Hybrid deep modeling of a CHO-K1 fed-batch process: combining first-principles with deep neural networks.

Introduction: Hybrid modeling combining First-Principles with machine learning is becoming a pivotal methodology for Biopharma 4.0 enactment. Chinese Hamster Ovary (CHO) cells, being the workhorse for industrial glycoproteins production, have been the object of several hybrid modeling studies. Most previous studies pursued a shallow hybrid modeling approach based on three-layered Feedforward Neural Networks (FFNNs) combined with macroscopic material balance equations. Only recently, the hybrid modeling field is incorporating deep learning into its framework with significant gains in descriptive and predictive power. Methods: This study compares, for the first time, deep and shallow hybrid modeling in a CHO process development context. Data of 24 fed-batch cultivations of a CHO-K1 cell line expressing a target glycoprotein, comprising 30 measured state variables over time, were used to compare both methodologies. Hybrid models with varying FFNN depths (3-5 layers) were systematically compared using two training methodologies. The classical training is based on the Levenberg-Marquardt algorithm, indirect sensitivity equations and cross-validation. The deep learning is based on the Adaptive Moment Estimation Method (ADAM), stochastic regularization and semidirect sensitivity equations. Results and conclusion: The results point to a systematic generalization improvement of deep hybrid models over shallow hybrid models. Overall, the training and testing errors decreased by 14.0% and 23.6% respectively when applying the deep methodology. The Central Processing Unit (CPU) time for training the deep hybrid model increased by 31.6% mainly due to the higher FFNN complexity. The final deep hybrid model is shown to predict the dynamics of the 30 state variables within the error bounds in every test experiment. Notably, the deep hybrid model could predict the metabolic shifts in key metabolites (e.g., lactate, ammonium, glutamine and glutamate) in the test experiments. We expect deep hybrid modeling to accelerate the deployment of high-fidelity digital twins in the biopharma sector in the near future.

Stimulation of cholesterol biosynthesis in mitochondrial complex I-deficiency lowers reductive stress and improves motor function and survival in mice.

The majority of cellular energy is produced by the mitochondrial oxidative phosphorylation (OXPHOS) system. Failure of the first OXPHOS enzyme complex, NADH:ubiquinone oxidoreductase or complex I (CI), is associated with multiple signs and symptoms presenting at variable ages of onset. There is no approved drug treatment yet to slow or reverse the progression of CI-deficient disorders. Here, we present a comprehensive human metabolic network model of genetically characterized CI-deficient patient-derived fibroblasts. Model calculations predicted that increased cholesterol production, export, and utilization can counterbalance the surplus of reducing equivalents in patient-derived fibroblasts, as these pathways consume considerable amounts of NAD(P)H. We show that fibrates attenuated increased NAD(P)H levels and improved CI-deficient fibroblast growth by stimulating the production of cholesterol via enhancement of its cellular efflux. In CI-deficient (Ndufs4-/-) mice, fibrate treatment resulted in prolonged survival and improved motor function, which was accompanied by an increased cholesterol efflux from peritoneal macrophages. Our results shine a new light on the use of compensatory biological pathways in mitochondrial dysfunction, which may lead to novel therapeutic interventions for mitochondrial diseases for which currently no cure exists.

Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm.

MOTIVATION: Genome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental "omics" data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more "flexible" metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions. RESULTS: Here, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information. AVAILABILITY: MMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.

Identification of potential drug targets in Salmonella enterica sv. Typhimurium using metabolic modelling and experimental validation.

Salmonella enterica sv. Typhimurium is an established model organism for Gram-negative, intracellular pathogens. Owing to the rapid spread of resistance to antibiotics among this group of pathogens, new approaches to identify suitable target proteins are required. Based on the genome sequence of S. Typhimurium and associated databases, a genome-scale metabolic model was constructed. Output was based on an experimental determination of the biomass of Salmonella when growing in glucose minimal medium. Linear programming was used to simulate variations in the energy demand while growing in glucose minimal medium. By grouping reactions with similar flux responses, a subnetwork of 34 reactions responding to this variation was identified (the catabolic core). This network was used to identify sets of one and two reactions that when removed from the genome-scale model interfered with energy and biomass generation. Eleven such sets were found to be essential for the production of biomass precursors. Experimental investigation of seven of these showed that knockouts of the associated genes resulted in attenuated growth for four pairs of reactions, whilst three single reactions were shown to be essential for growth.

Inferring metabolic states in uncharacterized environments using gene-expression measurements.

The large size of metabolic networks entails an overwhelming multiplicity in the possible steady-state flux distributions that are compatible with stoichiometric constraints. This space of possibilities is largest in the frequent situation where the nutrients available to the cells are unknown. These two factors: network size and lack of knowledge of nutrient availability, challenge the identification of the actual metabolic state of living cells among the myriad possibilities. Here we address this challenge by developing a method that integrates gene-expression measurements with genome-scale models of metabolism as a means of inferring metabolic states. Our method explores the space of alternative flux distributions that maximize the agreement between gene expression and metabolic fluxes, and thereby identifies reactions that are likely to be active in the culture from which the gene-expression measurements were taken. These active reactions are used to build environment-specific metabolic models and to predict actual metabolic states. We applied our method to model the metabolic states of Saccharomyces cerevisiae growing in rich media supplemented with either glucose or ethanol as the main energy source. The resulting models comprise about 50% of the reactions in the original model, and predict environment-specific essential genes with high sensitivity. By minimizing the sum of fluxes while forcing our predicted active reactions to carry flux, we predicted the metabolic states of these yeast cultures that are in large agreement with what is known about yeast physiology. Most notably, our method predicts the Crabtree effect in yeast cells growing in excess glucose, a long-known phenomenon that could not have been predicted by traditional constraint-based modeling approaches. Our method is of immediate practical relevance for medical and industrial applications, such as the identification of novel drug targets, and the development of biotechnological processes that use complex, largely uncharacterized media, such as biofuel production.

Quantitative analysis of flux regulation through hierarchical regulation analysis.

Regulation analysis is a methodology that quantifies to what extent a change in the flux through a metabolic pathway is regulated by either gene expression or metabolism. Two extensions to regulation analysis were developed over the past years: (i) the regulation of V(max) can be dissected into the various levels of the gene-expression cascade, such as transcription, translation, protein degradation, etc. and (ii) a time-dependent version allows following flux regulation when cells adapt to changes in their environment. The methodology of the original form of regulation analysis as well as of the two extensions will be described in detail. In addition, we will show what is needed to apply regulation analysis in practice. Studies in which the different versions of regulation analysis were applied revealed that flux regulation was distributed over various processes and depended on time, enzyme, and condition of interest. In the case of the regulation of glycolysis in baker's yeast, it appeared, however, that cells that remain under respirofermentative conditions during a physiological challenge tend to invoke more gene-expression regulation, while a shift between respirofermentative and respiratory conditions invokes an important contribution of metabolic regulation. The complexity of the regulation observed in these studies raises the question what is the advantage of this highly distributed and condition-dependent flux regulation.

Towards a quantitative prediction of the fluxome from the proteome.

The promise of proteomics and fluxomics is limited by our current inability to integrate these two levels of cellular organization. Here we present the derivation, experimental parameterization, and appraisal of flux functions that enable the quantitative prediction of changes in metabolic fluxes from changes in enzyme levels. We based our derivation on the hypothesis that, in the determination of steady-state flux changes, the direct proportionality between enzyme concentrations and reaction rates is principal, whereas the complexity of enzyme-metabolite interactions is secondary and can be described using an approximate kinetic format. The quality of the agreement between predicted and experimental fluxes in Lactococcus lactis, supports our hypothesis and demonstrates the need and usefulness of approximative descriptions in the study of complex biological systems. Importantly, these flux functions are scalable to genome-wide networks, and thus drastically expand the capabilities of flux prediction for metabolic engineering efforts beyond those conferred by the currently used constraints-based models.

Effect of hxk2 deletion and HAP4 overexpression on fermentative capacity in Saccharomyces cerevisiae.

To describe the fermentative potential of a yeast cell, the fermentative capacity (FC) has been defined as the specific rate of ethanol and CO2 production under anaerobic conditions. The effect of growth rate on FC of glucose-limited grown Saccharomyces cerevisiae strains with altered expression of two major glycolytic regulators, Hap4p and Hxk2p, was compared with their parent strain. Whereas overproduction of Hap4p behaved similar to the wild-type strain, deletion of hxk2 resulted in a very different FC profile. Most importantly, with maltose as the carbon and energy source, the latter strain expressed an FC twofold that of the wild type. Further analysis at the level of gene expression showed large changes in ADH2 transcripts and to a lesser extent in hexose transporters and genes involved in the glyoxylate cycle. With respect to primary glucose metabolism, a shift in the type of hexose transport to one with high affinity was induced. In accordance with the phenotype of the mutant strain, the maltose transporter was constitutively expressed under glucose-limited conditions and synthesis increased in the presence of maltose.

Mixed and diverse metabolic and gene-expression regulation of the glycolytic and fermentative pathways in response to a HXK2 deletion in Saccharomyces cerevisiae.

In Saccharomyces cerevisiae the HXK2 gene, which encodes the glycolytic enzyme hexokinase II, is involved in the regulatory mechanism known as 'glucose repression'. Its deletion leads to fully respiratory growth at high glucose concentrations where the wild type ferments profusely. Here we describe that deletion of the HXK2 gene resulted in a 75% reduction in fermentative capacity. Using regulation analysis we found that the fluxes through most glycolytic and fermentative enzymes were regulated cooperatively by changes in their capacities (Vmax) and by changes in the way they interacted with the rest of the metabolism. Glucose transport and phosphofructokinase were regulated purely at the metabolic level. The reduction of fermentative capacity in the mutant was accompanied by a remarkable resilience of the remaining capacity to nutrient starvation. After starvation, the fermentative capacity of the hxk2Delta mutant was similar to that of the wild type. Based on our results and previous reports, we suggest an inverse correlation between glucose repression and the resilience of fermentative capacity towards nutrient starvation. Only a limited number of glycolytic enzyme activities changed upon starvation of the hxk2Delta mutant and we discuss to what extent this could explain the stability of the fermentative capacity.

The fluxes through glycolytic enzymes in Saccharomyces cerevisiae are predominantly regulated at posttranscriptional levels.

Metabolic fluxes may be regulated "hierarchically," e.g., by changes of gene expression that adjust enzyme capacities (V(max)) and/or "metabolically" by interactions of enzymes with substrates, products, or allosteric effectors. In the present study, a method is developed to dissect the hierarchical regulation into contributions by transcription, translation, protein degradation, and posttranslational modification. The method was applied to the regulation of fluxes through individual glycolytic enzymes when the yeast Saccharomyces cerevisiae was confronted with the absence of oxygen and the presence of benzoic acid depleting its ATP. Metabolic regulation largely contributed to the approximately 10-fold change in flux through the glycolytic enzymes. This contribution varied from 50 to 80%, depending on the glycolytic step and the cultivation condition tested. Within the 50-20% hierarchical regulation of fluxes, transcription played a minor role, whereas regulation of protein synthesis or degradation was the most important. These also contributed to 75-100% of the regulation of protein levels.

Unraveling the complexity of flux regulation: a new method demonstrated for nutrient starvation in Saccharomyces cerevisiae.

An important question is to what extent metabolic fluxes are regulated by gene expression or by metabolic regulation. There are two distinct aspects to this question: (i) the local regulation of the fluxes through the individual steps in the pathway and (ii) the influence of such local regulation on the pathway's flux. We developed regulation analysis so as to address the former aspect for all steps in a pathway. We demonstrate the method for the issue of how Saccharomyces cerevisiae regulates the fluxes through its individual glycolytic and fermentative enzymes when confronted with nutrient starvation. Regulation was dissected quantitatively into (i) changes in maximum enzyme activity (Vmax, called hierarchical regulation) and (ii) changes in the interaction of the enzyme with the rest of metabolism (called metabolic regulation). Within a single pathway, the regulation of the fluxes through individual steps varied from fully hierarchical to exclusively metabolic. Existing paradigms of flux regulation (such as single- and multisite modulation and exclusively metabolic regulation) were tested for a complete pathway and falsified for a major pathway in an important model organism. We propose a subtler mechanism of flux regulation, with different roles for different enzymes, i.e., "leader," "follower," or "conservative," the latter attempting to hold back the change in flux. This study makes this subtlety, so typical for biological systems, tractable experimentally and invites reformulation of the questions concerning the drives and constraints governing metabolic flux regulation.

Hierarchical and metabolic regulation of glucose influx in starved Saccharomyces cerevisiae.

A novel method dissecting the regulation of a cellular function into direct metabolic regulation and hierarchical (e.g., gene-expression) regulation is applied to yeast starved for nitrogen or carbon. Upon nitrogen starvation glucose influx is down-regulated hierarchically. Upon carbon starvation it is down-regulated both metabolically and hierarchically. The method is expounded in terms of its implications for diverse types of regulation. It is also fine-tuned for cases where isoenzymes catalyze the flux through a single metabolic step.

One-second time resolution brain microdialysis in fully awake rats. Protocol for the collection, separation and sorting of nanoliter dialysate volumes.

Capillary zone electrophoresis is capable of analyzing nanoliter volumes, reducing the challenge posed by brain microdialysis time resolution improvement to the management of nanoliter dialysate volumes. This fact has not been overlooked and 12- and 6-s time resolution microdialysis have been reported in anesthetized rats. However, behavioral experiments require fully awake and freely moving animals. To achieve high temporal resolution brain microdialysis in awake unrestrained rats, we have developed an online device that mixes the outflowing dialysate with fluorescein isothiocyanate and buffer within a 26-nl reactor. The mixture was continuously accumulated in a 99-micrometer-bore capillary tube. After the experiment the tube was cut into 4-mm pieces and the content of each piece (30 nl, equivalent to 1 s dialysate) was transferred to a test tube. After allowing 18 h for derivatization, the samples were diluted with water and injected into a capillary electrophoresis laser-induced fluorescence detection instrument. This protocol was tested first in an in vitro assay and proved to be capable of detecting glutamate concentration changes in only 1 s. For the in vivo assays, a probe was inserted into the primary somatosensory cortex of eight rats divided in two groups. One group was stimulated by gently moving its whiskers for 10 s. The other group had no whisker manipulation. Moving the whiskers released glutamate in the experimental group. The first and only change was observed at the 12th s. This method allows 1-s time resolution brain microdialysis in freely moving rats and multiple amino acid analysis every second during sensory perception or motor actions in behavioral experiments.

Loss of fermentative capacity in baker's yeast can partly be explained by reduced glucose uptake capacity.

Initial attempts to increase fermentative capacity of baker's yeast focussed on the overproduction of single enzymes, which proved to be insufficient. Nowadays many components of the system are monitored simultaneously in a search for a correlation with fermentative capacity. However, this strategy has not yet proven fruitful either. Here we investigate an element previously neglected, the glucose transporter, and find that a loss of glucose transport capacity correlates with a decrease of fermentative capacity during nutrient starvation. However the correlation is not unique, suggesting that the loss of fermentative capacity cannot be attributed to an inactivation of glucose transport alone. Our results suggest the necessity to use a detailed kinetic model as an underlying working hypothesis and to use Metabolic Control Analysis to examine the pathway's control properties.

Haloperidol abolished glutamate release evoked by photic stimulation of the visual cortex in rats.

There is evidence that systemic administration of haloperidol, a dopamine receptor blocker, attenuates visual cortex evoked potentials. However, there is scarce information on cortical neurochemical changes associated with haloperidol effects on visual function. The present experiment was designed to investigate: (1) the effect of photic stimulation on glutamate release in the visual cortex; and (2) whether systemic administration of haloperidol would affect those neurochemical changes. Microdialysis probes were implanted in the occipital cortex. Glutamate levels were measured every 30 s using capillary zone electrophoresis. Extracellular glutamate levels increased to about 282% 30 s after photic stimulation started and remain elevated for the 3 min that the photic stimulation lasted. Haloperidol (1.5 and 5 mg/kg, i.p.) completely suppressed the increased of glutamate efflux during photic stimulation. Finally, it was also found that the highest dose of haloperidol (5 mg/kg) did not change glutamate basal levels. The results are discussed with reference to possible dopaminergic actions on the visual system function.