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Patel H, Solanki N, Solanki A, Patel M, Patel S, Shah U. Mathematical modelling of Alzheimer's disease biomarkers: Targeting Amyloid beta, Tau protein, Apolipoprotein E and Apoptotic pathways. Am J Transl Res 2024; 16:2777-2792. [PMID: 39114703 PMCID: PMC11301479 DOI: 10.62347/ujqf5204] [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: 01/09/2024] [Accepted: 05/15/2024] [Indexed: 08/10/2024]
Abstract
Introduction: The kinetics of brain cell death in Alzheimer's disease (AD) is being studied using mathematical models. These mathematical models utilize techniques like differential equations, stochastic processes, and network theory to explore crucial signalling pathways and interactions between different cell types. One crucial area of research is the intentional cell death known as apoptosis, which is crucial for the nervous system. The main purpose behind the mathematical modelling of this is for identification of which biomarkers and pathways are most influential in the progression of AD. In addition, we can also predict the natural history of the disease, by which we can make early diagnosis. Mathematical modelling of AD: Current mathematical models include the Apolipoprotein E (APOE) Gene Model, the Tau Protein Kinetics Model, and the Amyloid Beta Peptide Kinetic Model. The Bcl-2 and Bax apoptosis theories postulate that the balance of pro- and anti-apoptotic proteins in cells determines whether a cell experiences apoptosis, where the Bcl-2 model, depicts the interaction of pro- and anti-apoptotic proteins, it is also being used in research on cell death in a range of cell types, including neurons and glial cells. How peptides are produced and eliminated in the brain is explained by the Amyloid beta Peptide (Aβ) Kinetics Model. The tau protein kinetics model focuses on production, aggregation, and clearance of tau protein processes, which are hypothesized to be involved in AD. The APOE gene model investigates the connection between the risk of Alzheimer's disease and the APOE gene. These models have been used to predict how Alzheimer's disease would develop and to evaluate how different inhibitors will affect the illness's course. Conclusion: These mathematical models reflect physiological meaningful characteristics and demonstrates robust fits to training data. Incorporating biomarkers like Aβ, Tau, APOE and markers of neuronal loss and cognitive impairment can generate sound predictions of biomarker trajectories over time in Alzheimer's disease.
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Affiliation(s)
- Hetvi Patel
- Ramanbhai Patel College of Pharmacy, Charotar University of Science and Technology (CHARUSAT), CHARUSAT CampusChanga 388421, Gujarat, India
| | - Nilay Solanki
- Ramanbhai Patel College of Pharmacy, Charotar University of Science and Technology (CHARUSAT), CHARUSAT CampusChanga 388421, Gujarat, India
| | - Arpita Solanki
- Parul Institute of Engineering and Technology, Department of Applied Sciences and Humanities (Mathematics), Parul UniversityVadodara 391760, Gujarat, India
| | - Mehul Patel
- Ramanbhai Patel College of Pharmacy, Charotar University of Science and Technology (CHARUSAT), CHARUSAT CampusChanga 388421, Gujarat, India
| | - Swayamprakash Patel
- Ramanbhai Patel College of Pharmacy, Charotar University of Science and Technology (CHARUSAT), CHARUSAT CampusChanga 388421, Gujarat, India
| | - Umang Shah
- Ramanbhai Patel College of Pharmacy, Charotar University of Science and Technology (CHARUSAT), CHARUSAT CampusChanga 388421, Gujarat, India
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2
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Targeted Quantification of Protein Phosphorylation and Its Contributions towards Mathematical Modeling of Signaling Pathways. Molecules 2023; 28:molecules28031143. [PMID: 36770810 PMCID: PMC9919559 DOI: 10.3390/molecules28031143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2022] [Revised: 01/12/2023] [Accepted: 01/18/2023] [Indexed: 01/26/2023] Open
Abstract
Post-translational modifications (PTMs) are key regulatory mechanisms that can control protein function. Of these, phosphorylation is the most common and widely studied. Because of its importance in regulating cell signaling, precise and accurate measurements of protein phosphorylation across wide dynamic ranges are crucial to understanding how signaling pathways function. Although immunological assays are commonly used to detect phosphoproteins, their lack of sensitivity, specificity, and selectivity often make them unreliable for quantitative measurements of complex biological samples. Recent advances in Mass Spectrometry (MS)-based targeted proteomics have made it a more useful approach than immunoassays for studying the dynamics of protein phosphorylation. Selected reaction monitoring (SRM)-also known as multiple reaction monitoring (MRM)-and parallel reaction monitoring (PRM) can quantify relative and absolute abundances of protein phosphorylation in multiplexed fashions targeting specific pathways. In addition, the refinement of these tools by enrichment and fractionation strategies has improved measurement of phosphorylation of low-abundance proteins. The quantitative data generated are particularly useful for building and parameterizing mathematical models of complex phospho-signaling pathways. Potentially, these models can provide a framework for linking analytical measurements of clinical samples to better diagnosis and treatment of disease.
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Ovchinnikov A, Pérez Verona I, Pogudin G, Tribastone M. CLUE: Exact maximal reduction of kinetic models by constrained lumping of differential equations. Bioinformatics 2021; 37:1732-1738. [PMID: 33532849 DOI: 10.1093/bioinformatics/btab010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Revised: 11/13/2020] [Accepted: 01/30/2021] [Indexed: 11/14/2022] Open
Abstract
MOTIVATION Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which each involved biochemical species can be found. Model reduction can help tame such complexity by providing a lower-dimensional model in which each macro-variable can be directly related to the original variables. RESULTS We present CLUE, an algorithm for exact model reduction of systems of polynomial differential equations by constrained linear lumping. It computes the smallest dimensional reduction as a linear mapping of the state space such that the reduced model preserves the dynamics of user-specified linear combinations of the original variables. Even though CLUE works with nonlinear differential equations, it is based on linear algebra tools, which makes it applicable to high-dimensional models. Using case studies from the literature, we show how CLUE can substantially lower model dimensionality and help extract biologically intelligible insights from the reduction. AVAILABILITY An implementation of the algorithm and relevant resources to replicate the experiments herein reported are freely available for download at https://github.com/pogudingleb/CLUE. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Alexey Ovchinnikov
- Department of Mathematics, CUNY Queens College, Queens, NY, 11367, and CUNY Graduate Center, New York, NY, 10016, USA
| | | | - Gleb Pogudin
- LIX, CNRS, École Polytechnique, Institute Polytechnique de Paris, Palaiseau, 91120, France
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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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Stepanov A, Karelina T, Markevich N, Demin O, Nicholas T. A mathematical model of multisite phosphorylation of tau protein. PLoS One 2018; 13:e0192519. [PMID: 29408874 PMCID: PMC5800643 DOI: 10.1371/journal.pone.0192519] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2017] [Accepted: 01/24/2018] [Indexed: 11/18/2022] Open
Abstract
Abnormal tau metabolism followed by formation of tau deposits causes a number of neurodegenerative diseases called tauopathies including Alzheimer's disease. Hyperphosphorylation of tau protein precedes tau aggregation and is a topic of interest for the development of pharmacological interventions to prevent pathology progression at early stages. The development of a mathematical model of multisite phosphorylation of tau would be helpful for searching for the targets of pharmacological interventions and candidates for biomarkers of pathology progression. In the present study, we for the first time developed a model of multisite phosphorylation of tau protein and elucidated the relative contribution of kinases to phosphorylation of distinct sites. The model describes phosphorylation of tau or PKA-prephosphorylated tau by GSK3β and CDK5 and dephosphorylation by PP2A, accurately reproducing the data for short-term kinetics of tau (de)phosphorylation. Our results suggest that kinase inhibition may more specifically prevent tau hyperphosphorylation, e.g., on PHF sites, which are key biomarkers of pathological changes in Alzheimer's disease. The main features of our model are partial phosphorylation of tau residues and merging of random and sequential mechanisms of multisite phosphorylation within the framework of the probability-based approach assuming independent phosphorylation events.
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Affiliation(s)
| | | | | | | | - Timothy Nicholas
- Pfizer Global R&D, Groton, Connecticut, United States of America
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6
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Straube R. Analysis of network motifs in cellular regulation: Structural similarities, input-output relations and signal integration. Biosystems 2017; 162:215-232. [PMID: 29107640 DOI: 10.1016/j.biosystems.2017.10.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Revised: 10/22/2017] [Accepted: 10/23/2017] [Indexed: 02/07/2023]
Abstract
Much of the complexity of regulatory networks derives from the necessity to integrate multiple signals and to avoid malfunction due to cross-talk or harmful perturbations. Hence, one may expect that the input-output behavior of larger networks is not necessarily more complex than that of smaller network motifs which suggests that both can, under certain conditions, be described by similar equations. In this review, we illustrate this approach by discussing the similarities that exist in the steady state descriptions of a simple bimolecular reaction, covalent modification cycles and bacterial two-component systems. Interestingly, in all three systems fundamental input-output characteristics such as thresholds, ultrasensitivity or concentration robustness are described by structurally similar equations. Depending on the system the meaning of the parameters can differ ranging from protein concentrations and affinity constants to complex parameter combinations which allows for a quantitative understanding of signal integration in these systems. We argue that this approach may also be extended to larger regulatory networks.
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Affiliation(s)
- Ronny Straube
- Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg, Sandtorstr. 1, D-39106 Magdeburg, Germany
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7
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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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Gough A, Stern AM, Maier J, Lezon T, Shun TY, Chennubhotla C, Schurdak ME, Haney SA, Taylor DL. Biologically Relevant Heterogeneity: Metrics and Practical Insights. SLAS DISCOVERY 2017; 22:213-237. [PMID: 28231035 DOI: 10.1177/2472555216682725] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Heterogeneity is a fundamental property of biological systems at all scales that must be addressed in a wide range of biomedical applications, including basic biomedical research, drug discovery, diagnostics, and the implementation of precision medicine. There are a number of published approaches to characterizing heterogeneity in cells in vitro and in tissue sections. However, there are no generally accepted approaches for the detection and quantitation of heterogeneity that can be applied in a relatively high-throughput workflow. This review and perspective emphasizes the experimental methods that capture multiplexed cell-level data, as well as the need for standard metrics of the spatial, temporal, and population components of heterogeneity. A recommendation is made for the adoption of a set of three heterogeneity indices that can be implemented in any high-throughput workflow to optimize the decision-making process. In addition, a pairwise mutual information method is suggested as an approach to characterizing the spatial features of heterogeneity, especially in tissue-based imaging. Furthermore, metrics for temporal heterogeneity are in the early stages of development. Example studies indicate that the analysis of functional phenotypic heterogeneity can be exploited to guide decisions in the interpretation of biomedical experiments, drug discovery, diagnostics, and the design of optimal therapeutic strategies for individual patients.
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Affiliation(s)
- Albert Gough
- 1 Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA, USA.,2 University of Pittsburgh Drug Discovery Institute, Pittsburgh, PA, USA
| | - Andrew M Stern
- 1 Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA, USA.,2 University of Pittsburgh Drug Discovery Institute, Pittsburgh, PA, USA
| | - John Maier
- 3 Department of Family Medicine, University of Pittsburgh, Pittsburgh, PA, USA
| | - Timothy Lezon
- 1 Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA, USA.,2 University of Pittsburgh Drug Discovery Institute, Pittsburgh, PA, USA
| | - Tong-Ying Shun
- 2 University of Pittsburgh Drug Discovery Institute, Pittsburgh, PA, USA
| | - Chakra Chennubhotla
- 1 Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA, USA.,2 University of Pittsburgh Drug Discovery Institute, Pittsburgh, PA, USA
| | - Mark E Schurdak
- 1 Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA, USA.,2 University of Pittsburgh Drug Discovery Institute, Pittsburgh, PA, USA.,4 University of Pittsburgh Cancer Institute, Pittsburgh, PA, USA
| | - Steven A Haney
- 5 Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN, USA
| | - D Lansing Taylor
- 1 Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA, USA.,2 University of Pittsburgh Drug Discovery Institute, Pittsburgh, PA, USA.,4 University of Pittsburgh Cancer Institute, Pittsburgh, PA, USA
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9
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Aliper AM, Korzinkin MB, Kuzmina NB, Zenin AA, Venkova LS, Smirnov PY, Zhavoronkov AA, Buzdin AA, Borisov NM. Mathematical Justification of Expression-Based Pathway Activation Scoring (PAS). Methods Mol Biol 2017; 1613:31-51. [PMID: 28849557 DOI: 10.1007/978-1-4939-7027-8_3] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Although modeling of activation kinetics for various cell signaling pathways has reached a high grade of sophistication and thoroughness, most such kinetic models still remain of rather limited practical value for biomedicine. Nevertheless, recent advancements have been made in application of signaling pathway science for real needs of prescription of the most effective drugs for individual patients. The methods for such prescription evaluate the degree of pathological changes in the signaling machinery based on two types of data: first, on the results of high-throughput gene expression profiling, and second, on the molecular pathway graphs that reflect interactions between the pathway members. For example, our algorithm OncoFinder evaluates the activation of molecular pathways on the basis of gene/protein expression data in the objects of the interest.Yet, the question of assessment of the relative importance for each gene product in a molecular pathway remains unclear unless one call for the methods of parameter sensitivity /stiffness analysis in the interactomic kinetic models of signaling pathway activation in terms of total concentrations of each gene product.Here we show two principal points: 1. First, the importance coefficients for each gene in pathways that were obtained using the extremely time- and labor-consuming stiffness analysis of full-scaled kinetic models generally differ from much easier-to-calculate expression-based pathway activation score (PAS) not more than by 30%, so the concept of PAS is kinetically justified. 2. Second, the use of pathway-based approach instead of distinct gene analysis, due to the law of large numbers, allows restoring the correlation between the similar samples that were examined using different transcriptome investigation techniques.
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Affiliation(s)
- Alexander M Aliper
- Drug Research and Design Department, Pathway Pharmaceuticals, Wan Chai, Hong Kong, Hong Kong SAR
- Department of Personalized Medicine, First Oncology Research and Advisory Center, Moscow, Russia
- Laboratory of Bioinformatics, D. Rogachev Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Michael B Korzinkin
- Department of Personalized Medicine, First Oncology Research and Advisory Center, Moscow, Russia
- Laboratory of Bioinformatics, D. Rogachev Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Natalia B Kuzmina
- Laboratory of Systems Biology, A.I. Burnazyan Federal Medical Biophysical Center, Moscow, 123182, Russia
| | - Alexander A Zenin
- Laboratory of Systems Biology, A.I. Burnazyan Federal Medical Biophysical Center, Moscow, 123182, Russia
| | - Larisa S Venkova
- Department of Personalized Medicine, First Oncology Research and Advisory Center, Moscow, Russia
- Laboratory of Bioinformatics, D. Rogachev Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Philip Yu Smirnov
- Laboratory of Systems Biology, A.I. Burnazyan Federal Medical Biophysical Center, Moscow, 123182, Russia
| | - Alex A Zhavoronkov
- Drug Research and Design Department, Pathway Pharmaceuticals, Wan Chai, Hong Kong, Hong Kong SAR
- Department of Personalized Medicine, First Oncology Research and Advisory Center, Moscow, Russia
- Laboratory of Bioinformatics, D. Rogachev Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
| | - Anton A Buzdin
- Drug Research and Design Department, Pathway Pharmaceuticals, Wan Chai, Hong Kong, Hong Kong SAR
- Department of Personalized Medicine, First Oncology Research and Advisory Center, Moscow, Russia
- Laboratory of Bioinformatics, D. Rogachev Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia
- Group for Genomic Regulation of Cell Signaling Systems, Shemyakin-Ovchinnikov Institute of Bioorganic Chemistry, Moscow, Russia
- National Research Centre "Kurchatov Institute", Centre for Convergence of Nano-, Bio-, Information and Cognitive Sciences and Technologies, Moscow, Russia
| | - Nikolay M Borisov
- Department of Personalized Medicine, First Oncology Research and Advisory Center, Moscow, Russia.
- Laboratory of Bioinformatics, D. Rogachev Federal Research Center of Pediatric Hematology, Oncology and Immunology, Moscow, Russia.
- National Research Centre "Kurchatov Institute", Centre for Convergence of Nano-, Bio-, Information and Cognitive Sciences and Technologies, Moscow, Russia.
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11
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Fey D, Halasz M, Dreidax D, Kennedy SP, Hastings JF, Rauch N, Munoz AG, Pilkington R, Fischer M, Westermann F, Kolch W, Kholodenko BN, Croucher DR. Signaling pathway models as biomarkers: Patient-specific simulations of JNK activity predict the survival of neuroblastoma patients. Sci Signal 2015; 8:ra130. [DOI: 10.1126/scisignal.aab0990] [Citation(s) in RCA: 118] [Impact Index Per Article: 13.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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12
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Birtwistle MR. Analytical reduction of combinatorial complexity arising from multiple protein modification sites. J R Soc Interface 2015; 12:rsif.2014.1215. [PMID: 25519995 DOI: 10.1098/rsif.2014.1215] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Combinatorial complexity is a major obstacle to ordinary differential equation (ODE) modelling of biochemical networks. For example, a protein with 10 sites that can each be unphosphorylated, phosphorylated or bound to adaptor protein requires 3(10) ODEs. This problem is often dealt with by making ad hoc assumptions which have unclear validity and disallow modelling of site-specific dynamics. Such site-specific dynamics, however, are important in many biological systems. We show here that for a common biological situation where adaptors bind modified sites, binding is slow relative to modification/demodification, and binding to one modified site hinders binding to other sites, for a protein with n modification sites and m adaptor proteins the number of ODEs needed to simulate the site-specific dynamics of biologically relevant, lumped bound adaptor states is independent of the number of modification sites and equal to m + 1, giving a significant reduction in system size. These considerations can be relaxed considerably while retaining reasonably accurate descriptions of the true system dynamics. We apply the theory to model, using only 11 ODEs, the dynamics of ligand-induced phosphorylation of nine tyrosines on epidermal growth factor receptor (EGFR) and primary recruitment of six signalling proteins (Grb2, PI3K, PLCγ1, SHP2, RasA1 and Shc1). The model quantitatively accounts for experimentally determined site-specific phosphorylation and dephosphorylation rates, differential affinities of binding proteins for the phosphorylated sites and binding protein expression levels. Analysis suggests that local concentration of site-specific phosphatases such as SHP2 in membrane subdomains by a factor of approximately 10(7) is critical for effective site-specific regulation. We further show how our framework can be extended with minimal effort to consider binding cooperativity between Grb2 and c-Cbl, which is important for receptor trafficking. Our theory has potentially broad application to reduce combinatorial complexity and allow practical simulation of a variety ODE models relevant to systems biology and pharmacology applications to allow exploration of key aspects of complexity that control signal flux.
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Affiliation(s)
- Marc R Birtwistle
- Department of Pharmacology and Systems Therapeutics, Icahn School of Medicine at Mount Sinai, One Gustave L. Levy Place, New York, NY 10029, USA
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13
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Hogg JS, Harris LA, Stover LJ, Nair NS, Faeder JR. Exact hybrid particle/population simulation of rule-based models of biochemical systems. PLoS Comput Biol 2014; 10:e1003544. [PMID: 24699269 PMCID: PMC3974646 DOI: 10.1371/journal.pcbi.1003544] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2013] [Accepted: 02/03/2014] [Indexed: 11/19/2022] Open
Abstract
Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility. Rule-based modeling is a modeling paradigm that addresses the problem of combinatorial complexity in biochemical systems. The key idea is to specify only those components of a biological macromolecule that are directly involved in a biochemical transformation. Until recently, this “pattern-based” approach greatly simplified the process of model building but did nothing to improve the performance of model simulation. This changed with the introduction of “network-free” simulation methods, which operate directly on the compressed rule set of a rule-based model rather than on a fully-enumerated set of reactions and species. However, these methods represent every molecule in a system as a particle, limiting their use to systems containing less than a few million molecules. Here, we describe an extension to the network-free approach that treats rare, complex species as particles and plentiful, simple species as population variables, while retaining the exact dynamics of the model system. By making more efficient use of computational resources for species that do not require the level of detail of a particle representation, this hybrid particle/population approach can simulate systems much larger than is possible using network-free methods and is an important step towards realizing the practical simulation of detailed, mechanistic models of whole cells.
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Affiliation(s)
- Justin S. Hogg
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Leonard A. Harris
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Lori J. Stover
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - Niketh S. Nair
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
| | - James R. Faeder
- Department of Computational and Systems Biology, University of Pittsburgh School of Medicine, Pittsburgh, Pennsylvania, United States of America
- * E-mail:
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14
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Santra T, Kolch W, Kholodenko BN. Navigating the multilayered organization of eukaryotic signaling: a new trend in data integration. PLoS Comput Biol 2014; 10:e1003385. [PMID: 24550716 PMCID: PMC3923657 DOI: 10.1371/journal.pcbi.1003385] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The ever-increasing capacity of biological molecular data acquisition outpaces our ability to understand the meaningful relationships between molecules in a cell. Multiple databases were developed to store and organize these molecular data. However, emerging fundamental questions about concerted functions of these molecules in hierarchical cellular networks are poorly addressed. Here we review recent advances in the development of publically available databases that help us analyze the signal integration and processing by multilayered networks that specify biological responses in model organisms and human cells
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Affiliation(s)
- Tapesh Santra
- Systems Biology Ireland, University College Dublin, Belfield, Dublin, Ireland
| | - Walter Kolch
- Systems Biology Ireland, University College Dublin, Belfield, Dublin, Ireland
- Conway Institute of Biomolecular and Biomedical Research, University College Dublin, Belfield, Dublin, Ireland
- School of Medicine and Medical Science, University College Dublin, Belfield, Dublin, Ireland
| | - Boris N. Kholodenko
- Systems Biology Ireland, University College Dublin, Belfield, Dublin, Ireland
- Conway Institute of Biomolecular and Biomedical Research, University College Dublin, Belfield, Dublin, Ireland
- School of Medicine and Medical Science, University College Dublin, Belfield, Dublin, Ireland
- * E-mail:
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Duan G, Walther D, Schulze WX. Reconstruction and analysis of nutrient-induced phosphorylation networks in Arabidopsis thaliana. FRONTIERS IN PLANT SCIENCE 2013; 4:540. [PMID: 24400017 PMCID: PMC3872036 DOI: 10.3389/fpls.2013.00540] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/24/2013] [Accepted: 12/12/2013] [Indexed: 05/23/2023]
Abstract
Elucidating the dynamics of molecular processes in living organisms in response to external perturbations is a central goal in modern systems biology. We investigated the dynamics of protein phosphorylation events in Arabidopsis thaliana exposed to changing nutrient conditions. Phosphopeptide expression levels were detected at five consecutive time points over a time interval of 30 min after nutrient resupply following prior starvation. The three tested inorganic, ionic nutrients NH(+) 4, NO(-) 3, PO(3-) 4 elicited similar phosphosignaling responses that were distinguishable from those invoked by the sugars mannitol, sucrose. When embedded in the protein-protein interaction network of Arabidopsis thaliana, phosphoproteins were found to exhibit a higher degree compared to average proteins. Based on the time-series data, we reconstructed a network of regulatory interactions mediated by phosphorylation. The performance of different network inference methods was evaluated by the observed likelihood of physical interactions within and across different subcellular compartments and based on gene ontology semantic similarity. The dynamic phosphorylation network was then reconstructed using a Pearson correlation method with added directionality based on partial variance differences. The topology of the inferred integrated network corresponds to an information dissemination architecture, in which the phosphorylation signal is passed on to an increasing number of phosphoproteins stratified into an initiation, processing, and effector layer. Specific phosphorylation peptide motifs associated with the distinct layers were identified indicating the action of layer-specific kinases. Despite the limited temporal resolution, combined with information on subcellular location, the available time-series data proved useful for reconstructing the dynamics of the molecular signaling cascade in response to nutrient stress conditions in the plant Arabidopsis thaliana.
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Affiliation(s)
- Guangyou Duan
- Max Planck Institute of Molecular Plant PhysiologyPotsdam, Germany
| | - Dirk Walther
- Max Planck Institute of Molecular Plant PhysiologyPotsdam, Germany
| | - Waltraud X. Schulze
- Max Planck Institute of Molecular Plant PhysiologyPotsdam, Germany
- Department of Plant Systems Biology, Universität HohenheimStuttgart, Germany
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16
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Rother M, Münzner U, Thieme S, Krantz M. Information content and scalability in signal transduction network reconstruction formats. MOLECULAR BIOSYSTEMS 2013; 9:1993-2004. [PMID: 23636168 DOI: 10.1039/c3mb00005b] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
One of the first steps towards holistic understanding of cellular networks is the integration of the available information in a human and machine readable format. This network reconstruction process is well established for metabolic networks, and numerous genome wide metabolic reconstructions are already available. Extending these strategies to signalling networks has proven difficult, primarily due to the combinatorial nature of regulatory modifications. The combinatorial nature of possible protein-protein interactions and post translational modifications affects both network size and the correspondence between the reconstructed network and the underlying empirical data. Here, we discuss different approaches to reconstruction of signal transduction networks. We divide the current approaches into topological, specific state based and reaction-contingency based, and discuss their different information content and scalability. The discussion focusses on graphical formats but the points are in general applicable also to mathematical models and databases. While the formats have complementary strengths especially for small networks, reaction-contingency based formats have a number of advantages in the light of global network reconstruction. In particular, they minimise the need for assumptions, maximise the congruence with empirical data, and scale efficiently with network size.
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Affiliation(s)
- Magdalena Rother
- Theoretical Biophysics, Humboldt-Universität zu Berlin, Invalidenstr. 42, 10115 Berlin, Germany
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17
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Moenke G, Falcke M, Thurley K. Hierarchic stochastic modelling applied to intracellular Ca(2+) signals. PLoS One 2012; 7:e51178. [PMID: 23300536 PMCID: PMC3531454 DOI: 10.1371/journal.pone.0051178] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2012] [Accepted: 10/30/2012] [Indexed: 11/19/2022] Open
Abstract
Important biological processes like cell signalling and gene expression have noisy components and are very complex at the same time. Mathematical analysis of such systems has often been limited to the study of isolated subsystems, or approximations are used that are difficult to justify. Here we extend a recently published method (Thurley and Falcke, PNAS 2011) which is formulated in observable system configurations instead of molecular transitions. This reduces the number of system states by several orders of magnitude and avoids fitting of kinetic parameters. The method is applied to Ca(2+) signalling. Ca(2+) is a ubiquitous second messenger transmitting information by stochastic sequences of concentration spikes, which arise by coupling of subcellular Ca(2+) release events (puffs). We derive analytical expressions for a mechanistic Ca(2+) model, based on recent data from live cell imaging, and calculate Ca(2+) spike statistics in dependence on cellular parameters like stimulus strength or number of Ca(2+) channels. The new approach substantiates a generic Ca(2+) model, which is a very convenient way to simulate Ca(2+) spike sequences with correct spiking statistics.
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Affiliation(s)
- Gregor Moenke
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - Martin Falcke
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
| | - Keven Thurley
- Mathematical Cell Physiology, Max Delbrück Center for Molecular Medicine, Berlin, Germany
- Institute for Theoretical Biology, Charité Universitätsmedizin, Berlin, Germany
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18
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Fey D, Croucher DR, Kolch W, Kholodenko BN. Crosstalk and signaling switches in mitogen-activated protein kinase cascades. Front Physiol 2012; 3:355. [PMID: 23060802 PMCID: PMC3449335 DOI: 10.3389/fphys.2012.00355] [Citation(s) in RCA: 121] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2012] [Accepted: 08/19/2012] [Indexed: 12/24/2022] Open
Abstract
Mitogen-activated protein kinase (MAPK) cascades control cell fate decisions, such as proliferation, differentiation, and apoptosis by integrating and processing intra- and extracellular cues. However, similar MAPK kinetic profiles can be associated with opposing cellular decisions depending on cell type, signal strength, and dynamics. This implies that signaling by each individual MAPK cascade has to be considered in the context of the entire MAPK network. Here, we develop a dynamic model of feedback and crosstalk for the three major MAPK cascades; extracellular signal-regulated kinase (ERK), p38 mitogen-activated protein kinase (p38), c-Jun N-terminal kinase (JNK), and also include input from protein kinase B (AKT) signaling. Focusing on the bistable activation characteristics of the JNK pathway, this model explains how pathway crosstalk harmonizes different MAPK responses resulting in pivotal cell fate decisions. We show that JNK can switch from a transient to sustained activity due to multiple positive feedback loops. Once activated, positive feedback locks JNK in a highly active state and promotes cell death. The switch is modulated by the ERK, p38, and AKT pathways. ERK activation enhances the dual specificity phosphatase (DUSP) mediated dephosphorylation of JNK and shifts the threshold of the apoptotic switch to higher inputs. Activation of p38 restores the threshold by inhibiting ERK activity via the PP1 or PP2A phosphatases. Finally, AKT activation inhibits the JNK positive feedback, thus abrogating the apoptotic switch and allowing only proliferative signaling. Our model facilitates understanding of how cancerous deregulations disturb MAPK signal processing and provides explanations for certain drug resistances. We highlight a critical role of DUSP1 and DUSP2 expression patterns in facilitating the switching of JNK activity and show how oncogene induced ERK hyperactivity prevents the normal apoptotic switch explaining the failure of certain drugs to induce apoptosis.
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Affiliation(s)
- Dirk Fey
- Systems Biology Ireland, University College Dublin Dublin, Ireland
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19
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Radulescu O, Gorban AN, Zinovyev A, Noel V. Reduction of dynamical biochemical reactions networks in computational biology. Front Genet 2012; 3:131. [PMID: 22833754 PMCID: PMC3400272 DOI: 10.3389/fgene.2012.00131] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2012] [Accepted: 06/26/2012] [Indexed: 12/23/2022] Open
Abstract
Biochemical networks are used in computational biology, to model mechanistic details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multiscaleness, an important property of these networks, can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler models, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state (QSS) and quasi-equilibrium approximations (QE), and provide practical recipes for model reduction of linear and non-linear networks. We also discuss the application of model reduction to the problem of parameter identification, via backward pruning machine learning techniques.
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Affiliation(s)
- O. Radulescu
- DIMNP UMR CNRS, University of Montpellier 2Montpellier, France
| | - A. N. Gorban
- Department of Mathematics, University of LeicesterLE, UK
| | - A. Zinovyev
- Institut Curie, INSERM/Curie/Mines ParisTechParis, France
| | - V. Noel
- IRMAR UMR, University of Rennes 1Rennes, France
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20
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Heitzler D, Durand G, Gallay N, Rizk A, Ahn S, Kim J, Violin JD, Dupuy L, Gauthier C, Piketty V, Crépieux P, Poupon A, Clément F, Fages F, Lefkowitz RJ, Reiter E. Competing G protein-coupled receptor kinases balance G protein and β-arrestin signaling. Mol Syst Biol 2012; 8:590. [PMID: 22735336 PMCID: PMC3397412 DOI: 10.1038/msb.2012.22] [Citation(s) in RCA: 65] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2011] [Accepted: 05/23/2012] [Indexed: 01/14/2023] Open
Abstract
The molecular mechanisms and hidden dynamics governing ERK activation by the angiotensin II type 1A receptor are studied and deciphered, revealing a signal balancing mechanism that is found to be relevant to a range of other seven transmembrane receptors. ![]()
An ODE-based dynamical model of ERK activation by the prototypical angiotensin II type-1A seven transmembrane receptor has been built and validated. In order to deal with a limited number of experimental read-outs, unknown parameters have been inferred by simultaneously fitting control and perturbed conditions. In addition to its well-established function in G-protein uncoupling, G protein-coupled receptor kinase 2 has been shown to exert a strong negative effect on β-arrestin-dependent signaling and by doing so, to balance G-protein and β-arrestin signaling. This novel function of G protein-coupled receptor kinase 2 has also been evidenced in primary vascular smooth muscle cells naturally expressing the AT1AR and in HEK293 cells expressing other 7TMRs.
Seven-transmembrane receptors (7TMRs) are involved in nearly all aspects of chemical communications and represent major drug targets. 7TMRs transmit their signals not only via heterotrimeric G proteins but also through β-arrestins, whose recruitment to the activated receptor is regulated by G protein-coupled receptor kinases (GRKs). In this paper, we combined experimental approaches with computational modeling to decipher the molecular mechanisms as well as the hidden dynamics governing extracellular signal-regulated kinase (ERK) activation by the angiotensin II type 1A receptor (AT1AR) in human embryonic kidney (HEK)293 cells. We built an abstracted ordinary differential equations (ODE)-based model that captured the available knowledge and experimental data. We inferred the unknown parameters by simultaneously fitting experimental data generated in both control and perturbed conditions. We demonstrate that, in addition to its well-established function in the desensitization of G-protein activation, GRK2 exerts a strong negative effect on β-arrestin-dependent signaling through its competition with GRK5 and 6 for receptor phosphorylation. Importantly, we experimentally confirmed the validity of this novel GRK2-dependent mechanism in both primary vascular smooth muscle cells naturally expressing the AT1AR, and HEK293 cells expressing other 7TMRs.
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Affiliation(s)
- Domitille Heitzler
- BIOS Group, INRA, UMR85, Unité Physiologie de la Reproduction et des Comportements, Nouzilly, France
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21
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Saiz L. The physics of protein-DNA interaction networks in the control of gene expression. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:193102. [PMID: 22516977 DOI: 10.1088/0953-8984/24/19/193102] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Protein-DNA interaction networks play a central role in many fundamental cellular processes. In gene regulation, physical interactions and reactions among the molecular components together with the physical properties of DNA control how genes are turned on and off. A key player in all these processes is the inherent flexibility of DNA, which provides an avenue for long-range interactions between distal DNA elements through DNA looping. Such versatility enables multiple interactions and results in additional complexity that is remarkably difficult to address with traditional approaches. This topical review considers recent advances in statistical physics methods to study the assembly of protein-DNA complexes with loops, their effects in the control of gene expression, and their explicit application to the prototypical lac operon genetic system of the E. coli bacterium. In the last decade, it has been shown that the underlying physical properties of DNA looping can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including the balance between robustness and sensitivity of the induction process. These physical properties are largely dependent on the free energy of DNA looping, which accounts for DNA bending and twisting effects. These new physical methods have also been used in reverse to uncover the actual in vivo free energy of looping double-stranded DNA in living cells, which was not possible with existing experimental techniques. The results obtained for DNA looping by the lac repressor inside the E. coli bacterium showed a more malleable DNA than expected as a result of the interplay of the simultaneous presence of two distinct conformations of looped DNA.
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Affiliation(s)
- Leonor Saiz
- Department of Biomedical Engineering, University of California, 451 East Health Sciences Drive, Davis, CA 95616, USA.
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22
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Kholodenko B, Yaffe MB, Kolch W. Computational approaches for analyzing information flow in biological networks. Sci Signal 2012; 5:re1. [PMID: 22510471 DOI: 10.1126/scisignal.2002961] [Citation(s) in RCA: 126] [Impact Index Per Article: 10.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
The advancements in "omics" (proteomics, genomics, lipidomics, and metabolomics) technologies have yielded large inventories of genes, transcripts, proteins, and metabolites. The challenge is to find out how these entities work together to regulate the processes by which cells respond to external and internal signals. Mathematical and computational modeling of signaling networks has a key role in this task, and network analysis provides insights into biological systems and has applications for medicine. Here, we review experimental and theoretical progress and future challenges toward this goal. We focus on how networks are reconstructed from data, how these networks are structured to control the flow of biological information, and how the design features of the networks specify biological decisions.
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Affiliation(s)
- Boris Kholodenko
- Systems Biology Ireland, University College Dublin, Belfield, Dublin 4, Ireland
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23
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Abstract
A kinase anchoring proteins (AKAPs) bind multiple signaling proteins and have subcellular targeting domains that allow them to greatly impact cellular signaling. AKAPs localize, specify, amplify, and accelerate signal transduction within the cell by bringing signaling proteins together in space and time. AKAPs also organize higher-order network motifs such as feed forward and feedback loops that may create complex network responses, including adaptation, oscillation, and ultrasensitivity. Computational models have begun to provide an insight into how AKAPs regulate signaling dynamics and cardiovascular pathophysiology. Models of mitogen-activated protein kinase and epidermal growth factor receptor scaffolds have revealed additional design principles and new methods for representing signaling scaffolds mathematically. Coupling computational modeling with quantitative experimental approaches will be increasingly necessary for dissecting the diverse information processing functions performed by AKAP signaling complexes.
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24
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Nguyen LK, Matallanas D, Croucher DR, von Kriegsheim A, Kholodenko BN. Signalling by protein phosphatases and drug development: a systems-centred view. FEBS J 2012; 280:751-65. [PMID: 22340367 DOI: 10.1111/j.1742-4658.2012.08522.x] [Citation(s) in RCA: 42] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Protein modification cycles catalysed by opposing enzymes, such as kinases and phosphatases, form the backbone of signalling networks. Although, historically, kinases have been at the research forefront, a systems-centred approach reveals predominant roles for phosphatases in controlling the network response times and spatio-temporal profiles of signalling activities. Emerging evidence suggests that phosphatase kinetics are critical for network function and cell-fate decisions. Protein phosphatases operate as both immediate and delayed regulators of signal transduction, capable of attenuating or amplifying signalling. This versatility of phosphatase action emphasizes the need for systems biology approaches to understand cellular signalling networks and predict the cellular outcomes of combinatorial drug interventions.
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Affiliation(s)
- Lan K Nguyen
- Systems Biology Ireland, University College Dublin, Belfield, Ireland
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25
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Modeling Signaling Networks Using High-throughput Phospho-proteomics. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2012; 736:19-57. [DOI: 10.1007/978-1-4419-7210-1_2] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
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26
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Yang J, Meng X, Hlavacek WS. Rule-based modelling and simulation of biochemical systems with molecular finite automata. IET Syst Biol 2011; 4:453-66. [PMID: 21073243 DOI: 10.1049/iet-syb.2010.0015] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
The authors propose a theoretical formalism, molecular finite automata (MFA), to describe individual proteins as rule-based computing machines. The MFA formalism provides a framework for modelling individual protein behaviours and systems-level dynamics via construction of programmable and executable machines. Models specified within this formalism explicitly represent the context-sensitive dynamics of individual proteins driven by external inputs and represent protein-protein interactions as synchronised machine reconfigurations. Both deterministic and stochastic simulations can be applied to quantitatively compute the dynamics of MFA models. They apply the MFA formalism to model and simulate a simple example of a signal-transduction system that involves an MAP kinase cascade and a scaffold protein.
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Affiliation(s)
- J Yang
- Chinese Academy of Sciences, Max Plank Society Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Shanghai, People's Republic of China.
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27
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28
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29
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Smith GR, Shanley DP. Modelling the response of FOXO transcription factors to multiple post-translational modifications made by ageing-related signalling pathways. PLoS One 2010; 5:e11092. [PMID: 20567500 PMCID: PMC2886341 DOI: 10.1371/journal.pone.0011092] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2010] [Accepted: 05/01/2010] [Indexed: 01/10/2023] Open
Abstract
FOXO transcription factors are an important, conserved family of regulators of cellular processes including metabolism, cell-cycle progression, apoptosis and stress resistance. They are required for the efficacy of several of the genetic interventions that modulate lifespan. FOXO activity is regulated by multiple post-translational modifications (PTMs) that affect its subcellular localization, half-life, DNA binding and transcriptional activity. Here, we show how a mathematical modelling approach can be used to simulate the effects, singly and in combination, of these PTMs. Our model is implemented using the Systems Biology Markup Language (SBML), generated by an ancillary program and simulated in a stochastic framework. The use of the ancillary program to generate the SBML is necessary because the possibility that many regulatory PTMs may be added, each independently of the others, means that a large number of chemically distinct forms of the FOXO molecule must be taken into account, and the program is used to generate them. Although the model does not yet include detailed representations of events upstream and downstream of FOXO, we show how it can qualitatively, and in some cases quantitatively, reproduce the known effects of certain treatments that induce various single and multiple PTMs, and allows for a complex spatiotemporal interplay of effects due to the activation of multiple PTM-inducing treatments. Thus, it provides an important framework to integrate current knowledge about the behaviour of FOXO. The approach should be generally applicable to other proteins experiencing multiple regulations.
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Affiliation(s)
- Graham R. Smith
- Henry Wellcome Laboratory for Biogerontology, Institute for Ageing and Health, Newcastle University, Newcastle upon Tyne, United Kingdom
| | - Daryl P. Shanley
- Henry Wellcome Laboratory for Biogerontology, Institute for Ageing and Health, Newcastle University, Newcastle upon Tyne, United Kingdom
- * E-mail:
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30
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Ghaffari N, Ivanov I, Qian X, Dougherty ER. A CoD-based reduction algorithm for designing stationary control policies on Boolean networks. ACTA ACUST UNITED AC 2010; 26:1556-63. [PMID: 20421196 DOI: 10.1093/bioinformatics/btq225] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
Abstract
MOTIVATION Gene regulatory networks serve as models from which to derive therapeutic intervention strategies, in particular, stationary control policies over time that shift the probability mass of the steady state distribution (SSD) away from states associated with undesirable phenotypes. Derivation of control policies is hindered by the high-dimensional state spaces associated with gene regulatory networks. Hence, network reduction is a fundamental issue for intervention. RESULTS The network model that has been most used for the study of intervention in gene regulatory networks is the probabilistic Boolean network (PBN), which is a collection of constituent Boolean networks (BNs) with perturbation. In this article, we propose an algorithm that reduces a BN with perturbation, designs a control policy on the reduced network and then induces that policy to the original network. The coefficient of determination (CoD) is used to choose a gene for deletion, and a reduction mapping is used to rewire the remaining genes. This CoD-reduction procedure is used to construct a reduced network, then either the previously proposed mean first-passage time (MFPT) or SSD stationary control policy is designed on the reduced network, and these policies are induced to the original network. The efficacy of the overall algorithm is demonstrated on networks of 10 genes or less, where it is possible to compare the steady state shifts of the induced and original policies (because the latter can be derived), and by applying it to a 17-gene gastrointestinal network where it is shown that there is substantial beneficial steady state shift. AVAILABILITY The code for the algorithms is available at: http://gsp.tamu.edu/Publications/supplementary/ghaffari10a/ Please Contact Noushin Ghaffari at nghaffari@tamu.edu for further questions. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Noushin Ghaffari
- Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843, USA.
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31
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Sunnåker M, Schmidt H, Jirstrand M, Cedersund G. Zooming of states and parameters using a lumping approach including back-translation. BMC SYSTEMS BIOLOGY 2010; 4:28. [PMID: 20298607 PMCID: PMC2853501 DOI: 10.1186/1752-0509-4-28] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2009] [Accepted: 03/18/2010] [Indexed: 12/17/2022]
Abstract
Background Systems biology models tend to become large since biological systems often consist of complex networks of interacting components, and since the models usually are developed to reflect various mechanistic assumptions of those networks. Nevertheless, not all aspects of the model are equally interesting in a given setting, and normally there are parts that can be reduced without affecting the relevant model performance. There are many methods for model reduction, but few or none of them allow for a restoration of the details of the original model after the simplified model has been simulated. Results We present a reduction method that allows for such a back-translation from the reduced to the original model. The method is based on lumping of states, and includes a general and formal algorithm for both determining appropriate lumps, and for calculating the analytical back-translation formulas. The lumping makes use of efficient methods from graph-theory and ϵ-decomposition and is derived and exemplified on two published models for fluorescence emission in photosynthesis. The bigger of these models is reduced from 26 to 6 states, with a negligible deviation from the reduced model simulations, both when comparing simulations in the states of the reduced model and when comparing back-translated simulations in the states of the original model. The method is developed in a linear setting, but we exemplify how the same concepts and approaches can be applied to non-linear problems. Importantly, the method automatically provides a reduced model with back-translations. Also, the method is implemented as a part of the systems biology toolbox for matlab, and the matlab scripts for the examples in this paper are available in the supplementary material. Conclusions Our novel lumping methodology allows for both automatic reduction of states using lumping, and for analytical retrieval of the original states and parameters without performing a new simulation. The two models can thus be considered as two degrees of zooming of the same model. This is a conceptually new development of model reduction approaches, which we think will stimulate much further research and will prove to be very useful in future modelling projects.
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Affiliation(s)
- Mikael Sunnåker
- Fraunhofer-Chalmers Research Centre for Industrial Mathematics, 412 88 Gothenburg, Sweden
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32
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Costa MN, Radhakrishnan K, Wilson BS, Vlachos DG, Edwards JS. Coupled stochastic spatial and non-spatial simulations of ErbB1 signaling pathways demonstrate the importance of spatial organization in signal transduction. PLoS One 2009; 4:e6316. [PMID: 19626123 PMCID: PMC2710010 DOI: 10.1371/journal.pone.0006316] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2009] [Accepted: 06/17/2009] [Indexed: 01/24/2023] Open
Abstract
Background The ErbB family of receptors activates intracellular signaling pathways that control cellular proliferation, growth, differentiation and apoptosis. Given these central roles, it is not surprising that overexpression of the ErbB receptors is often associated with carcinogenesis. Therefore, extensive laboratory studies have been devoted to understanding the signaling events associated with ErbB activation. Methodology/Principal Findings Systems biology has contributed significantly to our current understanding of ErbB signaling networks. However, although computational models have grown in complexity over the years, little work has been done to consider the spatial-temporal dynamics of receptor interactions and to evaluate how spatial organization of membrane receptors influences signaling transduction. Herein, we explore the impact of spatial organization of the epidermal growth factor receptor (ErbB1/EGFR) on the initiation of downstream signaling. We describe the development of an algorithm that couples a spatial stochastic model of membrane receptors with a nonspatial stochastic model of the reactions and interactions in the cytosol. This novel algorithm provides a computationally efficient method to evaluate the effects of spatial heterogeneity on the coupling of receptors to cytosolic signaling partners. Conclusions/Significance Mathematical models of signal transduction rarely consider the contributions of spatial organization due to high computational costs. A hybrid stochastic approach simplifies analyses of the spatio-temporal aspects of cell signaling and, as an example, demonstrates that receptor clustering contributes significantly to the efficiency of signal propagation from ligand-engaged growth factor receptors.
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Affiliation(s)
- Michelle N. Costa
- Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico, United States of America
| | - Krishnan Radhakrishnan
- Department of Pathology, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, United States of America
- Cancer Research and Treatment Center, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, United States of America
| | - Bridget S. Wilson
- Department of Pathology, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, United States of America
- Cancer Research and Treatment Center, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, United States of America
| | - Dionisios G. Vlachos
- Department of Chemical Engineering, University of Delaware, Newark, Delaware, United States of America
| | - Jeremy S. Edwards
- Department of Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico, United States of America
- Cancer Research and Treatment Center, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, United States of America
- Molecular Genetics and Microbiology, University of New Mexico Health Sciences Center, Albuquerque, New Mexico, United States of America
- * E-mail:
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Systems-level interactions between insulin-EGF networks amplify mitogenic signaling. Mol Syst Biol 2009; 5:256. [PMID: 19357636 PMCID: PMC2683723 DOI: 10.1038/msb.2009.19] [Citation(s) in RCA: 155] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2008] [Accepted: 02/23/2009] [Indexed: 01/01/2023] Open
Abstract
Crosstalk mechanisms have not been studied as thoroughly as individual signaling pathways. We exploit experimental and computational approaches to reveal how a concordant interplay between the insulin and epidermal growth factor (EGF) signaling networks can potentiate mitogenic signaling. In HEK293 cells, insulin is a poor activator of the Ras/ERK (extracellular signal-regulated kinase) cascade, yet it enhances ERK activation by low EGF doses. We find that major crosstalk mechanisms that amplify ERK signaling are localized upstream of Ras and at the Ras/Raf level. Computational modeling unveils how critical network nodes, the adaptor proteins GAB1 and insulin receptor substrate (IRS), Src kinase, and phosphatase SHP2, convert insulin-induced increase in the phosphatidylinositol-3,4,5-triphosphate (PIP3) concentration into enhanced Ras/ERK activity. The model predicts and experiments confirm that insulin-induced amplification of mitogenic signaling is abolished by disrupting PIP3-mediated positive feedback via GAB1 and IRS. We demonstrate that GAB1 behaves as a non-linear amplifier of mitogenic responses and insulin endows EGF signaling with robustness to GAB1 suppression. Our results show the feasibility of using computational models to identify key target combinations and predict complex cellular responses to a mixture of external cues.
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Colvin J, Monine MI, Faeder JR, Hlavacek WS, Von Hoff DD, Posner RG. Simulation of large-scale rule-based models. Bioinformatics 2009; 25:910-7. [PMID: 19213740 PMCID: PMC2660871 DOI: 10.1093/bioinformatics/btp066] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2008] [Revised: 01/13/2009] [Accepted: 01/27/2009] [Indexed: 01/26/2023] Open
Abstract
MOTIVATION Interactions of molecules, such as signaling proteins, with multiple binding sites and/or multiple sites of post-translational covalent modification can be modeled using reaction rules. Rules comprehensively, but implicitly, define the individual chemical species and reactions that molecular interactions can potentially generate. Although rules can be automatically processed to define a biochemical reaction network, the network implied by a set of rules is often too large to generate completely or to simulate using conventional procedures. To address this problem, we present DYNSTOC, a general-purpose tool for simulating rule-based models. RESULTS DYNSTOC implements a null-event algorithm for simulating chemical reactions in a homogenous reaction compartment. The simulation method does not require that a reaction network be specified explicitly in advance, but rather takes advantage of the availability of the reaction rules in a rule-based specification of a network to determine if a randomly selected set of molecular components participates in a reaction during a time step. DYNSTOC reads reaction rules written in the BioNetGen language which is useful for modeling protein-protein interactions involved in signal transduction. The method of DYNSTOC is closely related to that of StochSim. DYNSTOC differs from StochSim by allowing for model specification in terms of BNGL, which extends the range of protein complexes that can be considered in a model. DYNSTOC enables the simulation of rule-based models that cannot be simulated by conventional methods. We demonstrate the ability of DYNSTOC to simulate models accounting for multisite phosphorylation and multivalent binding processes that are characterized by large numbers of reactions. AVAILABILITY DYNSTOC is free for non-commercial use. The C source code, supporting documentation and example input files are available at http://public.tgen.org/dynstoc/. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Joshua Colvin
- Computational Biology Division, Translational Genomics Research Institute, Phoenix, AZ 85004, USA.
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Bruggeman FJ, Snoep JL, Westerhoff HV. Control, responses and modularity of cellular regulatory networks: a control analysis perspective. IET Syst Biol 2009; 2:397-410. [PMID: 19045835 DOI: 10.1049/iet-syb:20070065] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
Cells adapt to changes in environmental conditions through the concerted action of signalling, gene expression and metabolic subsystems. The authors will discuss a theoretical framework addressing such integrated systems. This 'hierarchical analysis' was first developed as an extension to a metabolic control analysis. It builds on the phenomenon that often the communication between signalling, gene expression and metabolic subsystems is almost exclusively via regulatory interactions and not via mass flow interactions. This allows for the treatment of the said subsystems as 'levels' in a hierarchical view of the organisation of the molecular reaction network of cells. Such a hierarchical approach has as a major advantage that levels can be analysed conceptually in isolation of each other (from a local intra-level perspective) and at a later stage integrated via their interactions (from a global inter-level perspective). Hereby, it allows for a modular approach with variable scope. A number of different approaches have been developed for the analysis of hierarchical systems, for example hierarchical control analysis and modular response analysis. The authors, here, review these methods and illustrate the strength of these types of analyses using a core model of a system with gene expression, metabolic and signal transduction levels.
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Affiliation(s)
- F J Bruggeman
- Vrije Universiteit, Molecular Cell Physiology, Faculty of Earth and Life sciences, Amsterdam, The Netherlands.
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36
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Collins SD, Chatterjee A, Vlachos DG. Coarse-grained kinetic Monte Carlo models: Complex lattices, multicomponent systems, and homogenization at the stochastic level. J Chem Phys 2009; 129:184101. [PMID: 19045380 DOI: 10.1063/1.3005225] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
On-lattice kinetic Monte Carlo (KMC) simulations have extensively been applied to numerous systems. However, their applicability is severely limited to relatively short time and length scales. Recently, the coarse-grained MC (CGMC) method was introduced to greatly expand the reach of the lattice KMC technique. Herein, we extend the previous spatial CGMC methods to multicomponent species and/or site types. The underlying theory is derived and numerical examples are presented to demonstrate the method. Furthermore, we introduce the concept of homogenization at the stochastic level over all site types of a spatially coarse-grained cell. Homogenization provides a novel coarsening of the number of processes, an important aspect for complex problems plagued by the existence of numerous microscopic processes (combinatorial complexity). As expected, the homogenized CGMC method outperforms the traditional KMC method on computational cost while retaining good accuracy.
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Affiliation(s)
- Stuart D Collins
- Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716, USA
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37
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Saiz L, Vilar JMG. Protein-protein/DNA interaction networks: versatile macromolecular structures for the control of gene expression. IET Syst Biol 2009; 2:247-55. [PMID: 19045820 DOI: 10.1049/iet-syb:20080091] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
The assembly of macromolecular structures consisting of proteins and DNA lies at the core of many fundamental cellular processes, such as transcription, recombination and replication. A common theme to all these processes is DNA looping, which provides the backbone for the required long-range interactions on DNA and results in further complexity that is exceptionally difficult to tackle with traditional quantitative approaches. Here, recent advances in mathematical and computational methods to study the assembly of protein-protein/DNA complexes with loops and their effects in the cellular behaviour through gene regulation are reviewed. The interplay between multisite DNA looping and DNA bending regulatory proteins, such as the catabolite activator protein (CAP), and on its physiological consequences is focused on. It has become clear in the last few years that the complexity that looping brings about can actively control transcriptional noise and cell-to-cell variability. Here, it is shown that the DNA looping, through the effects of CAP, can also control the balance between robustness and sensitivity of the induction of gene expression.
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Affiliation(s)
- L Saiz
- University of California, Department of Biomedical Engineering, Davis, CA 95616, USA.
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38
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Borisov NM, Chistopolsky AS, Faeder JR, Kholodenko BN. Domain-oriented reduction of rule-based network models. IET Syst Biol 2009; 2:342-51. [PMID: 19045829 DOI: 10.1049/iet-syb:20070081] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
The coupling of membrane-bound receptors to transcriptional regulators and other effector functions is mediated by multi-domain proteins that form complex assemblies. The modularity of protein interactions lends itself to a rule-based description, in which species and reactions are generated by rules that encode the necessary context for an interaction to occur, but also can produce a combinatorial explosion in the number of chemical species that make up the signalling network. The authors have shown previously that exact network reduction can be achieved using hierarchical control relationships between sites/domains on proteins to dissect multi-domain proteins into sets of non-interacting sites, allowing the replacement of each 'full' (progenitor) protein with a set of derived auxiliary (offspring) proteins. The description of a network in terms of auxiliary proteins that have fewer sites than progenitor proteins often greatly reduces network size. The authors describe here a method for automating domain-oriented model reduction and its implementation as a module in the BioNetGen modelling package. It takes as input a standard BioNetGen model and automatically performs the following steps: 1) detecting the hierarchical control relationships between sites; 2) building up the auxiliary proteins; 3) generating a raw reduced model and 4) cleaning up the raw model to provide the correct mass balance for each chemical species in the reduced network. The authors tested the performance of this module on models representing portions of growth factor receptor and immunoreceptor-mediated signalling networks and confirmed its ability to reduce the model size and simulation cost by at least one or two orders of magnitude. Limitations of the current algorithm include the inability to reduce models based on implicit site dependencies or heterodimerisation and loss of accuracy when dynamics are computed stochastically.
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Affiliation(s)
- N M Borisov
- Thomas Jefferson University, Department of Pathology, Anatomy and Cell Biology, Philadelphia, PA 19107, USA
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39
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Abstract
Rule-based modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate site-specific details about protein-protein interactions into a model for the dynamics of a signal-transduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of protein-protein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rule-based model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rule-based modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly large-scale models for other biochemical systems.
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Affiliation(s)
- James R Faeder
- Department of Computational Biology, University of Pittsburgh School of Medicine, PA, 15260, USA
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40
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Koschorreck M, Gilles ED. ALC: automated reduction of rule-based models. BMC SYSTEMS BIOLOGY 2008; 2:91. [PMID: 18973705 PMCID: PMC2636783 DOI: 10.1186/1752-0509-2-91] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/20/2008] [Accepted: 10/31/2008] [Indexed: 01/01/2023]
Abstract
Background Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously. Results ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website. Conclusion ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.
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Affiliation(s)
- Markus Koschorreck
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr, 1, 39106 Magdeburg, Germany.
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41
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Robust simplifications of multiscale biochemical networks. BMC SYSTEMS BIOLOGY 2008; 2:86. [PMID: 18854041 PMCID: PMC2654786 DOI: 10.1186/1752-0509-2-86] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/12/2008] [Accepted: 10/14/2008] [Indexed: 12/21/2022]
Abstract
Background Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed. Results We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in [1]. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-κB pathway. Conclusion Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.
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42
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Gaffney EA, Heath JK, Kwiatkowska MZ. A mass action model of a Fibroblast Growth Factor signaling pathway and its simplification. Bull Math Biol 2008; 70:2229-63. [PMID: 18841420 DOI: 10.1007/s11538-008-9342-1] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2007] [Accepted: 05/23/2008] [Indexed: 10/21/2022]
Abstract
We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951-966, 2005, Biosystems 83, 152-166, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925-19938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter.
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Affiliation(s)
- E A Gaffney
- Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, UK.
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43
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Yang J, Monine MI, Faeder JR, Hlavacek WS. Kinetic Monte Carlo method for rule-based modeling of biochemical networks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:031910. [PMID: 18851068 PMCID: PMC2652652 DOI: 10.1103/physreve.78.031910] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2007] [Revised: 06/29/2008] [Indexed: 05/09/2023]
Abstract
We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.
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Affiliation(s)
- Jin Yang
- Chinese Academy of Sciences-Max Planck Society Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Shanghai 200031, China.
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44
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Conzelmann H, Fey D, Gilles ED. Exact model reduction of combinatorial reaction networks. BMC SYSTEMS BIOLOGY 2008; 2:78. [PMID: 18755034 PMCID: PMC2570670 DOI: 10.1186/1752-0509-2-78] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/11/2008] [Accepted: 08/28/2008] [Indexed: 11/10/2022]
Abstract
BACKGROUND Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models. RESULTS We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs. CONCLUSION The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.
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Affiliation(s)
- Holger Conzelmann
- Max-Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr, 1, 39106, Magdeburg, Germany.
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45
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Saez-Rodriguez J, Hammerle-Fickinger A, Dalal O, Klamt S, Gilles ED, Conradi C. Multistability of signal transduction motifs. IET Syst Biol 2008; 2:80-93. [PMID: 18397119 DOI: 10.1049/iet-syb:20070012] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Protein domains are the basic units of signalling processes. The mechanisms they are involved in usually follow recurring patterns, such as phosphorylation/dephosphorylation cycles. A set of common motifs was defined and their dynamic models were analysed with respect to number and stability of steady states. In a first step, Feinberg's chemical reaction network theory was used to determine whether a motif can show multistationarity or not. The analysis revealed that, apart from double-step activation motifs including a distributive mechanism, only those motifs involving an autocatalytic reaction can show multistationarity. To further characterise these motifs, a large number of randomly chosen parameter sets leading to bistability was generated, followed by a bifurcation analysis of each parameter set and a statistical evaluation of the results. The statistical results can be used to explore robustness against noise, pointing to the observation that multistationarity at the single-motif level may not be a robust property; the range of protein concentrations compatible with multistationarity is fairly narrow. Furthermore, experimental evidence suggests that protein concentrations vary substantially between cells. Considering a motif designed to be a bistable switch, this implies that fluctuation of protein concentrations between cells would prevent a significant proportion of motifs from acting as a switch. The authors consider this to be a first step towards a catalogue of fully characterised signalling modules.
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46
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Gomez-Uribe C, Verghese GC, Mirny LA. Operating regimes of signaling cycles: statics, dynamics, and noise filtering. PLoS Comput Biol 2008; 3:e246. [PMID: 18159939 PMCID: PMC2230677 DOI: 10.1371/journal.pcbi.0030246] [Citation(s) in RCA: 92] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2007] [Accepted: 10/24/2007] [Indexed: 01/11/2023] Open
Abstract
A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input–output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input–output characteristics. These results are obtained using the total quasi–steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act—in all four regimes—as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways. A cell is subjected to constantly changing environments and time-varying stimuli. Signals sensed at the cell surface are transmitted inside the cell by signaling pathways. Such pathways can transform signals in diverse ways and perform some preliminary information processing. A ubiquitous building block of signaling pathways is a simple biochemical cycle involving covalent modification of an enzyme–substrate pair. Our paper is devoted to fully characterizing the static and dynamic behavior of this simple cycle, an essential first step in understanding the behavior of interconnections of such cycles. It is known that a signaling cycle can function as a static switch, with the steady-state output being an “ultrasensitive” function of the input, i.e., changing from a low to high value for only a small change in the input. We show that there are in fact precisely four major regimes of static and dynamic operation (with ultrasensitive being one of the static regimes). Each regime has its own input–output characteristics. Despite the distinctive features of these four regimes, they all respond to time-varying stimuli by filtering out high-frequency fluctuations or noise in their inputs, while passing through the lower-frequency information-bearing variations. A cell can select the regime and tune the noise-filtering characteristics of the individual cycles in a specific signaling pathway. This tunability makes signaling cycles versatile components of elaborate cell-signaling pathways.
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Affiliation(s)
- Carlos Gomez-Uribe
- Harvard–MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - George C Verghese
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Leonid A Mirny
- Harvard–MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
- * To whom correspondence should be addressed. E-mail:
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Conzelmann H, Gilles ED. Dynamic pathway modeling of signal transduction networks: a domain-oriented approach. Methods Mol Biol 2008; 484:559-78. [PMID: 18592201 DOI: 10.1007/978-1-59745-398-1_33] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
Mathematical models of biological processes become more and more important in biology. The aim is a holistic understanding of how processes such as cellular communication, cell division, regulation, homeostasis, or adaptation work, how they are regulated, and how they react to perturbations. The great complexity of most of these processes necessitates the generation of mathematical models in order to address these questions. In this chapter we provide an introduction to basic principles of dynamic modeling and highlight both problems and chances of dynamic modeling in biology. The main focus will be on modeling of s transduction pathways, which requires the application of a special modeling approach. A common pattern, especially in eukaryotic signaling systems, is the formation of multi protein signaling complexes. Even for a small number of interacting proteins the number of distinguishable molecular species can be extremely high. This combinatorial complexity is due to the great number of distinct binding domains of many receptors and scaffold proteins involved in signal transduction. However, these problems can be overcome using a new domain-oriented modeling approach, which makes it possible to handle complex and branched signaling pathways.
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Affiliation(s)
- Holger Conzelmann
- Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
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48
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Saiz L, Vilar JMG. Ab initio thermodynamic modeling of distal multisite transcription regulation. Nucleic Acids Res 2007; 36:726-31. [PMID: 18056082 PMCID: PMC2241893 DOI: 10.1093/nar/gkm1034] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Transcription regulation typically involves the binding of proteins over long distances on multiple DNA sites that are brought close to each other by the formation of DNA loops. The inherent complexity of assembling regulatory complexes on looped DNA challenges the understanding of even the simplest genetic systems, including the prototypical lac operon. Here we implement a scalable approach based on thermodynamic molecular properties to model ab initio systems regulated through multiple DNA sites with looping. We show that this approach applied to the lac operon accurately predicts the system behavior for a wide range of cellular conditions, which include the transcription rate over five orders of magnitude as a function of the repressor concentration for wild type and all seven combinations of deletions of three operators, as well as the observed induction curves for cells with and without active catabolite activator protein. Our results provide new insights into the detailed functioning of the lac operon and reveal an efficient avenue to incorporate the required underlying molecular complexity into fully predictive models of gene regulation.
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Affiliation(s)
- Leonor Saiz
- Integrative Biological Modeling Laboratory, Computational Biology Program, Memorial Sloan-Kettering Cancer Center, New York, NY 10021, USA
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49
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Koschorreck M, Conzelmann H, Ebert S, Ederer M, Gilles ED. Reduced modeling of signal transduction - a modular approach. BMC Bioinformatics 2007; 8:336. [PMID: 17854494 PMCID: PMC2216040 DOI: 10.1186/1471-2105-8-336] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2007] [Accepted: 09/13/2007] [Indexed: 12/18/2022] Open
Abstract
Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties.
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Affiliation(s)
- Markus Koschorreck
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
| | - Holger Conzelmann
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
| | - Sybille Ebert
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
| | - Michael Ederer
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
| | - Ernst Dieter Gilles
- Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106 Magdeburg, Germany
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Abstract
The developments in the molecular biosciences have made possible a shift to combined molecular and system-level approaches to biological research under the name of Systems Biology. It integrates many types of molecular knowledge, which can best be achieved by the synergistic use of models and experimental data. Many different types of modeling approaches are useful depending on the amount and quality of the molecular data available and the purpose of the model. Analysis of such models and the structure of molecular networks have led to the discovery of principles of cell functioning overarching single species. Two main approaches of systems biology can be distinguished. Top-down systems biology is a method to characterize cells using system-wide data originating from the Omics in combination with modeling. Those models are often phenomenological but serve to discover new insights into the molecular network under study. Bottom-up systems biology does not start with data but with a detailed model of a molecular network on the basis of its molecular properties. In this approach, molecular networks can be quantitatively studied leading to predictive models that can be applied in drug design and optimization of product formation in bioengineering. In this chapter we introduce analysis of molecular network by use of models, the two approaches to systems biology, and we shall discuss a number of examples of recent successes in systems biology.
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Affiliation(s)
- Frank J Bruggeman
- Molecular Cell Physiology, Institute for Molecular Cell Biology, BioCentrum Amsterdam, Faculty of Earth and Life Sciences, Vrije Universiteit, De Boelelaan 1085, NL-1081 HIV Amsterdam, The Netherlands.
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