Measuring size distribution in highly heterogeneous systems with fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) is a sensitive and widely used technique for measuring diffusion. FCS data are conventionally modeled with a finite number of diffusing components and fit with a least-square fitting algorithm. This approach is inadequate for analyzing data obtained from highly heterogeneous systems. We introduce a Maximum Entropy Method based fitting routine (MEMFCS) that analyzes FCS data in terms of a quasicontinuous distribution of diffusing components, and also guarantees a maximally wide distribution that is consistent with the data. We verify that for a homogeneous specimen (green fluorescent protein in dilute aqueous solution), both MEMFCS and conventional fitting yield similar results. Further, we incorporate an appropriate goodness of fit criterion in MEMFCS. We show that for errors estimated from a large number of repeated measurements, the reduced chi(2) value in MEMFCS analysis does approach unity. We find that the theoretical prediction for errors in FCS experiments overestimates the actual error, but can be empirically modified to serve as a guide for estimating the goodness of the fit where reliable error estimates are unavailable. Finally, we compare the performance of MEMFCS with that of a conventional fitting routine for analyzing simulated data describing a highly heterogeneous distribution containing 41 diffusing species. Both methods fit the data well. However, the conventional fit fails to reproduce the essential features of the input distribution, whereas MEMFCS yields a distribution close to the actual input.     

Measuring the distribution of plantar pressures during walking in patients with multiple sclerosis to evaluate treatment efficiency

The relationship between the parameters of the distribution of plantar pressure and the state of a patient with multiple sclerosis has been studied with repeated measurements, before and after (or during) treatment. The possibility of using this method for study of walking function impairment in a chronic demyelinating process is considered.     

Measuring the cost of reproduction

Gravid and barren Daphnia pulex were exposed to a variety of predators in laboratory aquaria. Small fish (guppies, sticklebacks and shiner fry) consistently preferred the gravid females, establishing the existence of a behavioural cost of reproduction. However, no such cost was associated with predation by more efficient visual predators (sunfish) or by nonvisual predators (hydras), and the excess of gravid females eaten by backswimmers was found to be attributable to their distribution in the water column. Moreover, the cost associated with predation by small fish was observed only when the Daphnia were presented against a light background, and was abolished when a dark background was substituted. In a further series of experiments with guppies we attempted to show that each egg added to the brood caused a decrease in survival; in two such experiments survival rate was related to body size but not to fecundity, while in a third the effect of body size did not appear, and a negative correlation between survival and fecundity could be demonstrated. Although these experiments unambiguously demonstrate a cost of reproduction they also illustrate the elusiveness of the phenomenom and emphasize the need to develop theories which specify the type and magnitude of costs generated by different ways of life.     

Measuring the cost of reproduction

Summary The timing of the first two broods and the number and size of offspring in each was measured in a series of three experiments for monoclonal cultures of the cladoceran Daphnia pulex reared under standard conditions of ration, temperature and photoperiod. The pattern of total correlations between pairs of life-history variables did not in general support predictions made by hypotheses of reproductive cost. A partial correlation analysis, involving initial size and subsequent growth as well as the life history variables themselves, was performed in an attempt to avoid potential fallacies introduced by the use of total correlations. The only consistent effect found was a positive relationship between the age at reproductive maturity and the mean size of offspring in the first brood. The structure of this segment of the life history is strongly influenced by interactions between size and reproduction, to an extent that precludes the use of simple optimality models.     

Measuring alignment of the hindfoot

In subtalar arthrodesis operations, correction of the hindfoot alignment is performed in about half of the cases. To improve the quality of the operation, a measurement system was developed which reliably measures the hindfoot angle pre-, per-, and postoperatively. This device was evaluated by measuring subjects in standing weightbearing position and in prone nonweightbearing position. The results were compared with hindfoot angles constructed on posterior photographic images. The results are similar to other studies (all maximum values): intratester accuracy 1.4 degrees, intertester accuracy 2.2 degrees, intratester reliability 0.9, and intertester reliability 0.74. The proposed device will improve the quality of correction, because it enables peroperative measurement of hindfoot alignment.     

Measuring the costs of reproduction

The measurement of costs of reproduction is of interest because such costs are generally assumed by life history theory. There is some controversy concerning how to measure costs: common methods include experimental manipulations of life history, such as preventing some individuals from reproducing, or estimates of genetic correlations. These two methods often yield similar results, suggesting that one can serve as a substitute for the other. There are now experiments which demonstrate that there are different mechanisms underlying the response to an experimental manipulation versus a genetic correlation, so the two methods are not equivalent in estimating costs.     

Measuring the influence of mycorrhizas

'The view that nutrient acquisition by most plants growing in natural ecosystems is mediated by mycorrhiza-forming symbiotic fungi is now largely accepted' (Read, 2000). Is this bold claim really true for the whole suite of mineral nutrients that plants require? The case is strongest for nutrients that are not very mobile in soil, especially when present in growth-limiting amounts, and phosphate (P) is the classic example. Arbuscular mycorrhizas are by far the most widespread mycorrhizal symbioses, and the ability of arbuscular mycorrhizal (AM) fungi to take up soil nutrients such as P and transfer them to the host plant is an area of intense research. However, there is great variation in the extent to which AM plants benefit in measurable terms from the symbiosis under a given set of environmental conditions, and a paper in this issue, by Koide et al ., addresses this problem (Koide et al ., pp. 163–168). The variability is especially apparent in the field, thus obscuring the possible roles of mycorrhizas in community structure and succession (Fitter, 1985; McGonigle, 1988).     

Measuring the fitness of symbiotic rhizobia

The legume-rhizobia symbiosis is an important model system for research on the evolution of cooperation and conflict. A key strength of this system is that the fitness consequences of greater or lesser investment in cooperative behaviors can be measured for each partner. Most empirical studies have characterized the fitness of symbiotic rhizobia exclusively by their numbers within nodules, often estimated using nodule size as a proxy. Here we show that the relationship between nodule size and rhizobial numbers can differ drastically between strains of the same species. We further show that differences in accumulation of the storage polyester poly-3-hydroxybutyrate (PHB), which can support future reproduction, can be large enough that even direct measurements of rhizobial numbers alone can lead to qualitatively incorrect conclusions. Both results come from a comparison of strains differing in production of the ethylene-inhibitor rhizobitoxine (Rtx). A broader study (using three legume-rhizobia species pairs) showed that PHB/cell cannot be reliably estimated from its correlation with rhizobia/nodule or nodule size. Differences in PHB between strains or treatments will not always make major contributions to differences in fitness, but situation-specific data are needed before PHB can safely be neglected.     

Measuring the temporal extension of the Now

Anticipatory systems require a model of time which takes account of both successive and simultaneous rhythms. Such a model should also incorporate the fact that both past and future determine the present state of anticipatory systems across multiple scales, from physical to biological and social ones. My Theory of Fractal Time meets these requirements and enables us to compare the Now’s temporal complexity of endo-observer-participants in terms of their boundary complexity.     

Measuring the geometry of DNA grooves

We present a new method for measuring the widths and depths of the grooves formed within DNA helices. This method overcomes the limitations of simply measuring interstrand phosphate–phosphate distances and has the advantage of yielding continuous values for groove geometry along a DNA fragment. In the case of oligonucleotides, it also clearly indicates the zones in which grooves exist, bounded by two phosphodiester backbones. The methodology has been developed within the Curves algorithm for studying irregular DNA geometries and is based on the optimal, and generally curved, helical axis obtained by this analysis. © 1994 John Wiley & Sons, Inc.     

Measuring the efficiency of sound production

Sound production efficiency is a complex phenotypic trait that incorporates biochemical and mechanical events beginning with substrate oxidation and ending with the radiation of sound. Its accurate measurement is significant in understanding the mechanisms and energetics underlying acoustic signaling and sexual selection. I show that in the short-tailed cricket Anurogryllus arboreus Walker, acoustic performance is apparently the same in acoustic free fields and in the reverberant conditions of a respirometry chamber. I present three methods for simultaneous and nearly simultaneous determination of calling metabolic rate and acoustic power output. The new methods yielded metabolic rates 3%-6% lower than matched controls using traditional flow-through respirometry (mean=8.1 mW); however, none of theses differences were statistically significant. I also evaluate four methods for determining the efficiency of sound production. The means of an individual's efficiencies calculated using these methods vary between 0.50% and 0.60%, with no statistically significant differences between the methods. I conclude with a critical evaluation of these techniques.     

Measuring the diffusion of linguistic change

We examine situations in which linguistic changes have probably been propagated via normal contact as opposed to via conquest, recent settlement and large-scale migration. We proceed then from two simplifying assumptions: first, that all linguistic variation is the result of either diffusion or independent innovation, and, second, that we may operationalize social contact as geographical distance. It is clear that both of these assumptions are imperfect, but they allow us to examine diffusion via the distribution of linguistic variation as a function of geographical distance. Several studies in quantitative linguistics have examined this relation, starting with Séguy (Séguy 1971 Rev. Linguist. Romane 35, 335-357), and virtually all report a sublinear growth in aggregate linguistic variation as a function of geographical distance. The literature from dialectology and historical linguistics has mostly traced the diffusion of individual features, however, so that it is sensible to ask what sort of dynamic in the diffusion of individual features is compatible with Séguy's curve. We examine some simulations of diffusion in an effort to shed light on this question.