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E A Murphy

Publications and source records attributed to E A Murphy.

At least 109 records · Page 6Linked to original sources
PubMed1984

The dynamics of quantifiable homeostasis. IV: Zero-order homeostasis.

A zero-order homeostatic process is one in which the corrective force a has sign opposite to that of what the displacement from the homing value was one lag (L) time earlier, but is unrelated to magnitude of displacement. The properties of a zero-order process are considered in some detail. Its stable state is an oscillation with a period of 4L and a maximum amplitude of aL. It is suggested that this property is exploited in evolution for intrinsically rhythmical processes, and several examples (respiration, menstruation, and heart beat) are discussed. The parameters may be modulated by an ancillary cybernetic (retreat) circuit and hence the properties of the oscillation controlled as need be. Zero-order oscillation has means of conserving information through phase shifts. Also, when it is combined with a linear cybernetic process (with restoration constant b), it prevents information in the latter from dying out, even if Lb is less than pi/2 (which in a pure linear process would ensure extinction of all signs of perturbation). A further elaboration is the Dilman process of zero order in which there is a threshold of displacement below which homeostatic responses are not evoked. The merits of the value of the threshold are discussed. The properties of the zero-order process with a first-order retreat function furnish a tentative explanation for why hormonal homeostasis does not operate directly through the pituitary but involves the hypothalamus and intermediate hormone-releasing factors.

Blood Pressure↗
PubMed1984

The dynamics of quantifiable homeostasis. V: Homeostasis of higher order.

The properties are explored of a cybernetic process with lag L and force of restoration equal to the size of displacement one lag unit earlier, raised to any arbitrary positive power (w greater than 1), multiplied by the restoration constant b, the sign being opposite to that of the displacement at that time. No closed-form solution is available, but a converging Taylor series expansion is presented that gives a solution of arbitrary precision. Unlike the linear system previously discussed, the amplitude of the displacement (A) is germane, and it is shown that the criterion that the effect of a perturbation be damped out is whether or not LbAw-1 exceeds a constant, kw, that depends only on w. The counterpart of this pattern of higher-order homeostasis is closer to the biological behavior of many forms of homeostasis than the scaled invariance characteristic of the linear process. kw is shown to be bounded between pi/2 and 2, and increases monotonically with w. Exactly computed values and large-sample approximations are given for the critical values below which no overshoot at all occurs. It is shown that where it does not, the minimum expected cost decreases with increasing w and reaches a minimum at infinite w. However, this evolutionary gain is vitiated where large displacements are involved, and may need to be redressed by a change in the restoration constant. Thus, the dynamic balance becomes much more subtle than with lower-order processes. Several brief clinical illustrations of these ideas are presented.

Biological Evolution↗
PubMed1983

The dynamics of quantifiable homeostasis. I. The individual.

In this field of enquiry, "homeostasis" is understood in the sense of Bernard, Cannon, and Wiener, that is, with the system of continuous adjustments, in a trait not inherently stable, to meet the challenges of the environment. It is shown that the clinical fitness of a trait may depend on factors other than the mean or the variance. In particular the broad pattern of variation of the phenotype may be of importance and hence the characteristics of the homeostatic mechanisms for the control of traits subject to variation: notably the homing value (the "setting" of the homeostat), and the strength with which the organism responds to departures from this value. These parameters are related, but perhaps only remotely, to the traditional notion of the value of a phenotype. In general, where the environmental value is variable, there exist circumstances in which the optimal control would be neither extremely tight nor extremely loose. For instance, anticipatory action on the part of the body may be vitiated by too tight a control. Some illustrations are given of genetic disorders in which there is a fault in the strength of control. While neither the pattern of inheritance nor the impact on the species is explored in detail, the broad implications are indicated. Compromise adjustments are explored where two or more traits are regulated through the same homeostatic device.

Adaptation, Biological↗
PubMed1983

The dynamics of quantifiable homeostasis. II. Characterization of linear processes.

This paper deals with the representation of physiological homeostatic processes by mathematical models that lead to lag-differential equations. It deals exclusively with feedback processes that are linear. It is surmised that in the response to standard perturbations from equilibrium, in many systems the strength at which the restorative force works (denoted by the constant b) is a genetic characteristic, while the average or homing value may or may not be. The class of equations with linear feedback is solved. The solution provides predictions against which experimental data may be tested. Three types of displacement from the homing value are recognized: drifts, catastrophes, and saccades. Several methods of evaluating the mathematical functions are described. They are forward recursion, backward recursion, numerical integration, steady-state solutions, and inversion of the Heaviside expansion of the Laplace transform. Conditions for homeostatic processes that result in damped nonoscillating responses, damped oscillating responses, stable oscillations, and uncontrolled oscillations are derived. The concept of an associated penalty that depends on the degree of displacement from the homing value is discussed. Penalties are evaluated by numerical integration for linear, quadratic, and cubic costs. Costs for polynomial functions may be found by linear weighting. The optimum strength of response (ie, the one that produces the minimum cost) is calculated for each of these cost functions.

Feedback↗
PubMed1983

Paradoxical fixation of deleterious alleles in two-locus systems with epistasis.

The dynamics of four deterministic models of interaction between two Mendelian loci are explored numerically. At one locus there are two hypostatic alleles: h, the wild type and H, a deleterious mutant that in either heterozygous or homozygous state (depending on the specifics of the model) produces an abnormal phenotype. At another arbitrarily linked epistatic locus there are two alleles: e, the wild type with no effect on the expression of the H locus, and E, an epistatic mutant that in heterozygous or homozygous state (again, depending on the specifics of the model) blocks the expression of H. The parameters are the initial gamete frequencies, the recombination fraction, the genotypic viabilities, and the forward and back mutation rates at each locus. The He haplotype is eventually eliminated (unless back mutation occurs) from the population. If mutation is ignored, the evolutionary outcome is determined by the initial gamete frequencies and is either (1) an edge equilibrium comprising one pair of haplotypes only (he and He, or he and hE, or hE and HE, or He and HE, or, if there is no recombination, he and HE or hE and He); or (2) a corner equilibrium consisting of a single gametic type. Given that the forward mutation rates at both loci are greater than the back mutation rates, then the outcome is always the corner equilibrium in which HE is universal (apart from transient perturbations by mutation). In the process of fixation, the phenotypic impact of the deleterious allele H becomes neutralized by the epistatic allele E. The rate at which the initially harmful gene replaces the wild type gene depends on the recombination fraction, the genotypic viabilities, and the mutation rates.

Alleles↗
PubMed1983

Genetic aspects of multiple polyposis coli.

Questions on this topic that concern the clinician are addressed: whether it is inherited and, if so, whether Mendelian; what the segregation ratios will be; whether it is heterogeneous; how its high frequency can be accounted for; and what preventive measures are available. In several cases the question has to be reworded in order to make it sufficiently precise for it to be used in practice without misleading the patient. Framed in this fashion applicable answers are relatively easily available although many genetic puzzles remain. To date, no antenatal diagnosis is available.

Age Factors↗
PubMed1983

Inheritance of the mitral valve prolapse syndrome. Discussion of a three-dimensional penetrance model.

The families of 12 probands with classic mitral valve prolapse were studied for evidence of mitral valve prolapse. Seventy parents, sibs, and progeny were included in the analysis. Forty-seven percent (16 of 34) of progeny were affected compared with 30 percent (3 of 10) of parents. Thirty-eight percent (10 of 26) of sibs were affected. A three-compartmental penetrance model was devised to account for the variation in expression with age. This includes a latent stage (time before onset of signs), an affected stage, and a stage in which the subjects are withdrawn (because of treatment, regression, or death). The implications of this model are discussed.

Adolescent↗
PubMed1982

Kinetics and distribution of 111Indium-labeled platelets in patients with homocystinuria.

Homocystinuria is an inborn error of metabolism involving a high incidence of thromboembolism. It sometimes improves with large doses of pyridoxine. We investigated the kinetics and distribution of 111Indoxine-labeled platelets in 11 normal volunteers and 12 patients with homocystinuria, none of whom had clinical evidence of acute thrombosis at the time of the study. Six of the patients were resistant to pyridoxine and had homocystinemia. There were no statistical differences in mean platelet-survival times between pyridoxine responders and nonresponders or between normal subjects and pyridoxine responders or nonresponders, regardless of whether a linear, exponential, or multiple-hit model was used to analyze the kinetic data. Plasma homocystine levels had no apparent effect on mean platelet-survival time. There was no abnormal accumulation of platelets in any of the patients, and the distribution of platelets in liver and spleen was similar to that in normal subjects. Our results suggest that the kinetics and distribution of platelets in patients with homocystinuria who have no clinical evidence of thromboembolism are normal. Thus, the data do not provide evidence for disordered platelet function or for an ongoing interaction of platelets with vessel walls in this condition.

Adolescent↗
PubMed1982

Theory of genetic counseling for rare recessive traits with consanguinity.

The theory of assessing genetic risk for rare autosomal recessive traits in the face of extensive consanguinity is explored. A general lemma is proved that justifies the partition of posterior probability and recursive incorporation of it, as a means of reducing the logic of analysis to steps of manageable complexity: the conditions are that either the components should be independent or that each component, as it is added, is conditioned on the occurrence of all earlier components. An example is given of a pedigree in which the tracing of a gene by the method of expected proportions is misleading, and another that points up the importance of the posterior information. Four classes of patterns are identified and appropriate methods devised for handling them: the single consanguineous loop, multiple mutually-external loops, nested loops, and multiple closures. The latter problem may be treated in general by the use of truncated generating functions, with or without the use of matrix methods.

Bayes Theorem↗
PubMed1982

The analysis and interpretation of experiments: some philosophical issues.

The epistemology and ontology of experimentation are discussed in depth with special reference to biology and medicine. Two types of experiments are distinguished: exploratory (or "blazing") and consolidating. They have objectives and canons that are strikingly different. A contrast is drawn between the literalism of the most pragmatic scientists and the formalism of most statisticians. The terms and notions of the one may have imperfect correspondence with those of the other, or perhaps none at all. The dangers are pointed out of both the conclusion that the gap between the two is unbridgeable and the contrary view that the gap is trivial and merits no serious attention. Substantive discussions address the choice and meaning of a metric, the idea of interaction and time series analysis, the ontology of variation, and the epistemology of randomization, hypothesis-seeking, and multiple comparisons.

Animals↗
PubMed1981

The genetic dynamics of disease.

The notional principles of the genetics of disease are broadly discussed. Disease is an intrinsically vague term that represents the incongruity between the inner milieu of the organism and the environment. Its dynamics, then, cannot be reduced to naive statements about selection which may operate, and operate conflictingly, on several different levels or organization. Evolutionary selection results from the advantage of complexity, and the fundamental theorem of genetic dynamics - that mutational debts must eventually be paid in full-may be false or, at best approximate. The traditional models (mendelian, galtonian, and threshold) are set in a context that identifies certain features of disease that hitherto have been totally ignored. Neither invention nor traditional analysis has been adequate. Models should be made individually adequate for the study of diseases; the diseases should not be trimmed to fit the models.

Biological Evolution↗
PubMed1981

Inheritance of Kartagener syndrome.

The surmised autosomal recessive inheritance of situs inversus of Kartagener syndrome is re-examined on the hypothesis that the homozygous state replaces lateralization of the viscera in normal ontogeny by an indifferent lateralization. The segregation ratio in the progeny of two carrier parents (if there were no ascertainment bias) would then be 1/8. The estimated segregation ratio under the assumption of complete (truncate) ascertainment is 0.124. The implications for genetic counseling are discussed.

Diseases in Twins↗
PubMed1981

Recurrence risks for autosomal, epistatic two-locus systems: the effects of linkage disequilibrium.

The properties of the recurrence risk functions for Mendelian models involving two loci with epistatic interaction are examined. The two loci, H (hypostatic) and E (epistatic), are arbitrarily linked and diallelic. The general parameters are the genotypic frequencies and recombination fraction; the particular arguments are the number of affected and unaffected offspring. Limiting properties of the models are first described. Then, the more detailed properties of the models such as the sensitivity of the recurrence risk to the number of affected offspring are examined. If linkage disequilibrium is present, ie, the determinant of the gametic matrix is not zero, the predicted recurrence risk may resemble that empirically found in certain heritable diseases not evidently Mendelian.

Alleles↗
PubMed1981

The bingo model of survivorship: 1. probabilistic aspects.

A "bingo" model is one in which the pattern of survival of a system is determined by whichever of several components, each with its own particular distribution for survival, fails first. The model is motivated by the study of lifespan in animals. A number of properties of such systems are discussed in general. They include the use of a special criterion of skewness that probably corresponds more closely than traditional measures to what the eye observes in casually inspecting data. This criterion is the ratio, r(h), of the probability density at a point an arbitrary distance, h, above the mode to that an equal distance below the mode. If this ratio is positive for all positive arguments, the distribution is considered positively asymmetrical and conversely. Details of the bingo model are worked out for several types of base distributions: the rectangular, the triangular, the logistic, and by numerical methods, the normal, lognormal, and gamma.

Actuarial Analysis↗
PubMed1981

Detection of genetic effects of environmental agents.

The fundamental problems in population monitoring for genetic effects are twofold: the binomialized nature of the data and the lower power due to small risk of finding positive results. The binomial character is artificial, even forced, and can with advantage be replaced by more refined analysis, and by a focus on all mutations, not merely harmful ones. Moreover, a binomial treatment ignores accessory information (birth order, clustering, etc.). But this objective requires that an explicit model be used instead of nonparametric methods; a cancer may represent multiple independent hits that should be separately scored; sequencing of a codon or its product may show multiple distinct changes.

Environmental Exposure↗
PubMed1981

Only authorized persons admitted: the quantitative genetics of health and disease.

The scope of quantitation in genetics ranges from traits that are defined by quantity to those that can be quantitated not at all, or only with difficulty and on artificial scales of specious interpretability. Since disease is a complex process, there is a serious risk that a projection of it on an arbitrary system of measurements may be insensitive or frankly misleading. A hypothetical but plausible example (the "brittle model") of a purely genetic trait (but one with zero heritability) is presented. In addition an illustration is given that competition in pathways to an endpoint (such as death) may lead to a counterintuitive reversal of the positive skewness in the component processes (the "bingo model"). These paradoxical results reflect the perils of inadequate descriptors and an irrational reliance on stock methods of looking at the inheritance of disease. Well-known studies by Brown and Goldstein, Knudson, Paigen. Armitage and Doll, and Moolgavkar are cited as examples of how medical geneticists might rationally approach the genetics of common and complicated diseases.

Decision Theory↗