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Most human cancers are characterized by genomic instability, the accumulation of multiple genetic alterations and allelic imbalance throughout the genome. Loss of heterozygosity (LOH) is a common form of allelic imbalance and the detection of LOH has been used to identify genomic regions that harbor tumor suppressor genes and to characterize tumor stages and progression. Here we describe the use of high-density oligonucleotide arrays for genome-wide scans for LOH and allelic imbalance in human tumors. The arrays contain redundant sets of probes for 600 genetic loci that are distributed across all human chromosomes. The arrays were used to detect allelic imbalance in two types of human tumors, and a subset of the results was confirmed using conventional gel-based methods. We also tested the ability to study heterogeneous cell populations and found that allelic imbalance can be detected in the presence of a substantial background of normal cells. The detection of LOH and other chromosomal changes using large numbers of single nucleotide polymorphism (SNP) markers should enable identification of patterns of allelic imbalance with potential prognostic and diagnostic utility.

Comparisons within and between the human, mouse and rabbit immunoglobulin‐kappa gene (J‐C region) DNA sequences are carried out in terms of three two‐letter nucleotide alphabets: (i) S‐W alphabet (W = A or T; S = G or C); (ii) P‐Q alphabet which distinguishes purines (P = A or G) from pyrimidines (Q = C or T); and (iii) a ‘control’ E‐F alphabet (E = A or C; F = G or T). All statistically significant direct repeats within each of the three sequences and all significant block identities (a set of consecutive matching letters) shared by two or more sequences are determined for each alphabet. By contrast to the S‐W and E‐F alphabets, the P‐Q alphabet comparisons reveal an abundance of statistically significant block identities not seen at the nucleotide level. Various interpretations of these P‐Q structures with respect to control and functional roles are considered.

Concepts and methods [Karlin, S. & Ghandour, G. (1985) Proc. Natl. Acad. Sci. USA 82, 5800-5804] for the analysis of patterns and relationships are extended to multiple DNA and protein sequences. Functionals include multiple sequence common word occurrence distributions, characterizations of high frequency shared words, and ascertainment of long block identities. Various comparisons of sequences using natural alphabets obtained from grouping nucleotides or amino acids by their chemical and functional characteristics are described. Specific applications are given to globin genes, mitochondrial genomes, and a variety of mammalian viruses.

Efficient (linear time) algorithms are described for identifying global molecular sequence features allowing for errors including repeats, matches between sequences, dyad symmetry pairings, and other sequence patterns. A multiple sequence alignment algorithm is also described. Specific applications are given to hepatitis B viruses and the J5-C (J, joining; C, constant) region of the immunoglobulin kappa gene.

High-density oligonucleotide arrays can be used to rapidly examine large amounts of DNA sequence in a high throughput manner. An array designed to determine the specific nucleotide sequence of 705 bp of the rpoB gene of Mycobacterium tuberculosis accurately detected rifampin resistance associated with mutations of 44 clinical isolates of M. tuberculosis. The nucleotide sequence diversity in 121 Mycobacterial isolates (comprised of 10 species) was examined by both conventional dideoxynucleotide sequencing of the rpoB and 16S genes and by analysis of the rpoB oligonucleotide array hybridization patterns. Species identification for each of the isolates was similar irrespective of whether 16S sequence, rpoB sequence, or the pattern of rpoB hybridization was used. However, for several species, the number of alleles in the 16S and rpoB gene sequences provided discordant estimates of the genetic diversity within a species. In addition to confirming the array's intended utility for sequencing the region of M. tuberculosis that confers rifampin resistance, this work demonstrates that this array can identify the species of nontuberculous Mycobacteria. This demonstrates the general point that DNA microarrays that sequence important genomic regions (such as drug resistance or pathogenicity islands) can simultaneously identify species and provide some insight into the organism's population structure.

Four categories of data representations are used to help interpret structures and similarities of nucleic acid and protein sequences. Statistical significance of the observed relationships revealed by these representations are assessed by a hierarchy of permutation procedures and by comparisons with theoretical random models. Applications are presented for various DNA sequences including papovaviruses, Epstein-Barr virus, mitochondrial genomes, and several globin and immunoglobulin genes.

A new high-speed computer algorithm is outlined that ascertains within and between nucleic acid and protein sequences all direct repeats, dyad symmetries, and other structural relationships. Large repeats, repeats of high frequency, dyad symmetries of specified stem length and loop distance, and their distributions are determined. Significance of homologies is assessed by a hierarchy of permutation procedures. Applications are made to papovaviruses, the human papillomavirus HPV, lambda phage, the human and mouse mitochondrial genomes, and the human and mouse immunoglobulin kappa-chain genes.

We compare the amino acid sequences of the constant domains of the immunoglobulin kappa chain of human, mouse, and rabbit by using four classification schemes ("alphabets") of the 20 amino acids based on their chemical, functional, charge, and structural properties. The comparison reveals three regions of pronounced similarity across the three species, independent of allotype. Two of these regions (residues 65-73 and 99-103) entail a high degree of identity at the DNA level and are distinguished from the rest of the constant domain in codon usage and in the dinucleotide sequence at abutting sites of adjacent codons. Residues 22-29 are highly conserved among the three species in the chemical and functional alphabets but do not show any three-sequence significant amino acid block identities. These results are discussed in terms of transcript processing, effector functions, and structural interactions within the constant domain and with the heavy chain.

Comparisons within and between the human, mouse and rabbit immunoglobulin‐kappa gene (J‐C region) DNA sequences are carried out in terms of three two‐letter nucleotide alphabets: (i) S‐W alphabet (W = A or T; S = G or C); (ii) P‐Q alphabet which distinguishes purines (P = A or G) from pyrimidines (Q = C or T); and (iii) a ‘control’ E‐F alphabet (E = A or C; F = G or T). All statistically significant direct repeats within each of the three sequences and all significant block identities (a set of consecutive matching letters) shared by two or more sequences are determined for each alphabet. By contrast to the S‐W and E‐F alphabets, the P‐Q alphabet comparisons reveal an abundance of statistically significant block identities not seen at the nucleotide level. Various interpretations of these P‐Q structures with respect to control and functional roles are considered.

The Schrödinger picture for the field Dirac theory is derived from a path integral over Grassmann fields and momenta. States and operators are described by wavefunctionals and functional differentiation. Unlike Bose fields, the free Fermi fields are shown to follow only their classical trajectories. An interacting theory is treated; integrating out the fermions gives the non-local effective Bose action.

A comparative analysis between human, mouse, and rabbit immunoglobulin (Ig) kappa-gene DNA sequences is presented. New formulas for determining the expected length and variance of the longest block identity (a succession of matching nucleotides) between multiple random sequences are given and are used to establish statistical criteria for ascertaining the significance of block identities shared in r out of s sequences. The statistically significant block identities within and between the Ig-kappa-gene sequences are ascertained, and alignment maps based on these similarities are constructed. The human and rabbit sequences (especially in the noncoding regions) and the human and mouse sequences (on the coding regions) show a similarity much stronger than that between the mouse and rabbit sequences. The existence of several highly significant shared oligonucleotides occurring in alignment with each other or with respect to the J- and C-gene segments suggests a configuration of multiple control sites. Discussion and interpretations of the form and distribution of the block identities are given.

The statistically significant shared oligonucleotides (block identities) of the intervening region (J5-C) in the human, mouse, and rabbit immunoglobulin (Ig)-kappa gene were determined. These identities maintain their order (do not cross) and never connect with any Ig-kappa segment external to the intron region. The two regions of pronounced similarity are (1) the vicinity of the established enhancer element (Queen and Baltimore 1983) and (2) a 200-bp region approximately 1 kb upstream that we have labeled the second enhancer element. Similarity is strong between the human and mouse sequences in the neighborhood of the first enhancer element and more pronounced between the human and rabbit sequences in the vicinity of the second enhancer region. The overall extent of similarity between the mouse and rabbit sequences is less than that between the human and mouse sequences and that between the human and rabbit sequences. All close and large dyad-symmetry pairings were ascertained and their possible relations to the enhancer elements discussed.

A method is presented for the analysis and comparison of nucleic acid and protein sequences utilizing all identity blocks (the term "identity block" refers to a set of consecutive matches between two sequences) above a prescribed length. Moreover, such identity blocks are determined for various groupings of amino acids according to chemical, functional, charge, and hydrophobic classifications. Alignment maps based on these classifications and containing all statistically significant identity blocks between two or more sequences are constructed. New theoretical results for determining the expected length of the longest identity block between sequences are also presented and are used, along with permutation procedures, to ascertain the significance of sequence identity blocks. As an example of the type of information that can be obtained, comparison has been made of the complete DNA sequences and the E1, E2, L1, and L2 genes of human and bovine papillomaviruses based on the classification schemes described above.