Recent interest in modeling biochemical networks raises questions about the relationship between often complex mathematical models and familiar arithmetic concepts from classical enzymology, and also about connections between modeling and experimental data. This review addresses both topics by familiarizing readers with key concepts (and terminology) in the construction, validation, and application of deterministic biochemical models, with particular emphasis on a simple enzyme-catalyzed reaction. Networks of coupled ordinary differential equations (ODEs) are the natural language for describing enzyme kinetics in a mass action approximation. We illustrate this point by showing how the familiar Briggs-Haldane formulation of Michaelis-Menten kinetics derives from the outer (or quasi-steady-state) solution of a dynamical system of ODEs describing a simple reaction under special conditions. We discuss how parameters in the Michaelis-Menten approximation and in the underlying ODE network can be estimated from experimental data, with a special emphasis on the origins of uncertainty. Finally, we extrapolate from a simple reaction to complex models of multiprotein biochemical networks. The concepts described in this review, hitherto of interest primarily to practitioners, are likely to become important for a much broader community of cellular and molecular biologists attempting to understand the promise and challenges of “systems biology” as applied to biochemical mechanisms.

/pdf/classic-and-contemporary-approaches-to-modeling-biochemical-3cxmseg6uz.pdf

Classic and contemporary approaches to modeling biochemical reactions

Regression is a method to estimate parameters in mathematical models of biological systems from experimental data. To ensure the validity of a model for a given data set, pre-regression and post-regression diagnostic tests must accompany the process of model fitting.

Linking data to models: data regression.

Yeast cells are often employed in industrial fermentation processes for their ability to efficiently convert relatively high concentrations of sugars into ethanol and carbon dioxide. Additionally, fermenting yeast cells produce a wide range of other compounds, including various higher alcohols, carbonyl compounds, phenolic compounds, fatty acid derivatives and sulfur compounds. Interestingly, many of these secondary metabolites are volatile and have pungent aromas that are often vital for product quality. In this review, we summarize the different biochemical pathways underlying aroma production in yeast as well as the relevance of these compounds for industrial applications and the factors that influence their production during fermentation. Additionally, we discuss the different physiological and ecological roles of aroma-active metabolites, including recent findings that point at their role as signaling molecules and attractants for insect vectors.

Physiology, ecology and industrial applications of aroma formation in yeast

https://bib.irb.hr/datoteka/389483.Arroyo-Lopez_et_al.pdf

Effects of temperature, pH and sugar concentration on the growth parameters of Saccharomyces cerevisiae, S. kudriavzevii and their interspecific hybrid

Process analytical technology (PAT), the regulatory initiative for building in quality to pharmaceutical manufacturing, has a great potential for improving biopharmaceutical production. The recommended analytical tools for building in quality, multivariate data analysis, mechanistic modeling, novel models for interpretation of systems biology data and new sensor technologies for cellular states, are instrumental in exploiting this potential. Industrial biopharmaceutical production has gradually become dependent on large-scale processes using sensitive mammalian cell cultures. This further emphasizes the need for improved PAT solutions. We summarize recent progress in this area based on an expert workshop held at the 8(th) European Symposium on Biochemical Engineering Sciences (Bologna, 2010), and highlight new opportunities for exploiting PAT when applied in biopharmaceutical production. We conclude with recommendations for advancing PAT applications in the biopharmaceutical industry.

/pdf/process-analytical-technology-pat-for-biopharmaceuticals-3k7vlw4fi9.pdf

Process analytical technology (PAT) for biopharmaceuticals

A physical and mathematical model for wine fermentation kinetics was adapted to include the influence of temperature, perhaps the most critical factor influencing fermentation kinetics. The model was based on flask-scale white wine fermentations at different temperatures (11 to 35°C) and different initial concentrations of sugar (265 to 300 g/liter) and nitrogen (70 to 350 mg N/liter). The results show that fermentation temperature and inadequate levels of nitrogen will cause stuck or sluggish fermentations. Model parameters representing cell growth rate, sugar utilization rate, and the inactivation rate of cells in the presence of ethanol are highly temperature dependent. All other variables (yield coefficient of cell mass to utilized nitrogen, yield coefficient of ethanol to utilized sugar, Monod constant for nitrogen-limited growth, and Michaelis-Menten-type constant for sugar transport) were determined to vary insignificantly with temperature. The resulting mathematical model accurately predicts the observed wine fermentation kinetics with respect to different temperatures and different initial conditions, including data from fermentations not used for model development. This is the first wine fermentation model that accurately predicts a transition from sluggish to normal to stuck fermentations as temperature increases from 11 to 35°C. Furthermore, this comprehensive model provides insight into combined effects of time, temperature, and ethanol concentration on yeast (Saccharomyces cerevisiae) activity and physiology.

Temperature-Dependent Kinetic Model for Nitrogen-Limited Wine Fermentations

The estimation of parameters for nonlinear process models is often accomplished through optimization routines that search for a global optimum with respect to a least squares or weighted least squares criterion. While such an approach is often reasonable, it fails to account for all of the information that is available from the data and practitioner. Here we focus on the inclusion of prior knowledge in the estimation of parameters in nonlinear dynamic systems. We use the Bayesian paradigm to define the probability distribution over process model parameters, called the Bayesian posterior. The quantities associated with this posterior distribution (e.g., credible regions, means, modes) are estimated via Markov Chain Monte Carlo (MCMC) integration. We first give a short introduction to Bayesian parameter estimation and the role of MCMC in evaluating arbitrary probability distributions. Bayesian parameter estimation (via MCMC) is then applied to three case studies. The first case study shows the basic methodology of assigning and evaluating a Bayesian posterior to a simple problem that consists of estimating the mean and variance of a sample. The second case study uses prior information that specifies a preference for a particular type of reaction mechanism over another for a simulated fermentation system; the inclusion of such prior information is shown to improve the estimated values of the model parameters in situations where data are sparse or noisy (compared to the more common weighted least squares approach). The third case study develops a hybrid semi-parametric neural network (NN) model to predict time-dependent observed state variables (cell and protein concentration) in Escherichia coli fermentations. An integral step in the development of this hybrid model is parameter estimation of a nonlinear dynamic model. A hybrid model developed from the Bayesian parameter estimates is shown to outperform a hybrid model developed from the weighted least squares parameter estimates for predicting the final protein yield of a test set. © 2005 American Institute of Chemical Engineers AIChE J, 2006

Bayesian parameter estimation with informative priors for nonlinear systems

Using a fermentation database for Escherichia coli producing green fluorescent protein (GFP), we have implemented a novel three-step optimization method to identify the process input variables most important in modeling the fermentation, as well as the values of those critical input variables that result in an increase in the desired output. In the first step of this algorithm, we use either decision-tree analysis (DTA) or information theoretic subset selection (ITSS) as a database mining technique to identify which process input variables best classify each of the process outputs (maximum cell concentration, maximum product concentration, and productivity) monitored in the experimental fermentations. The second step of the optimization method is to train an artificial neural network (ANN) model of the process input-output data, using the critical inputs identified in the first step. Finally, a hybrid genetic algorithm (hybrid GA), which includes both gradient and stochastic search methods, is used to identify the maximum output modeled by the ANN and the values of the input conditions that result in that maximum. The results of the database mining techniques are compared, both in terms of the inputs selected and the subsequent ANN performance. For the E. coli process used in this study, we identified 6 inputs from the original 13 that resulted in an ANN that best modeled the GFP fluorescence outputs of an independent test set. Values of the six inputs that resulted in a modeled maximum fluorescence were identified by applying a hybrid GA to the ANN model developed. When these conditions were tested in laboratory fermentors, an actual maximum fluorescence of 2.16E6 AU was obtained. The previous high value of fluorescence that was observed was 1.51E6 AU. Thus, this input condition set that was suggested by implementing the proposed optimization scheme on the available historical database increased the maximum fluorescence by 55%.

An integrated approach to optimization of Escherichia coli fermentations using historical data

We have previously shown the usefulness of historical data for fermentation process optimization. The methodology developed includes identification of important process inputs, training of an artificial neural network (ANN) process model, and ultimately use of the ANN model with a genetic algorithm to find the optimal values of each critical process input. However, this approach ignores the time-dependent nature of the system, and therefore, does not fully utilize the available information within a database. In this work, we propose a method for incorporating time-dependent optimization into our previously developed three-step optimization routine. This is achieved by an additional step that uses a fermentation model (consisting of coupled ordinary differential equations (ODE)) to interpret important time-course features of the collected data through adjustments in model parameters. Important process variables not explicitly included in the model were then identified for each model parameter using automatic relevance determination (ARD) with Gaussian process (GP) models. The developed GP models were then combined with the fermentation model to form a hybrid neural network model that predicted the time-course activity of the cell and protein concentrations of novel fermentation conditions. A hybrid-genetic algorithm was then used in conjunction with the hybrid model to suggest optimal time-dependent control strategies. The presented method was implemented upon an E. coli fermentation database generated in our laboratory. Optimization of two different criteria (final protein yield and a simplified economic criteria) was attempted. While the overall protein yield was not increased using this methodology, we were successful in increasing a simplified economic criterion by 15% compared to what had been previously observed. These process conditions included using 35% less arabinose (the inducer) and 33% less typtone in the media and reducing the time required to reach the maximum protein concentration by 10% while producing approximately the same level of protein as the previous optimum.

Retrospective optimization of time-dependent fermentation control strategies using time-independent historical data.

Novel criteria for designing experiments for nonlinear processes are presented These criteria improve on a previous methodology in that they can be used to suggest a batch of new experiments to perform (as opposed to a single new experiment) and are also optimized for discovering improved optima of the system response This is accomplished by using information theoretic criterion, which also heuristically penalize experiments that are likely to result in low (nonoptimal) results While the methods may be applied to any type of nonlinear-nonparametric model (radial basis functions and generalized linear regression), they are here exclusively considered in conjunction with Bayesian regularized feedforward neural networks A focus on the application of rapid process development, and how to use repeated experiments to optimize the training procedures of Bayesian regularized neural networks is shown The presented methods are applied to three case studies The first two case studies involve simulations of one and two-dimensional (2-D) nonlinear regression problems The third case study involves real historical data from bench-scale fermentations generated in our laboratory It is shown that using the presented criteria to design new experiments can greatly increase a feedforward neural network's ability to predict global optima © 2007 American Institute of Chemical Engineers AIChE J, 2007

Matthew C. Coleman

Papers

Temperature-Dependent Kinetic Model for Nitrogen-Limited Wine Fermentations

Bayesian parameter estimation with informative priors for nonlinear systems

An integrated approach to optimization of Escherichia coli fermentations using historical data

Retrospective optimization of time-dependent fermentation control strategies using time-independent historical data.

Nonlinear experimental design using Bayesian regularized neural networks