SummaryNatural variations in gene expression provide a mechanism for multiple phenotypes to arise in an isogenic bacterial population. In particular, a sub-group termed persisters show high tolerance to antibiotics. Previously, their formation has been attributed to cell dormancy. Here we demonstrate that bacterial persisters, under β-lactam antibiotic treatment, show less cytoplasmic drug accumulation as a result of enhanced efflux activity. Consistently, a number of multi-drug efflux genes, particularly the central component TolC, show higher expression in persisters. Time-lapse imaging and mutagenesis studies further establish a positive correlation between tolC expression and bacterial persistence. The key role of efflux systems, among multiple biological pathways involved in persister formation, indicates that persisters implement a positive defense against antibiotics prior to a passive defense via dormancy. Finally, efflux inhibitors and antibiotics together effectively attenuate persister formation, suggesting a combination strategy to target drug tolerance.

Graphical Abstract Highlights d The degree of drug-tolerant cells being dormant can be measured by ''dormancy depth'' d Cellular dark foci, proved to be protein aggresomes, indicate dormancy depth d Depletion of intracellular ATP is the major force driving aggresomes formation d DnaK is vital in the disaggregation of aggresomes when a dormant cell resuscitates In this work, Pu et al. introduced a concept of ''dormancy depth'' that provides a unifying framework for understanding both persisters and viable but non-culturable cells. Subsequent mechanistic investigations revealed how ATP-dependent dynamic protein aggregation regulates cellular dormancy and resuscitation, the fine control of which facilitates bacterial drug tolerance. SUMMARYCell dormancy is a widespread mechanism used by bacteria to evade environmental threats, including antibiotics. Here we monitored bacterial antibiotic tolerance and regrowth at the single-cell level and found that each individual survival cell shows different ''dormancy depth,'' which in return regulates the lag time for cell resuscitation after removal of antibiotic. We further established that protein aggresome-a collection of endogenous protein aggregates-is an important indicator of bacterial dormancy depth, whose formation is promoted by decreased cellular ATP level. For cells to leave the dormant state and resuscitate, clearance of protein aggresome and recovery of proteostasis are required. We revealed that the ability to recruit functional DnaK-ClpB machineries, which facilitate protein disaggregation in an ATP-dependent manner, determines the lag time for bacterial regrowth. Better understanding of the key factors regulating bacterial regrowth after surviving antibiotic attack could lead to new therapeutic strategies for combating bacterial antibiotic tolerance.

SummaryThe asymptotic behaviour of penalized spline estimators is studied in the univariate case. We use B -splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya-Watson kernel estimators with 'equivalent' kernels depending upon m. The equivalent kernels we obtain for penalized splines are the same as those found by Silverman for smoothing splines. The asymptotic distribution of the penalized spline estimator is Gaussian and we give simple expressions for the asymptotic mean and variance. Provided that it is fast enough, the rate at which the number of knots converges to infinity does not affect the asymptotic distribution. The optimal rate of convergence of the penalty parameter is given. Penalized splines are not design-adaptive.

Summary. We propose a fast penalized spline method for bivariate smoothing. Univariate Pspline smoothers Eilers and Marx (1996) are applied simultaneously along both coordinates.The new smoother has a sandwich form which suggested the name "sandwich smoother" to a referee. The sandwich smoother has a tensor product structure that simplifies an asymptotic analysis and it can be fast computed. We derive a local central limit theorem for the sandwich smoother, with simple expressions for the asymptotic bias and variance, by showing that the sandwich smoother is asymptotically equivalent to a bivariate kernel regression estimator with a product kernel. As far as we are aware, this is the first central limit theorem for a bivariate spline estimator of any type. Our simulation study shows that the sandwich smoother is orders of magnitude faster to compute than other bivariate spline smoothers, even when the latter are computed using a fast GLAM (Generalized Linear Array Model) algorithm, and comparable to them in terms of mean squared integrated errors. We extend the sandwich smoother to array data of higher dimensions, where a GLAM algorithm improves the computational speed of the sandwich smoother. One important application of the sandwich smoother is to estimate covariance functions in functional data analysis. In this application, our numerical results show that the sandwich smoother is orders of magnitude faster than local linear regression. The speed of the sandwich formula is important because functional data sets are becoming quite large.

Bacteria use subcellular proteinaceous liquid droplets to survive stress.

The paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are: 1) testing the null hypotheses that the mean of a functional process is parametric against a nonparametric alternative; and 2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo likelihood ratio test is proposed and its asymptotic distribution is derived. The size and power properties of the test are confirmed in realistic simulation scenarios. Finite sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized

In this paper, we systematically study the consistency of sliced average variance estimation (SAVE). The findings reveal that when the response is continuous, the asymptotic behavior of SAVE is rather different from that of sliced inverse regression (SIR). SIR can achieve $\sqrt{n}$ consistency even when each slice contains only two data points. However, SAVE cannot be $\sqrt{n}$ consistent and it even turns out to be not consistent when each slice contains a fixed number of data points that do not depend on n, where n is the sample size. These results theoretically confirm the notion that SAVE is more sensitive to the number of slices than SIR. Taking this into account, a bias correction is recommended in order to allow SAVE to be $\sqrt{n}$ consistent. In contrast, when the response is discrete and takes finite values, $\sqrt{n}$ consistency can be achieved. Therefore, an approximation through discretization, which is commonly used in practice, is studied. A simulation study is carried out for the purposes of illustration.Comment: Published at http://dx.doi.org/10.1214/009053606000001091 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The electrical membrane potential (V m) is one of the components of the electrochemical potential of protons across the biological membrane (proton motive force), which powers many vital cellular processes. Because V m also plays a role in signal transduction, measuring it is of great interest. Over the years, a variety of techniques have been developed for the purpose. In bacteria, given their small size, Nernstian membrane voltage probes are arguably the favorite strategy, and their cytoplasmic accumulation depends on V m according to the Nernst equation. However, a careful calibration of Nernstian probes that takes into account the tradeoffs between the ease with which the signal from the dye is observed and the dyes' interactions with cellular physiology is rarely performed. Here, we use a mathematical model to understand such tradeoffs and apply the results to assess the applicability of the Thioflavin T dye as a V m sensor in Escherichia coli. We identify the conditions in which the dye turns from a V m probe into an actuator and, based on the model and experimental results, propose a general workflow for the characterization of Nernstian dye candidates.