Samuel Karlin

Mathematical Methods in the Social Sciences

MMSS is an adjunct major and must be completed with a standalone major in a social science or other approved area. See the Mathematics Second Major or Minor for MMSS Students (https:// catalogs.northwestern.edu/undergraduate/arts-sciences/mathematics/ mathematics-second-major-minor-mmss-students) for information about the major or the minor in mathematics when combined with the MMSS adjunct major; see the program website (https:// www.mmss.northwestern.edu/undergraduate) and relevant sections of this Catalog for information on adjustments to requirements in other majors for students in MMSS.

Finding the genes in genomic DNA

Genome sequencing efforts will soon generate hundreds of millions of bases of human genomic DNA containing thousands of novel genes. In the past year, the accuracy of computational gene-finding methods has improved significantly, to the point where a reasonable approximation of the gene structures within an extended genomic region can often be predicted in advance of more detailed experimental studies.

Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions

A function f(x) defined on = 1 - 2 - ... - n where each i is totally ordered satisfying f(x [logical or] y) f(x [logical and] y) >= f(x) f(y), where the lattice operations [logical or] and [logical and] refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,..., Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix [Sigma] satisfies -D[Sigma]-1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications.

Detecting anomalous gene clusters and pathogenicity islands in diverse bacterial genomes

A gene in a genome is defined as putative alien (pA) if its codon usage difference from the average gene exceeds a high threshold and codon usage differences from ribosomal protein genes, chaperone genes and protein-synthesis-processing factors are also high. pA gene clusters in bacterial genomes are relevant for detecting genomic islands (GIs), including pathogenicity islands (PAIs). Four other analyses appropriate to this task are G+C genome variation (the standard method); genomic signature divergences (dinucleotide bias); extremes of codon bias; and anomalies of amino acid usage. For example, the cagA domain of Helicobacter pylori is highly deviant in its genome signature and codon bias from the rest of the genome. Using these methods we can detect two potential PAIs in the Neisseria meningitidis genome, which contain hemagglutinin and/or hemolysin-related genes. Additionally, G+C variation and genome signature differences of the Mycobacterium tuberculosis genome indicate two pA gene clusters.

Correlations between Shine-Dalgarno Sequences and Gene Features Such as Predicted Expression Levels and Operon Structures

This work assesses relationships for 30 complete prokaryotic genomes between the presence of the Shine-Dalgarno (SD) sequence and other gene features, including expression levels, type of start codon, and distance between successive genes. A significant positive correlation of the presence of an SD sequence and the predicted expression level of a gene based on codon usage biases was ascertained, such that predicted highly expressed genes are more likely to possess a strong SD sequence than average genes. Genes with AUG start codons are more likely than genes with other start codons, GUG or UUG, to possess an SD sequence. Genes in close proximity to upstream genes on the same coding strand in most genomes are significantly higher in SD presence. In light of these results, we discuss the role of the SD sequence in translation initiation and its relationship with predicted gene expression levels and with operon structure in both bacterial and archaeal genomes.

The classification of birth and death processes

In the applications one is given the matrix A and it is required to construct P(t) and to study the properties of the corresponding stochastic process. The existence, uniqueness, and the analytic properties of P(t) have been discussed in detail in [I]. The objective of this paper is to use the results of [1] to establish equivalences between properties of the stochastic process and properties of the sequences { Xn }, { n,u } and to evaluate, in terms of these sequences, some of the interesting probabilistic quantities associated with the process.

Codon usages in different gene classes of the Escherichia coli genome

A new measure for assessing codon bias of one group of genes with respect to a second group of genes is introduced. In this formulation, codon bias correlations for Escherichia coli genes are evaluated for level of expression, for contrasts along genes, for genes in different 200 kb (or longer) contigs around the genome, for effects of gene size, for variation over different function classes, for codon bias in relation to possible lateral transfer and for dicodon bias for some gene classes. Among the function classes, codon biases of ribosomal proteins are the most deviant from the codon frequencies of the average E. coli gene. Other classes of ‘highly expressed genes’ (e.g. amino acyl tRNA synthetases, chaperonins, modification genes essential to translation activities) show less extreme codon biases. Consistently for genes with experimentally determined expression rates in the exponential growth phase, those of highest molar abundances are more deviant from the average gene codon frequencies and are more similar in codon frequencies to the average ribosomal protein gene. Independent of gene size, the codon biases in the 5′ third of genes deviate by more than a factor of two from those in the middle and 3′ thirds. In this context, there appear to be conflicting selection pressures imposed by the constraints of ribosomal binding, or more generally the early phase of protein synthesis (about the first 50 codons) may be more biased than the complete nascent polypeptide. In partitioning the E. coli genome into 10 equal lengths, pronounced differences in codon site 3 G+C frequencies accumulate. Genes near to oriC have 5% greater codon site 3 G+C frequencies than do genes from the ter region. This difference also is observed between small (100–300 codons) and large (>800 codons) genes. This result contrasts with that for eukaryotic genomes (including human, Caenorhabditis elegans and yeast) where long genes tend to have site 3 more AT rich than short genes. Many of the above results are special for E. coli genes and do not apply to genes of most bacterial genomes. A gene is defined as alien (possibly horizontally transferred) if its codon bias relative to the average gene exceeds a high threshold and the codon bias relative to ribosomal proteins is also appropriately high. These are identified, including four clusters (operons). The bulk of these genes have no known function.

Predicted Highly Expressed Genes of Diverse Prokaryotic Genomes

Our approach in predicting gene expression levels relates to codon usage differences among gene classes. In prokaryotic genomes, genes that deviate strongly in codon usage from the average gene but are sufficiently similar in codon usage to ribosomal protein genes, to translation and transcription processing factors, and to chaperone-degradation proteins are predicted highly expressed (PHX). By these criteria, PHX genes in most prokaryotic genomes include those encoding ribosomal proteins, translation and transcription processing factors, and chaperone proteins and genes of principal energy metabolism. In particular, for the fast-growing species Escherichia coli, Vibrio cholerae, Bacillus subtilis, and Haemophilus influenzae, major glycolysis and tricarboxylic acid cycle genes are PHX. In Synechocystis, prime genes of photosynthesis are PHX, and in methanogens, PHX genes include those essential for methanogenesis. Overall, the three protein families-ribosomal proteins, protein synthesis factors, and chaperone complexes-are needed at many stages of the life cycle, and apparently bacteria have evolved codon usage to maintain appropriate growth, stability, and plasticity. New interpretations of the capacity of Deinococcus radiodurans for resistance to high doses of ionizing radiation is based on an excess of PHX chaperone-degradation genes and detoxification genes. Expression levels of selected classes of genes, including those for flagella, electron transport, detoxification, histidine kinases, and others, are analyzed. Flagellar PHX genes are conspicuous among spirochete genomes. PHX genes are positively correlated with strong Shine-Dalgarno signal sequences. Specific regulatory proteins, e.g., two-component sensor proteins, are rarely PHX. Genes involved in pathways for the synthesis of vitamins record low predicted expression levels. Several distinctive PHX genes of the available complete prokaryotic genomes are highlighted. Relationships of PHX genes with stoichiometry, multifunctionality, and operon structures are discussed. Our methodology may be used complementary to experimental expression analysis.

Amino acid runs in eukaryotic proteomes and disease associations.

We present a comparative proteome analysis of the five complete eukaryotic genomes (human, Drosophila melanogaster, Caenorhabditis elegans, Saccharomyces cerevisiae, Arabidopsis thaliana), focusing on individual and multiple amino acid runs, charge and hydrophobic runs. We found that human proteins with multiple long runs are often associated with diseases; these include long glutamine runs that induce neurological disorders, various cancers, categories of leukemias (mostly involving chromosomal translocations), and an abundance of Ca2 + and K+ channel proteins. Many human proteins with multiple runs function in development and/or transcription regulation and are Drosophila homeotic homologs. A large number of these proteins are expressed in the nervous system. More than 80% of Drosophila proteins with multiple runs seem to function in transcription regulation. The most frequent amino acid runs in Drosophila sequences occur for glutamine, alanine, and serine, whereas human sequences highlight glutamate, proline, and leucine. The most frequent runs in yeast are of serine, glutamine, and acidic residues. Compared with the other eukaryotic proteomes, amino acid runs are significantly more abundant in the fly. This finding might be interpreted in terms of innate differences in DNA-replication processes, repair mechanisms, DNA-modification systems, and mutational biases. There are striking differences in amino acid runs for glutamine, asparagine, and leucine among the five proteomes.

General two-locus selection models: Some objectives, results and interpretations☆

In a population we can consider traits determined at a single locus, several loci, or of a polygenic kind. The bulk of allozyme variation, most blood serum typing, numerous disease susceptibilities, the + or functioning of an enzyme, certain color morphological patterns, are all classic examples of a single gene trait. A number of mainly two-locus traits have been identified, in recent years, e.g., the HLA histocompatibility system in man involving primarily the LA and the four loci each manifesting a substantial number of alleles (see Bodmer et al., 1970, or McDevitt and Bodmer, 1972) or the equivalent H, system in mice (McDevitt and Benacerrof, 1969); the two pairs of two linked incompatibility loci (a and ,f3) determining mating types in the fungus Schizojillum commune (Raper et al., 1958), the pair of loci involved in sex determination in melons, coat color in mammals frequently involves two or three principal genes (Searle, 1968) Gosspyle content in cotton is controlled at three primary loci. There is now increasing biochemical evidence that supports two to four loci situations, see e.g., Roberts and Baker (1973) for a four-locus model, etc. There are examples of sets of linked loci that apparently arose from duplication of a single gene and subsequently developed partially differentiated functions while retaining strong linkage. It is contended that there are many polygenic traits involving two or three main gene effects and many small effects (Thoday, 1967; Lewontin, 1974, pp. 93-94). The consequences of constant selection forces acting on a one-locus two-allele monoecious random mating diploid population are well understo0d.l Substantial