An efficient approximate moment method for multi-dimensional population balance models – Application to virus replication in multi-cellular systems

Mechanistic modeling of viral particle production

Viral systems such as wild-type viruses, viral vectors, and virus-like particles are essential components of modern biotechnology and medicine. Despite their importance, the commercial-scale production of viral systems remains highly inefficient for multiple reasons. Computational strategies are a promising avenue for improving process development, optimization, and control, but require a mathematical description of the system. This article reviews mechanistic modeling strategies for the production of viral particles, both at the cellular and bioreactor scales. In many cases, techniques and models from adjacent fields such as epidemiology and wild-type viral infection kinetics can be adapted to construct a suitable process model. These process models can then be employed for various purposes such as in-silico testing of novel process operating strategies and/or advanced process control.

Multi-Rate Data Fusion for State and Parameter Estimation in (Bio-)Chemical Process Engineering

For efficient operation, modern control approaches for biochemical process engineering require information on the states of the process such as temperature, humidity or chemical composition. Those measurement are gathered from a set of sensors which differ with respect to sampling rates and measurement quality. Furthermore, for biochemical processes in particular, analysis of physical samples is necessary, e.g., to infer cellular composition resulting in delayed information. As an alternative for the use of this delayed measurement for control, so-called soft-sensor approaches can be used to fuse delayed multirate measurements with the help of a mathematical process model and provide information on the current state of the process. In this manuscript we present a complete methodology based on cascaded unscented Kalman filters for state estimation from delayed and multi-rate measurements. The approach is demonstrated for two examples, an exothermic chemical reactor and a recently developed model for biopolymer production. The results indicate that the the current state of the systems can be accurately reconstructed and therefore represent a promising tool for further application in advanced model-based control not only of the considered processes but also of related processes.

Model-based approach for predicting the impact of genetic modifications on product yield in biopharmaceutical manufacturing-Application to influenza vaccine production

A large group of biopharmaceuticals is produced in cell lines. The yield of such products can be increased by genetic engineering of the corresponding cell lines. The prediction of promising genetic modifications by mathematical modeling is a valuable tool to facilitate experimental screening. Besides information on the intracellular kinetics and genetic modifications the mathematical model has to account for ubiquitous cell-to-cell variability. In this contribution, we establish a novel model-based methodology for influenza vaccine production in cell lines with overexpressed genes. The manipulation of the expression level of genes coding for host cell factors relevant for virus replication is achieved by lentiviral transduction. Since lentiviral transduction causes increased cell-to-cell variability due to different copy numbers and integration sites of the gene constructs we use a population balance modeling approach to account for this heterogeneity in terms of intracellular viral components and distributed kinetic parameters. The latter are estimated from experimental data of intracellular viral RNA levels and virus titers of infection experiments using cells overexpressing a single host cell gene. For experiments with cells overexpressing multiple host cell genes, only final virus titers were measured and thus, no direct estimation of the parameter distributions was possible. Instead, we evaluate four different computational strategies to infer these from single gene parameter sets. Finally, the best computational strategy is used to predict the most promising candidates for future modifications that show the highest potential for an increased virus yield in a combinatorial study. As expected, there is a trend to higher yields the more modifications are included.

In the present work, we use a sophisticated simulation-based methodology to account for the impact of genetic modifications in producer cell lines on the yield of biomanufacturing processes. Furthermore, our approach opens the possibility to predict the most promising genetic modifications instead of identifying them in costly and time-consuming screening experiments. As an example, we apply our methodology to cell culture-based influenza vaccine production, a process that is of tremendous importance for the maintenance of public health. Here, we consider cell lines in which genes coding for one or more cellular factors are up-regulated by genetic engineering to increase the virus yield. However, the gene editing procedure increases the heterogeneity in the producer cell population because genetic modifications do not occur equally in each cell. This cell-to-cell variability is taken into account in a population balance modeling framework, thus providing a more accurate prediction of the virus yield in the heterogeneous population. Finally, we use our approach and a concise experimental data set from cell lines with one gene modification to predict the virus yield of cell lines with multiple genetic modifications. Thereby, we facilitate the experimental screening of potential candidates. We suggest that this methodology is transferable to a wide range of biomanufacturing processes and constitutes a valuable contribution to experimental design.

Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.

A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations

Multicellular systems play an important role in many biotechnological processes. Typically, these exhibit cell-to-cell variability, which has to be monitored closely for process control and optimization. However, some properties may not be measurable due to technical and financial restrictions. To improve the monitoring, model-based online estimators can be designed for their reconstruction. The multicellular dynamics is accounted for in the framework of population balance models (PBMs). These models are based on single cell kinetics, and each cellular state translates directly into an additional dimension of the obtained partial differential equations. As multicellular dynamics often require detailed single cell models and feature a high number of cellular components, the resulting population balance equations are often high-dimensional. Therefore, established state estimation concepts for PBMs based on discrete grids are not recommended due to the large computational effort. In this contribution a novel approach is proposed, which is based on the approximation of the underlying number density functions as the weighted sum of Gaussian distributions. Thus, the distribution is described by the characteristic properties of the individual Gaussians, like the mean and covariance. Thereby, the complex infinite dimensional estimation problem can be reduced to a finite dimension. The characteristic properties are estimated in a recursive approach. The method is evaluated for two academic benchmark examples, and the results indicate its potential for model-based online reconstruction for multicellular systems.