Analysis of 193 cDNA sequences obtained from three tetraploid and three diploid potato genotypes revealed a high level of natural allelic variation in five potato invertase genes. Fifty-five different full-length cDNA sequences were identified, none of which were previously represented in the databases. Most were genotype specific: only nine were isolated from more than one of the cultivars examined. The average SNP density in cultivated potato is one SNP per 21-24 bp [41, 42]. The genes Pain-1 and InvCD111 fell within this range with one SNP per 24 and 25 bp, respectively. The highest variability, with one SNP per 13 bp, was observed in the InvGE gene. InvGF and InvCD141, both with one SNP per 17 bp, also had higher than average variability. A total of 479 SNPs were detected, and nine (1.6%) were tri-allelic. The 55 identified sequence variants represent a minimum estimate of the number of invertase alleles present in the six genotypes. Other alleles may have been missed due to template bias during PCR amplification [40] or because sample sizes were small, e.g. InvCD141 and InvCD111 in some genotypes. The sequence variants encode 46 distinct invertase proteins that differ from each other by between 4 and 9%. We took various precautions to eliminate sequence variants resulting from mistakes in reverse transcription or PCR. High-fidelity Taq polymerases were used to minimize PCR-derived errors, and cDNAs were cloned from different PCR reactions. Three quarters of the cDNA alleles were supported by at least two cDNA sequences, and alleles were defined based on consensus sequences of all cDNA clones derived from an individual genotype, eliminating singletons (SNPs occurring only once in the multiple sequence alignments). Although we cannot prove that all of the 479 SNPs are authentic, it is highly unlikely that more than a tiny minority of the SNPs observed were generated in the test tube. The generally high level of DNA polymorphism in the genome of Solanum tuberosum is well documented [29, 33, 41, 42]. However, very few data are available on the range of natural allelic variation among specific potato genes, particularly across multiple genotypes as studied here. Usually, potato genes are cloned and functionally characterized in a single cultivar. However, five different full-length cDNA clones encoding potato allene oxide synthase 2 (StAOS2) have been cloned from three diploid genotypes and functionally characterized [43]. High sequence variability has also been observed among genuine cDNA clones encoding Kunitz-type inhibitors in two tetraploid varieties [44]. The reason for this high genetic plasticity of the cultivated potato can be found in its reproductive biology. Potatoes are clonally propagated on an annual cycle. At much larger intervals (on the order of decades), the vegetative cycle is interrupted by sexual reproduction in the context of breeding programs. These combine heterozygous parental clones, select recombinant seedlings and propagate them again clonally. Switching between clonal and sexual reproduction may have been exploited during potato domestication and evolution, when farmers observed and selected in the field spontaneous hybrid seedlings among their clonally propagated crop [45]. In such a reproductive system, somatic mutations occurring at random during clonal propagation can give rise to cell lineages that eventually enter the germ line. Clonal selection will remove deleterious and favor beneficial somatic mutations [45]. The buffering capacity of a tetraploid genome may also allow the propagation of recessive deleterious mutations. The potato genome therefore represents a rich natural reservoir of mutant genes. In this respect, the potato genome stands in sharp contrast to the genome of its close relative the tomato (Solanum lycopersicum). The two genomes are highly colinear, but tomato shows very little intraspecific variation [46]. In contrast to potato, tomato is self-compatible and is propagated exclusively via seeds. Comparative functional characterization of natural potato invertase alleles - which is now possible, promises to uncover some interesting structure-function relationships. Functional differences between the coding regions of potato invertase alleles may be uncovered by the complementation of a yeast invertase mutant and the biochemical characterization of the heterologous expressed proteins [28]. Differences in the expression of alleles can be detected by quantifying the expression based on allele specific SNPs and pyrosequencing technology (Draffehn et al., manuscript in preparation).

The work reported here was designed to identify full-length cDNA clones encoding invertase alleles that are associated with chip quality, tuber starch content and starch yield [25] for further functional analysis. This goal was achieved for the associated markers Pain1-9a, Pain1-8c, InvGE-6f/InvGF-4d and pCD141-3c, but not for Pain1-5b and Pain1-5c, perhaps because an insufficient number of cDNA clones was analyzed. Alternatively, these SSCP markers might result from intron polymorphism that is not detectable in cDNA sequences. The full range of invertase alleles present in a population of 219 tetraploid individuals can be captured by genotyping 15, 11 and 38 SNPs, respectively, at the three invertase loci. Association analysis of the SNPs identified two new associations, one between the SNP allele InvGE-A ₈₅ and TSC and TSY, and the other between InvCD141-G ₇₆₅ and CQS, TSC and TSY (Table 5). The Pain1-a alleles showed the most significant and positive effects on chip quality and tuber starch content. The corresponding SSCP markers also show epistatic interactions with other candidate loci, which increase starch yield [47]. However, the frequency of these alleles in the ALL population was less than 10%. Enrichment of Pain1-a alleles in breeding populations should facilitate the selection of cultivars with improved quality traits. Interestingly, the three SNPs diagnostic for Pain-1 alleles of group a (C ₅₅₂ , A ₇₁₈ and A ₁₅₄₄ ) differed in their associations. These SNPs are in strong but not absolute linkage disequilibrium with each other. Pain1-C ₅₅₂ and Pain1-A ₇₁₈ were more strongly associated with chip quality after cold storage, whereas Pain1-A ₁₅₄₄ was mainly associated with tuber starch content. Whereas the cDNA alleles Pain1-Da, Sa and P18a contained all three SNPs, the allele StPain1-a (AAA50305) contained only A ₁₅₄₄ . This and the four different haplotype models obtained for these three SNPs (haplotypes K, M, N, O, Table 6) suggest further structural and possibly functional differentiation between the associated Pain1-a alleles, which may be exploitable for marker-assisted selection. Pain1-snp552 causes a synonymous nucleotide change, whereas Pain1-snp718 and Pain1-snp1544 induce non-synonymous changes. Pain1-SNP1544 causes the non-conservative amino acid change Thr515Lys. Whether these differences between the coding sequences or differences in the corresponding promoter regions are causal for possibly functional variation remains to be elucidated.

The direct inference of haplotypes from amplicon sequences requires that loci be homozygous, which is rarely the case in diploid and tetraploid potato genotypes. In amplicon sequences derived from heterozygous loci, the phase of the SNPs is unknown. The SATlotyper software was developed to model haplotypes in polyploid species based on unphased SNP data [40]. Haplotype modeling with a subset of the SNPs scored in the invertase genes Pain-1, InvGE and InvCD141 resulted for each gene in two or three haplotypes with higher frequencies (above 10%) and a large number of minor haplotypes with low frequencies. This haplotype distribution might be typical for nuclear genes of the European potato and a signature of its domestication, introduction and breeding history [48–50]. More genes must be analyzed however, before any general conclusions can be drawn. The occurrence of numerous low-frequency haplotypes is compatible with introgressions from other tuber-bearing Solanum species during 20^th-century breeding programs [50] and/or sequence diversification due to fixation of somatic mutations as outlined above. The SNP information will be useful for tracing specific haplotypes back to their origin.

Haplotype modeling correctly predicted some, but not all cDNA alleles that were obtained experimentally from the cvs Satina, Diana and Theresa and could have been detected based on the chosen SNP set. This is because, based on the analysis of sequence trace files, the SNP allele dosage cannot be scored with complete accuracy in all individuals used for haplotype modeling. A small percentage of scoring errors leads to haplotype artefacts with low frequency. To eliminate such artefacts, we considered only haplotype models with a frequency above 1%. As this is an arbitrary threshold, we cannot exclude the possibility that some of the remaining low-frequency haplotypes are also artefacts. Nevertheless, our results demonstrate that SATlotyper is a valuable tool for the fast identification of the major haplotypes present in populations of tetraploid potatoes. The determination of the exact haplotype composition of a tetraploid individual, including rare haplotypes, calls for an allele cloning approach such as that performed in this study.

As in tomato [22], the four genes encoding cell wall-bound acidic invertases in potato are organized in two pairs of tandemly duplicated genes on chromosomes IX and X. The soluble acid invertase is encoded by a single gene on potato chromosome III. The existence of a sixth potato invertase gene is predicted, which is orthologous to the tomato gene SlLIN9 located on chromosome 8 (based on the draft genome sequence of tomato provided by "The International Tomato Genome Sequencing Consortium" available at http://solgenomics.net and on personal communication from Gisella Orjeda, Universidad Peruana Cayetano Heredia, Peru). This gene might encode a soluble neutral invertase not characterized so far in potato. The five characterized potato invertase genes are all located within segmental chromosome duplications of unknown size, which show structural conservation with other, distantly related plant species [51, 52]. Functionally essential parts of an ancestral plant genome might be preserved in such conserved chromosome segments. The important role invertases play in many aspects of plant life is consistent with their location in evolutionarily ancient parts of plant genomes.

Very high natural allelic variation in five potato invertase genes was uncovered by sequence analysis of full length cDNA clones from six different genotypes and SNP analysis in a larger association mapping population. This variability is explained by the potato's reproductive biology. Some of the structural variation found might be causal for functional variation, which influences important agronomic traits of the potato such as tuber starch and sugar content. The invertase cDNA clones described here are the basis for further functional studies. The associations found between specific invertase alleles and tuber starch content, starch yield and chip quality facilitate the selection of superior potato genotypes in breeding programs. Finally, our results point out that natural variation should be taken into account when conducting molecular and functional characterization of potato genes.