A mélange of curves – further dialogue about species–area relationships

Scheiner (2003) presented a classification of species–area curves into six types based on the pattern of sampling and how the data are combined to form the curves. Gray et al. (2004) contended that five of those types should be termed ‘species‐accumulation curves’, reserving ‘species–area curve’ for those based on island‐type data. Their proposition contradicts 70 years of usage and confounds curves that are area‐explicit with those that are area‐undefined. In exploring these issues, I highlight additional aspects of species–area and species‐accumulation curves, including the assumption of nesting in Type IV (island) curves, how to convert area‐unspecified curves into area curves, and the effects of the grain of the analysis on the properties of the curve. Further exploration, theoretical development, and dialogue are needed before we will understand all the biology that species–area curves summarize.     

Graphical Representation and Similarity Analysis of DNA Sequences Based on Trigonometric Functions

In this paper, we propose two four-base related 2D curves of DNA primary sequences (termed as F-B curves) and their corresponding single-base related 2D curves (termed as A-related, G-related, T-related and C-related curves). The constructions of these graphical curves are based on the assignments of individual base to four different sinusoidal (or tangent) functions; then by connecting all these points on these four sinusoidal (tangent) functions, we can get the F-B curves; similarly, by connecting the points on each of the four sinusoidal (tangent) functions, we get the single-base related 2D curves. The proposed 2D curves are all strictly non degenerate. Then, a 8-component characteristic vector is constructed to compare similarity among DNA sequences from different species based on a normalized geometrical centers of the proposed curves. As examples, we examine similarity among the coding sequences of the first exon of beta-globin gene from eleven species, similarity of cDNA sequences of beta-globin gene from eight species, and similarity of the whole mitochondrial genomes of 18 eutherian mammals. The experimental results well demonstrate the effectiveness of the proposed method.     

Reflectance and transmittance of light by leaves

Spectrophotometric transmittance and reflectance curves were recorded for wavelengths from 0.45 (in some cases 0.34) to 2.7 micrometers for faces and backs of leaves and for stacked leaves of several plant species. Measurements were made at different angles of illumination. Leaf spectrophotometric curves were compared with curves for leaf extracts, potato tuber tissue, glass beads in water, and frozen leaves to demonstrate the physical bases for the leaf curves. Leaves were infiltrated with liquids of different refractive indices for further comparison of spectrophotometric curves. Goniophotometric reflectance curves were recorded, giving visible reflectance and degree of polarization as functions of viewing angle for two different angles of illumination.     

Thermal Inactivation Characteristics of Bacillus subtilis Spores at Ultrahigh Temperatures

The thermal inactivation characteristics of Bacillus subtilis A spores suspended in skim milk with the use of large-scale ultrahigh temperature (UHT) processing equipment were investigated in terms of survival as measured with two plating media. Data on survival immediately after UHT treatments were recorded in temperature-survivor curves, time-survivor curves, and decimal reduction time (DRT) curves. The temperature-survivor curves emphasized that inactivation is accelerated more by increases in the treatment temperature than by increases in the exposure time. Time-survivor curves and DRT curves were not linear. Generally, exceedingly concave time-survivor curves were observed with the standard plating medium; however, only slightly concave curves were observed when CaCl(2) and sodium dipicolinate were added to the medium. For a given UHT sample, larger D values were obtained by use of the medium with the added CaCl(2) and sodium dipicolinate. The DRT curves of all data were concave and appeared to have two discrete slopes (z(D) values). The z(D) values observed in the upper UHT range (above 260 F; 127 C) were twice those observed at lower test temperatures.     

Sensitivity of Optical Fiber Sensor Based on Surface Plasmon Resonance: Modeling and Experiments

In this paper, surface plasmon resonance curves of an optical fiber-based sensor were investigated. From an experimental and theoretical perspective, the response curves were analyzed and discussed. Precisely, such curves were calculated by modeling the analyte/metallic layer interface using a multilayer system, including the effects of roughness. Then, the experimental response curves observed in solutions with different refractive indices were compared to the simulated curves. Good agreement was obtained with respect to the resonance peak location and the shape of the curves. Consequently, these results enabled us to predict the ideal functioning conditions of the sensor, i.e., the working parameters corresponding to the best sensitivities of detection.     

Xylem vulnerability to cavitation can be accurately characterised in species with long vessels using a centrifuge method

Vulnerability to cavitation curves describe the decrease in xylem hydraulic conductivity as xylem pressure declines. Several techniques for constructing vulnerability curves use centrifugal force to induce negative xylem pressure in stem or root segments. Centrifuge vulnerability curves constructed for long‐vesselled species have been hypothesised to overestimate xylem vulnerability to cavitation due to increased vulnerability of vessels cut open at stem ends that extend to the middle or entirely through segments. We tested two key predictions of this hypothesis: (i) centrifugation induces greater embolism than dehydration in long‐vesselled species, and (ii) the proportion of open vessels changes centrifuge vulnerability curves. Centrifuge and dehydration vulnerability curves were compared for a long‐ and short‐vesselled species. The effect of open vessels was tested in four species by comparing centrifuge vulnerability curves for stems of two lengths. Centrifuge and dehydration vulnerability curves agreed well for the long‐ and short‐vesselled species. Centrifuge vulnerability curves constructed using two stem lengths were similar. Also, the distribution of embolism along the length of centrifuged stems matched the theoretical pressure profile induced by centrifugation. We conclude that vulnerability to cavitation can be accurately characterised with vulnerability curves constructed using a centrifuge technique, even in long‐vesselled species.     

An 8000 year Holocene sea-level record from Jamaica: implications for interpretation of Caribbean reef and coastal history

Two coastal wetlands in western Jamaica have been investigated by means of extensive coring, stratigraphic study, determination of depositional environments and radiocarbon dating of 55 samples. The study has resulted in construction of two curves of the mid to late-Holocene sea-level rise in the area. The curves are regarded as good indicators of sea-surface movements during the last 8000 years, and represent the first curves from island settings within the Caribbean Plate. Probable absence of any significant Holocene tectonic disturbance allows direct comparison with sea-level curves from Florida and Bermuda. Observed differences between them highlight the problems involved in use of extra-regional curves in interpretation of Holocene reef growth, which has been the case, particularly in the eastern Caribbean. The curves provide a framework for study of Holocene reef growth and coastal history in Jamaica, and obviate the need for non-coral based sea-level-rise curves from other parts of the Caribbean for control in reef growth studies.     

A novel pattern recognition algorithm to classify membrane protein unfolding pathways with high-throughput single-molecule force spectroscopy

MOTIVATION: Misfolding of membrane proteins plays an important role in many human diseases such as retinitis pigmentosa, hereditary deafness and diabetes insipidus. Little is known about membrane proteins as there are only very few high-resolution structures. Single-molecule force spectroscopy is a novel technique, which measures the force necessary to pull a protein out of a membrane. Such force curves contain valuable information on the protein structure, conformation, and inter- and intra-molecular forces. High-throughput force spectroscopy experiments generate hundreds of force curves including spurious ones and good curves, which correspond to different unfolding pathways. Manual analysis of these data is a bottleneck and source of inconsistent and subjective annotation. RESULTS: We propose a novel algorithm for the identification of spurious curves and curves representing different unfolding pathways. Our algorithm proceeds in three stages: first, we reduce noise in the curves by applying dimension reduction; second, we align the curves with dynamic programming and compute pairwise distances and third, we cluster the curves based on these distances. We apply our method to a hand-curated dataset of 135 force curves of bacteriorhodopsin mutant P50A. Our algorithm achieves a success rate of 81% distinguishing spurious from good curves and a success rate of 76% classifying unfolding pathways. As a result, we discuss five different unfolding pathways of bacteriorhodopsin including three main unfolding events and several minor ones. Finally, we link folding barriers to the degree of conservation of residues. Overall, the algorithm tackles the force spectroscopy bottleneck and leads to more consistent and reproducible results paving the way for high-throughput analysis of structural features of membrane proteins.     

Mechanics of the compression wood response: I. Preliminary analyses

Righting of two tilted white pine (Pinus strobus L.) stem leaders by compression wood formation was followed for 16 weeks. The natural curves and three deflection curves under added end loads were determined from weekly field photographs. Data for self-loading and cross sectional diameters were interpolated from original estimated and final measurements. A mechanical-mathematical model was developed to predict curves under zero gravity for each stem each week. The model estimated stiffness of the leaders independently for each week, and the stiffnesses were consistent throughout the experiment. A second model was developed to simulate the deflection curves assumed when the zero gravity curves were subjected to different end loads. These predicted curves were nearly identical to the observed curves from the photographs, thus verifying the assumptions in the first model. Data from this study will be used to investigate the mechanical aspects of compression wood induction and action as the stem is bent upward toward the vertical.     

Variance Calculations for Direct Adjusted Survival Curves,with Applications to Testing for No Treatment Effect

Several investigators have recently constructed survival curves adjusted for imbalances in prognostic factors by a method which we call direct adjustment. We present methods for calculating variances of these direct adjusted survival curves and their differences. Estimates of the adjusted curves, their variances, and the variances of their differences are compared for non-parametric (Kaplan-Meier), semi-parametric (Cox) and parametric (Weibull) models applied to censored exponential data. Semi-parametric proportional hazards models were nearly fully efficient for estimating differences in adjusted curves, but parametric estimates of individual adjusted curves may be substantially more precise. Standardized differences between direct adjusted survival curves may be used to test the null hypothesis of no treatment effect. This procedure may prove especially useful when the proportional hazards assumption is questionable.     

Direction-dependent corticofugal modulation of frequency-tuning curves of inferior collicular neurons in the big brown bat, Eptesicus fuscus

This study examined if corticofugal modulation of subcortical frequency-tuning curves varied with sound direction. Both excitatory and inhibitory frequency tuning curves of inferior collicular neurons of the big brown bat, Eptesicus fuscus were plotted before and during electrical stimulation in the auditory cortex at two sound directions (contra-40 degrees and ipsi-40 degrees). Most collicular neurons had broader excitatory frequency-tuning curves at contra-40 degrees but had broader inhibitory frequency-tuning curves at ipsi-40 degrees. Cortical electrical stimulation changed the excitatory minimum thresholds of most collicular neurons at a greater degree at ipsi-40 degrees than at contra-40 degrees. However, cortical electrical stimulation produced a greater increase in the sharpness of excitatory frequency-tuning curves of most corticofugally inhibited collicular neurons at contra-40 degrees but produced a greater decrease in the sharpness of excitatory frequency-tuning curves of most corticofugally facilitated collicular neurons at ipsi-40 degrees. Cortical electrical stimulation also produced a greater change in the sharpness of inhibitory frequency-tuning curves of most corticofugally inhibited collicular neurons at contra-40 degrees than at ipsi-40 degrees. Possible mechanisms for this direction-dependent corticofugal modulation of frequency-tuning curves of collicular neurons are discussed.     

On the use of partial area under the ROC curve for comparison of two diagnostic tests

Evaluation of diagnostic performance is typically based on the receiver operating characteristic (ROC) curve and the area under the curve (AUC) as its summary index. The partial area under the curve (pAUC) is an alternative index focusing on the range of practical/clinical relevance. One of the problems preventing more frequent use of the pAUC is the perceived loss of efficiency in cases of noncrossing ROC curves. In this paper, we investigated statistical properties of comparisons of two correlated pAUCs. We demonstrated that outside of the classic model there are practically reasonable ROC types for which comparisons of noncrossing concave curves would be more powerful when based on a part of the curve rather than the entire curve. We argue that this phenomenon stems in part from the exclusion of noninformative parts of the ROC curves that resemble straight‐lines. We conducted extensive simulation studies in families of binormal, straight‐line, and bigamma ROC curves. We demonstrated that comparison of pAUCs is statistically more powerful than comparison of full AUCs when ROC curves are close to a “straight line”. For less flat binormal ROC curves an increase in the integration range often leads to a disproportional increase in pAUCs’ difference, thereby contributing to an increase in statistical power. Thus, efficiency of differences in pAUCs of noncrossing ROC curves depends on the shape of the curves, and for families of ROC curves that are nearly straight‐line shaped, such as bigamma ROC curves, there are multiple practical scenarios in which comparisons of pAUCs are preferable.     

Possibility of wide-angle neutron scattering in the study of proteins and nucleic acids in solutions

A method is proposed for calculating wide-angle neutron scattering curves of biopolymers at any fraction of heavy water (D2O) in solution. The method permits to accurately take into account the phenomenon of deuteroexchange. By this method neutron scattering curves of proteins and DNA have been calculated. The calculations have shown that at optimal fractions of D2O in solution the profiles of neutron scattering curves and their sensitivity to conformational rearrangements in protein molecules turned out to differ very little from those of corresponding X-ray curves. Thus the neutron scattering curves do not contain any additional information (as compared with those contained in X-ray scattering curves) on the structure of proteins in solution. On the contrary, neutron and X-ray scattering curves of DNA differ significantly at all fractions of D2O in solution and therefore the methods of wide-angle neutron and X-ray scattering could become mutually complementary in studying the structure of nucleic acids in solution.     

THE ANALYSIS AND RECONSTRUCTION OF DIURNAL FLIGHT CURVES IN ALIENICOLAE OF APHIS FABAE SCOP.

Experiments, in which alate aphids were marked immediately after eclosion from the last nymphal instar and observed until they took flight, gave information which, together with the measured rate of moulting and a continuous record of temperature, has been used to construct theoretical daily curves for numbers flying from a bean crop. These curves have been matched against the observed curves for the same days.
The differences between curves so constructed for a period of 17 days and the observed curves for the same period are of the same order and kind as the differences between two measured curves in different sites at the same time.
The different types of daily flight curve can thus be accounted for in terms of the rate of production of alatae by moulting, the effect of temperature on the teneral ('drying out') period and the effect of low light intensity and temperature on take-off behaviour.     

Enzymic product formation curves with the normal or diffusion limited reaction mechanism and in the presence of substrate receptors

1. The enzymic product formation curves for several enzymes have been studied. 2. The product formation kinetics was related to the initial velocity kinetics and to the diffusion rate limited kinetics. 3. The time curves revealed new constants characterizing structural and binding properties of the enzymic systems which are not revealed from initial velocities. 4. The influence of selected inhibitors on the time curves has been studied. 5. The time curves revealed the specific substrate-receptor binding which was not revealed from initial velocities. 6. The product formation kinetics of acid phosphatase, beta-amylase and NADPH2 cytochrome-c reductase in the absence and in the presence of inhibitors, mercuric acetate and o-iodosobenzoate is described. 7. The time curves revealed the binding of cytochrome-c to the specific natural protein receptors. 8. The activation energies of acid phosphatase and beta-amylase were determined from the time curves.     

Direct estimates of multi-mesh gillnet selectivity to Oreochromis shiranus chilwae

The selectivity of multi-mesh monofilament nylon gillnets to Oreochromis shiranus chilwae was estimated directly by gillnetting in a small reservoir containing a population marked by size class. Numbers in each size class were estimated using the adjusted Petersen estimate. Pearson Type I curves were fitted to plots of selectivity against the fish length/mesh perimeter ratio, for two modes of capture: wedging and tangling. The generality of the selectivity curves is tested and discussed. The tangling component of the selectivity was unimportant, and for many applications the selectivity curves may be approximated by normal curves obtainable through indirect methods. However, the increase in the amplitude of the curves with mesh size, deserves further study.     

A Bayesian model for sparse functional data

Summary.   We propose a method for analyzing data which consist of curves on multiple individuals, i.e., longitudinal or functional data. We use a Bayesian model where curves are expressed as linear combinations of B-splines with random coefficients. The curves are estimated as posterior means obtained via Markov chain Monte Carlo (MCMC) methods, which automatically select the local level of smoothing. The method is applicable to situations where curves are sampled sparsely and/or at irregular time points. We construct posterior credible intervals for the mean curve and for the individual curves. This methodology provides unified, efficient, and flexible means for smoothing functional data.     

Graphical Methods for Analysing Combination Effects in Dose-Response Experiments

An organbath experiment with bovine tracheal muscle strips with cumulative increases in concentrations of a substance A in the absence and presence of a fixed concentration of a second substance B is considered as an example for demonstrating graphical methods to analyse drug combination effects. The response of each strip is individually described and estimated by a nonlinear dose response curve. From the curves of the combined action theoretical curves of substance A are derived, which were expected if the combination effect was simple similar or independent, respectively. The first graphical method consists in comparing the derived curves for substance A with the curves for substance A directly fitted. It is cheeked by eye if the group of derived curves can clearly be distinguished from the group of directly fitted curves. The second graphical method differs from the first method in so far, as not the curves are visualized but the parameter vectors corresponding to them. In contrast to widely used analytical methods the proposed graphical methods allow to treat individual instead of averaged dose response relationships. The methods can help to decide if the combination effect may be considered as independent, simple similar or none of both.     

Interaction of lysine-rich histone and DNA in chromatin structure.

The heat denaturation and renaturation curves of rat liver and ascites hepatoma (AH 108A) chromatins were measured. In these renaturation curves, there are small sigmoidal regions. These sigmoidal regions remained in redenaturation curves and were largely stable to DNAase I digestion. When the chromatins were treated stepwise with NaClO4 and lysine-rich histones were removed, the sigmoidal regions in the renaturation curves disappeared. These results suggested that the sigmoidal regions reflected the interaction of DNA and lysine-rich histones.     

Small-angle diffuse x-ray scattering on fine muscle filaments

Theoretical small-angle diffuse scattering curves from muscle thin filament models have been calculated. The curves reveal a maximum at 115' scattering angle. It has been shown that the maximum is due to the pitch of F-actin helix. Theoretical curves are in good agreement with the earlier obtained curves of small-angle diffuse scattering from F-actin dilute solutions.