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Holmquist, R.

Publications and source records attributed to Holmquist, R..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

The spatial distribution of fixed mutations within genes coding for proteins

An examination has been conducted of the extensive amino acid sequence data now available for five protein families - the alpha crystallin A chain, myoglobin, alpha and beta hemoglobin, and the cytochromes c - with the goal of estimating the true spatial distribution of base substitutions within genes that code for proteins. In every case the commonly used Poisson density failed to even approximate the experimental pattern of base substitution. For the 87 species of beta hemoglobin examined, for example, the probability that the observed results were from a Poisson process was the minuscule 10 to the -44th. Analogous results were obtained for the other functional families. All the data were reasonably, but not perfectly, described by the negative binomial density. In particular, most of the data were described by one of the very simple limiting forms of this density, the geometric density. The implications of this for evolutionary inference are discussed. It is evident that most estimates of total base substitutions between genes are badly in need of revision.

Holmquist, R.↗
NASA NTRS1983

Transitions and transversions in evolutionary descent - An approach to understanding

A quantitative theoretical groundwork is presented for determining the proportions of the possible types of base substitutions observed between 12 genes sharing a common ancestor and isolated from extant species. Three methods (direct count, regression, and informational entropy maximization) are described by which conditional base substitution probabilities that determine evolutionary descent can be estimated from experimental data. These methods are utilized to study the ratio of transversions to transitions during gene divergence. The limiting ratio is directly calculated from a knowledge of the 12 conditional probabilities for each type of base substitution and from a knowledge of the equilibrium base composition of the DNAs compared. An expression is developed for this calculation. It is concluded that multiple substitutions per se do not lead to a decrease in transition differences with increasing evolutionary divergence.

Holmquist, R.↗
NASA NTRS1981

The estimation of genetic divergence

Consideration is given to the criticism of Nei and Tateno (1978) of the REH (random evolutionary hits) theory of genetic divergence in nucleic acids and proteins, and to their proposed alternative estimator of total fixed mutations designated X2. It is argued that the assumption of nonuniform amino acid or nucleotide substitution will necessarily increase REH estimates relative to those made for a model where each locus has an equal likelihood of fixing mutations, thus the resulting value will not be an overestimation. The relative values of X2 and measures calculated on the basis of the PAM and REH theories for the number of nucleotide substitutions necessary to explain a given number of observed amino acid differences between two homologous proteins are compared, and the smaller values of X2 are attributed to (1) a mathematical model based on the incorrect assumption that an entire structural gene is free to fix mutations and (2) the assumptions of different numbers of variable codons for the X2 and REH calculations. Results of a repeat of the computer simulations of Nei and Tateno are presented which, in contrast to the original results, confirm the REH theory. It is pointed out that while a negative correlation is observed between estimations of the fixation intensity per varion and the number of varions for a given pair of sequences, the correlation between the two fixation intensities and varion numbers of two different pairs of sequences need not be negative. Finally, REH theory is used to resolve a paradox concerning the high rate of covarion turnover and the nature of general function sites as permanent covarions.

Holmquist, R.↗
NASA NTRS1981

The current status of REH theory

A response is made to the evaluation of Fitch (1980) of REH (random evolutionary hits) theory for the evolutionary divergence of proteins and nucleic acids. Correct calculations for the beta hemoglobin mRNAs of the human, mouse and rabbit in the absence and presence of selective constraints are summarized, and it is shown that the alternative evolutionary analysis of Fitch underestimates the total fixed mutations. It is further shown that the model used by Fitch to test for the completeness of the count of total base substitutions is in fact a variant of REH theory. Considerations of the variance inherent in evolutionary estimations are also presented which show the REH model to produce no more variance than other evolutionary models. In the reply, it is argued that, despite the objections raised, REH theory applied to proteins gives inaccurate estimates of total gene substitutions. It is further contended that REH theory developed for nucleic sequences suffers from problems relating to the frequency of nucleotide substitutions, the identity of the codons accepting silent and amino acid-changing substitutions, and estimate uncertainties.

Holmquist, R.↗
NASA NTRS1980

Theoretical foundations for quantitative paleogenetics. III - The molecular divergence of nucleic acids and proteins for the case of genetic events of unequal probability

Theoretical equations are derived for molecular divergence with respect to gene and protein structure in the presence of genetic events with unequal probabilities: amino acid and base compositions, the frequencies of nucleotide replacements, the usage of degenerate codons, the distribution of fixed base replacements within codons and the distribution of fixed base replacements among codons. Results are presented in the form of tables relating the probabilities of given numbers of codon base changes with respect to the original codon for the alpha hemoglobin, beta hemoglobin, myoglobin, cytochrome c and parvalbumin group gene families. Application of the calculations to the rabbit alpha and beta hemoglobin mRNAs and proteins indicates that the genes are separated by about 425 fixed based replacements distributed over 114 codon sites, which is a factor of two greater than previous estimates. The theoretical results also suggest that many more base replacements are required to effect a given gene or protein structural change than previously believed.

Holmquist, R.↗
NASA NTRS1979

Molecular phylogenetic trees - On the validity of the Goodman-Moore augmentation algorithm

A response is made to the reply of Nei and Tateno (1979) to the letter of Holmquist (1978) supporting the validity of the augmentation algorithm of Moore (1977) in reconstructions of nucleotide substitutions by means of the maximum parsimony principle. It is argued that the overestimation of the augmented numbers of nucleotide substitutions (augmented distances) found by Tateno and Nei (1978) is due to an unrepresentative data sample and that it is only necessary that evolution be stochastically uniform in different regions of the phylogenetic network for the augmentation method to be useful. The importance of the average value of the true distance over all links is explained, and the relative variances of the true and augmented distances are calculated to be almost identical. The effects of topological changes in the phylogenetic tree on the augmented distance and the question of the correctness of ancestral sequences inferred by the method of parsimony are also clarified.

Holmquist, R.↗
NASA NTRS1979

Beta-galactosidase and selective neutrality

Three hypotheses to explain the amino acid composition of proteins are inconsistent (about 10 to the minus 9th) with the experimental data for beta-galactosidase from Escherichia coli. The exceptional length of this protein, 1021 residues, permits rigorous tests of these hypotheses without complication from statistical artifacts. Either this protein is not at compositional equilibrium, which is unlikely from knowledge about other proteins, or the evolution of this protein and its coding gene have not been selectively neutral. However, the composition of approximately 60% of the molecule is consistent with either a selectively neutral or nonneutral evolutionary process.

Holmquist, R.↗
NASA NTRS1978

The augmentation algorithm and molecular phylogenetic trees

Moore's (1977) augmentation procedure is discussed, and it is concluded that the procedure is valid for obtaining estimates of the total number of fixed nucleotide substitutions both theoretically and in practice, for both simulated and real data, and in agreement, for experimentally dense data sets, with stochastic estimates of the divergence, provided the restrictions on codon mutability resulting from natural selection are explicitly allowed for. Tateno and Nei's (1978) critique that the augmentation procedure has a systematic bias toward overestimation of the total number of nucleotide replacements is disputed, and a data analysis suggests that ancestral sequences inferred by the method of parsimony contain a large number of incorrectly assigned nucleotides.

Holmquist, R.↗
NASA NTRS1978

Evaluation of compositional nonrandomness in proteins

The finite sampling component of Q, a measure of nonrandomness in the amino acid composition of proteins, is quantitatively estimated by using the natural abundances of amino acids rather than the genetic code table frequencies, and the revised value of Q implies that the value of Q(c), a measure of selective effects above and beyond those imposed by the average natural abundance of the amino acids, should be 9.7 rather than its previous value of 24.3. Individual Q(c) values are given for 81 protein families. The standard deviation of the population of Q(c) values is 12.5 but the Q(c) value differs significantly from the value of zero expected were the natural abundances of the amino acids the only selective constraint. The small value of Q(c) indicates that quantitatively minimal adjustments away from the average protein composition are necessary to maintain many different biological functions.

Holmquist, R.↗
NASA NTRS1978

The REH theory of protein and nucleic acid divergence - A retrospective update

The random evolutionary hits (REH) theory of evolutionary divergence, originally proposed in 1972, is restated with attention to certain aspects of the theory that have caused confusion. The theory assumes that natural selection and stochastic processes interact and that natural selection restricts those codon sites which may fix mutations. The predicted total number of fixed nucleotide replacements agrees with data for cytochrome c, a-hemoglobin, beta-hemoglobin, and myoglobin. The restatement analyzes the magnitude of possible sources of errors and simplifies calculational methodology by supplying polynomial expressions to replace tables and graphs.

Holmquist, R.↗
NASA NTRS1978

A measure of the denseness of a phylogenetic network

An objective measure of phylogenetic denseness is developed to examine various phylogenetic criteria: alpha- and beta-hemoglobin, myoglobin, cytochrome c, and the parvalbumin family. Attention is given to the number of nucleotide replacements separating homologous sequences, and to the topology of the network (in other words, to the qualitative nature of the network as defined by how closely the studied species are related). Applications include quantitative comparisons of species origin, relation, and rates of evolution.

Holmquist, R.↗
NASA NTRS1976

Solution to a gene divergence problem under arbitrary stable nucleotide transition probabilities

A nucleic acid chain, L nucleotides in length, with the specific base sequence B(1)B(2) ... B(L) is defined by the L-dimensional vector B = (B(1), B(2), ..., B(L)). For twelve given constant non-negative transition probabilities that, in a specified position, the base B is replaced by the base B' in a single step, an exact analytical expression is derived for the probability that the position goes from base B to B' in X steps. Assuming that each base mutates independently of the others, an exact expression is derived for the probability that the initial gene sequence B goes to a sequence B' = (B'(1), B'(2), ..., B'(L)) after X = (X(1), X(2), ..., X(L)) base replacements. The resulting equations allow a more precise accounting for the effects of Darwinian natural selection in molecular evolution than does the idealized (biologically less accurate) assumption that each of the four nucleotides is equally likely to mutate to and be fixed as one of the other three. Illustrative applications of the theory to some problems of biological evolution are given.

Holmquist, R.↗
NASA NTRS1975

Tables of critical values for examining compositional non-randomness in proteins and nucleic acids

A binomially distributed statistic is defined to show whether or not the proportion of a particular amino acid in a protein deviates from random expectation. An analogous statistic is derived for nucleotides in nucleic acids. These new statistics are simply related to the classical chi-squared test. They explicitly account for the compositional fluctuations imposed by the finite length of proteins, and they are more accurate than previous tables.

Laird, M.↗
NASA NTRS1973

Recently published protein sequences. III

A listing of polypeptide sequences announced in published papers in 1972 and 1973 is given. The listing contains twenty one new sequencies which were selected by using the distinction of Asn, Asp, Gln, and Glu from Asx and Glx, and the absence of unsequenced peptides as criteria.

Jukes, T. H.↗
NASA NTRS1972

Sequence data - Magnitude and implications of some ambiguities.

A stochastic model is applied to the divergence of the horse-pig lineage from a common ansestor in terms of the alpha and beta chains of hemoglobin and fibrinopeptides. The results are compared with those based on the minimum mutation distance model of Fitch (1972). Buckwheat and cauliflower cytochrome c sequences are analyzed to demonstrate their ambiguities. A comparative analysis of evolutionary rates for various proteins of horses and pigs shows that errors of considerable magnitude are introduced by Glx and Asx ambiguities into evolutionary conclusions drawn from sequences of incompletely analyzed proteins.

Holmquist, R.↗
NASA NTRS1972

Evolutionary clock - Nonconstancy of rate in different species.

By using various methods for comparing polypeptide sequences we find that the evolutionary divergence of rattlesnake cytochrome c from cytochromes c of species in other classes has been more rapid than that of cytochrome c of another reptile, the snapping turtle. This suggests that the evolutionary rate of change of cytochromes c is species-dependent as well as time-dependent.

Jukes, T. H.↗