Using nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) for simultaneous determination of concentration and equilibrium constant

Nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) is a versatile tool for studying affinity binding. Here we describe a NECEEM-based approach for simultaneous determination of both the equilibrium constant, K(d), and the unknown concentration of a binder that we call a target, T. In essence, NECEEM is used to measure the unbound equilibrium fraction, R, for the binder with a known concentration that we call a ligand, L. The first set of experiments is performed at varying concentrations of T, prepared by serial dilution of the stock solution, but at a constant concentration of L, which is as low as its reliable quantitation allows. The value of R is plotted as a function of the dilution coefficient, and dilution corresponding to R = 0.5 is determined. This dilution of T is used in the second set of experiments in which the concentration of T is fixed but the concentration of L is varied. The experimental dependence of R on the concentration of L is fitted with a function describing their theoretical dependence. Both K(d) and the concentration of T are used as fitting parameters, and their sought values are determined as the ones that generate the best fit. We have fully validated this approach in silico by using computer-simulated NECEEM electropherograms and then applied it to experimental determination of the unknown concentration of MutS protein and K(d) of its interactions with a DNA aptamer. The general approach described here is applicable not only to NECEEM but also to any other method that can determine a fraction of unbound molecules at equilibrium.

A note on statistical and biological communication: a case study of the 2009 H1N1 pandemic

Background

Many academic fields contribute to medical and health research. As a result, due to the various backgrounds of these disciplines, inference and interpretation of study findings can be misconstrued.

Results

In a recent survey of the 2009 H1N1 literature we found many instances where semantic and statistical misinterpretation or miscommunication could potentially arise. We provide examples where miscommunication or misinterpretation of study results can mislead the interdisciplinary reader. We also provide some additional background on statistical methodology and theory for the interested reader.

Discussion

This work presented some examples where statistical misinterpretation or miscommunication could arise in the H1N1 literature. However, similar challenges are encountered in other subjects and disciplines. To reduce the probability of this occurring it is necessary that (1) readers consider papers with a critical eye and approach citations with caution; (2) authors take more care to present study methods with more clarity. Reproducibility of the study results would greatly aid readers in their ability to understand and interpret the given findings.

Nonparametric estimation of a convex bathtub-shaped hazard function

In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of n(2/5) at points x(0) where the true hazard function is positive and strictly convex. Moreover, we establish the pointwise asymptotic distribution theory of our estimator under these same assumptions. One notable feature of the nonparametric MLE studied here is that no arbitrary choice of tuning parameter (or complicated data-adaptive selection of the tuning parameter) is required.

Computation of nonparametric convex hazard estimators via profile methods

This paper proposes a profile likelihood algorithm to compute the nonparametric maximum likelihood estimator of a convex hazard function. The maximisation is performed in two steps: First the support reduction algorithm is used to maximise the likelihood over all hazard functions with a given point of minimum (or antimode). Then it is shown that the profile (or partially maximised) likelihood is quasi-concave as a function of the antimode, so that a bisection algorithm can be applied to find the maximum of the profile likelihood, and hence also the global maximum. The new algorithm is illustrated using both artificial and real data, including lifetime data for Canadian males and females.

Estimation of a discrete monotone distribution

We study and compare three estimators of a discrete monotone distribution: (a) the (raw) empirical estimator; (b) the "method of rearrangements" estimator; and (c) the maximum likelihood estimator. We show that the maximum likelihood estimator strictly dominates both the rearrangement and empirical estimators in cases when the distribution has intervals of constancy. For example, when the distribution is uniform on {0, … , y}, the asymptotic risk of the method of rearrangements estimator (in squared ℓ(2) norm) is y/(y + 1), while the asymptotic risk of the MLE is of order (log y)/(y + 1). For strictly decreasing distributions, the estimators are asymptotically equivalent.

Digital photography as a novel technique of measuring ocular surface dimensions

PURPOSE

To introduce a novel technique for measuring ocular surface dimensions using digital photography and computerized image analysis in the context of ptosis repair surgery.

METHODS

Digital photographs and patient questionnaires on dry eye symptoms were obtained from 31 patients before and after ptosis repair. Patients were examined preoperatively and at 1 and 6 weeks postoperatively. Adobe Photoshop 7.0 (Adobe Systems Incorporated, 345 Parkl Avenue, San Jose, CA 95110-2704, USA) was used to digitally measure palpebral fissure height, fissure width, and ocular surface area (OSA). Similar digital measurements were obtained on 30 control subjects as well. Digital calculations of OSA for control, preoperative, and postoperative groups were compared with other published techniques.

RESULTS

Graphical comparison between our method of measuring OSA and the mathematical estimations proposed by previous studies suggests that our method is more precise in measuring OSA, and that it is also better able to identify individual variations of OSA from general population trends.

CONCLUSION

Digital ocular photography combined with computerized image analysis is a fast, easy to use, and reliable method of measuring ocular surface dimensions. In addition to ptosis surgery, this method can be used in other ocular surface studies.