The Malthusian parameter of ascents: What prevents the exponential increase of one’s ancestors?

The reason that the indefinite exponential increase in the number of one’s ancestors does not take place is found in the law of sibling interference, which can be expressed by the following simple equation:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\begin{matrix}{\mathit{N}}_{{\mathit{n}}} \enskip & \\ {\mathit{{\blacksquare}}} \enskip & \\ {\mathit{ASZ}} \enskip & \end{matrix} {\mathrm{\hspace{.167em}{\times}\hspace{.167em}2\hspace{.167em}=\hspace{.167em}}}{\mathit{N_{n+1},}}\end{equation*}\end{document} where Nn is the number of ancestors in the nth generation, ASZ is the average sibling size of these ancestors, and Nn+1 is the number of ancestors in the next older generation (n + 1). Accordingly, the exponential increase in the number of one’s ancestors is an initial anomaly that occurs while ASZ remains at 1. Once ASZ begins to exceed 1, the rate of increase in the number of ancestors is progressively curtailed, falling further and further behind the exponential increase rate. Eventually, ASZ reaches 2, and at that point, the number of ancestors stops increasing for two generations. These two generations, named AN SA and AN SA + 1, are the most critical in the ancestry, for one’s ancestors at that point come to represent all the progeny-produced adults of the entire ancestral population. Thereafter, the fate of one’s ancestors becomes the fate of the entire population. If the population to which one belongs is a successful, slowly expanding one, the number of ancestors would slowly decline as you move toward the remote past. This is because ABZ would exceed 2. Only when ABZ is less than 2 would the number of ancestors increase beyond the AN SA and AN SA + 1 generations. Since the above is an indication of a failing population on the way to extinction, there had to be the previous AN SA involving a far greater number of individuals for such a population. Simulations indicated that for a member of a continuously successful population, the AN SA ancestors might have numbered as many as 5.2 million, the AN SA generation being the 28th generation in the past. However, because of the law of increasingly irrelevant remote ancestors, only a very small fraction of the AN SA ancestors would have left genetic traces in the genome of each descendant of today.

The optimization principle in phylogenetic analysis tends to give incorrect topologies when the number of nucleotides or amino acids used is small

In the maximum parsimony (MP) and minimum evolution (ME) methods of phylogenetic inference, evolutionary trees are constructed by searching for the topology that shows the minimum number of mutational changes required (M) and the smallest sum of branch lengths (S), respectively, whereas in the maximum likelihood (ML) method the topology showing the highest maximum likelihood (A) of observing a given data set is chosen. However, the theoretical basis of the optimization principle remains unclear. We therefore examined the relationships of M, S, and A for the MP, ME, and ML trees with those for the true tree by using computer simulation. The results show that M and S are generally greater for the true tree than for the MP and ME trees when the number of nucleotides examined (n) is relatively small, whereas A is generally lower for the true tree than for the ML tree. This finding indicates that the optimization principle tends to give incorrect topologies when n is small. To deal with this disturbing property of the optimization principle, we suggest that more attention should be given to testing the statistical reliability of an estimated tree rather than to finding the optimal tree with excessive efforts. When a reliability test is conducted, simplified MP, ME, and ML algorithms such as the neighbor-joining method generally give conclusions about phylogenetic inference very similar to those obtained by the more extensive tree search algorithms.

Telomeres in the mouse have large inter-chromosomal variations in the number of T2AG3 repeats

The ultra-long telomeres that have been observed in mice are not in accordance with the concept that critical telomere shortening is related to aging and immortalization. Here, we have used quantitative fluorescence in situ hybridization to estimate (T2AG3)n lengths of individual telomeres in various mouse strains. Telomere lengths were very heterogeneous, but specific chromosomes of bone marrow cells and skin fibroblasts from individual mice had similar telomere lengths. We estimate that the shortest telomeres are around 10 kb in length, indicating that each mouse cell has a few telomeres with (T2AG3)n lengths within the range of human telomeres. These short telomeres may be critical in limiting the replicative potential of murine cells.

Varying the number of telomere-bound proteins does not alter telomere length in tel1Δ cells

Yeast telomere DNA consists of a continuous, ≈330-bp tract of the heterogeneous repeat TG1-3 with irregularly spaced, high affinity sites for the protein Rap1p. Yeast monitor, or count, the number of telomeric Rap1p C termini in a negative feedback mechanism to modulate the length of the terminal TG1-3 repeats, and synthetic telomeres that tether Rap1p molecules adjacent to the TG1-3 tract cause wild-type cells to maintain a shorter TG1-3 tract. To identify trans-acting proteins required to count Rap1p molecules, these same synthetic telomeres were placed in two short telomere mutants: yku70Δ (which lack the yeast Ku70 protein) and tel1Δ (which lack the yeast ortholog of ATM). Although both mutants maintain telomeres with ≈100 bp of TG1-3, only yku70Δ cells maintained shorter TG1-3 repeats in response to internal Rap1p molecules. This distinct response to internal Rap1p molecules was not caused by a variation in Rap1p site density in the TG1-3 repeats as sequencing of tel1Δ and yku70Δ telomeres showed that both strains have only five to six Rap1p sites per 100-bp telomere. In addition, the tel1Δ short telomere phenotype was epistatic to the unregulated telomere length caused by deletion of the Rap1p C-terminal domain. Thus, the length of the TG1-3 repeats in tel1Δ cells was independent of the number of the Rap1p C termini at the telomere. These data indicate that tel1Δ cells use an alternative mechanism to regulate telomere length that is distinct from monitoring the number of telomere binding proteins.

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.

The number of unidentified amacrine cells in the mammalian retina

The three largest known populations of amacrine cells in the rabbit retina were stained with fluorescent probes in whole mounts and counted at a series of retinal eccentricities. The retinas were counterstained using a fluorescent DNA-binding molecule and the total number of nuclei in the inner nuclear layer were counted in confocal sections. From the total number of inner nuclear layer cells and the known fraction of them occupied by amacrine cells, the fraction of amacrine cells made up by the stained populations could be calculated. Starburst cells made up 3%, indoleamine-accumulating cells made up 4%, and AII cells made up 11% of all amacrine cells. By referring four smaller populations of amacrine cells to the number of indoleamine-accumulating cells, they were estimated to make up 4% of all amacrine cells. Thus, 78% of all amacrine cells in the rabbit’s retina are known only from isolated examples, if at all. This proportion is similar in the retinas of the mouse, cat, and monkey. It is likely that a substantial fraction of the local circuit neurons present in other regions of the central nervous system are also invisible as populations to current techniques.

An essential amino acid residue in the protein translocation channel revealed by targeted random mutagenesis of SecY

The SecY/Sec61α family of membrane proteins are the central subunits of the putative protein translocation channel. We introduced random mutations into a segment of Escherichia coli SecY within its cytoplasmic domain 5, which was shown previously to be important for the SecA-dependent translocation activity. Mutations were classified into those retaining function and those gaining a dominant-interfering ability caused by a loss of function. These analyses showed that Arg-357, Pro-358, Gly-359, and Thr-362 are functionally important; Arg-357, conserved in almost all organisms, was identified as an indispensable residue.

Heat effects on DNA repair after ionising radiation: hyperthermia commonly increases the number of non-repaired double-strand breaks and structural rearrangements

After ionising radiation double-strand breaks (dsb) are lethal if not repaired or misrepaired. Cell killing is greatly enhanced by hyperthermia and it is questioned here whether heat not only affects dsb repair capacity but also fidelity in a chromosomal context. dsb repair experiments were designed so as to mainly score non-homologous end joining, while homologous recombination was largely precluded. Human male G0 fibroblasts were either preheated (45°C, 20 min) or not before X-irradiation. dsb induction and repair were measured by conventional gel electrophoresis and an assay combining restriction digestion using a rare cutting enzyme (NotI) and Southern hybridisation, which detects large chromosomal rearrangements (>100 kb). dsb induction rate in an X-chromosomal NotI fragment was 4.8 × 10–3 dsb/Gy/Mb. Similar values were found for the genome overall and also when cells were preheated. After 50 Gy, fibroblasts were competent to largely restore the original restriction fragment size. Five per cent of dsb remained non-rejoined and 14% were misrejoined. Correct restitution of restriction fragments occurred preferably during the first hour but continued at a slow rate for 12–16 h. In addition, dsb appeared to misrejoin throughout the entire repair period. After hyperthermia the fractions of non-rejoined and misrejoined dsb were similarly increased to 13 and 51%, respectively. It is suggested that heat increases the probability of dsb being incorrectly rejoined but it is not likely to interfere with one dsb repair pathway in particular.

Random mutagenesis of Thermus aquaticus DNA polymerase I: concordance of immutable sites in vivo with the crystal structure.

Expression of Thermus aquaticus (Taq) DNA polymerase I (pol I) in Escherichia, coli complements the growth defect caused by a temperature-sensitive mutation in the host pol I. We replaced the nucleotide sequence encoding amino acids 659-671 of the O-helix of Taq DNA pol I, corresponding to the substrate binding site, with an oligonucleotide containing random nucleotides. Functional Taq pol I mutants were selected based on colony formation at the nonpermissive temperature. By using a library with 9% random substitutions at each of 39 positions, we identified 61 active Taq pol I mutants, each of which contained from one to four amino acid substitutions. Some amino acids, such as alanine-661 and threonine-664, were tolerant of several or even many diverse replacements. In contrast, no replacements or only conservative replacements were identified at arginine-659, lysine-663, and tyrosine-671. By using a library with totally random nucleotides at five different codons (arginine-659, arginine-660, lysine-663, phenylalanine-667, and glycine-668), we confirmed that arginine-659 and lysine-663 were immutable, and observed that only tyrosine substituted for phenylalanine-667. The two immutable residues and the two residues that tolerate only highly conservative replacements lie on the side of O-helix facing the incoming deoxynucleoside triphosphate, as determined by x-ray analysis. Thus, we offer a new approach to assess concordance of the active conformation of an enzyme, as interpreted from the crystal structure, with the active conformation inferred from in vivo function.

Multiplex genotype determination at a large number of gene loci.

To facilitate large-scale genotype analysis, an efficient PCR-based multiplex approach has been developed. For simultaneously amplifying the target sequences at a large number of genetic loci, locus-specific primers containing 5' universal tails are used. Attaching the universal tails to the target sequences in the initial PCR steps allows replacement of all specific primers with a pair of primers identical to the universal tails and converts the multiplex amplification into "uniplex." Simultaneous amplification of 26 genetic loci with this approach is described. The multiplex amplification can be coupled with genotype determination. By incorporating a single-base mismatch between a primer and the template into the target sequences, a polymorphic site can be converted into a desirable restriction fragment length polymorphism when it is necessary. In this way, the allelic PCR products for the polymorphic loci can be discriminated by gel electrophoresis after restriction enzyme digestion. In this study, 32 loci were typed in such a multiplex way.