Analysis of quantal response data from bacterial destruction studies in sterilization: the Stumbo estimate is biased

J. HACHIGIAN AND R.J. SCHLESINGER. 1991. Real and simulated experimental data and theoretical data from quantal response experiments were used to make a comparison between the analysis of data from a quantal response experiment and data from a direct enumeration experiment. The method of analysis for each is differentiated, thereby enhancing the utility of the quantal response experiment in sterilization studies. From this comparison it appears that the Stumbo estimate of the D value is biased. Furthermore, the Stumbo estimate depends upon the spore load per replicate in quantal response type experiments, which makes experimental comparisons difficult. Another estimate of D is demonstrated which overcomes some of these shortcomings.     

Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs.     

Fitting the linear-quadratic model using time of occurrence as the end-point for quantal response multifraction experiments

A statistical technique is given for fitting the linear-quadratic model to experimental quantal response multifraction data using the time of the response as the end-point. The analysis used is based on the Cox Proportional Hazards model. The technique is useful for late effects where the time of occurrence of the response is dose dependent. The technique is compared to logistic regression analysis and the advantages and disadvantages are discussed. Both methods are applied to a lung pneumonitis experiment and a kidney experiment.     

Estimation of radiation resistance values of microorganisms in food products

Several statistical methods, including the conventional technique of Schmidt and Nank, were evaluated for estimating radiation resistance values of various strains of Clostridium botulinum by the use of partial spoilage data from an inoculated ham pack study. Procedures based on quantal response were preferred. The tedious but rigorous probit maximum likelihood determination was used as a standard of comparison. Weibull's graphical treatment was the method of choice because it is simple to utilize, it is mathematically sound, and its ld(50) values agreed closely with the reference standard. In addition, it offers a means for analyzing the type of microbial death kinetics that occur in the pack (exponential, normal, log normal, or mixed distributions), and it predicts the probability of microbial death with any radiation dose used, as well as the dose needed to destroy any given number of organisms, without the need to assume the death pattern of the partial spoilage data. The Weibull analysis indicated a normal type kinetics of death for C. botulinum spores in irradiated cured ham rather than an exponential order of death, as assumed by the Schmidt-Nank formula. The Weibull 12D equivalent of a radiation process, or the minimal radiation dose (MRD), for cured ham was consistently higher than both the experimental sterilizing dose (ESD) and the Schmidt-Nank average MRD. The latter calculation was lower than the ESD in three of the five instances examined, which seems unrealistic. The Spearman-K?rber estimate was favored as the arithmetic technique on the bases of ease of computation, close agreement with the reference method, and providing confidence limits for the ld(50) values.     

Estimating synaptic parameters from mean, variance, and covariance in trains of synaptic responses

Fluctuation analysis of synaptic transmission using the variance-mean approach has been restricted in the past to steady-state responses. Here we extend this method to short repetitive trains of synaptic responses, during which the response amplitudes are not stationary. We consider intervals between trains, long enough so that the system is in the same average state at the beginning of each train. This allows analysis of ensemble means and variances for each response in a train separately. Thus, modifications in synaptic efficacy during short-term plasticity can be attributed to changes in synaptic parameters. In addition, we provide practical guidelines for the analysis of the covariance between successive responses in trains. Explicit algorithms to estimate synaptic parameters are derived and tested by Monte Carlo simulations on the basis of a binomial model of synaptic transmission, allowing for quantal variability, heterogeneity in the release probability, and postsynaptic receptor saturation and desensitization. We find that the combined analysis of variance and covariance is advantageous in yielding an estimate for the number of release sites, which is independent of heterogeneity in the release probability under certain conditions. Furthermore, it allows one to calculate the apparent quantal size for each response in a sequence of stimuli.     

Testing the fit of a quantal model of neurotransmission

Many studies of synaptic transmission have assumed a parametric model to estimate the mean quantal content and size or the effect upon them of manipulations such as the induction of long-term potentiation. Classical tests of fit usually assume that model parameters have been selected independently of the data. Therefore, their use is problematic after parameters have been estimated. We hypothesized that Monte Carlo (MC) simulations of a quantal model could provide a table of parameter-independent critical values with which to test the fit after parameter estimation, emulating Lilliefors's tests. However, when we tested this hypothesis within a conventional quantal model, the empirical distributions of two conventional goodness-of-fit statistics were affected by the values of the quantal parameters, falsifying the hypothesis. Notably, the tests' critical values increased when the combined variances of the noise and quantal-size distributions were reduced, increasing the distinctness of quantal peaks. Our results support two conclusions. First, tests that use a predetermined critical value to assess the fit of a quantal model after parameter estimation may operate at a differing unknown level of significance for each experiment. Second, a MC test enables a valid assessment of the fit of a quantal model after parameter estimation.     

Estimating the parameters in the two-component model for cell survival from experimental quantal response data

A statistical technique is given which can be used to estimate the parameters of the two-component model for cell survival from quantal response multifraction data. The method is a nonlinear logistic regression and relies on a mild assumption relating the probability of death to cell survival level. The method is demonstrated on mouse colon data, where more efficient estimates of the parameters are known, and the agreement is good. Also for some mouse lung LD50 data we obtain estimates of the parameters, and the fit to the data is shown to be better than that of linear-quadratic model.     

A Global Parallel Model Based Design of Experiments Method to Minimize Model Output Uncertainty

Model-based experiment design specifies the data to be collected that will most effectively characterize the biological system under study. Existing model-based design of experiment algorithms have primarily relied on Fisher Information Matrix-based methods to choose the best experiment in a sequential manner. However, these are largely local methods that require an initial estimate of the parameter values, which are often highly uncertain, particularly when data is limited. In this paper, we provide an approach to specify an informative sequence of multiple design points (parallel design) that will constrain the dynamical uncertainty of the biological system responses to within experimentally detectable limits as specified by the estimated experimental noise. The method is based upon computationally efficient sparse grids and requires only a bounded uncertain parameter space; it does not rely upon initial parameter estimates. The design sequence emerges through the use of scenario trees with experimental design points chosen to minimize the uncertainty in the predicted dynamics of the measurable responses of the system. The algorithm was illustrated herein using a T cell activation model for three problems that ranged in dimension from 2D to 19D. The results demonstrate that it is possible to extract useful information from a mathematical model where traditional model-based design of experiments approaches most certainly fail. The experiments designed via this method fully constrain the model output dynamics to within experimentally resolvable limits. The method is effective for highly uncertain biological systems characterized by deterministic mathematical models with limited data sets. Also, it is highly modular and can be modified to include a variety of methodologies such as input design and model discrimination.     

Experiment specific expression patterns

The differential analysis of genes between microarrays from several experimental conditions or treatments routinely estimates which genes change significantly between groups. As genes are never regulated individually, observed behavior may be a consequence of changes in other genes. Existing approaches like co-expression analysis aim to resolve such patterns from a wide range of experiments. The knowledge of such a background set of experiments can be used to compute expected gene behavior based on known links. It is particularly interesting to detect previously unseen specific effects in other experiments. Here, a new method to spot genes deviating from expected behavior (PAttern DEviation SCOring--Padesco) is devised. It uses linear regression models learned from a background set to arrive at gene specific prediction accuracy distributions. For a given experiment, it is then decided whether each gene is predicted better or worse than expected. This provides a novel way to estimate the experiment specificity of each gene. We propose a validation procedure to estimate the detection of such specific candidates and show that these can be identified with an average accuracy of about 85%.     

Simultaneous rapid estimation of sedimentation coefficient and molecular weight

Data obtained from the early portion of sedimentation velocity experiments may be analyzed to simultaneously estimate both s and s/D. The C versus r data obtained are analyzed using a nonlinear least squares algorithm and an approximate solution to the Lamm equation. This procedure was tested both with simulated noisy data and with experimental data obtained using ribonuclease, ovalbumin, and somatostatin.dodecylsulfate. The procedure assumes that both s and D are independent of concentration. The results suggest that optimal estimation of both s and s/D is obtained at values of (= 2D/(s.omega(2).r(a)(2))) in the range of 0.002 to 0.01 and values of tau(= 2 somega(2)t) less than 0.04. Appropriate selection of rotor speed allows the estimation of both s and s/D for nearly globular macromolecules in the range of 10(4) to 10(6) daltons with data obtained during the first 3000-5000 seconds of a sedimentation velocity experiment.     

Hierarchical analysis of large-scale two-dimensional gel electrophoresis experiments

Large-scale two-dimensional gel experiments have the potential to identify proteins that play an important role in elucidating cell mechanisms and in various stages of drug discovery. Such experiments, typically including hundreds or even thousands of related gels, are notoriously difficult to perform, and analysis of the gel images has until recently been virtually impossible. In this paper we describe a scalable computational model that permits the organization and analysis of a large gel collection. The model is implemented in Compugen's Z4000 system. Gels are organized in a hierarchical, multidimensional data structure that allow the user to view a large-scale experiment as a tree of numerous simpler experiments, and carry out the analysis one step at a time. Analyzed sets of gels form processing units that can be combined into higher level units in an iterative framework. The different conditions at the core of the experiment design, termed the dimensions of the experiment, are transformed from a multidimensional structure to a single hierarchy. The higher level comparison is performed with the aid of a synthetic "adaptor" gel image, called a Raw Master Gel (RMG). The RMG allows the inclusion of data from an entire set of gels to be presented as a gel image, thereby enabling the iterative process. Our model includes a flexible experimental design approach that allows the researcher to choose the condition to be analyzed a posteriori. It also enables data reuse, the performing of several different analysis designs on the same experimental data. The stability and reproducibility of a protein can be analyzed by tracking it up or down the hierarchical dimensions of the experiment.     

Asynchronous effect produced by neurotransmitter release at the frog neuromuscular junction

Hump-shaped distortion of motor nerve response, resembling spontaneous or single quanta in amplitude and time course were, observed at a temperature of 20°C, produced by stimulating this nerve during experiments on preparations of frog sartorius and cutaneous pectoral muscle involving focal extracellular recording. Having performed statistical analysis, the possibility could be excluded of this effect representing superposition of spontaneous over-evoked signals and the hypothesis could be put forward that it results from relatively unsynchronized release of separate quanta which go to make up a multiquantal response. This hypothesis would appear to be confirmed by clear-cut correlation between the distribution of synaptic delays in unitary response (when quantal content is low) and those observed in asynchronous response (when quantal content is high). Polymodal type distribution of synaptic delay is shown to be common to both cases. It is deduced that both asynchronous response and the discrete nature of variations in synaptic delay are standard features in the mechanisms of transmitter release.I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 18, No. 3, pp. 346–354, May–June, 1986.     

A model for analysis of the anesthetic response

When a dose d of an anesthetic is administered intravenously, either sleep will be observed for a period of time or no sleep will occur. We developed a general approach for formulating a model for this response which reduces to a quantal response model if the duration of sleep is ignored. Several specific models illustrate the general formulation. In each case the underlying dose response relationship that corresponds to the quantal response problem is the logistic. To include the duration of sleep in the model we introduced a concept of an "active dose" which is a function of the administered dose and time. We use a set of data from a study of the response of guinea pigs to ketamine for our numerical examples.     

Evaluation of the time course of neurotransmitter release from the measured PSC and MPSC

A method for obtaining delay histograms for the time course of neurotransmitter release is presented. The delay histogram is derived from the measured psc (or the sum of several psc's) and the mpsc (obtained experimentally or otherwise) by means of a simple, quick, mathematical procedure. The procedure may be automated for the greater part. No approximation of the mpsc shape is performed, and the method is applicable to all quantal contents. For low and medium quantal contents, the delay histograms obtained by the method are compared to those obtained by direct analysis. A reasonable agreement is achieved. An experiment of high quantal content, for which direct analysis is impossible, is then analysed using the new method. Difficulties which may arise when applying the procedure and methods to overcome them are discussed at length. Other methods are set forth in the Discussion.     

The Database for Reaching Experiments and Models

Reaching is one of the central experimental paradigms in the field of motor control, and many computational models of reaching have been published. While most of these models try to explain subject data (such as movement kinematics, reaching performance, forces, etc.) from only a single experiment, distinct experiments often share experimental conditions and record similar kinematics. This suggests that reaching models could be applied to (and falsified by) multiple experiments. However, using multiple datasets is difficult because experimental data formats vary widely. Standardizing data formats promises to enable scientists to test model predictions against many experiments and to compare experimental results across labs. Here we report on the development of a new resource available to scientists: a database of reaching called the Database for Reaching Experiments And Models (DREAM). DREAM collects both experimental datasets and models and facilitates their comparison by standardizing formats. The DREAM project promises to be useful for experimentalists who want to understand how their data relates to models, for modelers who want to test their theories, and for educators who want to help students better understand reaching experiments, models, and data analysis.     

A Symmetric Extended Logistic Model with Applications to Experimental Toxicity Data

The fit of the logit and probit models for quantal response data can be improved by embedding these classical models within a richer parametric family indexed by one or two shape parameters. In this paper, a symmetric extended logistic model indexed by a shape parameter λ is discussed with application to dose response curves. The usual maximum likelihood method is employed to estimate the parameters of the model. The need to include the shape parameter λ is illustrated by analyzing a set of real experimental data and comparing the fit of the extended logistic model to those obtained by the standard logit and probit models.     

Potential of a quantal response as a mechanism for oscillatory behavior: implications for our concepts of hormonal control mechanisms

This article describes the potential of a quantal (i.e., all-or-none) response as a model for understanding the interactions between endocrine, paracrine and autocrine hormones. We review the general features of continuous and discontinuous (i.e., oscillating) quantal models including the role of a threshold. In addition, we also describe a few of the many different biochemical mechanisms which may give rise to quantal behavior. One of the more attractive schemes involves the coordinate regulation of opposing biochemical pathways resulting from phosphorylation of hormone receptors and/or rate-limiting enzymes. At least one hormone receptor (i.e., that for insulin) and many rate-limiting enzymes which control the flow of metabolites through a variety of metabolic pathways can be phosphorylated at multiple sites by one or more protein kinases. Phosphorylation may enhance or inhibit the activities of these proteins depending on which sites are modified. Furthermore, since phosphorylation of some sites on a protein may enhance the ability of phosphoprotein phosphatases to dephosphorylate other sites responsible for biological activity of the protein, phosphorylation also has the potential to produce a discontinuous quantal response. Quantal response mechanisms may alter our notions of endocrine regulation. When a quantal response mechanism is applied to a simple negative feedback model similar to that which was originally postulated to explain the interactions between gonadotropin and steroid hormonal levels, the model can account for the oscillations in hormone levels even when the input is constant. Conversely, when a graded mechanism is applied to the same negative feedback model, the model will almost certainly result in constant hormone levels. Further, the model illustrates that small changes in rate constants and thresholds of response, amplification of hormonal signals, and degradation of intermediate regulators can produce large shifts in the output of the system. These may account for the variability in hormonal levels observed in some endocrine systems. Finally, the high sensitivity of the quantal response mechanism accounts for the data which suggest that gonadotropins may play permissive rather than causal roles in regulation of gonadal function. Since increasing evidence suggests that all cells of a given type may not be equal in terms of hormonal responsiveness, measurements of response in single cells over short time periods will be needed before the role of a quantal response can be determined and endocrine regulation will be fully understood.     

Design and analysis issues in quantitative proteomics studies

Quantitative proteomics is the comparison of distinct proteomes which enables the identification of protein species which exhibit changes in expression or post-translational state in response to a given stimulus. Many different quantitative techniques are being utilized and generate large datasets. Independent of the technique used, these large datasets need robust data analysis to ensure valid conclusions are drawn from such studies. Approaches to address the problems that arise with large datasets are discussed to give insight into the types of statistical analyses of data appropriate for the various experimental strategies that can be employed by quantitative proteomic studies. This review also highlights the importance of employing a robust experimental design and highlights various issues surrounding the design of experiments. The concepts and examples discussed within will show how robust design and analysis will lead to confident results that will ensure quantitative proteomics delivers.