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Pajoh-Casco M, Vinujudson A, Enciso G. Bounds on the Ultrasensitivity of Biochemical Reaction Cascades. Bull Math Biol 2024; 86:59. [PMID: 38637362 DOI: 10.1007/s11538-024-01287-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2023] [Accepted: 03/20/2024] [Indexed: 04/20/2024]
Abstract
The ultrasensitivity of a dose response function can be quantifiably defined using the generalized Hill coefficient of the function. We examined an upper bound for the Hill coefficient of the composition of two functions, namely the product of their individual Hill coefficients. We proved that this upper bound holds for compositions of Hill functions, and that there are instances of counterexamples that exist for more general sigmoidal functions. Additionally, we tested computationally other types of sigmoidal functions, such as the logistic and inverse trigonometric functions, and we provided computational evidence that in these cases the inequality also holds. We show that in large generality there is a limit to how ultrasensitive the composition of two functions can be, which has applications to understanding signaling cascades in biochemical reactions.
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Affiliation(s)
- Marcello Pajoh-Casco
- Department of Physics and Astronomy, University of California, Irvine, 92697, USA
| | | | - German Enciso
- Department of Mathematics, University of California, Irvine, 92697, USA.
- Department of Developmental and Cell Biology, University of California, Irvine, 92697, USA.
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2
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Borowicz P, Chan H, Hauge A, Spurkland A. Adaptor proteins: Flexible and dynamic modulators of immune cell signalling. Scand J Immunol 2020; 92:e12951. [DOI: 10.1111/sji.12951] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Revised: 07/22/2020] [Accepted: 07/26/2020] [Indexed: 12/16/2022]
Affiliation(s)
- Paweł Borowicz
- Department of Molecular Medicine Institute of Basic Medical Sciences University of Oslo Oslo Norway
| | - Hanna Chan
- Department of Molecular Medicine Institute of Basic Medical Sciences University of Oslo Oslo Norway
| | - Anette Hauge
- Department of Molecular Medicine Institute of Basic Medical Sciences University of Oslo Oslo Norway
| | - Anne Spurkland
- Department of Molecular Medicine Institute of Basic Medical Sciences University of Oslo Oslo Norway
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3
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Su Z, Dhusia K, Wu Y. Understand the Functions of Scaffold Proteins in Cell Signaling by a Mesoscopic Simulation Method. Biophys J 2020; 119:2116-2126. [PMID: 33113350 DOI: 10.1016/j.bpj.2020.10.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Revised: 08/24/2020] [Accepted: 10/07/2020] [Indexed: 02/02/2023] Open
Abstract
Scaffold proteins are central players in regulating the spatial-temporal organization of many important signaling pathways in cells. They offer physical platforms to downstream signaling proteins so that their transient interactions in a crowded and heterogeneous environment of cytosol can be greatly facilitated. However, most scaffold proteins tend to simultaneously bind more than one signaling molecule, which leads to the spatial assembly of multimeric protein complexes. The kinetics of these protein oligomerizations are difficult to quantify by traditional experimental approaches. To understand the functions of scaffold proteins in cell signaling, we developed a, to our knowledge, new hybrid simulation algorithm in which both spatial organization and binding kinetics of proteins were implemented. We applied this new technique to a simple network system that contains three molecules. One molecule in the network is a scaffold protein, whereas the other two are its binding targets in the downstream signaling pathway. Each of the three molecules in the system contains two binding motifs that can interact with each other and are connected by a flexible linker. By applying the new simulation method to the model, we show that the scaffold proteins will promote not only thermodynamics but also kinetics of cell signaling given the premise that the interaction between the two signaling molecules is transient. Moreover, by changing the flexibility of the linker between two binding motifs, our results suggest that the conformational fluctuations in a scaffold protein play a positive role in recruiting downstream signaling molecules. In summary, this study showcases the capability of computational simulation in understanding the general principles of scaffold protein functions.
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Affiliation(s)
- Zhaoqian Su
- Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, New York
| | - Kalyani Dhusia
- Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, New York
| | - Yinghao Wu
- Department of Systems and Computational Biology, Albert Einstein College of Medicine, Bronx, New York.
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4
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Suwanmajo T, Ramesh V, Krishnan J. Exploring cyclic networks of multisite modification reveals origins of information processing characteristics. Sci Rep 2020; 10:16542. [PMID: 33024185 PMCID: PMC7539153 DOI: 10.1038/s41598-020-73045-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 09/07/2020] [Indexed: 12/20/2022] Open
Abstract
Multisite phosphorylation (and generally multisite modification) is a basic way of encoding substrate function and circuits/networks of post-translational modifications (PTM) are ubiquitous in cell signalling. The information processing characteristics of PTM systems are a focal point of broad interest. The ordering of modifications is a key aspect of multisite modification, and a broad synthesis of the impact of ordering of modifications is still missing. We focus on a basic class of multisite modification circuits: the cyclic mechanism, which corresponds to the same ordering of phosphorylation and dephosphorylation, and examine multiple variants involving common/separate kinases and common/separate phosphatases. This is of interest both because it is encountered in concrete cellular contexts, and because it serves as a bridge between ordered (sequential) mechanisms (representing one type of ordering) and random mechanisms (which have no ordering). We show that bistability and biphasic dose response curves of the maximally modified phosphoform are ruled out for basic structural reasons independent of parameters, while oscillations can result with even just one shared enzyme. We then examine the effect of relaxing some basic assumptions about the ordering of modification. We show computationally and analytically how bistability, biphasic responses and oscillations can be generated by minimal augmentations to the cyclic mechanism even when these augmentations involved reactions operating in the unsaturated limit. All in all, using this approach we demonstrate (1) how the cyclic mechanism (with single augmentations) represents a modification circuit using minimal ingredients (in terms of shared enzymes and sequestration of enzymes) to generate bistability and oscillations, when compared to other mechanisms, (2) new design principles for rationally designing PTM systems for a variety of behaviour, (3) a basis and a necessary step for understanding the origins and robustness of behaviour observed in basic multisite modification systems.
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Affiliation(s)
- Thapanar Suwanmajo
- Center of Excellence in Materials Science and Technology, Chiang Mai University, Chiang Mai, 50200, Thailand
- Department of Chemistry, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand
| | - Vaidhiswaran Ramesh
- Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London, London, SW7 2AZ, UK
| | - J Krishnan
- Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London, London, SW7 2AZ, UK.
- Institute for Systems and Synthetic Biology, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK.
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5
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Suwanmajo T, Krishnan J. Exploring the intrinsic behaviour of multisite phosphorylation systems as part of signalling pathways. J R Soc Interface 2019; 15:rsif.2018.0109. [PMID: 29950514 DOI: 10.1098/rsif.2018.0109] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2018] [Accepted: 05/31/2018] [Indexed: 01/13/2023] Open
Abstract
Multisite phosphorylation is a basic way of chemically encoding substrate function and a recurring feature of cell signalling pathways. A number of studies have explored information processing characteristics of multisite phosphorylation, through studies of the intrinsic kinetics. Many of these studies focus on the module in isolation. In this paper, we build a bridge to connect the behaviour of multisite modification in isolation to that as part of pathways. We study the effect of activation of the enzymes (which are basic ways in which the module may be regulated), as well the effects of the modified substrates being involved in further modifications or exiting reaction compartments. We find that these effects can induce multiple kinds of transitions, including to behaviour not seen intrinsically in the multisite modification module. We then build on these insights to investigate how these multisite modification systems can be tuned by enzyme activation to realize a range of information processing outcomes for the design of synthetic phosphorylation circuits. Connecting the complexity of multisite modification kinetics, with the pathways in which they are embedded, serves as a basis for teasing out many aspects of their interaction, providing insights of relevance in systems biology, synthetic biology/chemistry and chemical information processing.
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Affiliation(s)
- Thapanar Suwanmajo
- Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, UK.,Centre of Excellence in Materials Science and Technology, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand.,Department of Chemistry, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
| | - J Krishnan
- Department of Chemical Engineering, Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, UK .,Institute for Systems and Synthetic Biology, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
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6
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Dynamics of Posttranslational Modification Systems: Recent Progress and Future Directions. Biophys J 2019; 114:507-515. [PMID: 29414696 DOI: 10.1016/j.bpj.2017.11.3787] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2017] [Revised: 10/23/2017] [Accepted: 11/27/2017] [Indexed: 12/13/2022] Open
Abstract
Posttranslational modification of proteins is important for signal transduction, and hence significant effort has gone toward understanding how posttranslational modification networks process information. This involves, on the theory side, analyzing the dynamical systems arising from such networks. Which networks are, for instance, bistable? Which networks admit sustained oscillations? Which parameter values enable such behaviors? In this Biophysical Perspective, we highlight recent progress in this area and point out some important future directions. Along the way, we summarize several techniques for analyzing general networks, such as eliminating variables to obtain steady-state parameterizations, and harnessing results on how incorporating intermediates affects dynamics.
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7
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Petrides A, Vinnicombe G. Enzyme sequestration by the substrate: An analysis in the deterministic and stochastic domains. PLoS Comput Biol 2018; 14:e1006107. [PMID: 29771922 PMCID: PMC5976211 DOI: 10.1371/journal.pcbi.1006107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Revised: 05/30/2018] [Accepted: 03/26/2018] [Indexed: 11/19/2022] Open
Abstract
This paper is concerned with the potential multistability of protein concentrations in the cell. That is, situations where one, or a family of, proteins may sit at one of two or more different steady state concentrations in otherwise identical cells, and in spite of them being in the same environment. For models of multisite protein phosphorylation for example, in the presence of excess substrate, it has been shown that the achievable number of stable steady states can increase linearly with the number of phosphosites available. In this paper, we analyse the consequences of adding enzyme docking to these and similar models, with the resultant sequestration of phosphatase and kinase by the fully unphosphorylated and by the fully phosphorylated substrates respectively. In the large molecule numbers limit, where deterministic analysis is applicable, we prove that there are always values for these rates of sequestration which, when exceeded, limit the extent of multistability. For the models considered here, these numbers are much smaller than the affinity of the enzymes to the substrate when it is in a modifiable state. As substrate enzyme-sequestration is increased, we further prove that the number of steady states will inevitably be reduced to one. For smaller molecule numbers a stochastic analysis is more appropriate, where multistability in the large molecule numbers limit can manifest itself as multimodality of the probability distribution; the system spending periods of time in the vicinity of one mode before jumping to another. Here, we find that substrate enzyme sequestration can induce bimodality even in systems where only a single steady state can exist at large numbers. To facilitate this analysis, we develop a weakly chained diagonally dominant M-matrix formulation of the Chemical Master Equation, allowing greater insights in the way particular mechanisms, like enzyme sequestration, can shape probability distributions and therefore exhibit different behaviour across different regimes.
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Affiliation(s)
- Andreas Petrides
- Department of Engineering, University of Cambridge, Cambridge, United Kingdom
| | - Glenn Vinnicombe
- Department of Engineering, University of Cambridge, Cambridge, United Kingdom
- * E-mail:
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8
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Feng S, Sáez M, Wiuf C, Feliu E, Soyer OS. Core signalling motif displaying multistability through multi-state enzymes. J R Soc Interface 2017; 13:rsif.2016.0524. [PMID: 27733693 PMCID: PMC5095215 DOI: 10.1098/rsif.2016.0524] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2016] [Accepted: 09/06/2016] [Indexed: 12/18/2022] Open
Abstract
Bistability, and more generally multistability, is a key system dynamics feature enabling decision-making and memory in cells. Deciphering the molecular determinants of multistability is thus crucial for a better understanding of cellular pathways and their (re)engineering in synthetic biology. Here, we show that a key motif found predominantly in eukaryotic signalling systems, namely a futile signalling cycle, can display bistability when featuring a two-state kinase. We provide necessary and sufficient mathematical conditions on the kinetic parameters of this motif that guarantee the existence of multiple steady states. These conditions foster the intuition that bistability arises as a consequence of competition between the two states of the kinase. Extending from this result, we find that increasing the number of kinase states linearly translates into an increase in the number of steady states in the system. These findings reveal, to our knowledge, a new mechanism for the generation of bistability and multistability in cellular signalling systems. Further the futile cycle featuring a two-state kinase is among the smallest bistable signalling motifs. We show that multi-state kinases and the described competition-based motif are part of several natural signalling systems and thereby could enable them to implement complex information processing through multistability. These results indicate that multi-state kinases in signalling systems are readily exploited by natural evolution and could equally be used by synthetic approaches for the generation of multistable information processing systems at the cellular level.
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Affiliation(s)
- Song Feng
- School of Life Sciences, University of Warwick, Coventry, UK
| | - Meritxell Sáez
- Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Carsten Wiuf
- Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Elisenda Feliu
- Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
| | - Orkun S Soyer
- School of Life Sciences, University of Warwick, Coventry, UK
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9
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Wagner N, Mukherjee R, Maity I, Peacock-Lopez E, Ashkenasy G. Bistability and Bifurcation in Minimal Self-Replication and Nonenzymatic Catalytic Networks. Chemphyschem 2017; 18:1842-1850. [PMID: 28112462 DOI: 10.1002/cphc.201601293] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2016] [Revised: 01/23/2017] [Indexed: 11/08/2022]
Abstract
Bistability and bifurcation, found in a wide range of biochemical networks, are central to the proper function of living systems. We investigate herein recent model systems that show bistable behavior based on nonenzymatic self-replication reactions. Such models were used before to investigate catalytic growth, chemical logic operations, and additional processes of self-organization leading to complexification. By solving for their steady-state solutions by using various analytical and numerical methods, we analyze how and when these systems yield bistability and bifurcation and discover specific cases and conditions producing bistability. We demonstrate that the onset of bistability requires at least second-order catalysis and results from a mismatch between the various forward and reverse processes. Our findings may have far-reaching implications in understanding early evolutionary processes of complexification, emergence, and potentially the origin of life.
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Affiliation(s)
- Nathaniel Wagner
- Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
| | - Rakesh Mukherjee
- Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
| | - Indrajit Maity
- Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
| | | | - Gonen Ashkenasy
- Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, 84105, Israel
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10
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Long XY, Zhang ZJ, Li JY, Sheng D, Lian HZ. A combination strategy using two novel cerium-based nanocomposite affinity probes for the selective enrichment of mono- and multi-phosphopeptides in mass spectrometric analysis. Chem Commun (Camb) 2017; 53:4620-4623. [DOI: 10.1039/c7cc00540g] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
The sequential enrichment of mono- and multi-phosphopeptides was successfully achieved using two novel Ce-based nanocomposite affinity probes.
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Affiliation(s)
- Xing-yu Long
- State Key Laboratory of Analytical Chemistry for Life Science
- Collaborative Innovation Center of Chemistry for Life Sciences
- School of Chemistry & Chemical Engineering and Center of Materials Analysis
- Nanjing University
- Nanjing 210023
| | - Zi-jin Zhang
- State Key Laboratory of Analytical Chemistry for Life Science
- Collaborative Innovation Center of Chemistry for Life Sciences
- School of Chemistry & Chemical Engineering and Center of Materials Analysis
- Nanjing University
- Nanjing 210023
| | - Jia-yuan Li
- State Key Laboratory of Analytical Chemistry for Life Science
- Collaborative Innovation Center of Chemistry for Life Sciences
- School of Chemistry & Chemical Engineering and Center of Materials Analysis
- Nanjing University
- Nanjing 210023
| | - Dong Sheng
- State Key Laboratory of Analytical Chemistry for Life Science
- Collaborative Innovation Center of Chemistry for Life Sciences
- School of Chemistry & Chemical Engineering and Center of Materials Analysis
- Nanjing University
- Nanjing 210023
| | - Hong-zhen Lian
- State Key Laboratory of Analytical Chemistry for Life Science
- Collaborative Innovation Center of Chemistry for Life Sciences
- School of Chemistry & Chemical Engineering and Center of Materials Analysis
- Nanjing University
- Nanjing 210023
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11
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Sun X, Xian H, Tian S, Sun T, Qin Y, Zhang S, Cui J. A Hierarchical Mechanism of RIG-I Ubiquitination Provides Sensitivity, Robustness and Synergy in Antiviral Immune Responses. Sci Rep 2016; 6:29263. [PMID: 27387525 PMCID: PMC4937349 DOI: 10.1038/srep29263] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Accepted: 06/13/2016] [Indexed: 12/12/2022] Open
Abstract
RIG-I is an essential receptor in the initiation of the type I interferon (IFN) signaling pathway upon viral infection. Although K63-linked ubiquitination plays an important role in RIG-I activation, the optimal modulation of conjugated and unanchored ubiquitination of RIG-I as well as its functional implications remains unclear. In this study, we determined that, in contrast to the RIG-I CARD domain, full-length RIG-I must undergo K63-linked ubiquitination at multiple sites to reach full activity. A systems biology approach was designed based on experiments using full-length RIG-I. Model selection for 7 candidate mechanisms of RIG-I ubiquitination inferred a hierarchical architecture of the RIG-I ubiquitination mode, which was then experimentally validated. Compared with other mechanisms, the selected hierarchical mechanism exhibited superior sensitivity and robustness in RIG-I-induced type I IFN activation. Furthermore, our model analysis and experimental data revealed that TRIM4 and TRIM25 exhibited dose-dependent synergism. These results demonstrated that the hierarchical mechanism of multi-site/type ubiquitination of RIG-I provides an efficient, robust and optimal synergistic regulatory module in antiviral immune responses.
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Affiliation(s)
- Xiaoqiang Sun
- Zhong-shan School of Medicine, Sun Yat-sen University, Guangzhou 510089, China
- School of Life Science, Sun Yat-sen University, Guangzhou, 510275, China
- School of Mathematical and Computational Science, Sun Yat-sen University, Guangzhou, 510000, China
| | - Huifang Xian
- School of Life Science, Sun Yat-sen University, Guangzhou, 510275, China
| | - Shuo Tian
- School of Life Science, Sun Yat-sen University, Guangzhou, 510275, China
| | - Tingzhe Sun
- School of Life Sciences, AnQing Normal University, AnQing, 246011, China
| | - Yunfei Qin
- School of Life Sciences, Zhengzhou University, Zhengzhou, Henan, 450001, China
| | - Shoutao Zhang
- School of Life Sciences, Zhengzhou University, Zhengzhou, Henan, 450001, China
| | - Jun Cui
- School of Life Science, Sun Yat-sen University, Guangzhou, 510275, China
- Collaborative Innovation Center of Cancer Medicine, Sun Yat-sen University, Guangzhou, 510060, China
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12
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Enciso GA, Ryerson S. The effect of site-to-site variability in ultrasensitive dose responses. J Math Biol 2016; 74:23-41. [DOI: 10.1007/s00285-016-1013-5] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2015] [Revised: 04/11/2016] [Indexed: 11/28/2022]
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13
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Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks. Bull Math Biol 2015; 77:1744-67. [PMID: 26376889 DOI: 10.1007/s11538-015-0102-8] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2014] [Accepted: 09/03/2015] [Indexed: 10/23/2022]
Abstract
We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth-death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.
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14
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Clinical Significance of SASH1 Expression in Glioma. DISEASE MARKERS 2015; 2015:383046. [PMID: 26424902 PMCID: PMC4575719 DOI: 10.1155/2015/383046] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/10/2015] [Revised: 08/20/2015] [Accepted: 08/23/2015] [Indexed: 01/26/2023]
Abstract
OBJECTIVE SAM and SH3 domain containing 1 (SASH1) is a recently discovered tumor suppressor gene. The role of SASH1 in glioma has not yet been described. We investigated SASH1 expression in glioma cases to determine its clinical significance on glioma pathogenesis and prognosis. METHODS We produced tissue microarrays using 121 patient-derived glioma samples and 30 patient-derived nontumor cerebral samples. Immunohistochemistry and Western blotting were used to evaluate SASH1 expression. We used Fisher's exact tests to determine relationships between SASH1 expression and clinicopathological characteristics; Cox regression analysis to evaluate the independency of different SASH1 expression; Kaplan-Meier analysis to determine any correlation of SASH1 expression with survival rate. RESULTS SASH1 expression was closely correlated with the WHO glioma grade. Of the 121 cases, 66.9% with low SASH1 expression were mostly grade III-IV cases, whereas 33.1% with high SASH1 expression were mostly grades I-II. Kaplan-Meier analysis revealed a significant positive correlation between SASH1 expression and postoperative survival. CONCLUSIONS SASH1 was widely expressed in normal and low-grade glioma tissues. SASH1 expression strongly correlated with glioma grades, showing higher expression at a lower grade, which decreased significantly as grade increased. Furthermore, SASH1 expression was positively correlated with better postoperative survival in patients with glioma.
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15
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A systems model of phosphorylation for inflammatory signaling events. PLoS One 2014; 9:e110913. [PMID: 25333362 PMCID: PMC4205014 DOI: 10.1371/journal.pone.0110913] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2014] [Accepted: 09/19/2014] [Indexed: 12/24/2022] Open
Abstract
Phosphorylation is a fundamental biochemical reaction that modulates protein activity in cells. While a single phosphorylation event is relatively easy to understand, multisite phosphorylation requires systems approaches for deeper elucidation of the underlying molecular mechanisms. In this paper we develop a mechanistic model for single- and multi-site phosphorylation. The proposed model is compared with previously reported studies. We compare the predictions of our model with experiments published in the literature in the context of inflammatory signaling events in order to provide a mechanistic description of the multisite phosphorylation-mediated regulation of Signal Transducer and Activator of Transcription 3 (STAT3) and Interferon Regulatory Factor 5 (IRF-5) proteins. The presented model makes crucial predictions for transcription factor phosphorylation events in the immune system. The model proposes potential mechanisms for T cell phenotype switching and production of cytokines. This study also provides a generic framework for the better understanding of a large number of multisite phosphorylation-regulated biochemical circuits.
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16
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Abstract
Cellular memory - conversion of a transient signal into a sustained response - is a common feature of biological systems. Synthetic biologists aim to understand and re-engineer such systems in a reliable and predictable manner. Synthetic memory circuits have been designed and built in vitro and in vivo based on diverse mechanisms, such as oligonucleotide hybridization, recombination, transcription, phosphorylation, and RNA editing. Thus far, building these circuits has helped us explore the basic principles required for stable memory and ask novel biological questions. Here we discuss strategies for building synthetic memory circuits, their use as research tools, and future applications of these devices in medicine and industry.
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Affiliation(s)
- Mara C Inniss
- Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA
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17
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Onal B, Unudurthi SD, Hund TJ. Modeling CaMKII in cardiac physiology: from molecule to tissue. Front Pharmacol 2014; 5:9. [PMID: 24550832 PMCID: PMC3912431 DOI: 10.3389/fphar.2014.00009] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2013] [Accepted: 01/16/2014] [Indexed: 12/02/2022] Open
Abstract
Post-translational modification of membrane proteins (e.g., ion channels, receptors) by protein kinases is an essential mechanism for control of excitable cell function. Importantly, loss of temporal and/or spatial control of ion channel post-translational modification is common in congenital and acquired forms of cardiac disease and arrhythmia. The multifunctional Ca2+/calmodulin-dependent protein kinase II (CaMKII) regulates a number of diverse cellular functions in heart, including excitation-contraction coupling, gene transcription, and apoptosis. Dysregulation of CaMKII signaling has been implicated in human and animal models of disease. Understanding of CaMKII function has been advanced by mathematical modeling approaches well-suited to the study of complex biological systems. Early kinetic models of CaMKII function in the brain characterized this holoenzyme as a bistable molecular switch capable of storing information over a long period of time. Models of CaMKII activity have been incorporated into models of the cell and tissue (particularly in the heart) to predict the role of CaMKII in regulating organ function. Disease models that incorporate CaMKII overexpression clearly demonstrate a link between its excessive activity and arrhythmias associated with congenital and acquired heart disease. This review aims at discussing systems biology approaches that have been applied to analyze CaMKII signaling from the single molecule to intact cardiac tissue. In particular, efforts to use computational biology to provide new insight into cardiac disease mechanisms are emphasized.
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Affiliation(s)
- Birce Onal
- The Dorothy M. Davis Heart and Lung Research Institute, Wexner Medical Center, The Ohio State University Columbus, OH, USA ; Department of Biomedical Engineering, College of Engineering, The Ohio State University Columbus, OH, USA
| | - Sathya D Unudurthi
- The Dorothy M. Davis Heart and Lung Research Institute, Wexner Medical Center, The Ohio State University Columbus, OH, USA
| | - Thomas J Hund
- The Dorothy M. Davis Heart and Lung Research Institute, Wexner Medical Center, The Ohio State University Columbus, OH, USA ; Department of Biomedical Engineering, College of Engineering, The Ohio State University Columbus, OH, USA ; Department of Internal Medicine, Wexner Medical Center, The Ohio State University Columbus, OH, USA
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18
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Enciso G, Kellogg DR, Vargas A. Compact modeling of allosteric multisite proteins: application to a cell size checkpoint. PLoS Comput Biol 2014; 10:e1003443. [PMID: 24516371 PMCID: PMC3916233 DOI: 10.1371/journal.pcbi.1003443] [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] [Received: 06/13/2013] [Accepted: 11/23/2013] [Indexed: 11/21/2022] Open
Abstract
We explore a framework to model the dose response of allosteric multisite phosphorylation proteins using a single auxiliary variable. This reduction can closely replicate the steady state behavior of detailed multisite systems such as the Monod-Wyman-Changeux allosteric model or rule-based models. Optimal ultrasensitivity is obtained when the activation of an allosteric protein by its individual sites is concerted and redundant. The reduction makes this framework useful for modeling and analyzing biochemical systems in practical applications, where several multisite proteins may interact simultaneously. As an application we analyze a newly discovered checkpoint signaling pathway in budding yeast, which has been proposed to measure cell growth by monitoring signals generated at sites of plasma membrane growth. We show that the known components of this pathway can form a robust hysteretic switch. In particular, this system incorporates a signal proportional to bud growth or size, a mechanism to read the signal, and an all-or-none response triggered only when the signal reaches a threshold indicating that sufficient growth has occurred.
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Affiliation(s)
- Germán Enciso
- Department of Mathematics, Department of Developmental and Cell Biology, University of California Irvine, Irvine, California, United States of America
| | - Douglas R. Kellogg
- Department of Molecular, Cell and Developmental Biology, University of California Santa Cruz, Santa Cruz, California, United States of America
| | - Arturo Vargas
- Computational and Applied Mathematics Department, Rice University, Houston, Texas, United States of America
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Feliu E, Wiuf C. Simplifying biochemical models with intermediate species. J R Soc Interface 2013; 10:20130484. [PMID: 23883954 PMCID: PMC3758008 DOI: 10.1098/rsif.2013.0484] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2013] [Accepted: 07/01/2013] [Indexed: 11/12/2022] Open
Abstract
Mathematical models are increasingly being used to understand complex biochemical systems, to analyse experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to the choice and uncertainties of the model. Using algebraic techniques, we study systematically the effects of intermediate, or transient, species in biochemical systems and provide a simple, yet rigorous mathematical classification of all models obtained from a core model by including intermediates. Main examples include enzymatic and post-translational modification systems, where intermediates often are considered insignificant and neglected in a model, or they are not included because we are unaware of their existence. All possible models obtained from the core model are classified into a finite number of classes. Each class is defined by a mathematically simple canonical model that characterizes crucial dynamical properties, such as mono- and multistationarity and stability of steady states, of all models in the class. We show that if the core model does not have conservation laws, then the introduction of intermediates does not change the steady-state concentrations of the species in the core model, after suitable matching of parameters. Importantly, our results provide guidelines to the modeller in choosing between models and in distinguishing their properties. Further, our work provides a formal way of comparing models that share a common skeleton.
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Affiliation(s)
| | - Carsten Wiuf
- Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
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20
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Ultrasensitivity in independent multisite systems. J Math Biol 2013; 69:977-99. [PMID: 24046085 DOI: 10.1007/s00285-013-0727-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2013] [Revised: 08/08/2013] [Indexed: 10/26/2022]
Abstract
Multisite modifications are widely recognized as an essential feature of many switch-like responses in signal transduction. It is usually assumed that the modification of one site directly or indirectly increases the rate of modification of neighboring sites. In this paper we provide a new set of assumptions for a multisite system to become highly ultrasensitive even in the absence of cooperativity or allostery. We assume that the individual sites are modified independently of each other, and that protein activity is an ultrasensitive function of the fraction of modified sites. These assumptions are particularly useful in the context of multisite systems with a large (8+) number of sites. We estimate the apparent Hill coefficient of the dose responses in the sequential and nonsequential cases, highlight their different qualitative properties, and discuss a formula to approximate dose responses in the nonsequential case. As an example we describe a model of bacterial chemotaxis that features robust ultrasensitivity and perfect adaptation over a wide range of ligand concentrations, based on non-allosteric multisite behavior at the level of receptors and flagella. We also include a model of the inactivation of the yeast pheromone protein Ste5 by cell cycle proteins.
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21
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Martins BMC, Swain PS. Ultrasensitivity in phosphorylation-dephosphorylation cycles with little substrate. PLoS Comput Biol 2013; 9:e1003175. [PMID: 23950701 PMCID: PMC3738489 DOI: 10.1371/journal.pcbi.1003175] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2012] [Accepted: 06/26/2013] [Indexed: 11/19/2022] Open
Abstract
Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with phosphosites, we find an upper bound of the Hill number of , and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells.
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Affiliation(s)
- Bruno M. C. Martins
- SynthSys – Synthetic and Systems Biology, The University of Edinburgh, Edinburgh, United Kingdom
- * E-mail: (BMCM); (PSS)
| | - Peter S. Swain
- SynthSys – Synthetic and Systems Biology, The University of Edinburgh, Edinburgh, United Kingdom
- * E-mail: (BMCM); (PSS)
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Zhong H, Xiao X, Zheng S, Zhang W, Ding M, Jiang H, Huang L, Kang J. Mass spectrometric analysis of mono- and multi-phosphopeptides by selective binding with NiZnFe2O4 magnetic nanoparticles. Nat Commun 2013; 4:1656. [DOI: 10.1038/ncomms2662] [Citation(s) in RCA: 73] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2012] [Accepted: 02/28/2013] [Indexed: 01/11/2023] Open
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Witzel F, Maddison L, Blüthgen N. How scaffolds shape MAPK signaling: what we know and opportunities for systems approaches. Front Physiol 2012; 3:475. [PMID: 23267331 PMCID: PMC3527831 DOI: 10.3389/fphys.2012.00475] [Citation(s) in RCA: 72] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2012] [Accepted: 12/04/2012] [Indexed: 11/13/2022] Open
Abstract
Scaffolding proteins add a new layer of complexity to the dynamics of cell signaling. Above their basic function to bring several components of a signaling pathway together, recent experimental research has found that scaffolds influence signaling in a much more complex way: scaffolds can exert some catalytic function, influence signaling by allosteric mechanisms, are feedback-regulated, localize signaling activity to distinct regions of the cell or increase pathway fidelity. Here we review experimental and theoretical approaches that address the function of two MAPK scaffolds, Ste5, a scaffold of the yeast mating pathway and KSR1/2, a scaffold of the classical mammalian MAPK signaling pathway. For the yeast scaffold Ste5, detailed mechanistic models have been valuable for the understanding of its function. For scaffolds in mammalian signaling, however, models have been rather generic and sketchy. For example, these models predicted narrow optimal scaffold concentrations, but when revisiting these models by assuming typical concentrations, rather a range of scaffold levels optimally supports signaling. Thus, more realistic models are needed to understand the role of scaffolds in mammalian signal transduction, which opens a big opportunity for systems biology.
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Affiliation(s)
- Franziska Witzel
- Institute of Pathology, Charité-Universitätsmedizin Berlin Berlin, Germany ; Institute for Theoretical Biology, Humboldt University Berlin Berlin, Germany
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