Extensions of ℓ1 regularization increase detection specificity for cell-type specific parameters in dynamic models

Uncovering specific mechanisms across cell types in dynamical models

Ordinary differential equations are frequently employed for mathematical modeling of biological systems. The identification of mechanisms that are specific to certain cell types is crucial for building useful models and to gain insights into the underlying biological processes. Regularization techniques have been proposed and applied to identify mechanisms specific to two cell types, e.g., healthy and cancer cells, including the LASSO (least absolute shrinkage and selection operator). However, when analyzing more than two cell types, these approaches are not consistent, and require the selection of a reference cell type, which can affect the results. To make the regularization approach applicable to identifying cell-type specific mechanisms in any number of cell types, we propose to incorporate the clustered LASSO into the framework of ordinary differential equation modeling by penalizing the pairwise differences of the logarithmized fold-change parameters encoding a specific mechanism in different cell types. The symmetry introduced by this approach renders the results independent of the reference cell type. We discuss the necessary adaptations of state-of-the-art numerical optimization techniques and the process of model selection for this method. We assess the performance with realistic biological models and synthetic data, and demonstrate that it outperforms existing approaches. Finally, we also exemplify its application to published biological models including experimental data, and link the results to independent biological measurements.

Elucidating yeast glycolytic dynamics at steady state growth and glucose pulses through kinetic metabolic modeling

Microbial cell factories face changing environments during industrial fermentations. Kinetic metabolic models enable the simulation of the dynamic metabolic response to these perturbations, but their development is challenging due to model complexity and experimental data requirements. An example of this is the well-established microbial cell factory Saccharomyces cerevisiae, for which no consensus kinetic model of central metabolism has been developed and implemented in industry. Here, we aim to bring the academic and industrial communities closer to this consensus model. We developed a physiology informed kinetic model of yeast glycolysis connected to central carbon metabolism by including the effect of anabolic reactions precursors, mitochondria and the trehalose cycle. To parametrize such a large model, a parameter estimation pipeline was developed, consisting of a divide and conquer approach, supplemented with regularization and global optimization. Additionally, we show how this first mechanistic description of a growing yeast cell captures experimental dynamics at different growth rates and under a strong glucose perturbation, is robust to parametric uncertainty and explains the contribution of the different pathways in the network. Such a comprehensive model could not have been developed without using steady state and glucose perturbation data sets. The resulting metabolic reconstruction and parameter estimation pipeline can be applied in the future to study other industrially-relevant scenarios. We show this by generating a hybrid CFD-metabolic model to explore intracellular glycolytic dynamics for the first time. The model suggests that all intracellular metabolites oscillate within a physiological range, except carbon storage metabolism, which is sensitive to the extracellular environment.

Using Kinetic Modelling to Infer Adaptations in Saccharomyces cerevisiae Carbohydrate Storage Metabolism to Dynamic Substrate Conditions

Microbial metabolism is strongly dependent on the environmental conditions. While these can be well controlled under laboratory conditions, large-scale bioreactors are characterized by inhomogeneities and consequently dynamic conditions for the organisms. How Saccharomyces cerevisiae response to frequent perturbations in industrial bioreactors is still not understood mechanistically. To study the adjustments to prolonged dynamic conditions, we used published repeated substrate perturbation regime experimental data, extended it with proteomic measurements and used both for modelling approaches. Multiple types of data were combined; including quantitative metabolome, ¹³C enrichment and flux quantification data. Kinetic metabolic modelling was applied to study the relevant intracellular metabolic response dynamics. An existing model of yeast central carbon metabolism was extended, and different subsets of enzymatic kinetic constants were estimated. A novel parameter estimation pipeline based on combinatorial enzyme selection supplemented by regularization was developed to identify and predict the minimum enzyme and parameter adjustments from steady-state to dynamic substrate conditions. This approach predicted proteomic changes in hexose transport and phosphorylation reactions, which were additionally confirmed by proteome measurements. Nevertheless, the modelling also hints at a yet unknown kinetic or regulation phenomenon. Some intracellular fluxes could not be reproduced by mechanistic rate laws, including hexose transport and intracellular trehalase activity during substrate perturbation cycles.

Disentangling ERBB Signaling in Breast Cancer Subtypes-A Model-Based Analysis

Targeted therapies have shown striking success in the treatment of cancer over the last years. However, their specific effects on an individual tumor appear to be varying and difficult to predict. Using an integrative modeling approach that combines mechanistic and regression modeling, we gained insights into the response mechanisms of breast cancer cells due to different ligand-drug combinations. The multi-pathway model, capturing ERBB receptor signaling as well as downstream MAPK and PI3K pathways was calibrated on time-resolved data of the luminal breast cancer cell lines MCF7 and T47D across an array of four ligands and five drugs. The same model was then successfully applied to triple negative and HER2-positive breast cancer cell lines, requiring adjustments mostly for the respective receptor compositions within these cell lines. The additional relevance of cell-line-specific mutations in the MAPK and PI3K pathway components was identified via L1 regularization, where the impact of these mutations on pathway activation was uncovered. Finally, we predicted and experimentally validated the proliferation response of cells to drug co-treatments. We developed a unified mathematical model that can describe the ERBB receptor and downstream signaling in response to therapeutic drugs targeting this clinically relevant signaling network in cell line that represent three major subtypes of breast cancer. Our data and model suggest that alterations in this network could render anti-HER therapies relevant beyond the HER2-positive subtype.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

Metabolic Modeling Combined With Machine Learning Integrates Longitudinal Data and Identifies the Origin of LXR-Induced Hepatic Steatosis

Temporal multi-omics data can provide information about the dynamics of disease development and therapeutic response. However, statistical analysis of high-dimensional time-series data is challenging. Here we develop a novel approach to model temporal metabolomic and transcriptomic data by combining machine learning with metabolic models. ADAPT (Analysis of Dynamic Adaptations in Parameter Trajectories) performs metabolic trajectory modeling by introducing time-dependent parameters in differential equation models of metabolic systems. ADAPT translates structural uncertainty in the model, such as missing information about regulation, into a parameter estimation problem that is solved by iterative learning. We have now extended ADAPT to include both metabolic and transcriptomic time-series data by introducing a regularization function in the learning algorithm. The ADAPT learning algorithm was (re)formulated as a multi-objective optimization problem in which the estimation of trajectories of metabolic parameters is constrained by the metabolite data and refined by gene expression data. ADAPT was applied to a model of hepatic lipid and plasma lipoprotein metabolism to predict metabolic adaptations that are induced upon pharmacological treatment of mice by a Liver X receptor (LXR) agonist. We investigated the excessive accumulation of triglycerides (TG) in the liver resulting in the development of hepatic steatosis. ADAPT predicted that hepatic TG accumulation after LXR activation originates for 80% from an increased influx of free fatty acids. The model also correctly estimated that TG was stored in the cytosol rather than transferred to nascent very-low density lipoproteins. Through model-based integration of temporal metabolic and gene expression data we discovered that increased free fatty acid influx instead of de novo lipogenesis is the main driver of LXR-induced hepatic steatosis. This study illustrates how ADAPT provides estimates for biomedically important parameters that cannot be measured directly, explaining (side-)effects of pharmacological treatment with LXR agonists.

Personalized computational model quantifies heterogeneity in postprandial responses to oral glucose challenge

Plasma glucose and insulin responses following an oral glucose challenge are representative of glucose tolerance and insulin resistance, key indicators of type 2 diabetes mellitus pathophysiology. A large heterogeneity in individuals' challenge test responses has been shown to underlie the effectiveness of lifestyle intervention. Currently, this heterogeneity is overlooked due to a lack of methods to quantify the interconnected dynamics in the glucose and insulin time-courses. Here, a physiology-based mathematical model of the human glucose-insulin system is personalized to elucidate the heterogeneity in individuals' responses using a large population of overweight/obese individuals (n = 738) from the DIOGenes study. The personalized models are derived from population level models through a systematic parameter selection pipeline that may be generalized to other biological systems. The resulting personalized models showed a 4-5 fold decrease in discrepancy between measurements and model simulation compared to population level. The estimated model parameters capture relevant features of individuals' metabolic health such as gastric emptying, endogenous insulin secretion and insulin dependent glucose disposal into tissues, with the latter also showing a significant association with the Insulinogenic index and the Matsuda insulin sensitivity index, respectively.