The best models of metabolism

Mathematical Modeling of Non-Small-Cell Lung Cancer Biology through the Experimental Data on Cell Composition and Growth of Patient-Derived Organoids

Mathematical models of non-small-cell lung cancer are powerful tools that use clinical and experimental data to describe various aspects of tumorigenesis. The developed algorithms capture phenotypic changes in the tumor and predict changes in tumor behavior, drug resistance, and clinical outcomes of anti-cancer therapy. The aim of this study was to propose a mathematical model that predicts the changes in the cellular composition of patient-derived tumor organoids over time with a perspective of translation of these results to the parental tumor, and therefore to possible clinical course and outcomes for the patient. Using the data on specific biomarkers of cancer cells (PD-L1), tumor-associated macrophages (CD206), natural killer cells (CD8), and fibroblasts (αSMA) as input, we proposed a model that accurately predicts the cellular composition of patient-derived tumor organoids at a desired time point. Combining the obtained results with "omics" approaches will improve our understanding of the nature of non-small-cell lung cancer. Moreover, their implementation into clinical practice will facilitate a decision-making process on treatment strategy and develop a new personalized approach in anti-cancer therapy.

Hepatic cholesterol biosynthesis and dioxin-induced dysregulation: A multiscale computational approach

Humans are constantly exposed to lipophilic persistent organic pollutants (POPs) that accumulate in fatty foods. Among the numerous POPs, dioxins, in particular 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), can impact several organ systems. While the hazard is clearly recognized, it is still difficult to develop a comprehensive understanding of the overall health impacts of dioxins. As chemical toxicity testing is steadily adopting new approach methodologies (NAMs), it becomes imperative to develop computational models that can bridge the data gaps between in vitro testing and in vivo outcomes. As an effort to address this challenge, we propose a multiscale computational approach using a "template-and-anchor" (T&A) structure. A template is a high-level umbrella model that permits the integration of information from various, detailed anchor models. In the present study, we use this T&A approach to describe the effect of TCDD on cholesterol dynamics. Specifically, we represent hepatic cholesterol biosynthesis as an anchor model that is perturbed by TCDD, leading to steatosis, along with alterations of plasma cholesterol. In the future, incorporating pertinent information from all anchor models into the template model will allow the characterization of the global effects of dioxin, which can subsequently be translated into overall - and ultimately personalized - human health risk assessment.

A dynamic compartment model for xylem loading and long-distance transport of iron explains the effect of kanamycin on metal uptake in Arabidopsis

Arabidopsis plants exposed to the antibiotic kanamycin (Kan) display altered metal homeostasis. Further, mutation of the WBC19 gene leads to increased sensitivity to kanamycin and changes in iron (Fe) and zinc (Zn) uptake. Here we propose a model that explain this surprising relationship between metal uptake and exposure to Kan. We first use knowledge about the metal uptake phenomenon to devise a transport and interaction diagram on which we base the construction of a dynamic compartment model. The model has three pathways for loading Fe and its chelators into the xylem. One pathway, involving an unknown transporter, loads Fe as a chelate with citrate (Ci) into the xylem. This transport step can be significantly inhibited by Kan. In parallel, FRD3 transports Ci into the xylem where it can chelate with free Fe. A third critical pathway involves WBC19, which transports metal-nicotianamine (NA), mainly as Fe-NA chelate, and possibly NA itself. To permit quantitative exploration and analysis, we use experimental time series data to parameterize this explanatory and predictive model. Its numerical analysis allows us to predict responses by a double mutant and explain the observed differences between data from wildtype, mutants and Kan inhibition experiments. Importantly, the model provides novel insights into metal homeostasis by permitting the reverse-engineering of mechanistic strategies with which the plant counteracts the effects of mutations and of the inhibition of iron transport by kanamycin.

Discrete Biochemical Systems Theory

Almost every biomedical systems analysis requires early decisions regarding the choice of the most suitable representations to be used. De facto the most prevalent choice is a system of ordinary differential equations (ODEs). This framework is very popular because it is flexible and fairly easy to use. It is also supported by an enormous array of stand-alone programs for analysis, including many distinct numerical solvers that are implemented in the main programming languages. Having selected ODEs, the modeler must then choose a mathematical format for the equations. This selection is not trivial as nearly unlimited options exist and there is seldom objective guidance. The typical choices include ad hoc representations, default models like mass-action or Lotka-Volterra equations, and generic approximations. Within the realm of approximations, linear models are typically successful for analyses of engineered systems, but they are not as appropriate for biomedical phenomena, which often display nonlinear features such as saturation, threshold effects or limit cycle oscillations, and possibly even chaos. Power-law approximations are simple but overcome these limitations. They are the key ingredient of Biochemical Systems Theory (BST), which uses ODEs exclusively containing power-law representations for all processes within a model. BST models cover a vast repertoire of nonlinear responses and, at the same time, have structural properties that are advantageous for a wide range of analyses. Nonetheless, as all ODE models, the BST approach has limitations. In particular, it is not always straightforward to account for genuine discreteness, time delays, and stochastic processes. As a new option, we therefore propose here an alternative to BST in the form of discrete Biochemical Systems Theory (dBST). dBST models have the same generality and practicality as their BST-ODE counterparts, but they are readily implemented even in situations where ODEs struggle. As a case study, we illustrate dBST applied to the dynamics of the aryl hydrocarbon receptor (AhR), a signal transduction system that simultaneously involves time delays and stochasticity.

Queueing theory model of pentose phosphate pathway

Due to its role in maintaining the proper functioning of the cell, the pentose phosphate pathway (PPP) is one of the most important metabolic pathways. It is responsible for regulating the concentration of simple sugars and provides precursors for the synthesis of amino acids and nucleotides. In addition, it plays a critical role in maintaining an adequate level of NADPH, which is necessary for the cell to fight oxidative stress. These reasons prompted the authors to develop a computational model, based on queueing theory, capable of simulating changes in PPP metabolites’ concentrations. The model has been validated with empirical data from tumor cells. The obtained results prove the stability and accuracy of the model. By applying queueing theory, this model can be further expanded to include successive metabolic pathways. The use of the model may accelerate research on new drugs, reduce drug costs, and reduce the reliance on laboratory animals necessary for this type of research on which new methods are tested.

Queueing theory model of Krebs cycle

MOTIVATION

Queueing theory can be effective in simulating biochemical reactions taking place in living cells, and the article paves a step toward development of a comprehensive model of cell metabolism. Such a model could help to accelerate and reduce costs for developing and testing investigational drugs reducing number of laboratory animals needed to evaluate drugs.

RESULTS

The article presents a Krebs cycle model based on queueing theory. The model allows for tracking of metabolites concentration changes in real time. To validate the model, a drug-induced inhibition affecting activity of enzymes involved in Krebs cycle was simulated and compared with available experimental data.

AVAILABILITYAND IMPLEMENTATION

The source code is freely available for download at https://github.com/UTP-WTIiE/KrebsCycleUsingQueueingTheory, implemented in C# supported in Linux or MS Windows.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A model of dopamine and serotonin-kynurenine metabolism in cortisolemia: Implications for depression

A major factor contributing to the etiology of depression is a neurochemical imbalance of the dopaminergic and serotonergic systems, which is caused by persistently high levels of circulating stress hormones. Here, a computational model is proposed to investigate the interplay between dopaminergic and serotonergic-kynurenine metabolism under cortisolemia and its consequences for the onset of depression. The model was formulated as a set of nonlinear ordinary differential equations represented with power-law functions. Parameter values were obtained from experimental data reported in the literature, biological databases, and other general information, and subsequently fine-tuned through optimization. Model simulations predict that changes in the kynurenine pathway, caused by elevated levels of cortisol, can increase the risk of neurotoxicity and lead to increased levels of 3,4-dihydroxyphenylaceltahyde (DOPAL) and 5-hydroxyindoleacetaldehyde (5-HIAL). These aldehydes contribute to alpha-synuclein aggregation and may cause mitochondrial fragmentation. Further model analysis demonstrated that the inhibition of both serotonin transport and kynurenine-3-monooxygenase decreased the levels of DOPAL and 5-HIAL and the neurotoxic risk often associated with depression. The mathematical model was also able to predict a novel role of the dopamine and serotonin metabolites DOPAL and 5-HIAL in the ethiology of depression, which is facilitated through increased cortisol levels. Finally, the model analysis suggests treatment with a combination of inhibitors of serotonin transport and kynurenine-3-monooxygenase as a potentially effective pharmacological strategy to revert the slow-down in monoamine neurotransmission that is often triggered by inflammation.

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

A multistationary loop model of ALS unveils critical molecular interactions involving mitochondria and glucose metabolism

Amyotrophic lateral sclerosis (ALS) is a poor-prognosis disease with puzzling pathogenesis and inconclusive treatments. We develop a mathematical model of ALS based on a system of interactive feedback loops, focusing on the mutant SOD1G93A mouse. Misfolded mutant SOD1 aggregates in motor neuron (MN) mitochondria and triggers a first loop characterized by oxidative phosphorylation impairment, AMP kinase over-activation, 6-phosphofructo-2-kinase (PFK3) rise, glucose metabolism shift from pentose phosphate pathway (PPP) to glycolysis, cell redox unbalance, and further worsening of mitochondrial dysfunction. Oxidative stress then triggers a second loop, involving the excitotoxic glutamatergic cascade, with cytosolic Ca2+ overload, increase of PFK3 expression, and further metabolic shift from PPP to glycolysis. Finally, cytosolic Ca2+ rise is also detrimental to mitochondria and oxidative phosphorylation, thus closing a third loop. These three loops are overlapped and positive (including an even number of inhibitory steps), hence they form a candidate multistationary (bistable) system. To describe the system dynamics, we model the interactions among the functional agents with differential equations. The system turns out to admit two stable equilibria: the healthy state, with high oxidative phosphorylation and preferential PPP, and the pathological state, with AMP kinase activation, PFK3 over expression, oxidative stress, excitotoxicity and MN degeneration. We demonstrate that the loop system is monotone: all functional agents consistently act toward the healthy or pathological condition, depending on low or high mutant SOD1 input. We also highlight that molecular interactions involving PFK3 are crucial, as their deletion disrupts the system's bistability leading to a single healthy equilibrium point. Hence, our mathematical model unveils that promising ALS management strategies should be targeted to mechanisms that keep low PFK3 expression and activity within MNs.

Biotransformation of 2,4-dinitrotoluene in a phototrophic co-culture of engineered Synechococcus elongatus and Pseudomonas putida

In contrast to the current paradigm of using microbial mono-cultures in most biotechnological applications, increasing efforts are being directed towards engineering mixed-species consortia to perform functions that are difficult to programme into individual strains. In this work, we developed a synthetic microbial consortium composed of two genetically engineered microbes, a cyanobacterium (Synechococcus elongatus PCC 7942) and a heterotrophic bacterium (Pseudomonas putida EM173). These microbial species specialize in the co-culture: cyanobacteria fix CO2 through photosynthetic metabolism and secrete sufficient carbohydrates to support the growth and active metabolism of P. putida, which has been engineered to consume sucrose and to degrade the environmental pollutant 2,4-dinitrotoluene (2,4-DNT). By encapsulating S. elongatus within a barium-alginate hydrogel, cyanobacterial cells were protected from the toxic effects of 2,4-DNT, enhancing the performance of the co-culture. The synthetic consortium was able to convert 2,4-DNT with light and CO2 as key inputs, and its catalytic performance was stable over time. Furthermore, cycling this synthetic consortium through low nitrogen medium promoted the sucrose-dependent accumulation of polyhydroxyalkanoate, an added-value biopolymer, in the engineered P. putida strain. Altogether, the synthetic consortium displayed the capacity to remediate the industrial pollutant 2,4-DNT while simultaneously synthesizing biopolymers using light and CO2 as the primary inputs.

Systematic Multi-Omics Integration (MOI) Approach in Plant Systems Biology

Across all facets of biology, the rapid progress in high-throughput data generation has enabled us to perform multi-omics systems biology research. Transcriptomics, proteomics, and metabolomics data can answer targeted biological questions regarding the expression of transcripts, proteins, and metabolites, independently, but a systematic multi-omics integration (MOI) can comprehensively assimilate, annotate, and model these large data sets. Previous MOI studies and reviews have detailed its usage and practicality on various organisms including human, animals, microbes, and plants. Plants are especially challenging due to large poorly annotated genomes, multi-organelles, and diverse secondary metabolites. Hence, constructive and methodological guidelines on how to perform MOI for plants are needed, particularly for researchers newly embarking on this topic. In this review, we thoroughly classify multi-omics studies on plants and verify workflows to ensure successful omics integration with accurate data representation. We also propose three levels of MOI, namely element-based (level 1), pathway-based (level 2), and mathematical-based integration (level 3). These MOI levels are described in relation to recent publications and tools, to highlight their practicality and function. The drawbacks and limitations of these MOI are also discussed for future improvement toward more amenable strategies in plant systems biology.

Stochastic Simulation of Cellular Metabolism

Increased technological methods have enabled the investigation of biology at nanoscale levels. Such systems require the use of computational methods to comprehend the complex interactions that occur. The dynamics of metabolic systems have been traditionally described utilizing differential equations without fully capturing the heterogeneity of biological systems. Stochastic modeling approaches have recently emerged with the capacity to incorporate the statistical properties of such systems. However, the processing of stochastic algorithms is a computationally intensive task with intrinsic limitations. Alternatively, the queueing theory approach, historically used in the evaluation of telecommunication networks, can significantly reduce the computational power required to generate simulated results while simultaneously reducing the expansion of errors. We present here the application of queueing theory to simulate stochastic metabolic networks with high efficiency. With the use of glycolysis as a well understood biological model, we demonstrate the power of the proposed modeling methods discussed herein. Furthermore, we describe the simulation and pharmacological inhibition of glycolysis to provide an example of modeling capabilities.

Model-based Comparisons of the Abundance Dynamics of Bacterial Communities in Two Lakes

Lake Lanier (Georgia, USA) is home to more than 11,000 microbial Operational Taxonomic Units (OTUs), many of which exhibit clear annual abundance patterns. To assess the dynamics of this microbial community, we collected time series data of 16S and 18S rRNA gene sequences, recovered from 29 planktonic shotgun metagenomic datasets. Based on these data, we constructed a dynamic mathematical model of bacterial interactions in the lake and used it to analyze changes in the abundances of OTUs. The model accounts for interactions among 14 sub-communities (SCs), which are composed of OTUs blooming at the same time of the year, and three environmental factors. It captures the seasonal variations in abundances of the SCs quite well. Simulation results suggest that changes in water temperature affect the various SCs differentially and that the timing of perturbations is critical. We compared the model results with published results from Lake Mendota (Wisconsin, USA). These comparative analyses between lakes in two very different geographical locations revealed substantially more cooperation and less competition among species in the warmer Lake Lanier than in Lake Mendota.

The role of dynamic enzyme assemblies and substrate channelling in metabolic regulation

Transient physical association between enzymes appears to be a cardinal feature of metabolic systems, yet the purpose of this metabolic organisation remains enigmatic. It is generally assumed that substrate channelling occurs in these complexes. However, there is a lack of information concerning the mechanisms and extent of substrate channelling and confusion regarding the consequences of substrate channelling. In this review, we outline recent advances in the structural characterisation of enzyme assemblies and integrate this with new insights from reaction-diffusion modelling and synthetic biology to clarify the mechanistic and functional significance of the phenomenon.

Ensemble methods for stochastic networks with special reference to the biological clock of Neurospora crassa

A major challenge in systems biology is to infer the parameters of regulatory networks that operate in a noisy environment, such as in a single cell. In a stochastic regime it is hard to distinguish noise from the real signal and to infer the noise contribution to the dynamical behavior. When the genetic network displays oscillatory dynamics, it is even harder to infer the parameters that produce the oscillations. To address this issue we introduce a new estimation method built on a combination of stochastic simulations, mass action kinetics and ensemble network simulations in which we match the average periodogram and phase of the model to that of the data. The method is relatively fast (compared to Metropolis-Hastings Monte Carlo Methods), easy to parallelize, applicable to large oscillatory networks and large (~2000 cells) single cell expression data sets, and it quantifies the noise impact on the observed dynamics. Standard errors of estimated rate coefficients are typically two orders of magnitude smaller than the mean from single cell experiments with on the order of ~1000 cells. We also provide a method to assess the goodness of fit of the stochastic network using the Hilbert phase of single cells. An analysis of phase departures from the null model with no communication between cells is consistent with a hypothesis of Stochastic Resonance describing single cell oscillators. Stochastic Resonance provides a physical mechanism whereby intracellular noise plays a positive role in establishing oscillatory behavior, but may require model parameters, such as rate coefficients, that differ substantially from those extracted at the macroscopic level from measurements on populations of millions of communicating, synchronized cells.

The three-legged stool of understanding metabolism: integrating metabolomics with biochemical genetics and computational modeling

Traditional biochemical research has resulted in a good understanding of many aspects of metabolism. However, this reductionist approach is time consuming and requires substantial resources, thus raising the question whether modern metabolomics and genomics should take over and replace the targeted experiments of old. We proffer that such a replacement is neither feasible not desirable and propose instead the tight integration of modern, system-wide omics with traditional experimental bench science and dedicated computational approaches. This integration is an important prerequisite toward the optimal acquisition of knowledge regarding metabolism and physiology in health and disease. The commentary describes advantages and drawbacks of current approaches to assessing metabolism and highlights the challenges to be overcome as we strive to achieve a deeper level of metabolic understanding in the future.

Mathematical models of lignin biosynthesis

BACKGROUND

Lignin is a natural polymer that is interwoven with cellulose and hemicellulose within plant cell walls. Due to this molecular arrangement, lignin is a major contributor to the recalcitrance of plant materials with respect to the extraction of sugars and their fermentation into ethanol, butanol, and other potential bioenergy crops. The lignin biosynthetic pathway is similar, but not identical in different plant species. It is in each case comprised of a moderate number of enzymatic steps, but its responses to manipulations, such as gene knock-downs, are complicated by the fact that several of the key enzymes are involved in several reaction steps. This feature poses a challenge to bioenergy production, as it renders it difficult to select the most promising combinations of genetic manipulations for the optimization of lignin composition and amount.

RESULTS

Here, we present several computational models than can aid in the analysis of data characterizing lignin biosynthesis. While minimizing technical details, we focus on the questions of what types of data are particularly useful for modeling and what genuine benefits the biofuel researcher may gain from the resulting models. We demonstrate our analysis with mathematical models for black cottonwood (Populus trichocarpa), alfalfa (Medicago truncatula), switchgrass (Panicum virgatum) and the grass Brachypodium distachyon.

CONCLUSIONS

Despite commonality in pathway structure, different plant species show different regulatory features and distinct spatial and topological characteristics. The putative lignin biosynthes pathway is not able to explain the plant specific laboratory data, and the necessity of plant specific modeling should be heeded.