The limitations of heart rate as a predictor of metabolic rate in fish

Although telemetered heart rate (f_H) has been used as a physiological correlate to predict the metabolic rate (as oxygen consumption, V?O₂) of fish in the field, it is our contention that the method has not been validated adequately for fish. If f_H in fish is to be used to estimate V?O₂, a single linear (or log-linear) relationship must be established for each species between the two variables which allows V?O₂ to be predicted accurately under all environmentally relevant conditions. Our analyses of existing data indicate that while a good linear (or log-linear) relationship can be established between f_H and V?O₂, the conditions under which the relationship applies may be quite restricted. Physiological states and environmental factors affect the relationship between f_H and V?O₂ significantly such that several curves can exist for a single species. In addition, there are situations in which f_H and V?O₂ do not covary in a significant manner. In some situations f_H can vary over much of its physiological range while V?O₂ remains constant; in others V?O₂ may vary while f_H is invariate. The theoretical basis for this variability is examined to explain why the use of telemetered f_H in predicting V?O₂ of fish may be limited to certain specified applications.     

Growth rate and rupture rate of unruptured intracranial aneurysms: a population approach

Background  

Understanding aneurysm growth rate allows us to predict not only the current rupture risk, but also accumulated rupture risk in the future. However, determining growth rate of unruptured intracranial aneurysms often requires follow-up of patients for a long period of time so that significant growth can be observed and measured. We investigate a relationship between growth rate and rupture rate and develop a theoretical model that can predict average behavior of unruptured intracranial aneurysms based on existing clinical data.     

The rate of mutation of a single gene

The rate of mutation refers to the probability that a unit length of DNA (generally a base pair) mutates with time. Fluctuation analysis or mutant accumulation assays applied to phenotypic changes measure mutation rates of cells. However, only a few phenotypic changes indicative of mutations are known thus limiting the analysis to those rare genes. Direct sequencing overcomes the limitations imposed by phenotypic analysis but is limited by the extensive number of clones or cells that have to be analyzed in fluctuation or mutant accumulation assays. We propose a strategy to determine the rate of mutation of a gene by limited direct sequencing of a few single cells of a defined lineage. To accomplish this, we determined the average number of mutations per position in each DNA length sequenced from the proportion of the non-mutated positions, according to the Poisson process and/or the Taylor series. Measuring the rate of mutation by direct sequencing of genes does not require ascertaining a phenotype and can be applied to any area of the genome in a cell. The approach avoids fluctuation errors.     

Polypeptide-chain-elongation rate in Escherichia coli B/r as a function of growth rate.

By evaluating the kinetics of radioactive labelling of nascent and finished polypeptides, the peptide-chain elongation rate for Escherichia coli B/r at three different growth rates (mu) was determined to be 17 amino acids/s for the fast-growing cells (mu equals 1.3 and 2.0 doublings/h) and 12 amino acids/s for slow-growing cells (mu equals 0.67 doublings/h). The results agree with the growth-rate-dependence of the rate of peptide-chain elongation found for the translation of newly induced beta-galactosidase messenger in this strain and under these conditions of growth [Dalbow & Young (1975) Biochem. J. 150, 13-20]. Together with the previously observed ribosome efficiency at these growth rates [Dennis & Bremer (1974) J. Mol. Biol. 84, 407-422] the results indicate that the fraction of ribosomes engaged in protein synthesis is about 0.8 at all three growth rates.     

Does the presence of an observer affect a bird's occurrence rate or singing rate during a point count?

The approach or presence of an observer may affect the behavior of nearby birds, rendering them either more or less detectable than when no observer is present due to a change in singing rates. To test whether there are systematic detection biases associated with the presence of an observer during point count bird surveys, we compared the occurrence and singing rates of birds during a 10-min period immediately preceding the time when an observer arrived to conduct a count and during the formal count itself by extracting song information from autonomous sound recorders. We obtained recordings of 36 species of birds detected at ≥5 locations in one of three vegetation types, including burned conifer forest, green conifer/riparian streamside forest, and riparian bottomland/marshland. We found that species richness and both the probability of occurrence and singing rate for any of the species recorded were unaffected by the presence of an observer. In addition, the probability of occurrence did not differ significantly among four 2.5-min recording sessions during 10-min counts when an observer was present. Thus, the presence of an observer did not appear to introduce any detectable systematic bias that would make bird lists or unadjusted occurrence rates inaccurate on that basis alone. In addition, rates of bird occurrence across 2.5-min temporal subsets of a 10-min count did not vary in a systematic way that would violate the assumption of equal occupancy across adjacent time periods as sometimes used to build detection histories in occupancy modeling.     

SecA supports a constant rate of preprotein translocation

In Escherichia coli, secretory proteins (preproteins) are translocated across the cytoplasmic membrane by the Sec system composed of a protein-conducting channel, SecYEG, and an ATP-dependent motor protein, SecA. After binding of the preprotein to SecYEG-bound SecA, cycles of ATP binding and hydrolysis by SecA are thought to drive the stepwise translocation of the preprotein across the membrane. To address how the length of a preprotein substrate affects the SecA-driven translocation process, we constructed derivatives of the precursor of the outer membrane protein A (proOmpA) with 2, 4, 6, and 8 in-tandem repeats of the periplasmic domain. With increasing polypeptide length, an increasing delay in the time before full-length translocation was observed, but the translocation rate expressed as amino acid translocation per minute remained constant. These data indicate that in the ATP-dependent reaction, SecA drives a constant rate of preprotein translocation consistent with a stepping mechanism of translocation.     

Superoxide dismutase: a comparison of rate constants

O₂^?was introduced, at a constant rate, into buffered aqueous solutions, either by mechanical infusion of KO₂, dissolved in tetrahydrofuran, or by the in situ action of xanthine oxidase on xanthine plus oxygen. This O₂^? was allowed to react with ferricytochrome c or with tetranitromethane and the formation of the reaction products, ferrocytochrome c or nitroform, respectively, was monitored spectrophotometrically. That concentration of Superoxide dismutase, which competed equally with given levels of cytochrome c or tetranitromethane and which thus caused 50% inhibition of the rates of accumulation of ferrocytochrome c or of nitroform, was determined. The rate constant for the enzymatic dismutation of O₂^? by the copper and zinc containing enzyme from bovine erythrocytes was then calculated from the known rate constants for the reaction of O₂^? with ferricytochrome c and with tetranitromethane and was found to be 2 × 10⁹m^?1 sec^?1 at pH 7.8 and 8.5. This rate constant was obtained at steady-state concentrations of O₂^? in the 10^?8m → 10^?13m range and is in full agreement with the results of pulse radiolytic investigations which were performed at O₂^? concentrations in the 10^?5m range. The second order rate constant for the enzymatic dismutation of O₂^? is thus independent of the concentration of O₂^? in the range 10^?5 → 10^?13m.Several distinct types of Superoxide dismutase have been described. These include the mangano-enzymes from Escherichia coli and from chicken liver mitochondria and the iron-enzyme from E. coli. The rate constants for the dismutations catalyzed by these enzymes have also been investigated as a function of pH.     

Spread rate for a nonlinear stochastic invasion

Despite the recognized importance of stochastic factors, models for ecological invasions are almost exclusively formulated using deterministic equations [29]. Stochastic factors relevant to invasions can be either extrinsic (quantities such as temperature or habitat quality which vary randomly in time and space and are external to the population itself) or intrinsic (arising from a finite population of individuals each reproducing, dying, and interacting with other individuals in a probabilistic manner). It has been long conjectured [27] that intrinsic stochastic factors associated with interacting individuals can slow the spread of a population or disease, even in a uniform environment. While this conjecture has been borne out by numerical simulations, we are not aware of a thorough analytical investigation. In this paper we analyze the effect of intrinsic stochastic factors when individuals interact locally over small neighborhoods. We formulate a set of equations describing the dynamics of spatial moments of the population. Although the full equations cannot be expressed in closed form, a mixture of a moment closure and comparison methods can be used to derive upper and lower bounds for the expected density of individuals. Analysis of the upper solution gives a bound on the rate of spread of the stochastic invasion process which lies strictly below the rate of spread for the deterministic model. The slow spread is most evident when invaders occur in widely spaced high density foci. In this case spatial correlations between individuals mean that density dependent effects are significant even when expected population densities are low. Finally, we propose a heuristic formula for estimating the true rate of spread for the full nonlinear stochastic process based on a scaling argument for moments. Received: 19 October 1998 / Revised version: 1 September 1999 / Published online: 4 October 2000     

Metabolic turnover rate: a physiological meaning of the metabolic rate per unit body weight.

In analogy to “specific gravity” or “specific heat” the expression “weight specific metabolic rate” (Ultsch, 1973) would be correct if the metabolic rate were directly proportional to body weight. In that case the quotient metabolic rate divided by body weight would be a constant, independent of body weight like density or specific heat are constants. The metabolic rate, however, is not proportional to body weight but to its $\text{3}\text{4}$ power. I have stated that heat flow per unit body weight has no proper physical or physiological meaning (Kleiber, 1970), but since found such a physiological meaning: in work with tracers turnover rates are measured as quotients of transfer rates/pool content. For similometric animals pool contents are proportional to body weight. For such animals therefore the quotient metabolic rate/body weight may have a proper physiological meaning, namely the turnover rate of chemical energy in the animal body.The usefulness of the turnover rate is limited. For the calculation of the energy requirement of horizontal animal locomotion, for example, the calculation from the metabolic rate per animal is preferable to the calculation based on the metabolic rate per unit body weight.     

The rate of spontaneous mutation of a human gene

Summary The rate of mutation at which the gene for haemophilia appears in the population of London is estimated at about once in 50,000 human life cycles. There are probably two distinct allelomorphs at the same locus, the milder type arising less frequently by mutation than the severe type. I have to thank Dr Julia Bell and Dr C. V. Green for most generously placing at my disposal data collected on behalf of the Medical Research Council and the Research Committee of the American Medical Association.     

The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

Determination of the mutation rate of a retrovirus.

The mutation rate of Rous sarcoma virus (RSV) was measured. Progeny descended from a single virion were collected after one replication cycle, and seven regions of the genome were analyzed for mutations by denaturing-gradient gel electrophoresis. In all, 65,250 nucleotides were screened, yielding nine mutations, and the RSV mutation rate was calculated as 1.4 x 10(-4) mutations per nucleotide per replication cycle. These results indicate that RSV is an extremely mutable virus. We speculate that the mutation rate of a virus may correlate inversely with the effectiveness of vaccination against a given virus and suggest that prevention of retrovirus-mediated disease via vaccination may prove difficult.