Model Testing in Radioligand/Receptor Interaction by Monte Carlo Simulation

Abstract

Monte Carlo simulations have been applied for evaluating the reliability of parameter estimates as well as for testing models in radioligand saturation binding experiments. Scatchard analysis was compared to the nonlinear least-square curve fitting method for one-site saturation binding curves. It was found that linear regression analysis from the transformed data in the Scatchard plot yielded generally less accurate parameter estimates than nonlinear regression analysis of untransformed data. The advantage of the nonlinear least-squares curve fitting method was especially pronounced in cases where the scatter and number of data points, as well as the radioligand concentration range, were chosen similar to less optimal experimental conditions. Under such circumstances, several K_D and B_max values derived by Scatchard analysis led to physically impossible negative values whereas the same data analyzed by nonlinear regression yielded reasonable parameter estimates. Furthermore, it was found that for both means of analysis, K_D and B_max correlated positively. In another set of Monte Carlo experiments, saturation binding curves involving two receptor sites were generated and subsequently analyzed according to both a one-site and a two-site model. The confidence with which one is able to distinguish the two-site model from nonlinear least-squares curve fitting was then estimated for optimal, as well as for, less ideal experimental condigions.     

Modulation by dexamethasone of insulin binding and insulin receptor mRNA levels in U-937 human promonocytic cells.

Treatment with 5 x 10(-6) M dexamethasone stimulated insulin binding in human promonocytic U-937 cells. When curvilinear Scatchard plots were examined according to the one-site model, only changes in affinity, but not in receptor numbers, were observed. However, when the two-site model was applied, an increase in both the affinity and the number of the high affinity-low capacity sites was observed, with maximum values at 15 h. By contrast, the low affinity-high capacity sites did not undergo significant alterations. Northern blot assays revealed two insulin receptor-related mRNAs of approximately 11 and 7 kb in size. Dexamethasone increased the levels of these RNAs, following similar kinetics to those of high affinity receptor expression. This suggests that the 11 and 7 kb species carry information for high affinity insulin receptors, and that in U-937 cells the expression of this receptor subclass is primarily regulated at the mRNA level.     

Efficient and accurate experimental design for enzyme kinetics: Bayesian studies reveal a systematic approach

In areas such as drug development, clinical diagnosis and biotechnology research, acquiring details about the kinetic parameters of enzymes is crucial. The correct design of an experiment is critical to collecting data suitable for analysis, modelling and deriving the correct information. As classical design methods are not targeted to the more complex kinetics being frequently studied, attention is needed to estimate parameters of such models with low variance. We demonstrate that a Bayesian approach (the use of prior knowledge) can produce major gains quantifiable in terms of information, productivity and accuracy of each experiment. Developing the use of Bayesian Utility functions, we have used a systematic method to identify the optimum experimental designs for a number of kinetic model data sets. This has enabled the identification of trends between kinetic model types, sets of design rules and the key conclusion that such designs should be based on some prior knowledge of K(M) and/or the kinetic model. We suggest an optimal and iterative method for selecting features of the design such as the substrate range, number of measurements and choice of intermediate points. The final design collects data suitable for accurate modelling and analysis and minimises the error in the parameters estimated.     

Analysis of protein-mediated 3-O-methylglucose transport in rat erythrocytes: rejection of the alternating conformation carrier model for sugar transport

3-O-Methylglucose (3OMG) transport in rat erythrocytes (RBCs) is mediated by a low-capacity, facilitated diffusion-type process. This study examines whether the characteristics of sugar transport in rat RBCs are consistent with the predictions of two diametric, theoretical mechanisms for sugar transport. The one-site carrier describes a transport mechanism in which sugar influx and efflux substrate binding sites are mutually exclusive. The two-site carrier describes a transport mechanism in which sugar influx and efflux substrate binding sites can exist simultaneously but may interact in a cooperative fashion when occupied by substrate. Michaelis and velocity parameters for saturable 3OMG transport in rat erythrocytes at 24 degrees C were obtained from initial rate measurements of 3OMG transport. The results are incompatible with the predictions of the one-site carrier but are consistent with the predictions of a symmetric two-site carrier, displaying negligible cooperativity between substrate binding sites. This allows reduction of the two-site carrier transport equations to a form containing fewer constants than the one-site carrier equations without limiting their predictive success. While the available evidence does not prove that rat erythrocyte sugar transport is mediated by a two-site mechanism, we conclude that adoption of the formally more complex one-site model for sugar transport in rat erythrocytes is unnecessary and unwarranted. Counterflow experiments have also been performed in which the time course of radiolabeled 3OMG uptake is measured in cells containing saturating levels of 3OMG. The results of these experiments are consistent with the hypothesis [Naftalin et al. (1985) Biochim. Biophys. Acta 820, 235-249] that exchange of sugar between intracellular compartments (cell water and hemoglobin) can be rate limiting for transport under certain conditions.     

Design of experiments for the precise estimation of dose-response parameters: the Hill equation

Optimal experimental designs were evaluated for the precise estimation of parameters of the Hill model. The optimally effective designs were obtained by using the criterion of D-optimization. For the Hill model, optimal designs replicate 3 sampling points. These points were shown to be quite sensitive to the behavior of the experimental error. Since an investigator is often uncertain about error conditions in biological studies, a practical approach would use the sampling scheme calculated for an intermediate error condition. Thus, if the behavior of error variances is not known, precise parameters of the Hill model are obtained by choosing concentrations which yield fractional responses (responses divided by their asymptotic, maximum value) of 0.086, 0.581 and 1.0. When experimental constraints limit the maximum attainable concentration and response, all design points are lowered. Appropriate designs can be constructed based on the design which is optimal when constraints result in a maximum attainable fractional response of 0.5. The optimal designs were found to be robust when the parameter values assumed by the investigator did not equal their true values. The estimating efficiencies obtained by using two frequently applied designs were assessed. Uniformly spaced concentrations yielded imprecise parameters. Six-point, geometrically spaced designs gave generally good results. However, their estimating efficiency was generally exceeded by the recommended sampling schemes even in the presence of uncertainty about error conditions. The method exemplified in this paper can be used for other models.     

Glaucoma triple procedure: a one-site vs. a two-site approach

The purpose of this study is to describe and evaluate the success rate of combined glaucoma and small cataract surgery by means of a one-site versus two-site approach. Fifty-eight eyes of fifty-five patients undergoing combined surgery were operated: thirty-one eyes underwent two-site approach and twenty-seven eyes underwent one-site approach. Short term and long term mean intraocular pressure (IOP) was similar in both groups. There was no significant difference in postoperative inflammation and complication rates between two groups. There is no significant difference in the postoperative results in those two different approaches to perform combined operations of cataract and glaucoma.     

Optimal designs for a multiresponse Emax model and efficient parameter estimation

The aim of dose finding studies is sometimes to estimate parameters in a fitted model. The precision of the parameter estimates should be as high as possible. This can be obtained by increasing the number of subjects in the study, N, choosing a good and efficient estimation approach, and by designing the dose finding study in an optimal way. Increasing the number of subjects is not always feasible because of increasing cost, time limitations, etc. In this paper, we assume fixed N and consider estimation approaches and study designs for multiresponse dose finding studies. We work with diabetes dose–response data and compare a system estimation approach that fits a multiresponse Emax model to the data to equation‐by‐equation estimation that fits uniresponse Emax models to the data. We then derive some optimal designs for estimating the parameters in the multi‐ and uniresponse Emax model and study the efficiency of these designs.     

Reliability of Confidence Interval Estimators under Various Nested Design Parental Sample Sizes

The coverage probabilities of several confidence limit estimators of genetic parameters, obtained from North Carolina I designs, were assessed by means of Monte Carlo simulations. The reliability of the estimators was compared under three different parental sample sizes. The coverage of confidence intervals set on the Normal distribution, and using standard errors either computed by the “delta” method or derived using an approximation for the variance of a variance component estimated by means of a linear combination of mean squares, was affected by the number of males and females included in the experiment. The “delta” method was found to provide reliable standard errors of the genetic parameters only when at least 48 males were each mated to six different females randomly selected from the reference population. Formulae are provided for obtaining “delta” method standard errors, and appropriate statistical software procedures are discussed. The error rates of confidence limits based on the Normal distribution and using standard errors obtained by an approximation for the variance of a variance component varied widely. The coverage of F-distribution confidence intervals for heritability estimates was not significantly affected by parental sample size and consistently provided a mean coverage near the stated coverage. For small parental sample sizes, confidence intervals for heritability estimates should be based on the F-distribution.     

Experimental designs for estimating the kinetic parameters for enzyme-catalysed reactions

The problem of evaluating the kinetic parameters associated with an enzyme-catalysed reaction is examined. If the errors associated with velocity measurements are unknown, or are known to deviate from a normal distribution, then methods based on the minimization of the sum of squares are inappropriate. It is shown that by using a proper experimental design then the kinetic parameters may be estimated unambiguously while making only minimal assumptions regarding the error structure of the data. The design consists of several replicate measurements of the velocity at as many experimental conditions as there are parameters to be estimated. Formulae are presented for choosing the experimental conditions for selected kinetic equations and a computer program is described for designing experiments for any kinetic model. The designs formulated are optimal in the sense that they minimize the overall variance of the parameter estimates.     

D-optimal design applied to binding saturation curves of an enkephalin analog in rat brain

The D-optimal design, a minimal sample design that minimizes the volume of the joint confidence region for the parameters, was used to evaluate binding parameters in a saturation curve with a view to reducing the number of experimental points without loosing accuracy in binding parameter estimates. Binding saturation experiments were performed in rat brain crude membrane preparations with the opioid mu-selective ligand [3H]-[D-Ala2,MePhe4,Gly-ol5]enkephalin (DAGO), using a sequential procedure. The first experiment consisted of a wide-range saturation curve, which confirmed that [3H]-DAGO binds only one class of specific sites and non-specific sites, and gave information on the experimental range and a first estimate of binding affinity (Ka), capacity (Bmax) and non-specific constant (k). On this basis the D-optimal design was computed and sequential experiments were performed each covering a wide-range traditional saturation curve, the D-optimal design and a splitting of the D-optimal design with the addition of 2 points (+/- 15% of the central point). No appreciable differences were obtained with these designs in parameter estimates and their accuracy. Thus sequential experiments based on D-optimal design seem a valid method for accurate determination of binding parameters, using far fewer points with no loss in parameter estimation accuracy.     

Temporal Data Set Reduction Based on D-Optimality for Quantitative FLIM-FRET Imaging

Fluorescence lifetime imaging (FLIM) when paired with Förster resonance energy transfer (FLIM-FRET) enables the monitoring of nanoscale interactions in living biological samples. FLIM-FRET model-based estimation methods allow the quantitative retrieval of parameters such as the quenched (interacting) and unquenched (non-interacting) fractional populations of the donor fluorophore and/or the distance of the interactions. The quantitative accuracy of such model-based approaches is dependent on multiple factors such as signal-to-noise ratio and number of temporal points acquired when sampling the fluorescence decays. For high-throughput or in vivo applications of FLIM-FRET, it is desirable to acquire a limited number of temporal points for fast acquisition times. Yet, it is critical to acquire temporal data sets with sufficient information content to allow for accurate FLIM-FRET parameter estimation. Herein, an optimal experimental design approach based upon sensitivity analysis is presented in order to identify the time points that provide the best quantitative estimates of the parameters for a determined number of temporal sampling points. More specifically, the D-optimality criterion is employed to identify, within a sparse temporal data set, the set of time points leading to optimal estimations of the quenched fractional population of the donor fluorophore. Overall, a reduced set of 10 time points (compared to a typical complete set of 90 time points) was identified to have minimal impact on parameter estimation accuracy (≈5%), with in silico and in vivo experiment validations. This reduction of the number of needed time points by almost an order of magnitude allows the use of FLIM-FRET for certain high-throughput applications which would be infeasible if the entire number of time sampling points were used.     

Quantification of gliadin levels to the picogram level by flow cytometry.

BACKGROUND: Celiac disease is a widely prevalent enteropathy caused by intolerance to gliadin, one of the gluten proteins. We developed two methods for the analysis of gliadin levels. Both methods use flow cytometry and rat antibodies against a 16-residue peptide of gliadin. The peptide is common to the alpha-, beta-, gamma-, and omega-gliadins. METHODS: In the one-site assay, the antigen (gliadin standard or food extract) was adsorbed on 3-mum latex particles. Sensitized particles were then incubated, in this order, with rat anti-gliadin peptide antibodies and anti-rat immunoglobulin G antibodies labeled with fluorescein isothiocyanate. In the two-site assay, the antigen was trapped on the latex particles by rat anti-gliadin antibodies and then measured by the same antibodies labeled with fluorescein. RESULTS: Detection limits were 1 ng/ml for the one-site assay and 10 pg/ml for the two-site assay. The two-site assay displayed gliadin at concentrations above the limit proposed by the Codex Alimentarius in 2 of 40 gluten-free products. CONCLUSION: There is a growing concern that gliadin, even when present in gluten-free foods within the limit fixed by the Codex Alimentarius, over the long term may become toxic to patients with celiac disease. The techniques described in this study provide an opportunity to further decrease the acceptable limit of gliadin in gluten-free foods.     

Variance component estimation techniques compared for two mating designs with forest genetic architecture through computer simulation

Computer simulation was used to compare minimum variance quadratic estimation (MIVQUE), minimum norm quadratic unbiased estimation (MINQUE), restricted maximum likelihood (REML), maximum likelihood (ML), and Henderson's Method 3 (HM3) on the basis of variance among estimates, mean square error (MSE), bias and probability of nearness for estimation of both individual variance components and three ratios of variance components. The investigation also compared three procedures for dealing with negative estimates and included the use of both individual observations and plot means as the experimental unit of the analysis. The structure of data simulated (field design, mating designs, genetic architecture and imbalance) represented typical analysis problems in quantitative forest genetics. Results of comparing the estimation techniques demonstrated that: estimates of probability of nearness did not discriminate among techniques; bias was discriminatory among procedures for dealing with negative estimates but not among estimation techniques (except ML); sampling variance among estimates was discriminatory among procedures for dealing with negative estimates, estimation techniques and unit of observation; and MSE provided no additional information to variance of the estimates. HM3 and REML were the closest competitors under these criteria; however, REML demonstrated greater robustness to imbalance. Of the three negative estimate procedures, two are of practical significance and guidelines for their application are presented. Estimates from individual observations were always preferable to those from plot means over the experimental levels of this study.This is Journal Series NO. R-03768 of the Institute of Food and Agricultural Sciences     

Multiple sensitive estimation and optimal sample size allocation in the item sum technique

For surveys of sensitive issues in life sciences, statistical procedures can be used to reduce nonresponse and social desirability response bias. Both of these phenomena provoke nonsampling errors that are difficult to deal with and can seriously flaw the validity of the analyses. The item sum technique (IST) is a very recent indirect questioning method derived from the item count technique that seeks to procure more reliable responses on quantitative items than direct questioning while preserving respondents' anonymity. This article addresses two important questions concerning the IST: (i) its implementation when two or more sensitive variables are investigated and efficient estimates of their unknown population means are required; (ii) the determination of the optimal sample size to achieve minimum variance estimates. These aspects are of great relevance for survey practitioners engaged in sensitive research and, to the best of our knowledge, were not studied so far. In this article, theoretical results for multiple estimation and optimal allocation are obtained under a generic sampling design and then particularized to simple random sampling and stratified sampling designs. Theoretical considerations are integrated with a number of simulation studies based on data from two real surveys and conducted to ascertain the efficiency gain derived from optimal allocation in different situations. One of the surveys concerns cannabis consumption among university students. Our findings highlight some methodological advances that can be obtained in life sciences IST surveys when optimal allocation is achieved.     

Blinded sample size reestimation in non-inferiority trials with binary endpoints

Sample size calculations in the planning of clinical trials depend on good estimates of the model parameters involved. When the estimates of these parameters have a high degree of uncertainty attached to them, it is advantageous to reestimate the sample size after an internal pilot study. For non-inferiority trials with binary outcome we compare the performance of Type I error rate and power between fixed-size designs and designs with sample size reestimation. The latter design shows itself to be effective in correcting sample size and power of the tests when misspecification of nuisance parameters occurs with the former design.     

Optimal experimental design for a nonlinear response in environmental toxicology

A start-stop experiment in environmental toxicology provides a backdrop for this design discussion. The basic problem is to decide when to sample a nonlinear response in order to minimize the generalized variance of the estimated parameters. An easily coded heuristic optimization strategy can be applied to this problem to obtain optimal or nearly optimal designs. The efficiency of the heuristic approach allows a straightforward exploration of the sensitivity of the suggested design with respect to such problem-specific concerns as variance heterogeneity, time-grid resolution, design criteria, and interval specification of planning values for parameters. A second illustration of design optimization is briefly presented in the context of concentration spacing for a reproductive toxicity study.     

A model-based meta-analysis of monoclonal antibody pharmacokinetics to guide optimal first-in-human study design

The objectives of this retrospective analysis were (1) to characterize the population pharmacokinetics (popPK) of four different monoclonal antibodies (mAbs) in a combined analysis of individual data collected during first-in-human (FIH) studies and (2) to provide a scientific rationale for prospective design of FIH studies with mAbs. The data set was composed of 171 subjects contributing a total of 2716 mAb serum concentrations, following intravenous (IV) and subcutaneous (SC) doses. mAb PK was described by an open 2-compartment model with first-order elimination from the central compartment and a depot compartment with first-order absorption. Parameter values obtained from the popPK model were further used to generate optimal sampling times for a single dose study. A robust fit to the combined data from four mAbs was obtained using the 2-compartment model. Population parameter estimates for systemic clearance and central volume of distribution were 0.20 L/day and 3.6 L with intersubject variability of 31% and 34%, respectively. The random residual error was 14%. Differences (> 2-fold) in PK parameters were not apparent across mAbs. Rich designs (22 samples/subject), minimal designs for popPK (5 samples/subject), and optimal designs for non-compartmental analysis (NCA) and popPK (10 samples/subject) were examined by stochastic simulation and estimation. Single-dose PK studies for linear mAbs executed using the optimal designs are expected to yield high-quality model estimates, and accurate capture of NCA estimations. This model-based meta-analysis has determined typical popPK values for four mAbs with linear elimination and enabled prospective optimization of FIH study designs, potentially improving the efficiency of FIH studies for this class of therapeutics.     

A model-based meta-analysis of monoclonal antibody pharmacokinetics to guide optimal first-in-human study design

The objectives of this retrospective analysis were (1) to characterize the population pharmacokinetics (popPK) of four different monoclonal antibodies (mAbs) in a combined analysis of individual data collected during first-in-human (FIH) studies and (2) to provide a scientific rationale for prospective design of FIH studies with mAbs. The data set was composed of 171 subjects contributing a total of 2716 mAb serum concentrations, following intravenous (IV) and subcutaneous (SC) doses. mAb PK was described by an open 2-compartment model with first-order elimination from the central compartment and a depot compartment with first-order absorption. Parameter values obtained from the popPK model were further used to generate optimal sampling times for a single dose study. A robust fit to the combined data from four mAbs was obtained using the 2-compartment model. Population parameter estimates for systemic clearance and central volume of distribution were 0.20 L/day and 3.6 L with intersubject variability of 31% and 34%, respectively. The random residual error was 14%. Differences (> 2-fold) in PK parameters were not apparent across mAbs. Rich designs (22 samples/subject), minimal designs for popPK (5 samples/subject), and optimal designs for non-compartmental analysis (NCA) and popPK (10 samples/subject) were examined by stochastic simulation and estimation. Single-dose PK studies for linear mAbs executed using the optimal designs are expected to yield high-quality model estimates, and accurate capture of NCA estimations. This model-based meta-analysis has determined typical popPK values for four mAbs with linear elimination and enabled prospective optimization of FIH study designs, potentially improving the efficiency of FIH studies for this class of therapeutics.     

Differential effects of temperature and maturity stage on hepatic estrogen receptor characteristics of Atlantic salmon

In order to determine if elevated temperature during vitellogenesis had a detrimental effect on hepatic estrogen receptors of Atlantic salmon (Salmo salar), 3H-estradiol saturation binding analysis, using one- and two-site binding models, was carried out on extracts of hepatic cytosols from fish held at 14, 18 or 22 degrees C over the austral period of peak vitellogenesis (February to April). With one-site binding analysis, no temperature related difference in either receptor affinity (Kd) or number (Bmax) was found at each sampling point, but there was an apparent decrease in both affinity and number at each temperature over the period of the study. However, some analyses, notably at 22 degrees C during February, were best described using a two-site binding model. At this temperature and time, there was a clear separation of binding affinity into high and low components (Kd = 0.67+/-S.E. 0.05 and 20+/-S.E. 5.6 nM, respectively) (n = 4), which suggests that February was a critical time of temperature related hepatic sensitivity to estrogen. These results support those of other studies where we found that February was also a sensitive time with respect to temperature impairment of in vitro follicular estrogen synthesis, and the greatest period of in vivo temperature sensitivity.     

Robust and efficient design of experiments for the Monod model

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.