The N-linked glycosylation pattern is an important quality attribute of therapeutic glycoproteins. It has been reported by our group and by others that different carbon sources, such as glucose, mannose and galactose, can differently impact the glycosylation profile of glycoproteins in mammalian cell culture. Acting on the sugar feeding is thus an attractive strategy to tune the glycan pattern. However, in case of feeding of more than one carbon source simultaneously, the cells give priority to the one with the highest uptake rate, which limits the usage of this tuning, e.g. the cells favor consuming glucose in comparison to galactose. We present here a new feeding strategy (named ‘TAFE’ for targeted feeding) for perfusion culture to adjust the concentrations of fed sugars influencing the glycosylation. The strategy consists in setting the sugar feeding such that the cells are forced to consume these substrates at a target cell specific consumption rate decided by the operator and taking into account the cell specific perfusion rate (CSPR). This strategy is applied in perfusion cultures of Chinese hamster ovary (CHO) cells, illustrated by ten different regimes of sugar feeding, including glucose, galactose and mannose. Applying the TAFE strategy, different glycan profiles were obtained using the different feeding regimes. Furthermore, we successfully forced the cells to consume higher proportions of non-glucose sugars, which have lower transport rates than glucose in presence of this latter, in a controlled way. In previous work, a mathematical model named Glycan Residues Balance Analysis (GReBA) was developed to model the glycosylation profile based on the fed carbon sources. The present data were applied to the GReBA to design a feeding regime targeting a given glycosylation profile. The ability of the model to achieve this objective was confirmed by a multi-round of leave-one-out cross-validation (LOOCV), leading to the conclusion that the GReBA model can be used to design the feeding regime of a perfusion cell culture to obtain a desired glycosylation profile.

Glycosylation is a critical quality attribute of therapeutic monoclonal antibodies (mAbs). The glycan pattern can have a large impact on the immunological functions, serum half-life and stability. The medium components and cultivation parameters are known to potentially influence the glycosylation profile. Mathematical modelling provides a strategy for rational design and control of the upstream bioprocess. However, the kinetic models usually contain a very large number of unknown parameters, which limit their practical applications. In this article, we consider the metabolic network of N-linked glycosylation as a Bayesian network (BN) and calculate the fluxes of the glycosylation process as joint probability using the culture parameters as inputs. The modelling approach is validated with data of different Chinese hamster ovary cell cultures in pseudo perfusion, perfusion, and fed batch cultures, all showing very good predictive capacities. In cases where a large number of cultivation parameters is available, it is shown here that principal components analysis can efficiently be employed for a dimension reduction of the inputs compared to Pearson correlation analysis and feature importance by decision tree. The present study demonstrates that BN model can be a powerful tool in upstream process and medium development for glycoprotein productions. 

In this paper, we propose an estimation method for heteroscedastic multilinear systems. The system consists of a multilinear map of latent functions and an input-dependent noise process. We assume Gaussian-process priors on the unknowns to embed non-parametric models. This leads to a hierarchical model called heteroscedastic multilinear Gaussian processes which do not admit closed-form posterior and predictive distributions. The model is treated in an empirical Bayes fashion where the hyperparameters are estimated by maximizing the marginal distribution. To achieve that, we use a Monte Carlo expectation maximization method based on a Gibbs sampling algorithm. The predictive inference is also introduced where the mean is used as an approximation of the unknown functions. The performance of the proposed method is illustrated in a simulation study. 

The structure of N-linked glycosylation is a very important quality attribute for therapeutic monoclonal antibodies. Different carbon sources in cell culture media, such as mannose and galactose, have been reported to have different influences on the glycosylation patterns. Accurate prediction and control of the glycosylation profile are important for the process development of mammalian cell cultures. In this study, a mathematical model, that we named Glycan Residues Balance Analysis (GReBA), was developed based on the concept of Elementary Flux Mode (EFM), and used to predict the glycosylation profile for steady state cell cultures. Experiments were carried out in pseudo-perfusion cultivation of antibody producing Chinese Hamster Ovary (CHO) cells with various concentrations and combinations of glucose, mannose and galactose. Cultivation of CHO cells with mannose or the combinations of mannose and galactose resulted in decreased lactate and ammonium production, and more matured glycosylation patterns compared to the cultures with glucose. Furthermore, the growth rate and IgG productivity were similar in all the conditions. When the cells were cultured with galactose alone, lactate was fed as well to be used as complementary carbon source, leading to cell growth rate and IgG productivity comparable to feeding the other sugars. The data of the glycoprofiles were used for training the model, and then to simulate the glycosylation changes with varying the concentrations of mannose and galactose. In this study we showed that the GReBA model had a good predictive capacity of the N-linked glycosylation. The GReBA can be used as a guidance for development of glycoprotein cultivation processes.

In biological systems, nonlinear kinetic relationships between metabolites of interest are modeled for various purposes. Usually, little a priori knowledge is available in such models. Identifying the unknown kinetics is, therefore, a critical step which can be very challenging due to the problems of (i) model selection and (ii) nonlinear parameter estimation. In this paper, we aim to address these problems systematically in a framework based on multilinear Gaussian processes using a family of kernels tailored to typical behaviours of modulation effects such as activation and inhibition or combinations thereof. Using one such process as a model for each modulation effect leads to a much more flexible model than conventional parametric models, e.g., the Monod model. The resulting models of the modulation effects can also be used as a starting point for estimating parametric kinetic models. As each modulation effect is modeled separately, this task is greatly simplified compared to the conventional approach where the parameters in all modulation functions have to be estimated simultaneously. We also show how the type of modulation effect can be selected automatically by way of regularization, thus by-passing the model selection problem. The resulting parameter estimates can be used as initial estimates in the conventional approach where the full model is estimated. Numerical experiments, including fed-batch simulations, are conducted to demonstrate our methods.

In this paper, we propose an unscented Bayes method for hierarchical Gaussian processes. The hierarchical Gaussian process consists of multiple layers of Gaussian process, which leads to intractable marginal likelihood and posterior distributions. Instead of resorting to the traditional sampling approach, we use the unscented transform to compute the intractable quantities in a hierarchical model, which allows us to optimize the hyperparameters using a gradient based approach and to obtain the predictive distributions. We develop the proposed approach to different application scenarios. The performance of the proposed method is validated in two experiments with comparison to the state-of-art methods.

Models rational in the parameters arise frequently in biosystems and other applications. As with all models that are non-linear in the parameters, direct parameter estimation, using e.g. nonlinear least-squares, can become challenging due to the issues of local minima and finding good initial estimates. Here we propose a multi-step least-squares method for a class of nonlinear rational models. The proposed method is applied to an extended Monod-type model. Numerical simulations indicate that the proposed method is consistent.