Logarithmic and Power Law Input-Output Relations in Sensory Systems with Fold-Change Detection

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.     

Quality determination and the repair of poor quality spots in array experiments

Background  

A common feature of microarray experiments is the occurence of missing gene expression data. These missing values occur for a variety of reasons, in particular, because of the filtering of poor quality spots and the removal of undefined values when a logarithmic transformation is applied to negative background-corrected intensities. The efficiency and power of an analysis performed can be substantially reduced by having an incomplete matrix of gene intensities. Additionally, most statistical methods require a complete intensity matrix. Furthermore, biases may be introduced into analyses through missing information on some genes. Thus methods for appropriately replacing (imputing) missing data and/or weighting poor quality spots are required.     

RAPD assessment of novelties resulting in a new species of Vaccinium L. (Ericaceae) from Vietnam

A molecular technique (RAPD-PCR) is used to determine the relationship of an unknown Vaccinium from Vietnam to Vaccinia from throughout the south-east Pacific region. Based on the RAPD and morphological data, a new taxon, Vaccinium hiepii vander Kloet, sp. nov., is described. Cluster analyses (UPGMA, Neighbour-joining) clearly group V. hiepii with V. chunii , placing the new taxon within V. S Galeopetalum. Furthermore, Vaccinium S Bracteata sensu Sleumer (1941) is strongly supported by high bootstrap values within the dendrograms. Placement of V. petelotii within V. S Conchophyllum sensu Stevens (1969) is also possible.     

Stable isotope fractionation by Clostridium pasteurianum. 2. Regulation of sulfite reductases by sulfur amino acids and their influence on sulfur isotope fractionation during SO32- and SO42- reduction

In addition to an assimilatory sulfite reductase, studies of cultures of Clostridium pasteurianum supplemented with methionine, cysteine, and 35SO42- provides evidence for another reductase which is induced by SO32-. This inducible reductase appears to be dissimaltory because of the copious sulfide production arising when the cells are grown on SO32-. Cysteine can repress the assimilatory sulfite reductase but does not affect the inducible reductase. During late logarithmic growth on 1 mM SO42- + 10mM cysteine, depression of the inducible reductase occurred along with increased sulfide production. The presence of 1 mM cysteine and (or) 1 mM cysteine and (or) 1 mM methionine does not affect the inverse sulfur isotope effect for evolved H2S. However, 5 and 10 mM cysteine reduce the maximum delta34S value for released H2S from +40 to 10%. A small conversion of cysteine to H2S by C. pasteurianum occurs, but only in the stationary phase.     

Phylogenetic position of Licnophora,Lechriopyla, and Schizocaryum,three unusual ciliates (phylum Ciliophora) endosymbiotic in echinoderms (phylum Echinodermata)

Various echinoderms are colonized by species from several classes of the Phylum Ciliophora, indicating that the echinoderm "habitat" has been invaded independently on numerous occasions throughout evolutionary history. Two "echinoderm" ciliates whose phylogenetic positions have been problematic are Licnophora macfarlandi Stevens, 1901 and Schizocaryum dogieli Poljansky and Golikova, 1957. Licnophora macfarlandi is an endosymbiont of the respiratory trees of holothuroids, and S. dogieli is found in the esophagus of echinoids. A third species, Lechriopyla mystax Lynch, 1930, is a plagiopylid ciliate found in the intestine of echinoids. Host echinoderms were collected near the Friday Harbor Laboratories, San Juan Island, WA. Specimens of S. dogieli and L. mystax were obtained from the esophagus and intestine, respectively, of the sea urchin Strongylocentrotus pallidus. Specimens of L. macfarlandi were collected from the fluid obtained from the respiratory trees of Parastichopus californicus. Using small subunit ribosomal RNA (SSrRNA) sequences of these three ciliates and a global alignment of SSrRNA sequences of other ciliates, we established the following. 1) Licnophora is a spirotrich ciliate, clearly related to the hypotrichs and stichotrichs; this is corroborated by its possession of macronuclear replication bands. 2) Lechriopyla is the sister genus to Plagiopyla and is a member of the Class Plagiopylea, which was predicted based on its cytology. 3) Schizocaryum clusters in the Class Oligohymenophorea and is most closely related to the scuticociliates; there are currently no morphological features known to relate Schizocaryum to the scuticociliates.     

Functional interactions between the alpha1b-adrenoceptor and Galpha11 are compromised by de-palmitoylation of the G protein but not of the receptor

Both the alpha1b-adrenoceptor and Galpha11 are targets for post-translational thio-acylation that is regulated by agonist occupancy of the receptor [P.A. Stevens, J. Pediani, J.J. Carrillo, G. Milligan, J. Biol. Chem. 276 (2001) 35883]. In co-expression studies mutation of the sites of thio-acylation in the G protein or treatment of cell membranes with hydroxylamine greatly reduced agonist stimulation of guanosine 5'-[gamma-[35S]thio]triphosphate ([35S]GTPgammaS) binding. In alpha1b-adrenoceptor-Galpha11 fusion proteins mutation of thio-acylation sites in receptor or G protein did not alter the binding affinity of the antagonist [3H]prazosin or the agonist phenylephrine. Although the potency of phenylephrine to stimulate binding of [35S]GTPgammaS to alpha1b-adrenoceptor-Galpha11 fusion proteins was unaffected by the thio-acylation potential of either element, the maximal effect was reduced by some 50% when the G protein but not the receptor was mutated to prevent thio-acylation. This reflected lack of thio-acylation of the G protein rather than mutation of Cys9 and Cys10 to Ser because treatment with hydroxylamine mimicked this in fusions containing the wild type G protein but was without effect in those mutated to prevent thio-acylation. Mutation to reduce binding of beta/gamma to Galpha11 markedly reduced phenylephrine stimulation of [35S]GTPgammaS binding. Combination of mutations to prevent thio-acylation and beta/gamma binding did not, however, have an additive effect on [35S]GTPgammaS binding. These results indicate that the thio-acylation status of the alpha1b-adrenoceptor does not regulate G protein activation whereas thio-acylation of Galpha11 plays a key role in activation by the receptor beyond providing membrane association and proximity.     

On two tests of fit for HLA data with no double blanks.

Stevens suggests a test of fit, based on Bernstein's estimators, of the Hardy-Weinberg law for the ABO system. Nam and Gart extend this test to the generalized ABO-like system and apply it to HLA data. When the recessive gene is rare, Huether and Murphy recall Haldane's point that its Bernstein's estimator is negatively biased and go on to suggest novel corrected versions of it. With the identification of more HLA antigens, it is not uncommon to find, in certain populations, that the sample data contain no double blanks; that is, every individual reacts to at least one antigen for a given locus. Gart and Nam give a simple score test of a zero true recessive-gene frequency for such situations. Here we examine the extended test of Stevens as a test of this hypothesis. We find that it is fully efficient for two codominant alleles but that when the number exceeds two its efficiency may be 50% or lower or as high as 100%, depending on the number of alleles and the pattern of gene frequencies. The tests are applied to a set of HLA data.     

Rate of CO uptake by canine erythrocytes as a function of PO2

We used a continuous-flow rapid-mixing apparatus with spectroscopic analysis to measure the rate of CO uptake by canine erythrocytes at 37 degrees C at five different PO2 values from 0 to 553 Torr. Fresh blood from five different dogs was used for the experiments. PCO approximated 80 Torr. Corrections for the lower capillary PCO during a measurement of the diffusing capacity of lung CO, as made by Roughton and Forster in 1957 (J. Appl. Physiol. 11: 290-302, 1957), were not used. The regression equation for 1/theta, where theta is milliliters of CO combining for each milliliter of whole blood (capacity 0.2 ml/ml) per minute for a PCO of 1 Torr was 1/theta = 1.45 +/- 0.0042 PO2. This equation is very similar to that for human erythrocytes under the same conditions.     

The use of Taylor's power law to describe the aggregated distribution of gastro-intestinal nematodes of sheep.

The distribution of gastro-intestinal nematodes collected from lambs was investigated using the Taylor's power law index of aggregation beta, which is known to be independent of the mean population size. For 12 out of the 15 nematode species investigated the estimate of beta was not significantly different from 2.0. For these species a logarithmic transformation would stabilize the variance of the distributions prior to further statistical analysis. The remaining species had values of beta which were significantly lower than 2.0. For these species a variance-stabilizing transformation is given by z = x1-beta/2.     

Logarithmic Transformation is Essential for Statistical Analysis of Fungicide EC50 Values

Half maximal (50%) effective concentration (EC50) values are widely used to express fungicide potency and sensitivity of plant pathogens. This study explored the necessity of logarithmic transformation for statistical analysis of EC50 values. The results demonstrated that without logarithmic transformation, none of the five sets of epoxiconazole EC50 data (n = 26–33) against Sclerotinia sclerotiorum fitted a normal distribution. But after logarithmic transformation, four of the five datasets became normally distributed. Of the five sets of pyraclostrobin EC50 data (n = 29–32), only one dataset fitted a normal distribution. After logarithmic transformation, four datasets became normally distributed. Logarithmic transformation transformed the heterogeneity of variance across the five sets of epoxiconazole EC50 data to homogeneity but failed to improve the heterogeneity of variance across the five sets of pyraclostrobin EC50 data. For 150 isolates' EC50 values to epoxiconazole and 153 isolates' EC50 values to pyraclostrobin, the intervals of arithmetic means ± standard deviations (SD) covered 85.3% and 90.2% of data points, respectively, whereas the intervals of geometric means (*) multiplied/divided by the multiplicative SD (S*) covered 69.3% and 70.9% of data points, respectively, which approximated the theoretical value of 68.3%. Distribution normality and homogeneity of variance are prerequisites for analysis of variance (anova ) and the two parameters could be improved by logarithmic transformation, therefore, power and efficiency of statistical tests on EC50 data will be greatly enhanced by this kind of transformation.     

Modelling the Time Course of Self-thinning in Crowded Plant Populations

A logarithmic model for the self-thinning of plants is proposed.This model describes the time course of self-thinning very welland fits data from forest stands and yield tables, which followthe 3/2 power law. An approximated expression of this modelshows that plant density decreases with age along a Gompertzcurve. This appears to be a basic property of the time courseof self-thinning in plants. Pinus strobus L., Pinus densiflora Sieb, et Zucc., stand development, self-thinning, 3/2 power law, logarithmic model, mortality     

Thermal susceptibility of Streptococcus faecium strains isolated from frankfurters

The heat resistance of nine strains of Streptococcus faecium isolated from frankfurters was determined at 63 and 68 degrees C in brain heart infusion broth. Exponential-phase cultures (approximately 10(7) colonies/mL) were used as inoculants. The heat resistance of S. faecium DP2181, a moderately resistant isolate, was further examined in broth (55, 63, and 68 degrees C) and frankfurter emulsion (63 and 68 degrees C). The decimal reduction times (D values) were determined by regression. In broth, both time-temperature combinations resulted in a 3-4 log decline in bacterial numbers for the nine S. faecium strains tested. For S. faecium DP2181, the survivor curves deviated from the logarithmic order of death at all three heating temperatures. An initial slow period of death was evident at 55 degrees C and a resistant tail of organisms was observed at 55, 63, and 68 degrees C. The D55D63, and, D68 values for the logarithmic portion of the corresponding survivor curves were 105.6, 9.36, and 3.34 min, respectively. The survival of DP2181 was enhanced by the frankfurter emulsion. The results indicate that populations of S. faecium existed that were very heat resistant and could survive normal frankfurter processing if initially present in high numbers.     

Defining the stimulus—A memoir

The eminent psychophysicist, S.S. Stevens, once remarked that, “the basic problem of psychology was the definition of the stimulus” (Stevens, 1951, p. 46). By expanding the traditional definition of the stimulus, the study of animal learning has metamorphosed into animal cognition. The main impetus for that change was the recognition that it is often necessary to postulate a representation between the traditional S and R of learning theory. Representations allow a subject to represent a stimulus it learned previously that is currently absent. Thus, in delayed matching-to-sample, one has to assume that a subject responds to a representation of the sample during test if it responds correctly. Other examples, to name but a few, include concept formation, spatial memory, serial memory, learning a numerical rule, imitation and metacognition. Whereas a representation used to be regarded as a mentalistic phenomenon that was unworthy of scientific inquiry, it can now be operationally defined. To accommodate representations, the traditional discriminative stimulus has to be expanded to allow for the role of representations. The resulting composite can account for a significantly larger portion of the variance of performance measures than the exteroceptive stimulus could by itself.     

Estimation of growth yield and maintenance coefficient of plant cell suspensions

Methodology is presented for the determination of growth yield (Y(g)) and maintenance coefficient (m) for carbon utilization of plant cells grown in suspension culture. Estimation of Y(g) and m requires measurements of specific growth rate (micro) and specific rate of substrate uptake (q) at different growth limiting substrate concentrations. Batch culture of tobacco cells did not permit evaluation of Y(g) and m because micro is constant and maximal during most of the growth cycle. In batch culture, the period of declining specific growth rate is extremely brief because of the rapid transition from logarithmic growth to stationary phase. This occurs because the K(m) for growth is relatively small compared to the initial sucrose concentration. Thus, when the substrate level reaches the K(m), the large mass of cells rapidly depletes the remaining substrate. In contrast, semicontinuous culture facilitates the determination of Y(g) and m because various steady-state growth rates can be achieved. Mathematical expressions were developed to determine the effective values of micro and q over the semicontinuous replacement interval. The validity of this approach was verified by conducting simulations using experimentally determined parameters.     

Das Adenosinphosphat-System während Wachstum und Entwicklung von Acanthamoeba castellanii

The concentration of adenosine tri-, adenosine di-, and adenosine monophosphate in cells of Acanthamoeba castellanii was measured during the logarithmic growth phase and the stationary growth phase in which trophozoites were transformed into cysts. This developmental process was induced in three ways: by growth in nutrient medium to high cell density, by transferring cells in the logarithmic phase into a nutrient-free medium, and by mixing logarithmically growing cells with ethidium bromide. In all cases, encystment is accompanied with a reduction of total adenosine phosphate content to about 85%, mainly because of a depletion of cellular ATP. The value of the adenosine phosphate energy charge in logarithmically growing amoebae is 0.83. During development the energy charge becomes stabilized at different values (between 0.58 and 0.81), characteristic to the mode of encystation. A possible functional relationship between changes of the adenosine phosphate concentration and developmental processes of the amoeba is discussed.     

The Structure of Evolution by Natural Selection

We attempt a conclusive resolution of the debate over whether the principle of natural selection (PNS), especially conceived as the `principle' of the `survival of the fittest', is a tautology. This debate has been largely ignored for the past 15 years but not, we think, because it has actually been settled. We begin by describing the tautology objection, and situating the problem in the philosophical and biology literature. We then demonstrate the inadequacy of six prima facie plausible reasons for believing that the tautology debate has been satisfactorily resolved (the PNS is strictly a methodological principle; scientific theories can contain tautologies; the scope of the PNS has been reduced; theories should be understood as models and not exceptionless laws; the widespread acceptance of the propensity interpretation of fitness; and the abandonment of operationalism and verificationism). We proceed to a detailed discussion of Brandon's law (D) describing the PNS, and show that law (D) seriously misrepresents the structure of evolution by natural selection. In the final sections, we provide and defend a novel reinterpretation of the structure of the principle (or, we prefer, model) of evolution by natural selection.     

Age estimations of wild pallid sturgeon (Scaphirhynchus albus,Forbes & Richardson 1905) based on pectoral fin spines,otoliths and bomb radiocarbon: inferences on recruitment in the dam‐fragmented Missouri River

An extant stock of wild pallid sturgeon Scaphirhynchus albus persists in the fragmented upper Missouri River basin of Montana and North Dakota. Although successful spawning and hatch of embryos has been verified, long‐term catch records suggest that recruitment has not occurred for several decades as the extant stock lacks juvenile size classes and is comprised exclusively of large, presumably old individuals. Ages of 11 deceased (death years 1997–2007) wild S. albus (136–166 cm fork length) were estimated based on pectoral fin spines, sagittal otoliths and bomb radiocarbon (¹⁴C) assays of otoliths to test the hypothesis that members of this stock are old and to provide inferences on recruitment years that produced the extant stock. Age estimations based on counts of presumed annuli were about 2 years greater for otoliths (mean = 51 years, range = 43–57 years) than spines (mean = 49 years, range = 37–59 years). Based on ¹⁴C assays, confirmed birth years for all individuals occurred prior to 1957, thus establishing known longevity of at least 50 years. Estimated age based on presumed otolith annuli for one S. albus was validated to at least age 49. Although ¹⁴C assays confirmed pre‐1957 birth years for all S. albus, only 56% of estimated ages from spines and 91% of estimated ages from otoliths depicted pre‐1957 birth years. Both ageing structures were subject to under‐ageing error (up to 15 years). Lack of or severe curtailment of S. albus recruitment in the upper Missouri River basin since the mid‐1950s closely parallels the 1953–1957 timeframe when a mainstem reservoir was constructed and started to fill. This reservoir may function as a system‐wide stressor to diminish recruitment success of S. albus in the upper Missouri River basin.     

THE SIZE OF BACTERIA AS THE CAUSE OF THE LOGARITHMIC ORDER OF DEATH

Death of unicellular organisms is brought about by the inactivation of a certain number of essential molecules in the cell. If the number of these essential molecules is only one per cell, the order of death is the same as if the cell were identical with this molecule; the order of death is logarithmic following the mass law. If more than one molecule must be inactivated before the cell dies, the order of death is not logarithmic. With 2 or 3 molecules, it still resembles the logarithmic order, but with an increasing number of reacting molecules, it approaches more and more the order of death known with higher organisms, namely a period of no death, followed by a comparatively short period of rapid death. The decision whether or not the logarithmic order exists, should be based upon the constancy of the death rate See PDF for Equation. The existence of a straight line when logarithms of survivors are plotted against time, is not sufficient proof unless the initial number of cells is included. These deductions are made with the assumption that all organisms are exactly alike, and show no individual variations or graded resistance. With most bacteria, the order of death is so nearly logarithmic that death must be brought about by the inactivation of only one molecule, though there may be several molecules of this same type in each cell.