1
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Roussel MR, Soares T. Graph-based, dynamics-preserving reduction of (bio)chemical systems. J Math Biol 2024; 89:42. [PMID: 39271540 DOI: 10.1007/s00285-024-02138-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Revised: 08/20/2024] [Accepted: 08/27/2024] [Indexed: 09/15/2024]
Abstract
Complex dynamical systems are often governed by equations containing many unknown parameters whose precise values may or may not be important for the system's dynamics. In particular, for chemical and biochemical systems, there may be some reactions or subsystems that are inessential to understanding the bifurcation structure and consequent behavior of a model, such as oscillations, multistationarity and patterning. Due to the size, complexity and parametric uncertainties of many (bio)chemical models, a dynamics-preserving reduction scheme that is able to isolate the necessary contributors to particular dynamical behaviors would be useful. In this contribution, we describe model reduction methods for mass-action (bio)chemical models based on the preservation of instability-generating subnetworks known as critical fragments. These methods focus on structural conditions for instabilities and so are parameter-independent. We apply these results to an existing model for the control of the synthesis of the NO-detoxifying enzyme Hmp in Escherichia coli that displays bistability.
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Affiliation(s)
- Marc R Roussel
- Department of Chemistry and Biochemistry, Alberta RNA Research and Training Institute, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada.
| | - Talmon Soares
- Department of Chemistry and Biochemistry, Alberta RNA Research and Training Institute, University of Lethbridge, Lethbridge, AB, T1K 3M4, Canada
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2
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Samarth N, Gulhane P, Singh S. Investigation through naphtho[2,3-a]pyrene on mutated EGFR mediated autophagy in NSCLC: Cellular model system unleashing therapeutic potential. IUBMB Life 2024. [PMID: 39275879 DOI: 10.1002/iub.2914] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2024] [Accepted: 07/30/2024] [Indexed: 09/16/2024]
Abstract
Mutant epidermal growth factor receptor (EGFR) signaling has emerged as a key cause of carcinogenesis and therapy resistance in non-small cell lung cancer (NSCLC), which continues to pose a serious threat to world health. In this study, we aimed to elucidate the complex molecular pathways of EGFR-mediated autophagy signaling in NSCLC. We identified naphtho[2,3-a]pyrene, an anthraquinolone derivative, to be a promising investigational drug that targets EGFR-mediated autophagy using a cellular model system. By utilizing systems biology, we developed a computational model that explained the signaling of EGFR-mediated autophagy and identified critical crosstalk sites that could be inhibited therapeutically. As a lead compound, naphtho[2,3-a]pyrene was confirmed by molecular docking experiments. It was found to be cytotoxic to NSCLC cells, impact migration, induce apoptosis, and arrest cell cycle, both on its own and when combined with standard drugs. The anticancer efficacy of naphtho[2,3-a]pyrene was validated in vivo on CDX nude mice. It showed synergistic activity against NSCLC when coupled with gefitinib, chloroquine, and radiation. Altogether, our study highlights naphtho[2,3-a]pyrene's therapeutic promise in NSCLC by focusing on EGFR-mediated autophagy and providing a new strategy to fight drug resistance and tumor survival.
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Affiliation(s)
- Nikhil Samarth
- Systems Medicine Laboratory, Biotechnology Research and Innovation Council-National Centre for Cell Science (BRIC-NCCS), NCCS Complex, Pune, India
| | - Pooja Gulhane
- Systems Medicine Laboratory, Biotechnology Research and Innovation Council-National Centre for Cell Science (BRIC-NCCS), NCCS Complex, Pune, India
| | - Shailza Singh
- Systems Medicine Laboratory, Biotechnology Research and Innovation Council-National Centre for Cell Science (BRIC-NCCS), NCCS Complex, Pune, India
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3
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Jayathilaka C, Araujo R, Nguyen L, Flegg M. Two wrongs do not make a right: the assumption that an inhibitor acts as an inverse activator. J Math Biol 2024; 89:26. [PMID: 38967811 PMCID: PMC11226533 DOI: 10.1007/s00285-024-02118-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2023] [Revised: 05/10/2024] [Accepted: 06/09/2024] [Indexed: 07/06/2024]
Abstract
Models of biochemical networks are often large intractable sets of differential equations. To make sense of the complexity, relationships between genes/proteins are presented as connected graphs, the edges of which are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions in many cases by the identifying recurring of topological motifs, for example positive and negative feedback loops. These topological features are usually classified under the presumption that activation and inhibition are inverse relationships. For example, inhibition of an inhibitor is often classified the same as activation of an activator within a motif classification, effectively treating them as equivalent. Whilst in many contexts this may not lead to catastrophic errors, drawing conclusions about the behavior of motifs, pathways or networks from these broad classes of topological feature without adequate mathematical descriptions can lead to obverse outcomes. We investigate the extent to which a biochemical pathway/network will behave quantitatively dissimilar to pathway/ networks with similar typologies formed by swapping inhibitors as the inverse of activators. The purpose of the study is to determine under what circumstances rudimentary qualitative assessment of network structure can provide reliable conclusions as to the quantitative behaviour of the network. Whilst there are others, We focus on two main mathematical qualities which may cause a divergence in the behaviour of two pathways/networks which would otherwise be classified as similar; (i) a modelling feature we label 'bias' and (ii) the precise positioning of activators and inhibitors within simple pathways/motifs.
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Affiliation(s)
| | - Robyn Araujo
- School of Mathematics and Statistics, The University of Melbourne, Victoria, 3010, Australia
- ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems (MACSYS), Parkville, VIC, 3010, Australia
| | - Lan Nguyen
- Monash Biomedicine Discovery Institute, Monash University, Clayton, VIC, Australia
- ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems (MACSYS), Parkville, VIC, 3010, Australia
| | - Mark Flegg
- Department of Mathematics, Monash University, Clayton, VIC, Australia.
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4
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Khilwani R, Singh S. Traversing through the Mechanistic Event Analysis in IL-6 and IL-17 Signaling for a New Therapeutic Paradigm in NSCLC. Int J Mol Sci 2024; 25:1216. [PMID: 38279220 PMCID: PMC10816370 DOI: 10.3390/ijms25021216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Revised: 01/08/2024] [Accepted: 01/10/2024] [Indexed: 01/28/2024] Open
Abstract
IL-6 and IL-17 are paradoxical cytokines that progress inflammatory states in chronic diseases, including cancer. In lung cancer, their role has been elucidated to favor cancer development by modulating signaling mechanisms critical to cellular growth. The intrinsic ability of these cytokines to influence macroautophagy is yet another reason to facilitate lung cancer. Here, we employed a systems immunology approach to discover the mechanistic role of these cytokines in cancer development. In a biological system, at later stages, the activation of NFkB stimulates immunosuppressive phenotypes to achieve tolerating effects in a transformed cell. We found that the upregulation of cytokines signaled M2 macrophages to modulate tumor responses through the activation of autophagic intermediates and inflammasome mediators. This caused immune perturbations in the tumor microenvironment, which were associated with cancer inflammation. To address these inflammatory states, we performed triggered event analysis to examine whether overexpressing immune effectors or downregulating immune suppressors may have an effect on cancer reversal. Interestingly, the inhibition of immune regulators opposed the model outcome to an increased immune response. Therefore, IL6-IL17-mediated regulation of lung cancer may address tumor malignancy and potentiate the development of newer therapeutics for NSCLC.
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Affiliation(s)
| | - Shailza Singh
- Systems Medicine Laboratory, National Centre for Cell Science, NCCS Complex, Ganeshkhind, SPPU Campus, Pune 411007, India;
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5
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Gasparyan M, Rao S. Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species' Concentrations. Bioengineering (Basel) 2023; 10:1056. [PMID: 37760158 PMCID: PMC10526083 DOI: 10.3390/bioengineering10091056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 08/23/2023] [Accepted: 08/31/2023] [Indexed: 09/29/2023] Open
Abstract
The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species' concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.
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Affiliation(s)
- Manvel Gasparyan
- School of Environmental Engineering, University of Seoul, Seoul 02504, Republic of Korea
- Center for Biosystems and Biotech Data Science, Ghent University Global Campus, Incheon 21985, Republic of Korea;
- Department of Data Analysis and Mathematical Modelling, Ghent University, 9000 Ghent, Belgium
| | - Shodhan Rao
- Center for Biosystems and Biotech Data Science, Ghent University Global Campus, Incheon 21985, Republic of Korea;
- Department of Data Analysis and Mathematical Modelling, Ghent University, 9000 Ghent, Belgium
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6
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Küken A, Wendering P, Langary D, Nikoloski Z. A structural property for reduction of biochemical networks. Sci Rep 2021; 11:17415. [PMID: 34465818 PMCID: PMC8408245 DOI: 10.1038/s41598-021-96835-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2021] [Accepted: 07/19/2021] [Indexed: 11/28/2022] Open
Abstract
Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.
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Affiliation(s)
- Anika Küken
- Bioinformatics, Institute of Biochemistry and Biology, University of Potsdam, Potsdam, Germany
| | - Philipp Wendering
- Bioinformatics, Institute of Biochemistry and Biology, University of Potsdam, Potsdam, Germany
| | - Damoun Langary
- Systems Biology and Mathematical Modeling, Max Planck Institute of Molecular Plant Physiology, Potsdam, Germany
| | - Zoran Nikoloski
- Bioinformatics, Institute of Biochemistry and Biology, University of Potsdam, Potsdam, Germany.
- Systems Biology and Mathematical Modeling, Max Planck Institute of Molecular Plant Physiology, Potsdam, Germany.
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7
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A modular approach for modeling the cell cycle based on functional response curves. PLoS Comput Biol 2021; 17:e1009008. [PMID: 34379640 PMCID: PMC8382204 DOI: 10.1371/journal.pcbi.1009008] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Revised: 08/23/2021] [Accepted: 07/19/2021] [Indexed: 12/02/2022] Open
Abstract
Modeling biochemical reactions by means of differential equations often results in systems with a large number of variables and parameters. As this might complicate the interpretation and generalization of the obtained results, it is often desirable to reduce the complexity of the model. One way to accomplish this is by replacing the detailed reaction mechanisms of certain modules in the model by a mathematical expression that qualitatively describes the dynamical behavior of these modules. Such an approach has been widely adopted for ultrasensitive responses, for which underlying reaction mechanisms are often replaced by a single Hill function. Also time delays are usually accounted for by using an explicit delay in delay differential equations. In contrast, however, S-shaped response curves, which by definition have multiple output values for certain input values and are often encountered in bistable systems, are not easily modeled in such an explicit way. Here, we extend the classical Hill function into a mathematical expression that can be used to describe both ultrasensitive and S-shaped responses. We show how three ubiquitous modules (ultrasensitive responses, S-shaped responses and time delays) can be combined in different configurations and explore the dynamics of these systems. As an example, we apply our strategy to set up a model of the cell cycle consisting of multiple bistable switches, which can incorporate events such as DNA damage and coupling to the circadian clock in a phenomenological way. Bistability plays an important role in many biochemical processes and typically emerges from complex interaction patterns such as positive and double negative feedback loops. Here, we propose to theoretically study the effect of bistability in a larger interaction network. We explicitly incorporate a functional expression describing an S-shaped input-output curve in the model equations, without the need for considering the underlying biochemical events. This expression can be converted into a functional module for an ultrasensitive response, and a time delay is easily included as well. Exploiting the fact that several of these modules can easily be combined in larger networks, we construct a cell cycle model consisting of multiple bistable switches and show how this approach can account for a number of known properties of the cell cycle.
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8
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Padoan A, Forni F, Sepulchre R. Balanced truncation for model reduction of biological oscillators. BIOLOGICAL CYBERNETICS 2021; 115:383-395. [PMID: 34382116 PMCID: PMC8382660 DOI: 10.1007/s00422-021-00888-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 07/14/2021] [Indexed: 06/13/2023]
Abstract
Model reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the quantitative analysis of its properties, like sensitivity to parameter variations and resilience to exogenous perturbations. However, available model reduction methods often fail to capture a diverse range of nonlinear behaviors observed in biology, such as multistability and limit cycle oscillations. The paper addresses this need using differential analysis. This approach leads to a nonlinear enhancement of classical balanced truncation for biological systems whose behavior is not restricted to the stability of a single equilibrium. Numerical results suggest that the proposed framework may be relevant to the approximation of classical models of biological systems.
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Affiliation(s)
- Alberto Padoan
- Department of Engineering, University of Cambridge, Cambridge, UK
| | - Fulvio Forni
- Department of Engineering, University of Cambridge, Cambridge, UK
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9
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O'Brien CM, Zhang Q, Daoutidis P, Hu WS. A hybrid mechanistic-empirical model for in silico mammalian cell bioprocess simulation. Metab Eng 2021; 66:31-40. [PMID: 33813033 DOI: 10.1016/j.ymben.2021.03.016] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2020] [Revised: 01/10/2021] [Accepted: 03/27/2021] [Indexed: 12/20/2022]
Abstract
In cell culture processes cell growth and metabolism drive changes in the chemical environment of the culture. These environmental changes elicit reactor control actions, cell growth response, and are sensed by cell signaling pathways that influence metabolism. The interplay of these forces shapes the culture dynamics through different stages of cell cultivation and the outcome greatly affects process productivity, product quality, and robustness. Developing a systems model that describes the interactions of those major players in the cell culture system can lead to better process understanding and enhance process robustness. Here we report the construction of a hybrid mechanistic-empirical bioprocess model which integrates a mechanistic metabolic model with subcomponent models for cell growth, signaling regulation, and the bioreactor environment for in silico exploration of process scenarios. Model parameters were optimized by fitting to a dataset of cell culture manufacturing process which exhibits variability in metabolism and productivity. The model fitting process was broken into multiple steps to mitigate the substantial numerical challenges related to the first-principles model components. The optimized model captured the dynamics of metabolism and the variability of the process runs with different kinetic profiles and productivity. The variability of the process was attributed in part to the metabolic state of cell inoculum. The model was then used to identify potential mitigation strategies to reduce process variability by altering the initial process conditions as well as to explore the effect of changing CO2 removal capacity in different bioreactor scales on process performance. By incorporating a mechanistic model of cell metabolism and appropriately fitting it to a large dataset, the hybrid model can describe the different metabolic phases in culture and the variability in manufacturing runs. This approach of employing a hybrid model has the potential to greatly facilitate process development and reactor scaling.
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Affiliation(s)
- Conor M O'Brien
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN, 55455-0132, USA
| | - Qi Zhang
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN, 55455-0132, USA
| | - Prodromos Daoutidis
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN, 55455-0132, USA
| | - Wei-Shou Hu
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, MN, 55455-0132, USA.
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10
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Inferring phenomenological models of first passage processes. PLoS Comput Biol 2021; 17:e1008740. [PMID: 33667218 PMCID: PMC7968746 DOI: 10.1371/journal.pcbi.1008740] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 03/17/2021] [Accepted: 01/25/2021] [Indexed: 11/19/2022] Open
Abstract
Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.
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11
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Khazaaleh M, Samarasinghe S, Kulasiri D. A new hierarchical approach to multi-level model abstraction for simplifying ODE models of biological networks and a case study: The G1/S Checkpoint/DNA damage signalling pathways of mammalian cell cycle. Biosystems 2021; 203:104374. [PMID: 33556446 DOI: 10.1016/j.biosystems.2021.104374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2020] [Revised: 01/19/2021] [Accepted: 01/25/2021] [Indexed: 11/15/2022]
Abstract
Model reduction is an important topic in studies of biological systems. By reducing the complexity of large models through multi-level models while keeping the essence (biological meaning) of the model, model reduction can help answer many important questions about these systems. In this paper, we present a new reduction method based on hierarchical representation and a lumping approach. We used G1/S checkpoint pathway represented in Ordinary Differential Equations (ODE) in Iwamoto et al. (2011) as a case study to present this reduction method. The approach consists of two parts; the first part represents the biological network as a hierarchy (multiple levels) based on protein binding relations, which allowed us to model the biological network at different levels of abstraction. The second part applies different levels (level 1, 2 and 3) of lumping the species together depending on the level of the hierarchy, resulting in a reduced and transformed model for each level. The model at each level is a representation of the whole system and can address questions pertinent to that level. We develop and simulate reduced models for levels-1, 2 and 3 of lumping for the G1/S checkpoint pathway and evaluate the biological plausibility of the proposed method by comparing the results with the original ODE model of Iwamoto et al. (2011). The results for continuous dynamics of the G1/S checkpoint pathway with or without DNA-damage for reduced models of level- 1, 2 and 3 of lumping are in very good agreement and consistent with the original model results and with biological findings. Therefore, the reduced models (level-1, 2 and 3) can be used to study cell cycle progression in G1 and the effects of DNA damage on it. It is suitable for reducing complex ODE biological network models while retaining accurate continuous dynamics of the system. The 3 levels of the reduced models respectively achieved 20%, 26% and 31% reduction of the base model. Moreover, the reduced model is more efficient to run (30%, 44% and 52% time reduction for the three levels) and generate solutions than the original ODE model. Simplification of complex mathematical models is possible and the proposed reduction method has the potential to make an impact across many fields of biomedical research.
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Affiliation(s)
- Mutaz Khazaaleh
- Complex Systems, Big Data and Informatics Initiative (CSBII), New Zealand
| | - Sandhya Samarasinghe
- Complex Systems, Big Data and Informatics Initiative (CSBII), New Zealand; Centre for Advanced Computational Solutions, Lincoln University, Christchurch, New Zealand.
| | - Don Kulasiri
- Complex Systems, Big Data and Informatics Initiative (CSBII), New Zealand; Centre for Advanced Computational Solutions, Lincoln University, Christchurch, New Zealand
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12
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Kryazhimskiy S. Emergence and propagation of epistasis in metabolic networks. eLife 2021; 10:e60200. [PMID: 33527897 PMCID: PMC7924954 DOI: 10.7554/elife.60200] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 02/01/2021] [Indexed: 12/11/2022] Open
Abstract
Epistasis is often used to probe functional relationships between genes, and it plays an important role in evolution. However, we lack theory to understand how functional relationships at the molecular level translate into epistasis at the level of whole-organism phenotypes, such as fitness. Here, I derive two rules for how epistasis between mutations with small effects propagates from lower- to higher-level phenotypes in a hierarchical metabolic network with first-order kinetics and how such epistasis depends on topology. Most importantly, weak epistasis at a lower level may be distorted as it propagates to higher levels. Computational analyses show that epistasis in more realistic models likely follows similar, albeit more complex, patterns. These results suggest that pairwise inter-gene epistasis should be common, and it should generically depend on the genetic background and environment. Furthermore, the epistasis coefficients measured for high-level phenotypes may not be sufficient to fully infer the underlying functional relationships.
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Affiliation(s)
- Sergey Kryazhimskiy
- Division of Biological Sciences, University of California, San DiegoLa JollaUnited States
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13
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van Rosmalen RP, Smith RW, Martins Dos Santos VAP, Fleck C, Suarez-Diez M. Model reduction of genome-scale metabolic models as a basis for targeted kinetic models. Metab Eng 2021; 64:74-84. [PMID: 33486094 DOI: 10.1016/j.ymben.2021.01.008] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Revised: 01/05/2021] [Accepted: 01/15/2021] [Indexed: 11/26/2022]
Abstract
Constraint-based, genome-scale metabolic models are an essential tool to guide metabolic engineering. However, they lack the detail and time dimension that kinetic models with enzyme dynamics offer. Model reduction can be used to bridge the gap between the two methods and allow for the integration of kinetic models into the Design-Built-Test-Learn cycle. Here we show that these reduced size models can be representative of the dynamics of the original model and demonstrate the automated generation and parameterisation of such models. Using these minimal models of metabolism could allow for further exploration of dynamic responses in metabolic networks.
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Affiliation(s)
- R P van Rosmalen
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands
| | - R W Smith
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands
| | - V A P Martins Dos Santos
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands; Lifeglimmer GmbH, Berlin, Germany
| | - C Fleck
- Freiburg Center for Data Analysis and Modelling University of Freiburg Freiburg Germany; Control Theory and Systems Biology Laboratory, Department of Biosystems Science and En- gineering, ETH Zürich, Basel, Switzerland
| | - M Suarez-Diez
- Laboratory of Systems and Synthetic Biology, Department of Agrotechnology and Food Sciences, Wageningen University & Research, Wageningen, the Netherlands.
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14
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Johnson ME, Chen A, Faeder JR, Henning P, Moraru II, Meier-Schellersheim M, Murphy RF, Prüstel T, Theriot JA, Uhrmacher AM. Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry. Mol Biol Cell 2021; 32:186-210. [PMID: 33237849 PMCID: PMC8120688 DOI: 10.1091/mbc.e20-08-0530] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2020] [Revised: 10/13/2020] [Accepted: 11/17/2020] [Indexed: 12/29/2022] Open
Abstract
Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.
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Affiliation(s)
- M. E. Johnson
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD, 21218
| | - A. Chen
- Thomas C. Jenkins Department of Biophysics, Johns Hopkins University, Baltimore, MD, 21218
| | - J. R. Faeder
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, PA, 15260
| | - P. Henning
- Institute for Visual and Analytic Computing, University of Rostock, 18055 Rostock, Germany
| | - I. I. Moraru
- Department of Cell Biology, Center for Cell Analysis and Modeling, University of Connecticut Health Center, Farmington, CT 06030
| | - M. Meier-Schellersheim
- Laboratory of Immune System Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD 20892
| | - R. F. Murphy
- Computational Biology Department, Department of Biological Sciences, Department of Biomedical Engineering, Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA 15289
| | - T. Prüstel
- Laboratory of Immune System Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, MD 20892
| | - J. A. Theriot
- Department of Biology and Howard Hughes Medical Institute, University of Washington, Seattle, WA 98195
| | - A. M. Uhrmacher
- Institute for Visual and Analytic Computing, University of Rostock, 18055 Rostock, Germany
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15
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Sensitivity Based Order Reduction of a Chemical Membrane Degradation Model for Low-Temperature Proton Exchange Membrane Fuel Cells. ENERGIES 2020. [DOI: 10.3390/en13215611] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The chemical degradation of the perfluorinated sulfonic acid (PFSA) ion-exchange membrane as a result of an attack from a radical species, originating as a by-product of the oxygen reduction reaction, represents a significant limiting factor in a wider adoption of low-temperature proton exchange membrane fuel cells (LT-PEMFCs). The efficient mathematical modeling of these processes is therefore a crucial step in the further development of proton exchange membrane fuel cells. Starting with an extensive kinetic modeling framework, describing the whole range of chemical processes leading to the membrane degradation, we use the mathematical method of sensitivity analysis to systematically reduce the number of both chemical species and reactions needed to efficiently and accurately describe the chemical degradation of the membrane. The analysis suggests the elimination of chemical reactions among the radical species, which is supported by the physicochemical consideration of the modeled reactions, while the degradation of Nafion backbone can be significantly simplified by lumping several individual species concentrations. The resulting reduced model features only 12 species coupled by 8 chemical reactions, compared to 19 species coupled by 23 reactions in the original model. The time complexity of the model, analyzed on the basis of its stiffness, however, is not significantly improved in the process. Nevertheless, the significant reduction in the model system size and number of parameters represents an important step in the development of a computationally efficient coupled model of various fuel cell degradation processes. Additionally, the demonstrated application of sensitivity analysis method shows a great potential for further use in the optimization of models of operation and degradation of fuel cell components.
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16
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Abstract
We propose a new approach to the model reduction of biochemical reaction networks governed by various types of enzyme kinetics rate laws with non-autocatalytic reactions, each of which can be reversible or irreversible. This method extends the approach for model reduction previously proposed by Rao et al. which proceeds by the step-wise reduction in the number of complexes by Kron reduction of the weighted Laplacian corresponding to the complex graph of the network. The main idea in the current manuscript is based on rewriting the mathematical model of a reaction network as a model of a network consisting of linkage classes that contain more than one reaction. It is done by joining certain distinct linkage classes into a single linkage class by using the conservation laws of the network. We show that this adjustment improves the extent of applicability of the method proposed by Rao et al. We automate the entire reduction procedure using Matlab. We test our automated model reduction to two real-life reaction networks, namely, a model of neural stem cell regulation and a model of hedgehog signaling pathway. We apply our reduction approach to meaningfully reduce the number of complexes in the complex graph corresponding to these networks. When the number of species’ concentrations in the model of neural stem cell regulation is reduced by 33.33%, the difference between the dynamics of the original model and the reduced model, quantified by an error integral, is only 4.85%. Likewise, when the number of species’ concentrations is reduced by 33.33% in the model of hedgehog signaling pathway, the difference between the dynamics of the original model and the reduced model is only 6.59%.
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17
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Khazaaleh M, Samarasinghe S. Using activity time windows and logical representation to reduce the complexity of biological network models: G1/S checkpoint pathway with DNA damage. Biosystems 2020; 191-192:104128. [DOI: 10.1016/j.biosystems.2020.104128] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Revised: 02/25/2020] [Accepted: 02/25/2020] [Indexed: 01/14/2023]
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18
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Pucci F, Rooman M. Deciphering noise amplification and reduction in open chemical reaction networks. J R Soc Interface 2019; 15:20180805. [PMID: 30958227 DOI: 10.1098/rsif.2018.0805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The impact of fluctuations on the dynamical behaviour of complex biological systems is a longstanding issue, whose understanding would elucidate how evolutionary pressure tends to modulate intrinsic noise. Using the Itō stochastic differential equation formalism, we performed analytic and numerical analyses of model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. For networks of zero deficiency, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated and their Fano factors are Poissonian. Systems of higher deficiency have non-equilibrium steady states and non-zero reaction fluxes flowing between the complexes. When they model homo-oligomerization, the noise on each species is reduced when the flux flows from the oligomers of lowest to highest degree, and amplified otherwise. In the case of hetero-oligomerization systems, only the noise on the highest-degree species shows this behaviour.
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Affiliation(s)
- Fabrizio Pucci
- 2 Department of BioModeling, BioInformatics and BioProcesses, Université Libre de Bruxelles , 50 Roosevelt Ave, 1050 Brussels , Belgium
| | - Marianne Rooman
- 1 Department of Theoretical Physics, BioInformatics and BioProcesses, Université Libre de Bruxelles , 50 Roosevelt Ave, 1050 Brussels , Belgium.,2 Department of BioModeling, BioInformatics and BioProcesses, Université Libre de Bruxelles , 50 Roosevelt Ave, 1050 Brussels , Belgium
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19
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Cova TFGG, Bento DJ, Nunes SCC. Computational Approaches in Theranostics: Mining and Predicting Cancer Data. Pharmaceutics 2019; 11:E119. [PMID: 30871264 PMCID: PMC6471740 DOI: 10.3390/pharmaceutics11030119] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2019] [Revised: 02/26/2019] [Accepted: 03/07/2019] [Indexed: 02/02/2023] Open
Abstract
The ability to understand the complexity of cancer-related data has been prompted by the applications of (1) computer and data sciences, including data mining, predictive analytics, machine learning, and artificial intelligence, and (2) advances in imaging technology and probe development. Computational modelling and simulation are systematic and cost-effective tools able to identify important temporal/spatial patterns (and relationships), characterize distinct molecular features of cancer states, and address other relevant aspects, including tumor detection and heterogeneity, progression and metastasis, and drug resistance. These approaches have provided invaluable insights for improving the experimental design of therapeutic delivery systems and for increasing the translational value of the results obtained from early and preclinical studies. The big question is: Could cancer theranostics be determined and controlled in silico? This review describes the recent progress in the development of computational models and methods used to facilitate research on the molecular basis of cancer and on the respective diagnosis and optimized treatment, with particular emphasis on the design and optimization of theranostic systems. The current role of computational approaches is providing innovative, incremental, and complementary data-driven solutions for the prediction, simplification, and characterization of cancer and intrinsic mechanisms, and to promote new data-intensive, accurate diagnostics and therapeutics.
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Affiliation(s)
- Tânia F G G Cova
- Coimbra Chemistry Centre, Department of Chemistry, Faculty of Sciences and Technology, University of Coimbra, 3004-535 Coimbra, Portugal.
| | - Daniel J Bento
- Coimbra Chemistry Centre, Department of Chemistry, Faculty of Sciences and Technology, University of Coimbra, 3004-535 Coimbra, Portugal.
| | - Sandra C C Nunes
- Coimbra Chemistry Centre, Department of Chemistry, Faculty of Sciences and Technology, University of Coimbra, 3004-535 Coimbra, Portugal.
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20
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Strutz J, Martin J, Greene J, Broadbelt L, Tyo K. Metabolic kinetic modeling provides insight into complex biological questions, but hurdles remain. Curr Opin Biotechnol 2019; 59:24-30. [PMID: 30851632 DOI: 10.1016/j.copbio.2019.02.005] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2018] [Revised: 01/25/2019] [Accepted: 02/04/2019] [Indexed: 01/16/2023]
Abstract
Metabolic models containing kinetic information can answer unique questions about cellular metabolism that are useful to metabolic engineering. Several kinetic modeling frameworks have recently been developed or improved. In addition, techniques for systematic identification of model structure, including regulatory interactions, have been reported. Each framework has advantages and limitations, which can make it difficult to choose the most appropriate framework. Common limitations are data availability and computational time, especially in large-scale modeling efforts. However, recently developed experimental techniques, parameter identification algorithms, as well as model reduction techniques help alleviate these computational bottlenecks. Opportunities for additional improvements may come from the rich literature in catalysis and chemical networks. In all, kinetic models are positioned to make significant impact in cellular engineering.
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Affiliation(s)
- Jonathan Strutz
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, USA; Center for Synthetic Biology, Northwestern University, Evanston, IL, USA
| | - Jacob Martin
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, USA; Center for Synthetic Biology, Northwestern University, Evanston, IL, USA
| | - Jennifer Greene
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, USA; Center for Synthetic Biology, Northwestern University, Evanston, IL, USA
| | - Linda Broadbelt
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, USA
| | - Keith Tyo
- Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL, USA; Center for Synthetic Biology, Northwestern University, Evanston, IL, USA.
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21
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Frøysa HG, Fallahi S, Blaser N. Evaluating model reduction under parameter uncertainty. BMC SYSTEMS BIOLOGY 2018; 12:79. [PMID: 30053887 PMCID: PMC6062951 DOI: 10.1186/s12918-018-0602-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/13/2017] [Accepted: 07/09/2018] [Indexed: 11/10/2022]
Abstract
BACKGROUND The dynamics of biochemical networks can be modelled by systems of ordinary differential equations. However, these networks are typically large and contain many parameters. Therefore model reduction procedures, such as lumping, sensitivity analysis and time-scale separation, are used to simplify models. Although there are many different model reduction procedures, the evaluation of reduced models is difficult and depends on the parameter values of the full model. There is a lack of a criteria for evaluating reduced models when the model parameters are uncertain. RESULTS We developed a method to compare reduced models and select the model that results in similar dynamics and uncertainty as the original model. We simulated different parameter sets from the assumed parameter distributions. Then, we compared all reduced models for all parameter sets using cluster analysis. The clusters revealed which of the reduced models that were similar to the original model in dynamics and variability. This allowed us to select the smallest reduced model that best approximated the full model. Through examples we showed that when parameter uncertainty was large, the model should be reduced further and when parameter uncertainty was small, models should not be reduced much. CONCLUSIONS A method to compare different models under parameter uncertainty is developed. It can be applied to any model reduction method. We also showed that the amount of parameter uncertainty influences the choice of reduced models.
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Affiliation(s)
- Håvard G Frøysa
- Department of Mathematics, University of Bergen, Mailbox 7803, Bergen, 5020, Norway.
| | - Shirin Fallahi
- Department of Mathematics, University of Bergen, Mailbox 7803, Bergen, 5020, Norway
| | - Nello Blaser
- Department of Mathematics, University of Bergen, Mailbox 7803, Bergen, 5020, Norway
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22
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Smith RW, van Rosmalen RP, Martins Dos Santos VAP, Fleck C. DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems. BMC SYSTEMS BIOLOGY 2018; 12:72. [PMID: 29914475 PMCID: PMC6006996 DOI: 10.1186/s12918-018-0584-8] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/18/2017] [Accepted: 05/14/2018] [Indexed: 12/21/2022]
Abstract
Background Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. Results In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. Conclusion The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future. Electronic supplementary material The online version of this article (10.1186/s12918-018-0584-8) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Robert W Smith
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands.,LifeGlimmer GmbH, Markelstrasse 38, Berlin, 12163, Germany
| | - Rik P van Rosmalen
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands
| | - Vitor A P Martins Dos Santos
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands.,LifeGlimmer GmbH, Markelstrasse 38, Berlin, 12163, Germany
| | - Christian Fleck
- Laboratory of Systems & Synthetic Biology, Wageningen UR, Stippeneng 4, Wageningen, 6708WE, The Netherlands.
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23
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Ogilvie LA, Kovachev A, Wierling C, Lange BMH, Lehrach H. Models of Models: A Translational Route for Cancer Treatment and Drug Development. Front Oncol 2017; 7:219. [PMID: 28971064 PMCID: PMC5609574 DOI: 10.3389/fonc.2017.00219] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2017] [Accepted: 09/01/2017] [Indexed: 12/12/2022] Open
Abstract
Every patient and every disease is different. Each patient therefore requires a personalized treatment approach. For technical reasons, a personalized approach is feasible for treatment strategies such as surgery, but not for drug-based therapy or drug development. The development of individual mechanistic models of the disease process in every patient offers the possibility of attaining truly personalized drug-based therapy and prevention. The concept of virtual clinical trials and the integrated use of in silico, in vitro, and in vivo models in preclinical development could lead to significant gains in efficiency and order of magnitude increases in the cost effectiveness of drug development and approval. We have developed mechanistic computational models of large-scale cellular signal transduction networks for prediction of drug effects and functional responses, based on patient-specific multi-level omics profiles. However, a major barrier to the use of such models in a clinical and developmental context is the reliability of predictions. Here we detail how the approach of using “models of models” has the potential to impact cancer treatment and drug development. We describe the iterative refinement process that leverages the flexibility of experimental systems to generate highly dimensional data, which can be used to train and validate computational model parameters and improve model predictions. In this way, highly optimized computational models with robust predictive capacity can be generated. Such models open up a number of opportunities for cancer drug treatment and development, from enhancing the design of experimental studies, reducing costs, and improving animal welfare, to increasing the translational value of results generated.
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Affiliation(s)
| | | | | | | | - Hans Lehrach
- Alacris Theranostics GmbH, Berlin, Germany.,Max Planck Institute for Molecular Genetics, Berlin, Germany
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24
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Snowden TJ, van der Graaf PH, Tindall MJ. Methods of Model Reduction for Large-Scale Biological Systems: A Survey of Current Methods and Trends. Bull Math Biol 2017; 79:1449-1486. [PMID: 28656491 PMCID: PMC5498684 DOI: 10.1007/s11538-017-0277-2] [Citation(s) in RCA: 56] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2016] [Accepted: 03/30/2017] [Indexed: 01/31/2023]
Abstract
Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed.
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Affiliation(s)
- Thomas J Snowden
- Department of Mathematics and Statistics, University of Reading, Reading, RG6 6AX, UK.,Certara QSP, University of Kent Innovation Centre, Canterbury, CT2 7FG, UK
| | - Piet H van der Graaf
- Certara QSP, University of Kent Innovation Centre, Canterbury, CT2 7FG, UK.,Leiden Academic Centre for Drug Research, Universiteit Leiden, Leiden, 2333 CC, Netherlands
| | - Marcus J Tindall
- Department of Mathematics and Statistics, University of Reading, Reading, RG6 6AX, UK. .,The Institute for Cardiovascular and Metabolic Research (ICMR), University of Reading, Reading, RG6 6AX, UK.
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25
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Sáez M, Wiuf C, Feliu E. Graphical reduction of reaction networks by linear elimination of species. J Math Biol 2016; 74:195-237. [PMID: 27221101 DOI: 10.1007/s00285-016-1028-y] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2015] [Revised: 05/08/2016] [Indexed: 12/27/2022]
Abstract
The quasi-steady state approximation and time-scale separation are commonly applied methods to simplify models of biochemical reaction networks based on ordinary differential equations (ODEs). The concentrations of the "fast" species are assumed effectively to be at steady state with respect to the "slow" species. Under this assumption the steady state equations can be used to eliminate the "fast" variables and a new ODE system with only the slow species can be obtained. We interpret a reduced system obtained by time-scale separation as the ODE system arising from a unique reaction network, by identification of a set of reactions and the corresponding rate functions. The procedure is graphically based and can easily be worked out by hand for small networks. For larger networks, we provide a pseudo-algorithm. We study properties of the reduced network, its kinetics and conservation laws, and show that the kinetics of the reduced network fulfil realistic assumptions, provided the original network does. We illustrate our results using biological examples such as substrate mechanisms, post-translational modification systems and networks with intermediates (transient) steps.
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Affiliation(s)
- Meritxell Sáez
- Department of Mathematical Sciences. University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark
| | - Carsten Wiuf
- Department of Mathematical Sciences. University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark
| | - Elisenda Feliu
- Department of Mathematical Sciences. University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark.
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26
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Tummler K, Kühn C, Klipp E. Dynamic metabolic models in context: biomass backtracking. Integr Biol (Camb) 2016; 7:940-51. [PMID: 26189715 DOI: 10.1039/c5ib00050e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
Mathematical modeling has proven to be a powerful tool to understand and predict functional and regulatory properties of metabolic processes. High accuracy dynamic modeling of individual pathways is thereby opposed by simplified but genome scale constraint based approaches. A method that links these two powerful techniques would greatly enhance predictive power but is so far lacking. We present biomass backtracking, a workflow that integrates the cellular context in existing dynamic metabolic models via stoichiometrically exact drain reactions based on a genome scale metabolic model. With comprehensive examples, for different species and environmental contexts, we show the importance and scope of applications and highlight the improvement compared to common boundary formulations in existing metabolic models. Our method allows for the contextualization of dynamic metabolic models based on all available information. We anticipate this to greatly increase their accuracy and predictive power for basic research and also for drug development and industrial applications.
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Affiliation(s)
- Katja Tummler
- Theoretische Biophysik, Humboldt-Universität zu Berlin, Germany.
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27
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Johnson T, Bartol T, Sejnowski T, Mjolsness E. Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics. Phys Biol 2015; 12:045005. [PMID: 26086598 PMCID: PMC4489159 DOI: 10.1088/1478-3975/12/4/045005] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, 'graph-constrained correlation dynamics', requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice.
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Affiliation(s)
- Todd Johnson
- Department of Computer Science, University of California Irvine CA92697, USA
| | | | | | - Eric Mjolsness
- Department of Computer Science, University of California Irvine CA92697, USA
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28
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Auley MTM, Mooney KM, Angell PJ, Wilkinson SJ. Mathematical modelling of metabolic regulation in aging. Metabolites 2015; 5:232-51. [PMID: 25923415 PMCID: PMC4495371 DOI: 10.3390/metabo5020232] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2014] [Revised: 03/24/2015] [Accepted: 03/25/2015] [Indexed: 12/20/2022] Open
Abstract
The underlying cellular mechanisms that characterize aging are complex and multifaceted. However, it is emerging that aging could be regulated by two distinct metabolic hubs. These hubs are the pathway defined by the mammalian target of rapamycin (mTOR) and that defined by the NAD+-dependent deacetylase enzyme, SIRT1. Recent experimental evidence suggests that there is crosstalk between these two important pathways; however, the mechanisms underpinning their interaction(s) remains poorly understood. In this review, we propose using computational modelling in tandem with experimentation to delineate the mechanism(s). We briefly discuss the main modelling frameworks that could be used to disentangle this relationship and present a reduced reaction pathway that could be modelled. We conclude by outlining the limitations of computational modelling and by discussing opportunities for future progress in this area.
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Affiliation(s)
- Mark T Mc Auley
- Faculty of Science & Engineering, University of Chester, Thornton Science Park, CH2 4NU, UK.
| | - Kathleen M Mooney
- Faculty of Health and Social Care, Edge Hill University, Ormskirk, Lancashire, L39 4QP, UK.
| | - Peter J Angell
- School of Health Sciences, Liverpool Hope University, Taggart Avenue, Liverpool, L16 9JD, UK.
| | - Stephen J Wilkinson
- Faculty of Science & Engineering, University of Chester, Thornton Science Park, CH2 4NU, UK.
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29
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Zhang W, Tian T, Zou X. Negative feedback contributes to the stochastic expression of the interferon-β gene in virus-triggered type I interferon signaling pathways. Math Biosci 2015; 265:12-27. [PMID: 25892253 DOI: 10.1016/j.mbs.2015.04.003] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2014] [Revised: 04/05/2015] [Accepted: 04/06/2015] [Indexed: 12/28/2022]
Abstract
Type I interferon (IFN) signaling pathways play an essential role in the defense against early viral infections; however, the diverse and intricate molecular mechanisms of virus-triggered type I IFN responses are still poorly understood. In this study, we analyzed and compared two classes of models i.e., deterministic ordinary differential equations (ODEs) and stochastic models to elucidate the dynamics and stochasticity of type I IFN signaling pathways. Bifurcation analysis based on an ODE model reveals that the system exhibits a bistable switch and a one-way switch at high or low levels when the strengths of the negative and positive feedbacks are tuned. Furthermore, we compared the stochastic simulation results under the Master and Langevin equations. Both of the stochastic equations generate the bistable switch phenomenon, and the distance between two stable states are smaller than normal under the simulation of the Langevin equation. The quantitative computations also show that a moderate ratio between positive and negative feedback strengths is required to ensure a reliable switch between the different IFN concentrations that regulate the immune response. Moreover, we propose a multi-state stochastic model based on the above deterministic model to describe the multi-cellular system coupled with the diffusion of IFNs. The perturbation and inhibition analysis showed that the positive feedback, as well as noises, has little effect on the stochastic expression of IFNs, but the negative feedback of ISG56 on the activation of IRF7 has a great influence on IFN stochastic expression. Together, these results reveal that positive feedback stabilizes IFN gene expression, and negative feedback may be the main contribution to the stochastic expression of the IFN gene in the virus-triggered type I IFN response. These findings will provide new insight into the molecular mechanisms of virus-triggered type I IFN signaling pathways.
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Affiliation(s)
- Wei Zhang
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China; School of Sciences, East China Jiaotong University, Nanchang 330013, China
| | - Tianhai Tian
- School of Mathematical Science, Monash University, Melbourne Vic 3800, Australia
| | - Xiufen Zou
- School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China.
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30
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Cilfone NA, Kirschner DE, Linderman JJ. Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems. Cell Mol Bioeng 2015; 8:119-136. [PMID: 26366228 PMCID: PMC4564133 DOI: 10.1007/s12195-014-0363-6] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.
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Affiliation(s)
- Nicholas A. Cilfone
- Department of Chemical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Denise E. Kirschner
- Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI, USA
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