A general approach to confidence regions for optimal factor levels of response surfaces

For a response surface experiment, an approximate hypothesis test and an associated confidence region is proposed for the minimizing (or maximizing) factor-level configuration. Carter et al. (1982, Cancer Research 42, 2963-2971) show that confidence regions for optimal conditions provide a way to make decisions about therapeutic synergism. The response surface may be constrained to be within a specified, bounded region. These constraint regions can be quite general. This allows for more realistic constraint modeling and a wide degree of applicability, including constraints occurring in mixture experiments. The usual assumption of a quadratic model is also generalized to include any regression model that is linear in the model parameters. An intimate connection is established between this confidence region and the Box-Hunter (1954, Biometrika 41, 190-199) confidence region for a stationary point. As a byproduct, this methodology also provides a way to construct a confidence interval for the difference between the optimal mean response and the mean response at a specified factor-level configuration. The application of this confidence region is illustrated with two examples. Extensive simulations indicate that this confidence region has good coverage properties.     

A note on the estimation of evoked response

The traditional average evoked response is compared and contrasted with several alternate estimates, derived from frequency domain considerations, for a model of evoked responses superimposed upon a stationary noise series. Further, a means of constructing approximate confidence intervals for the values of an evoked response is indicated. The case of several simultaneously recorded series is also considered.Prepared with the support of the National Science Foundation Grant MCS 76-06117     

Analyzing optima in the exploration of multiple response surfaces

A method is presented for testing the equality of some or all (constrained or unconstrained) optima in a response surface analysis. An estimator of a common location of stationary points is obtained by a standard multivariate testing procedure and a confidence region associated with the common optimum is derived. The procedure is illustrated by the estimation of a common optimum in a multiple response experiment. The multivariate approach facilitates a more efficient estimation of the optimum than the usual univariate response surface analysis and provides additional tests of the response surface model.     

The response of cortical neurons to in vivo-like input current: theory and experiment

The study of several aspects of the collective dynamics of interacting neurons can be highly simplified if one assumes that the statistics of the synaptic input is the same for a large population of similarly behaving neurons (mean field approach). In particular, under such an assumption, it is possible to determine and study all the equilibrium points of the network dynamics when the neuronal response to noisy, in vivo-like, synaptic currents is known. The response function can be computed analytically for simple integrate-and-fire neuron models and it can be measured directly in experiments in vitro. Here we review theoretical and experimental results about the neural response to noisy inputs with stationary statistics. These response functions are important to characterize the collective neural dynamics that are proposed to be the neural substrate of working memory, decision making and other cognitive functions. Applications to the case of time-varying inputs are reviewed in a companion paper (Giugliano et al. in Biol Cybern, 2008). We conclude that modified integrate-and-fire neuron models are good enough to reproduce faithfully many of the relevant dynamical aspects of the neuronal response measured in experiments on real neurons in vitro.     

Xenohormesis: health benefits from an eon of plant stress response evolution

Xenohormesis is a biological principle that explains how environmentally stressed plants produce bioactive compounds that can confer stress resistance and survival benefits to animals that consume them. Animals can piggyback off products of plants' sophisticated stress response which has evolved as a result of their stationary lifestyle. Factors eliciting the plant stress response can judiciously be employed to maximize yield of health-promoting plant compounds. The xenohormetic plant compounds can, when ingested, improve longevity and fitness by activating the animal's cellular stress response and can be applied in drug discovery, drug production, and nutritional enhancement of diet.     

Comparison between the movement detection systems underlying the optomotor and the landing response in the housefly

Flies evaluate movement within their visual field in order to control the course of flight and to elicit landing manoeuvres. Although the motor output of the two types of responses is quite different, both systems can be compared with respect to the underlying movement detection systems. For a quantitative comparison, both responses were measured during tethered flight under identical conditions. The stimulus was a sinusoidal periodic pattern of vertical stripes presented bilaterally in the fronto-lateral eye region of the fly. To release the landing response, the pattern was moved on either side from front to back. The latency of the response depends on the stimulus conditions and was measured by means of an infrared light-beam that was interrupted whenever the fly lifted its forelegs to assume a preprogrammed landing posture (Borst and Bahde 1986). As an optomotor stimulus the pattern moved on one side from front to back and on the other side in the opposite direction. The induced turning tendency was measured by a torque meter (Götz 1964). The response values which will be compared are the inverse latencies of the landing response and the amplitude of the yaw torque.

1. Optomotor course-control is more sensitive to pattern movement at small spatial wavelengths (10° and 20°) than the landing response (Fig. 1a and b). This suggests that elementary movement detectors (EMDs, Buchner 1976) with large detection base (the distance between interacting visual elements) contribute more strongly to the landing than to the optomotor system.
2. The optimum contrast frequencies of the different responses obtained at a comparatively high pattern contrast of about 0.6 was found to be between 1 and 10 Hz for the optomotor response, and around 20 Hz for the landing response (Fig. 2a and b). This discrepancy can be explained by the fact that the optomotor response was tested under stationary conditions (several seconds of stimulation) while for the landing response transient response characteristics of the movement detectors have to be taken into account (landing occurs under these conditions within less than 100 ms after onset of the movement stimulus). To test the landing system under more stationary conditions, the pattern contrast had to be reduced to low values. This led to latencies of several seconds. Then the optimum of the landing response is around 4 Hz. This is in the optimum range of the optomotor course-control response. The result suggests the same filter time constants for the movement detectors of both systems.
3. The dependence of both responses on the position and the size of the pattern was examined. The landing response has its optimum sensitivity more ventrally than the optomotor response (Fig. 3a and b). Both response amplitudes increase with the size of the pattern in a similar progression (Fig. 3c and d).

In first approximation, the present results are compatible with the assumption of a common set of movement detectors for both the optomotor course-control and the landing system. Movement detectors with different sampling bases and at different positions in the visual field seem to contribute with different gain to both responses. Accordingly, the control systems underlying both behaviors are likely to be independent already at the level of spatial integration of the detector output.     

Dynamics of the yeast transcriptome during wine fermentation reveals a novel fermentation stress response

In this study, genome-wide expression analyses were used to study the response of Saccharomyces cerevisiae to stress throughout a 15-day wine fermentation. Forty per cent of the yeast genome significantly changed expression levels to mediate long-term adaptation to fermenting grape must. Among the genes that changed expression levels, a group of 223 genes was identified, which was designated as fermentation stress response (FSR) genes that were dramatically induced at various points during fermentation. FSR genes sustain high levels of induction up to the final time point and exhibited changes in expression levels ranging from four- to 80-fold. The FSR is novel; 62% of the genes involved have not been implicated in global stress responses and 28% of the FSR genes have no functional annotation. Genes involved in respiratory metabolism and gluconeogenesis were expressed during fermentation despite the presence of high concentrations of glucose. Ethanol, rather than nutrient depletion, seems to be responsible for entry of yeast cells into the stationary phase.     

Statistical analysis of functional response experiments

The aim of this paper is to highlight the benefits of a full data analysis of a functional response data set, compared to the usual one‐pass regression analysis. In a biological control setting where the choice of organism is often based on comparative studies of the functional responses, it is imperative to have both reliable estimates and a feeling of the degree of confidence one is willing to put on the figures. We analyzed a data set involving the freshwater predator Notonecta glauca (Hemiptera) preying on Asellus aquaticus during 24 h. The specific aim of the analysis was to test whether the functional response is of type II or type III. The different stages of a complete analysis are (1) a preliminary inspection of the data, (2) model building, (3) a model check and (4) a combination of the results with independent information. We argue that the analysis is best done with the predation rate as response and define a test for the location of its maximum. The existence of a maximum is typical for type III functional response. We explain why the binomial distribution is a natural error distribution, and how to implement the regression analysis within the family of generalized linear models using two competing link functions, the logit and the reciprocal. There is marked overdispersion which increases with increasing prey numbers. We use prior weights to take account of it. Using all available data, a type III functional response is warranted with the reciprocal link, but not with the logit link Model checks using Pearson residuals and regression diagnostics based on point deletions show that three points have a particularly strong influence on the parameter estimates. If these are deleted, the functional response type III is then warranted for both link functions. The complete analysis enables us to determine the various degrees of uncertainty and to draw biological conclusions with corresponding confidence. We are convinced that the data set shows a type III functional response, but we are less sure about which link function to choose. Furthermore, the marked overdispersion at high density, the regression diagnostics, as well as independent information on a change in the behaviour of the prey at high density, indicate that the experimental conditions may have changed as a function of the prey density.     

Kernel estimates of dose response

A nonparametric method for analyzing quantal response data from an indirect bioassay experiment is proposed. Kernel estimates of the dose-response curve are used to develop approximate confidence intervals for (i) the optimal combination dose of a drug with therapeutic effects at low doses and toxic effects at high doses, and (ii) the lethal dose levels of a toxic chemical. This nonparametric procedure was implemented on real and simulated data. The confidence interval for problem (i) has high coverage probabilities when the dose-response curve is symmetric about the optima. However, the coverage probabilities are adversely affected by asymmetry about the optima and consequently are not reliable unless the sample sizes are large. The use of kernel estimators with higher-order kernels may alleviate this sensitivity to asymmetry. The confidence interval for problem (ii) has high coverage probabilities robust with respect to the shape or symmetry of the underlying dose-response curve.     

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.     

Qualitative simulation of the carbon starvation response in Escherichia coli

In case of nutritional stress, like carbon starvation, Escherichia coli cells abandon their exponential-growth state to enter a more resistant, non-growth state called stationary phase. This growth-phase transition is controlled by a genetic regulatory network integrating various environmental signals. Although E. coli is a paradigm of the bacterial world, it is little understood how its response to carbon starvation conditions emerges from the interactions between the different components of the regulatory network. Using a qualitative method that is able to overcome the current lack of quantitative data on kinetic parameters and molecular concentrations, we model the carbon starvation response network and simulate the response of E. coli cells to carbon deprivation. This allows us to identify essential features of the transition between exponential and stationary phase and to make new predictions on the qualitative system behavior following a carbon upshift.     

Understanding the acid tolerance response of bifidobacteria

Aims: To investigate the effect of pH on the viability and the acid tolerance response (ATR) of bifidobacteria. Methods and Results: The impact of low pH on the viability of five species of bifidobacteria was examined under conditions of strict anaerobiosis. Although differences in the ability to resist the lethal effects of low pH were apparent among the species, cell viability could be improved by the provision of fermentable substrate during an acidic pH stress or through the use of stationary phase cells. While a stationary phase ATR was found to occur in two species of bifidobacteria, there was no adaptive response in exponential phase cells. Proteomic analysis of exponential phase Bifidobacterium longum subjected to a mild acid pre‐exposure (pH 4·5, 2 h) prior to an acid challenge revealed a substantial loss in the total number of cellular proteins. In contrast, proteomic analysis of stationary phase cells revealed an increased abundance of proteins associated with the general stress response as well as the β‐subunit of the F₀F₁‐ATPase, known to be important in bifidobacteria acid tolerance. Conclusion: Neither Bif. longum or Bifidobacterium breve possesses an inducible exponential phase ATR. Significance and Impact of the Study: These findings provide further insights into the impact of pH on the viability of bifidobacteria and may partially explain the loss in viability associated with their storage in acid foods.     

On the autocorrelation of one class of non-stationary random point processes

The autocorrelation of those non-stationary random point processes that can be transformed by a time transformation into a stationary process is derived. As an application, a closed form formula is obtained for the autocorrelation of those processes where the average number of points is sinusoidally modulated and the corresponding stationary process is defined by independent intervals identically distributed according to a gamma density of integer order.     

Collective response of human populations to large-scale emergencies

Despite recent advances in uncovering the quantitative features of stationary human activity patterns, many applications, from pandemic prediction to emergency response, require an understanding of how these patterns change when the population encounters unfamiliar conditions. To explore societal response to external perturbations we identified real-time changes in communication and mobility patterns in the vicinity of eight emergencies, such as bomb attacks and earthquakes, comparing these with eight non-emergencies, like concerts and sporting events. We find that communication spikes accompanying emergencies are both spatially and temporally localized, but information about emergencies spreads globally, resulting in communication avalanches that engage in a significant manner the social network of eyewitnesses. These results offer a quantitative view of behavioral changes in human activity under extreme conditions, with potential long-term impact on emergency detection and response.     

Identification of the Clostridium perfringens genes involved in the adaptive response to oxidative stress

Clostridium perfringens is a ubiquitous gram-positive pathogen that is present in the air, soil, animals, and humans. Although C. perfringens is strictly anaerobic, vegetative and stationary cells can survive in a growth-arrested stage in the presence of oxygen and/or low concentrations of superoxide and hydroxyl radicals. Indeed, it possesses an adaptive response to oxidative stress, which can be activated in both aerobic and anaerobic conditions. To identify the genes involved in this oxidative stress response, C. perfringens strain 13 mutants were generated by Tn916 insertional mutagenesis and screened for resistance or sensitivity to various oxidative stresses. Three of the 12 sensitive mutants examined harbored an independently inserted single copy of the transposon in the same operon as two genes orthologous to the ydaD and ycdF genes of Bacillus subtilis, which encode a putative NADPH dehydrogenase. Complementation experiments and knockout experiments demonstrated that these genes are both required for efficient resistance to oxidative stress in C. perfringens and are probably responsible for the production of NADPH, which is required for maintenance of the intracellular redox balance in growth-arrested cells. Other Tn916 disrupted genes were also shown to play important roles in the oxidative stress response. This is the first time that some of these genes (e.g., a gene encoding an ATP-dependent RNA helicase, the beta-glucuronidase gene, and the gene encoding the atypical iron sulfur prismane protein) have been shown to be involved in the oxidative response.     

Gravitational compensation and the phototropic response of oat coleoptiles

Avena seedlings were germinated and grown while continuously rotated on the horizontal axis of a clinostat. The coleoptiles of these gravity-compensated plants were phototropically more responsive than those of plants rotated on a vertical axis. When the plants were compensated after unilateral irradiation, phototropic curvature of the shoot progressed for the next 6 hours, with the rate of curving decreasing about 3 hours after irradiation. The decrease in rate was less in the plants gravity-compensated before irradiation than in those vertically rotated. In the period 70 to 76 hours after planting, the growth rate of the compensated coleoptiles was significantly less than that of the vertically rotated seedlings. The greater phototropic curvature, the decreased growth rate, and the slower rate of straightening of the curved, compensated shoot can be correlated with several consequences of compensation: an increase in sensitivity to auxin, a lowering of auxin content in the coleoptile tip, and possibly, from an interaction between compensation and phototropic stimulation, an enhanced difference in auxin transport between the illuminated and shaded halves of the unilaterally irradiated shoot.

The phototropic response of the vertically rotated seedling was significantly different from that of the vertical stationary, indicating the importance of vertically rotated controls in clinostat experiments.

     

Rats' memory for event duration in delayed matching-to-sample with nonspatial comparison response alternatives

Previous research has suggested that using stationary and moving levers as nonspatial response alternatives can significantly enhance the speed of acquiring a temporal discrimination in rats. In Experiment 1, rats were trained to discriminate 2 and 8s of magazine light illumination by responding to either a stationary lever or a moving lever with a cue light illuminated above it. Rats learned to discriminate event durations at a high level of accuracy after 25 sessions of training. During subsequent delay tests, rats exhibited a strong choose-long bias, indicating that they were timing from the onset of the magazine light until the entry of levers into the chamber. This occurred regardless of whether intertrial intervals and delay intervals were dark or illuminated. On test trials in which the sample was omitted, rats responded as if the short sample had been presented. In Experiment 2, the rats received extensive training with dark and illuminated variable delay intervals (1-4 s). However, they continued to exhibit a tendency to time from the onset of the magazine light until entry of the levers into the chamber. Although the use of stationary/uncued and moving/cued levers as response alternatives enhanced the speed of acquisition of the event duration discrimination in rats, additional procedural modifications will be necessary to prevent rats from timing during the delay interval.     

Estimating divergence times in the presence of an overdispersed molecular clock

Molecular loci that fail relative-rate tests are said to be "overdispersed." Traditional molecular-clock approaches to estimating divergence times do not take this into account. In this study, a method was developed to estimate divergence times using loci that may be overdispersed. The approach was to replace the traditional Poisson process assumption with a more general stationary process assumption. A probability model was developed, and an accompanying computer program was written to find maximum-likelihood estimates of divergence times under both the Poisson process and the stationary process assumptions. In simulation, it was shown that confidence intervals under the traditional Poisson assumptions often vastly underestimate the true confidence limits for overdispersed loci. Both models were applied to two data sets: one from land plants, the other from the higher metazoans. In both cases, the traditional Poisson process model could be rejected with high confidence. Maximum-likelihood analysis of the metazoan data set under the more general stationary process suggested that their radiation occurred well over a billion years ago, but confidence intervals were extremely wide. It was also shown that a model consistent with a Cambrian (or nearly Cambrian) origination of the animal phyla, although significantly less likely than a much older divergence, fitted the data well. It is argued that without an a priori understanding of the variance in the time between substitutions, molecular data sets may be incapable of ever establishing the age of the metazoan radiation.