The cutoff phenomenon in finite Markov chains.

Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists.

The hexapeptide LFPWMR in Hoxb-8 is required for cooperative DNA binding with Pbx1 and Pbx2 proteins.

The Hox gene products are DNA-binding proteins, containing a homeodomain, which function as a class of master control proteins establishing the body plan in organisms as diverse as Drosophila and vertebrates. Hox proteins have recently been shown to bind cooperatively to DNA with another class of homeodomain proteins that include extradenticle, Pbx1, and Pbx2. Hox gene products contain a highly conserved hexapeptide connected by a linker of variable length to the homeodomain. We show that the hexapeptide and the linker region are required for cooperativity with Pbx1 and Pbx2 proteins. Many of the conserved residues present in the Hoxb-8 hexapeptide are required to modulate the DNA binding of the Pbx proteins. Position of the hexapeptide relative to the homeodomain is important. Although deletions of two and four residues of the linker peptide still show cooperative DNA binding, removal of all six linker residues strongly reduces cooperativity. In addition, an insertion of 10 residues within the linker peptide significantly lowers cooperative DNA binding. These results show that the hexapeptide and the position of the hexapeptide relative to the homeodomain are important determinants to allow cooperative DNA binding involving Hox and Pbx gene products.

A very limited number of keywords (main patterns) describes all sequences of the human variable heavy (VH) and κ (Vκ) domains

Sequences of the variable heavy (VH) and κ (Vκ) domains of Ig structures were divided into 21 fragments that correspond to strands, loops, or parts of these structural units of the variable domains. Amino acid sequences of fragments (termed “words”) were collected from the 1,172 human heavy and 668 human κ chains available in the Kabat database. Statistical analysis of words of 17 fragments was performed (fragments that comprise the complementary determining regions′ fragments will not be discussed in this paper). The number of different words (those with different residues in at least one position) ranged, for various fragments, from 11 to 75 in the κ chains, and from 23 to 189 in the heavy chains. The main result of this study is that very few keywords, or main patterns of words, were necessary to describe over 90% of the sequences (no more than two keywords per fragment in the κ and no more than five per fragment in the heavy chains). No identical keywords were found for different fragments of the variable domains. Keywords of aligned fragments of the VH and Vκ domains were different in all but two instances. Thus, knowing the keywords, one can determine whether any given small part of a sequence belongs to a heavy or κ chain and predict its precise localization in the sequence. In addition, by using all of the keywords obtained through analysis of the Kabat database, it was possible to describe completely the sequences of the human VH and Vκ germ-line segments.

Regulation of product chain length by isoprenyl diphosphate synthases

An analysis of the x-ray structure of homodimeric avian farnesyl diphosphate synthase (geranyltransferase, EC 2.5.1.10) coupled with information about conserved amino acids obtained from a sequence alignment of 35 isoprenyl diphosphate synthases that synthesize farnesyl (C15), geranylgeranyl (C20), and higher chain length isoprenoid diphosphates suggested that the side chains of residues corresponding to F112 and F113 in the avian enzyme were important for determining the ultimate length of the hydrocarbon chains. This hypothesis was supported by site-directed mutagenesis to transform wild-type avian farnesyl diphosphate synthase (FPS) into synthases capable of producing geranylgeranyl diphosphate (F112A), geranylfarnesyl (C25) diphosphate (F113S), and longer chain prenyl diphosphates (F112A/F113S). An x-ray analysis of the structure of the F112A/F113S mutant in the apo state and with allylic substrates bound produced the strongest evidence that these mutations caused the observed change in product specificity by directly altering the size of the binding pocket for the growing isoprenoid chain in the active site of the enzyme. The proposed binding pocket in the apo mutant structure was increased in depth by 5.8 Å as compared with that for the wild-type enzyme. Allylic diphosphates were observed in the holo structures, bound through magnesium ions to the aspartates of the first of two conserved aspartate-rich sequences (D117–D121), with the hydrocarbon tails of all the ligands growing down the hydrophobic pocket toward the mutation site. A model was constructed to show how the growth of a long chain prenyl product may proceed by creation of a hydrophobic passageway from the FPS active site to the outside surface of the enzyme.

Temperature and length scale dependence of hydrophobic effects and their possible implications for protein folding

The Lum–Chandler–Weeks theory of hydrophobicity [Lum, K., Chandler, D. & Weeks, J. D. (1999) J. Phys. Chem. 103, 4570–4577] is applied to treat the temperature dependence of hydrophobic solvation in water. The application illustrates how the temperature dependence for hydrophobic surfaces extending less than 1 nm differs significantly from that for surfaces extending more than 1 nm. The latter is the result of water depletion, a collective effect, that appears at length scales of 1 nm and larger. Because of the contrasting behaviors at small and large length scales, hydrophobicity by itself can explain the variable behavior of entropies of protein folding.

Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations

We describe and test a Markov chain model of microsatellite evolution that can explain the different distributions of microsatellite lengths across different organisms and repeat motifs. Two key features of this model are the dependence of mutation rates on microsatellite length and a mutation process that includes both strand slippage and point mutation events. We compute the stationary distribution of allele lengths under this model and use it to fit DNA data for di-, tri-, and tetranucleotide repeats in humans, mice, fruit flies, and yeast. The best fit results lead to slippage rate estimates that are highest in mice, followed by humans, then yeast, and then fruit flies. Within each organism, the estimates are highest in di-, then tri-, and then tetranucleotide repeats. Our estimates are consistent with experimentally determined mutation rates from other studies. The results suggest that the different length distributions among organisms and repeat motifs can be explained by a simple difference in slippage rates and that selective constraints on length need not be imposed.

Defining the minimal length of sequence homology required for selective gene isolation by TAR cloning

The transformation-associated recombination (TAR) cloning technique allows selective and accurate isolation of chromosomal regions and genes from complex genomes. The technique is based on in vivo recombination between genomic DNA and a linearized vector containing homologous sequences, or hooks, to the gene of interest. The recombination occurs during transformation of yeast spheroplasts that results in the generation of a yeast artificial chromosome (YAC) containing the gene of interest. To further enhance and refine the TAR cloning technology, we determined the minimal size of a specific hook required for gene isolation utilizing the Tg.AC mouse transgene as a targeted region. For this purpose a set of vectors containing a B1 repeat hook and a Tg.AC-specific hook of variable sizes (from 20 to 800 bp) was constructed and checked for efficiency of transgene isolation by a radial TAR cloning. When vectors with a specific hook that was ≥60 bp were utilized, ∼2% of transformants contained circular YACs with the Tg.AC transgene sequences. Efficiency of cloning dramatically decreased when the TAR vector contained a hook of 40 bp or less. Thus, the minimal length of a unique sequence required for gene isolation by TAR is ∼60 bp. No transgene-positive YAC clones were detected when an ARS element was incorporated into a vector, demonstrating that the absence of a yeast origin of replication in a vector is a prerequisite for efficient gene isolation by TAR cloning.

Enhancing the catalytic repertoire of nucleic acids: a systematic study of linker length and rigidity

The incorporation of potentially catalytic groups in DNA is of interest for the in vitro selection of novel deoxyribozymes. A series of 10 C5-modified analogues of 2′-deoxyuridine triphosphate have been synthesised that possess side chains of differing flexibility and bearing a primary amino or imidazole functionality. For each series of nucleotide analogues differing degrees of flexibility of the C5 side chain was achieved through the use of alkynyl, alkenyl and alkyl moieties. The imidazole function was conjugated to these C5-amino-modified nucleotides using either imidazole 4-acetic acid or imidazole 4-acrylic acid (urocanic acid). The substrate properties of the nucleotides (fully replacing dTTP) with Taq polymerase during PCR have been investigated in order to evaluate their potential applications for in vitro selection experiments. 5-(3-Aminopropynyl)dUTP and 5-(E-3-aminopropenyl)dUTP and their imidazole 4-acetic acid- and urocanic acid-modified conjugates were found to be substrates. In contrast, C5-amino-modified dUTPs with alkane or Z-alkene linkers and their corresponding conjugates were not substrates. The incorporation of these analogues during PCR has been confirmed by inhibition of restriction enzyme digestion using XbaI and by mass spectrometry of the PCR products.

A modified gambler's ruin model of polyethylene chains in the amorphous region.

Polyethylene chains in the amorphous region between two crystalline lamellae M unit apart are modeled as random walks with one-step memory on a cubic lattice between two absorbing boundaries. These walks avoid the two preceding steps, though they are not true self-avoiding walks. Systems of difference equations are introduced to calculate the statistics of the restricted random walks. They yield that the fraction of loops is (2M - 2)/(2M + 1), the fraction of ties 3/(2M + 1), the average length of loops 2M - 0.5, the average length of ties 2/3M2 + 2/3M - 4/3, the average length of walks equals 3M - 3, the variance of the loop length 16/15M3 + O(M2), the variance of the tie length 28/45M4 + O(M3), and the variance of the walk length 2M3 + O(M2).

Novel unconventional binding site in the variable region of immunoglobulins.

The variable immunoglobulin (Ig) domains contain hypervariable regions that are involved in the formation of the antigen binding site. Besides the canonical antigen binding site, so-called unconventional sites also reside in the variable region that bind bacterial and viral proteins. Docking to these unconventional sites does not typically interfere with antigen binding, which suggests that these sites may be a part of the biological functions of Igs. Herein, a novel unconventional binding site is described. The site is detected with 8-azidopurine nucleotide photoaffinity probes that label antibodies efficiently and under mild conditions. Tryptic peptides were isolated from photolabeled monoclonal antibodies and aligned with the variable antibody domains of heavy and light chains. The structure of a variable Ig fragment was used to model the binding of the purine nucleotide to invariant residues in a hydrophobic pocket of the Ig molecule at a location distant from the antigen binding site. Monoclonal and polyclonal antibodies were biotinylated with the photoaffinity linker and used in fluorescence-activated cell sorter and ELISA analyses. The data support the utility of this site for tethering diagnostic and therapeutic agents to the variable Ig fragment region without impairing the structural and functional integrity of antibodies.

A new high molecular weight immunoglobulin class from the carcharhine shark: implications for the properties of the primordial immunoglobulin.

All immunoglobulins and T-cell receptors throughout phylogeny share regions of highly conserved amino acid sequence. To identify possible primitive immunoglobulins and immunoglobulin-like molecules, we utilized 3' RACE (rapid amplification of cDNA ends) and a highly conserved constant region consensus amino acid sequence to isolate a new immunoglobulin class from the sandbar shark Carcharhinus plumbeus. The immunoglobulin, termed IgW, in its secreted form consists of 782 amino acids and is expressed in both the thymus and the spleen. The molecule overall most closely resembles mu chains of the skate and human and a new putative antigen binding molecule isolated from the nurse shark (NAR). The full-length IgW chain has a variable region resembling human and shark heavy-chain (VH) sequences and a novel joining segment containing the WGXGT motif characteristic of H chains. However, unlike any other H-chain-type molecule, it contains six constant (C) domains. The first C domain contains the cysteine residue characteristic of C mu1 that would allow dimerization with a light (L) chain. The fourth and sixth domains also contain comparable cysteines that would enable dimerization with other H chains or homodimerization. Comparison of the sequences of IgW V and C domains shows homology greater than that found in comparisons among VH and C mu or VL, or CL thereby suggesting that IgW may retain features of the primordial immunoglobulin in evolution.

Yeast artificial chromosome contigs reveal that distal variable-region genes reside at least 3 megabases from the joining regions in the murine immunoglobulin kappa locus.

The immunoglobulin kappa gene locus encodes 95% of the light chains of murine antibody molecules and is thought to contain up to 300 variable (V kappa)-region genes generally considered to comprise 20 families. To delineate the locus we have isolated 29 yeast artificial chromosome genomic clones that form two contigs, span > 3.5 megabases, and contain two known non-immunoglobulin kappa markers. Using PCR primers specific for 19 V kappa gene families and Southern analysis, we have refined the genetically defined order of these V kappa gene families. Of these, V kappa 2 maps at least 3.0 Mb from the joining (J kappa) region and appears to be the most distal V kappa gene segment.

Restricted and conserved T-cell repertoires involved in allorecognition of class II major histocompatibility complex.

The nature of the alloreactive T-cell response is not yet clearly understood. These strong cellular responses are thought to be the basis of allograft rejection and graft-vs.-host disease. The question of the extent of responding T-cell repertoires has so far been addressed by cellular cloning, often combined with molecular T-cell receptor (TCR) analysis. Here we present a broad repertoire analysis of primed responder cells from mixed lymphocyte cultures in which two different DR1/3 responders were stimulated with DR3/4 cells. Repertoire analysis was performed by TCR spectratyping, a method by which T cells are analyzed on the basis of the complementarity-determining region 3 length of different variable region (V) families. Strikingly, both responders showed very similar repertoires when the TCR V beta was used as a lineage marker. This was not seen when TCR V alpha was analyzed. A different pattern of TCR V beta was observed if the stimulating alloantigen was changed. This finding indicates that alloreactive T cells form a specific repertoire for each alloantigen. Since conservation appears to be linked to TCR V beta, the question of different roles of alpha and beta chains in allorecognition is raised.

Evolutionary consequences of food chain length in kelp forest communities.

Kelp forests are strongly influenced by macroinvertebrate grazing on fleshy macroalgae. In the North Pacific Ocean, sea otter predation on macroinvertebrates substantially reduces the intensity of herbivory on macroalgae. Temperate Australasia, in contrast, has no known predator of comparable influence. These ecological and biogeographic patterns led us to predict that (i) the intensity of herbivory should be greater in temperate Australasia than in the North Pacific Ocean; thus (ii) Australasian seaweeds have been under stronger selection to evolve chemical defenses and (iii) Australasian herbivores have been more strongly selected to tolerate these compounds. We tested these predictions first by measuring rates of algal tissue loss to herbivory at several locations in Australasian and North Pacific kelp forests. There were significant differences in grazing rates among sea otter-dominated locations in the North Pacific (0-2% day-1), Australasia (5-7% day-1), and a North Pacific location lacking sea otters (80% day-1). The expectations that chronically high rates of herbivory in Australasia have selected for high concentrations of defensive secondary metabolites (phlorotannins) in brown algae and increased tolerance of these defenses in the herbivores also were supported. Phlorotannin concentrations in kelps and fucoids from Australasia were, on average, 5-6 times higher than those in a comparable suite of North Pacific algae, confirming earlier findings. Furthermore, feeding rates of Australasian herbivores were largely unaffected by phlorotannins, regardless of the compounds' regional source. North Pacific herbivores, in contrast, were consistently deterred by phlorotannins from both Australasia and the North Pacific. These findings suggest that top-level consumers, acting through food chains of various lengths, can strongly influence the ecology and evolution of plantherbivore interactions.