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Biomedical subjects

W J Wilbur

Publications and source records attributed to W J Wilbur.

12 recordsLinked to original sources
PubMed1991

Modelling neutral and selective evolution of protein folding.

We examine a model evolutionary space consisting of genotypes mapped to their corresponding phenotypes. This mapping is derived from a lattice model for proteins which, despite its highly idealized nature, has been shown to share general properties with real proteins. Large evolutionary networks are observed, with genotypes corresponding to non-lethal phenotypes linked by unit mutational steps. Neutral mutations are necessary for traversing the evolutionary networks, and even one neutral mutation in a genotype can change the phenotypes attainable by a unit mutational step.

Biological Evolution↗
PubMed1986

A biophysical model of cochlear processing: intensity dependence of pure tone responses.

A mathematical model of cochlear processing is developed to account for the nonlinear dependence of frequency selectivity on intensity in inner hair cell and auditory nerve fiber responses. The model describes the transformation from acoustic stimulus to intracellular hair cell potentials in the cochlea. It incorporates a linear formulation of basilar membrane mechanics and subtectorial fluid-cilia displacement coupling, and a simplified description of the inner hair cell nonlinear transduction process. The analysis at this stage is restricted to low-frequency single tones. The computed responses to single tone inputs exhibit the experimentally observed nonlinear effects of increasing intensity such as the increase in the bandwidth of frequency selectivity and the downward shift of the best frequency. In the model, the first effect is primarily due to the saturating effect of the hair cell nonlinearity. The second results from the combined effects of both the nonlinearity and of the inner hair cell low-pass transfer function. In contrast to these shifts along the frequency axis, the model does not exhibit intensity dependent shifts of the spatial location along the cochlea of the peak response for a given single tone. The observed shifts therefore do not contradict an intensity invariant tonotopic code.

Acoustic Stimulation↗
PubMed1985

On the PAM matrix model of protein evolution.

The internal consistency of the PAM matrix model of protein evolution is here investigated. The 1 PAM matrix has been constructed from amino acid replacements observed in closely related sequences. Such replacements are of two types, those that do not require an intermediate amino acid replacement and those that do. The second type of replacement must generally be produced by a repetition of the first. This allows data on the first type to be used in predicting data on the second type so that some elements of the 1 PAM matrix may be used to predict others. A discrepancy of more than two orders of magnitude is found between the predictions and the data when this is carried out. This is partly accounted for by an error in constructing the matrix. However, it also seems necessary that the basic model be modified. Several possibilities are considered. One of these is to incorporate a site-dependent spectrum of mutabilities associated with each amino acid.

Amino Acid Sequence↗
PubMed1984

On the statistical significance of nucleic acid similarities.

When evaluating sequence similarities among nucleic acids by the usual methods, statistical significance is often found when the biological significance of the similarity is dubious. We demonstrate that the known statistical properties of nucleic acid sequences strongly affect the statistical distribution of similarity values when calculated by standard procedures. We propose a series of models which account for some of these known statistical properties. The utility of the method is demonstrated in evaluating high relative similarity scores in four specific cases in which there is little biological context by which to judge the similarities. In two of the cases we identify the statistical properties which are responsible for the apparent similarity. In the other two cases the statistical significance of the similarity persists even when the known statistical properties of sequences are modelled. For one of these cases biological significance is likely while the other case remains an enigma.

Base Sequence↗
PubMed1983

A theoretical basis for large coefficient of variation and bimodality in neuronal interspike interval distributions.

We consider the classic Stein (1965) model for stochastic neuronal firing under random synaptic input. Our treatment includes the additional effect of synaptic reversal potentials. We develop and employ two numerical methods (in addition to Monte Carlo simulations) to study the relation of the various parameters of the model to the shape of the theoretical interspike interval distribution. Contrary to the results of Tuckwell (1979) we are unable to account, on the basis of substantial synaptic inhibition and with parameter settings in the known physiologic range, for experimental interspike interval distributions which exhibit large coefficients of variation or bimodality. We therefore introduce a time varying threshold into the model, which readily allows for such distributions and which has physiological justification.

Action Potentials↗
PubMed1983

Contextual constraints on synonymous codon choice.

We have studied the statistical constraints on synonymous codon choice to evaluate various proposals regarding the origin of the bias in synonymous codon usage observed by Fiers et al. (1975), Air et al. (1976), Grantham et al. (1980) and others. We have determined the statistical dependence of the degenerate third base on either of its nearest neighbors in mitochondrial, prokaryotic, and eukaryotic coding sequences. We noted an increasing dependence of the third base on its nearest neighbors in moving from mitochondria to prokaryotes to eukaryotes. A statistical model assuming random equiprobable selection of synonymous codons was found grossly adequate for the mitochondria, but totally inadequate for prokaryotes and eukaryotes. A model assuming selection of synonymous codons reflecting a genomic strategy, i.e. the genome hypothesis of Grantham et al. (1980), gave a good approximation of the mitochondrial sequences. A statistical model which exactly maintains codon frequency, but allows the position of corresponding synonymous codons to vary was only grossly adequate for prokaryotes and totally inadequate for eukaryotes. The results of these simulations are consistent with the measures on experimental sequences and suggest that a "frequency constraint" model such as that of Grantham et al. (1980) may be an adequate explanation of the codon usage in mitochondria. However, in addition to this frequency constraint, there may be constraints on synonymous codon choice in prokaryotes due to codon context. Furthermore, any proposal to explain codon usage in eukaryotes must involve a constraint on the context of a codon in the sequence.

Amino Acid Sequence↗
PubMed1983

Rapid similarity searches of nucleic acid and protein data banks.

With the development of large data banks of protein and nucleic acid sequences, the need for efficient methods of searching such banks for sequences similar to a given sequence has become evident. We present an algorithm for the global comparison of sequences based on matching k-tuples of sequence elements for a fixed k. The method results in substantial reduction in the time required to search a data bank when compared with prior techniques of similarity analysis, with minimal loss in sensitivity. The algorithm has also been adapted, in a separate implementation, to produce rigorous sequence alignments. Currently, using the DEC KL-10 system, we can compare all sequences in the entire Protein Data Bank of the National Biomedical Research Foundation with a 350-residue query sequence in less than 3 min and carry out a similar analysis with a 500-base query sequence against all eukaryotic sequences in the Los Alamos Nucleic Acid Data Base in less than 2 min.

Amino Acid Sequence↗
PubMed1978

Water exchange in the placenta: a mathematical model.

To better understand the complicated interplay of forces affecting human placental water exchange, we developed a system of differential equations describing the flows of water, glucose, bicarbonate ion, amino acids, CO2, O2, passive cations (such as Na+ and K+), and chloride ion transplacentally and across the erythrocytes. The equations are based largely on the flux equations of irreversible thermodynamics, although Goldman's hypothesis and equation are employed to treat the ionic currents across the erythrocyte membrane. Bicarbonate ion and dissolved carbon dioxide were found to be major forces acting early in capillary transit to produce a large flow of water toward the fetus. Near the end of the capillary an almost equal amount of water returns to the mother, an effect due predominantly to the effect of glucose. For small deviations from accepted normal values, water transfer is most sensitive to changes in passive cations and chloride, followed by bicarbonate and CO2, plasma solutes (including lactate and glucose), hydrostatic pressure, and amino acids. A simple equation is given to summarize the model's results for water transfer when many factors change simultaneously. Uneven distribution of maternal-to-fetal blood flows tends to favor fetal water acquisition.

Cell Membrane Permeability↗
PubMedDate not supplied

Interaction of silent and replacement changes in eukaryotic coding sequences.

We examined the codon usages in well-conserved and less-well-conserved regions of vertebrate protein genes and found them to be similar. Despite this similarity, there is a statistically significant decrease in codon bias in the less-well-conserved regions. Our analysis suggests that although those codon changes initially fixed under amino acid replacements tend to follow the overall codon usage pattern, they also reduce the bias in codon usage. This decrease in codon bias leads one to predict that the rate of change of synonymous codons should be greater in those regions that are less well conserved at the amino acid level than in the better-conserved regions. Our analysis supports this prediction. Furthermore, we demonstrate a significantly elevated rate of change of synonymous codons among the adjacent codons 5' to amino acid replacement positions. This provides further support for the idea that there are contextual constraints on the choice of synonymous codons in eukaryotes.

Cell Physiological Phenomena↗
PubMedDate not supplied

Codon equilibrium I: Testing for homogeneous equilibrium.

We present theoretical considerations that suggest that synonymous-codon usage might be expected to be close to an equilibrium distribution given a very homogeneous process of silent substitution. By homogeneous we mean that substitution depends only on the two bases involved, so that 12 base-substitution rates completely describe the silent substitution process. We have developed a method of statistically testing for such homogeneous equilibrium and applied it to reported data on the codon usages of different classes of organisms. Weakly expressed bacterial sequences and both mammalian and nonmammalian eukaryotic sequences deviate significantly from a random pattern of codon usage, in the direction of homogeneous equilibrium. On the other hand, highly expressed bacterial sequences do not exhibit homogeneous equilibrium, which may be correlated with recent experimental results showing that they are optimized to accept the most abundant tRNAs. To examine the effect of amino acid replacements on the homogeneous model of silent substitution, we divided the amino acids with degenerate codes into two classes, those with high mutabilities and those with low, and performed the same analysis on bacterial and eukaryotic data sets. The codon sets of the highly mutable class of amino acids are not further from homogeneous equilibrium than are the codon sets of the class with low mutabilities. We also found for the eukaryotic data that these independent classes of codon sets show very similar equilibrium patterns. The various results suggest a high level of uniformity in the process of silent fixation in the different synonymous-codon sets, especially in eukaryotes.

Amino Acid Sequence↗
PubMedDate not supplied

Codon equilibrium II: Its use in estimating silent-substitution rates.

We study the equilibrium in the use of synonymous codons by eukaryotic organisms and find five equations involving substitution rates that we believe embody the important implications of equilibrium for the process of silent substitution. We then combine these five equations with additional criteria to determine sets of substitution rates applicable to eukaryotic organisms. One method employs the equilibrium equations and a principle of maximum entropy to find the most uniform set of rates consistent with equilibrium. In a second method we combine the equilibrium equations with data on the man-mouse divergence to determine that set of rates that is most neutral yet consistent with both types of data (i.e., equilibrium and divergence data). Simulations show this second method to be quite reliable in spite of significant saturation in the substitution process. We find that when divergence data are included in the calculation of rates, even though these rates are chosen to be as neutral as possible, the strength of selection inferred from the nonuniformity of the rates is approximately doubled. Both sets of rates are applied to estimate the human-mouse divergence time based on several independent subsets of the divergence data consisting of the quartet, C- or T-ending duet, and A- or G-ending duet codon sets. Both rate sets produce patterns of divergence times that are shortest for the quartet data, intermediate for the CT-ending duets, and longest for the AG-ending duets. This indicates that rates of transitions in the duet-codon sets are significantly higher than those in the quartet-codon sets; this effect is especially marked for A----G, the rate of which in duets must be about double that in quartets.

Animals↗