Design issues for the Michaelis-Menten model

Optimal experimental design for cytogenetic dose-response calibration curves

Purpose: To introduce optimal experimental design techniques in the cytogenetic biological dosimetry practice. This includes the development of a new optimality criterion for the calibration of radiation doses.Materials and methods: The most typical optimal design criterion and the one developed in this research are introduced and applied in an example from the literature. In another example from the literature, a simulation study has been performed to compare the standard error of the dose estimation using different experimental designs. An RStudio project and a GitHub project have been developed to reproduce these results.Results: In the paper, it is observed that the application of optimal experimental design techniques can reduce the standard error of biodosimetric dose estimations.Conclusions: Optimal experimental design techniques jointly with practitioners' requirements may be applied. This practice would not involve an additional laboratory work.

A low cost mobile phone dark-field microscope for nanoparticle-based quantitative studies

Dark-field microscope (DFM) analysis of nanoparticle binding signal is highly useful for a variety of research and biomedical applications, but current applications for nanoparticle quantification rely on expensive DFM systems. The cost, size, limited robustness of these DFMs limits their utility for non-laboratory settings. Most nanoparticle analyses use high-magnification DFM images, which are labor intensive to acquire and subject to operator bias. Low-magnification DFM image capture is faster, but is subject to background from surface artifacts and debris, although image processing can partially compensate for background signal. We thus mated an LED light source, a dark-field condenser and a 20× objective lens with a mobile phone camera to create an inexpensive, portable and robust DFM system suitable for use in non-laboratory conditions. This proof-of-concept mobile DFM device weighs less than 400g and costs less than $2000, but analysis of images captured with this device reveal similar nanoparticle quantitation results to those acquired with a much larger and more expensive desktop DFMM system. Our results suggest that similar devices may be useful for quantification of stable, nanoparticle-based activity and quantitation assays in resource-limited areas where conventional assay approaches are not practical.

Standardized maximim D-optimal designs for enzyme kinetic inhibition models

Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters. An alternative is the maximin approach that allows the user to specify a range of values for each parameter of interest. However, the maximin approach is difficult because we first have to determine the locally optimal design for each set of nominal values before maximin types of optimal designs can be found via a nested optimization process. We show that particle swarm optimization (PSO) techniques can solve such complex optimization problems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae for standardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact and nonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibition models are not necessarily supported at a minimum number of points. To facilitate use of such designs, we create a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs.

Design optimality for models defined by a system of ordinary differential equations

Many scientific processes, specially in pharmacokinetics (PK) and pharmacodynamics (PD) studies, are defined by a system of ordinary differential equations (ODE). If there are unknown parameters that need to be estimated, the optimal experimental design approach offers quality estimators for the different objectives of the practitioners. When computing optimal designs the standard procedure uses the linearization of the analytical expression of the ODE solution, which is not feasible when this analytical form does not exist. In this work some methods to solve this problem are described and discussed. Optimal designs for two well-known example models, Iodine and Michaelis-Menten, have been computed using the proposed methods. A thorough study has been done for a specific two-parameter PK model, the biokinetic model of ciprofloxacin and ofloxacin, computing the best designs for different optimality criteria and numbers of points. The designs have been compared according to their efficiency, and the goodness of the designs for the estimation of each parameter has been checked. Although the objectives of the paper are focused on the optimal design field, the methodology can be used as well for a sensitivity analysis of ordinary differential equation systems.

Experimental designs for a benign paroxysmal positional vertigo model

BACKGROUND

The pathology of the Benign Paroxysmal Positional Vertigo (BPPV) is detected by a clinician through maneuvers consisting of a series of consecutive head turns that trigger the symptoms of vertigo in patient. A statistical model based on a new maneuver has been developed in order to calculate the volume of endolymph displaced after the maneuver.

METHODS

A simplification of the Navier-Stokes problem from the fluids theory has been used to construct the model. In addition, the same cubic splines that are commonly used in kinematic control of robots were used to obtain an appropriate description of the different maneuvers. Then experimental designs were computed to obtain an optimal estimate of the model.

RESULTS

D-optimal and c-optimal designs of experiments have been calculated. These experiments consist of a series of specific head turns of duration Δt and angle α that should be performed by the clinician on the patient. The experimental designs obtained indicate the duration and angle of the maneuver to be performed as well as the corresponding proportion of replicates. Thus, in the D-optimal design for 100 experiments, the maneuver consisting of a positive 30° pitch from the upright position, followed by a positive 30° roll, both with a duration of one and a half seconds is repeated 47 times. Then the maneuver with 60° /6° pitch/roll during half a second is repeated 16 times and the maneuver 90° /90° pitch/roll during half a second is repeated 37 times. Other designs with significant differences are computed and compared.

CONCLUSIONS

A biomechanical model was derived to provide a quantitative basis for the detection of BPPV. The robustness study for the D-optimal design, with respect to the choice of the nominal values of the parameters, shows high efficiencies for small variations and provides a guide to the researcher. Furthermore, c-optimal designs give valuable assistance to check how efficient the D-optimal design is for the estimation of each of the parameters. The experimental designs provided in this paper allow the physician to validate the model. The authors of the paper have held consultations with an ENT consultant in order to align the outline more closely to practical scenarios.

Classification of difference between inhibition constants of an inhibitor to facilitate identifying the inhibition type

To identify the common inhibition types, the putative decision system is unsatisfactory. In a new decision system, Michaelis-Menten constants and maximal reaction rates were plotted versus inhibitor concentrations for deriving K(ik) and K(iv) as the inhibition constants, respectively; their difference was quantified as the ratio of the larger one to the smaller one. Such ratios below 2.0 suggested uncompetitive inhibitors, over 5.0 suggested noncompetitive or competitive inhibitors, and from 2.0 to 5.0 suggested mixed inhibitors. By the new decision system, (i) the simulation recovery of uncompetitive inhibitors under CVs of 2% or 5% was improved by four times, but that of competitive or noncompetitive inhibitors was improved slightly; (ii) the recovery of L-phenylalanine as an uncompetitive inhibitor of intestinal alkaline phosphatase reached 38%, while the putative decision system lost all; the recovery of xanthine as a competitive inhibitor of uricase was improved slightly. Therefore, the new decision system was better.

The comparison of the estimation of enzyme kinetic parameters by fitting reaction curve to the integrated Michaelis-Menten rate equations of different predictor variables

The estimation of enzyme kinetic parameters by nonlinear fitting reaction curve to the integrated Michaelis-Menten rate equation ln(S(0)/S)+(S(0)-S)/K(m)=(V(m)/K(m))xt was investigated and compared to that by fitting to (S(0)-S)/t=V(m)-K(m)x[ln(S(0)/S)/t] (Atkins GL, Nimmo IA. The reliability of Michaelis-Menten constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. Biochem J 1973;135:779-84) with uricase as the model. Uricase reaction curve was simulated with random absorbance error of 0.001 at 0.075 mmol/l uric acid. Experimental reaction curve was monitored by absorbance at 293 nm. For both CV and deviation <20% by simulation, K(m) from 5 to 100 micromol/l was estimated with Eq. (1) while K(m) from 5 to 50 micromol/l was estimated with Eq. (2). The background absorbance and the error in the lag time of steady-state reaction resulted in negative K(m) with Eq. (2), but did not affect K(m) estimated with Eq. (1). Both equations gave better estimation of V(m). The computation time and the goodness of fit with Eq. (1) were 40-fold greater than those with Eq. (2). By experimentation, Eq. (1) yielded K(m) consistent with the Lineweaver-Burk plot analysis, but Eq. (2) gave many negative parameters. Apparent K(m) by Eq. (1) linearly increased, while V(m) were constant, vs. xanthine concentrations, and the inhibition constant was consistent with the Lineweaver-Burk plot analysis. These results suggested that the integrated rate equation that uses the predictor variable of reaction time was reliable for the estimation of enzyme kinetic parameters and applicable for the characterization of enzyme inhibitors.

Optimal design of experiments with anticipated pattern of missing observations

We propose a general method of designing an experiment when there are potentially failing trials. We use polynomial models and the Michaelis-Menten model as examples and construct different types of optimal designs under a broad class of response probability functions. We show that the usual optimal designs, that assume all observations are available at the end of the experiment, can be quite inefficient if the anticipated missingness pattern is not accounted for at the design stage. We also investigate robustness properties of the proposed designs to specification of their nominal values and the response probability functions.

Optimal designs for Michaelis-Menten kinetic studies

Many reactions in enzymology are governed by the Michaelis-Menten equation. Characterising these reactions requires the estimation of the parameters K(M) and V(max) which determine the Michaelis-Menten equation and this is done by observing rates of reactions at a set of substrate concentrations. The choice of substrate concentrations is investigated by determining Bayesian D-optimal designs for a model in which residuals have a normal distribution with constant variance. Designs which focus on alternative quantities, such as K(M) or the ratio V(max)/K(M) are also considered. The effect on the optimal designs of alternative error distributions is also considered.