Monte Carlo Simulations for the Analysis of Non-linear Parameter Confidence Intervals in Optimal Experimental Design.

Especially in biomanufacturing, methods to design optimal experiments are a valuable technique to fully exploit the potential of the emerging technical possibilities that are driving experimental miniaturization and parallelization. The general objective is to reduce the experimental effort while maximizing the information content of an experiment, speeding up knowledge gain in R&D. The approach of model-based design of experiments (known as MBDoE) utilizes the information of an underlying mathematical model describing the system of interest. A common method to predict the accuracy of the parameter estimates uses the Fisher information matrix to approximate the 90% confidence intervals of the estimates. However, for highly non-linear models, this method might lead to wrong conclusions. In such cases, Monte Carlo sampling gives a more accurate insight into the parameter's estimate probability distribution and should be exploited to assess the reliability of the approximations made through the Fisher information matrix. We first introduce the model-based optimal experimental design for parameter estimation including parameter identification and validation by means of a simple non-linear Michaelis-Menten kinetic and show why Monte Carlo simulations give a more accurate depiction of the parameter uncertainty. Secondly, we propose a very robust and simple method to find optimal experimental designs using Monte Carlo simulations. Although computational expensive, the method is easy to implement and parallelize. This article focuses on practical examples of bioprocess engineering but is generally applicable in other fields.

Stretching and breaking of a molecular junction.

Density functional theory (DFT) calculations based on band structure are used to investigate the electromechanical properties of a molecular junction consisting of a dithiolbenzene molecule sandwiched between two gold slabs. This represents a prototypical system for the field of molecular electronics; such a system has previously been studied in break-junction measurements and electron-transport calculations. The stretching and breaking behavior of the junction is analyzed for different geometric conformations, and it is found that the breakage occurs through dissociation of one of the sulfur-gold bonds with a maximum force of 1.25 nN. The molecular electronic states shift during stretching, and, at the point of highest stress in the junction, the highest occupied molecular orbital (HOMO) of the molecule is located exactly at the Fermi level.