Structural identifiability of a model for the acetic acid fermentation process

Modelling Acetification with Artificial Neural Networks and Comparison with Alternative Procedures

Modelling techniques allow certain processes to be characterized and optimized without the need for experimentation. One of the crucial steps in vinegar production is the biotransformation of ethanol into acetic acid by acetic bacteria. This step has been extensively studied by using two predictive models: first-principles models and black-box models. The fact that first-principles models are less accurate than black-box models under extreme bacterial growth conditions suggests that the kinetic equations used by the former, and hence their goodness of fit, can be further improved. By contrast, black-box models predict acetic acid production accurately enough under virtually any operating conditions. In this work, we trained black-box models based on Artificial Neural Networks (ANNs) of the multilayer perceptron (MLP) type and containing a single hidden layer to model acetification. The small number of data typically available for a bioprocess makes it rather difficult to identify the most suitable type of ANN architecture in terms of indices such as the mean square error (MSE). This places ANN methodology at a disadvantage against alternative techniques and, especially, polynomial modelling.

Gravito-inertial ambiguity resolved through head stabilization

It has been frequently observed that humans and animals spontaneously stabilize their heads with respect to the gravitational vertical during body movements even in the absence of vision. The interpretations of this intriguing behaviour have so far not included the need, for survival, to robustly estimate verticality. Here we use a mechanistic model of the head/otolith organ to analyse the possibility for this system to render verticality 'observable', a fundamental prerequisite to the determination of the angular position and acceleration of the head from idiothetic, inertial measurements. The intrinsically nonlinear head-vestibular dynamics is shown to generally lack observability unless the head is stabilized in orientation by feedback. Thus, our study supports the hypothesis that a central function of the physiologically costly head stabilization strategy is to enable an organism to estimate the gravitational vertical and head acceleration during locomotion. Moreover, our result exhibits a rare peculiarity of certain nonlinear systems to fortuitously alter their observability properties when feedback is applied.

Structural identifiability analyses of candidate models for in vitro Pitavastatin hepatic uptake

In this paper a review of the application of four different techniques (a version of the similarity transformation approach for autonomous uncontrolled systems, a non-differential input/output observable normal form approach, the characteristic set differential algebra and a recent algebraic input/output relationship approach) to determine the structural identifiability of certain in vitro nonlinear pharmacokinetic models is provided. The Organic Anion Transporting Polypeptide (OATP) substrate, Pitavastatin, is used as a probe on freshly isolated animal and human hepatocytes. Candidate pharmacokinetic non-linear compartmental models have been derived to characterise the uptake process of Pitavastatin. As a prerequisite to parameter estimation, structural identifiability analyses are performed to establish that all unknown parameters can be identified from the experimental observations available.

Compartmental modelling of the pharmacokinetics of a breast cancer resistance protein

A mathematical model for the pharmacokinetics of Hoechst 33342 following administration into a culture medium containing a population of transfected cells (HEK293 hBCRP) with a potent breast cancer resistance protein inhibitor, Fumitremorgin C (FTC), present is described. FTC is reported to almost completely annul resistance mediated by BCRP in vitro. This non-linear compartmental model has seven macroscopic sub-units, with 14 rate parameters. It describes the relationship between the concentration of Hoechst 33342 and FTC, initially spiked in the medium, and the observed change in fluorescence due to Hoechst 33342 binding to DNA. Structural identifiability analysis has been performed using two methods, one based on the similarity transformation/exhaustive modelling approach and the other based on the differential algebra approach. The analyses demonstrated that all models derived are uniquely identifiable for the experiments/observations available. A kinetic modelling software package, namely FACSIMILE (MPCA Software, UK), was used for parameter fitting and to obtain numerical solutions for the system equations. Model fits gave very good agreement with in vitro data provided by AstraZeneca across a variety of experimental scenarios.

Parameter identifiability of power-law biochemical system models

Mathematical modeling has become an integral component in biotechnology, in which these models are frequently used to design and optimize bioprocesses. Canonical models, like power-laws within the Biochemical Systems Theory, offer numerous mathematical and numerical advantages, including built-in flexibility to simulate general nonlinear behavior. The construction of such models relies on the estimation of unknown case-specific model parameters by way of experimental data fitting, also known as inverse modeling. Despite the large number of publications on this topic, this task remains the bottleneck in canonical modeling of biochemical systems. The focus of this paper concerns with the question of identifiability of power-law models from dynamic data, that is, whether the parameter values can be uniquely and accurately identified from time-series data. Existing and newly developed parameter identifiability methods were applied to two power-law models of biochemical systems, and the results pointed to the lack of parametric identifiability as the root cause of the difficulty faced in the inverse modeling. Despite the focus on power-law models, the analyses and conclusions are extendable to other canonical models, and the issue of parameter identifiability is expected to be a common problem in biochemical system modeling.