101
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Shirin A, Della Rossa F, Klickstein I, Russell J, Sorrentino F. Optimal regulation of blood glucose level in Type I diabetes using insulin and glucagon. PLoS One 2019; 14:e0213665. [PMID: 30893335 PMCID: PMC6426249 DOI: 10.1371/journal.pone.0213665] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2018] [Accepted: 02/26/2019] [Indexed: 12/11/2022] Open
Abstract
The Glucose-Insulin-Glucagon nonlinear model accurately describes how the body responds to exogenously supplied insulin and glucagon in patients affected by Type I diabetes. Based on this model, we design infusion rates of either insulin (monotherapy) or insulin and glucagon (dual therapy) that can optimally maintain the blood glucose level within desired limits after consumption of a meal and prevent the onset of both hypoglycemia and hyperglycemia. This problem is formulated as a nonlinear optimal control problem, which we solve using the numerical optimal control package PSOPT. Interestingly, in the case of monotherapy, we find the optimal solution is close to the standard method of insulin based glucose regulation, which is to assume a variable amount of insulin half an hour before each meal. We also find that the optimal dual therapy (that uses both insulin and glucagon) is better able to regulate glucose as compared to using insulin alone. We also propose an ad-hoc rule for both the dosage and the time of delivery of insulin and glucagon.
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Affiliation(s)
- Afroza Shirin
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131, United States of America
- * E-mail:
| | - Fabio Della Rossa
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131, United States of America
| | - Isaac Klickstein
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131, United States of America
| | - John Russell
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131, United States of America
| | - Francesco Sorrentino
- Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131, United States of America
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102
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Zañudo JGT, Guinn MT, Farquhar K, Szenk M, Steinway SN, Balázsi G, Albert R. Towards control of cellular decision-making networks in the epithelial-to-mesenchymal transition. Phys Biol 2019; 16:031002. [PMID: 30654341 PMCID: PMC6405305 DOI: 10.1088/1478-3975/aaffa1] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
We present the epithelial-to-mesenchymal transition (EMT) from two perspectives: experimental/technological and theoretical. We review the state of the current understanding of the regulatory networks that underlie EMT in three physiological contexts: embryonic development, wound healing, and metastasis. We describe the existing experimental systems and manipulations used to better understand the molecular participants and factors that influence EMT and metastasis. We review the mathematical models of the regulatory networks involved in EMT, with a particular emphasis on the network motifs (such as coupled feedback loops) that can generate intermediate hybrid states between the epithelial and mesenchymal states. Ultimately, the understanding gained about these networks should be translated into methods to control phenotypic outcomes, especially in the context of cancer therapeutic strategies. We present emerging theories of how to drive the dynamics of a network toward a desired dynamical attractor (e.g. an epithelial cell state) and emerging synthetic biology technologies to monitor and control the state of cells.
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Affiliation(s)
- Jorge Gómez Tejeda Zañudo
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
- Department of Medical Oncology, Dana-Farber Cancer Center, Boston, MA 02215, USA
- Cancer Program, Eli and Edythe L. Broad Institute of Harvard and Massachusetts Institute of Technology, Cambridge, MA 02142, USA
| | - M. Tyler Guinn
- Biomedical Engineering Department, Stony Brook University, Stony Brook, NY 11794 USA
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA
- Stony Brook Medical Scientist Training Program, 101 Nicolls Road, Stony Brook, NY 11794, USA
| | - Kevin Farquhar
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA
| | - Mariola Szenk
- Biomedical Engineering Department, Stony Brook University, Stony Brook, NY 11794 USA
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA
| | - Steven N. Steinway
- Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA
| | - Gábor Balázsi
- Biomedical Engineering Department, Stony Brook University, Stony Brook, NY 11794 USA
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794, USA
| | - Réka Albert
- Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
- Department of Biology, Pennsylvania State University, University Park, PA 16802, USA
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103
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Network controllability analysis of intracellular signalling reveals viruses are actively controlling molecular systems. Sci Rep 2019; 9:2066. [PMID: 30765882 PMCID: PMC6375943 DOI: 10.1038/s41598-018-38224-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Accepted: 12/21/2018] [Indexed: 12/19/2022] Open
Abstract
In recent years control theory has been applied to biological systems with the aim of identifying the minimum set of molecular interactions that can drive the network to a required state. However, in an intra-cellular network it is unclear how control can be achieved in practice. To address this limitation we use viral infection, specifically human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV), as a paradigm to model control of an infected cell. Using a large human signalling network comprised of over 6000 human proteins and more than 34000 directed interactions, we compared two states: normal/uninfected and infected. Our network controllability analysis demonstrates how a virus efficiently brings the dynamically organised host system into its control by mostly targeting existing critical control nodes, requiring fewer nodes than in the uninfected network. The lower number of control nodes is presumably to optimise exploitation of specific sub-systems needed for virus replication and/or involved in the host response to infection. Viral infection of the human system also permits discrimination between available network-control models, which demonstrates that the minimum dominating set (MDS) method better accounts for how the biological information and signals are organised during infection by identifying most viral proteins as critical driver nodes compared to the maximum matching (MM) method. Furthermore, the host driver nodes identified by MDS are distributed throughout the pathways enabling effective control of the cell via the high ‘control centrality’ of the viral and targeted host nodes. Our results demonstrate that control theory gives a more complete and dynamic understanding of virus exploitation of the host system when compared with previous analyses limited to static single-state networks.
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104
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Prediction of Optimal Drug Schedules for Controlling Autophagy. Sci Rep 2019; 9:1428. [PMID: 30723233 PMCID: PMC6363771 DOI: 10.1038/s41598-019-38763-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2018] [Accepted: 12/27/2018] [Indexed: 12/19/2022] Open
Abstract
The effects of molecularly targeted drug perturbations on cellular activities and fates are difficult to predict using intuition alone because of the complex behaviors of cellular regulatory networks. An approach to overcoming this problem is to develop mathematical models for predicting drug effects. Such an approach beckons for co-development of computational methods for extracting insights useful for guiding therapy selection and optimizing drug scheduling. Here, we present and evaluate a generalizable strategy for identifying drug dosing schedules that minimize the amount of drug needed to achieve sustained suppression or elevation of an important cellular activity/process, the recycling of cytoplasmic contents through (macro)autophagy. Therapeutic targeting of autophagy is currently being evaluated in diverse clinical trials but without the benefit of a control engineering perspective. Using a nonlinear ordinary differential equation (ODE) model that accounts for activating and inhibiting influences among protein and lipid kinases that regulate autophagy (MTORC1, ULK1, AMPK and VPS34) and methods guaranteed to find locally optimal control strategies, we find optimal drug dosing schedules (open-loop controllers) for each of six classes of drugs and drug pairs. Our approach is generalizable to designing monotherapy and multi therapy drug schedules that affect different cell signaling networks of interest.
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105
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Nacher JC, Ishitsuka M, Miyazaki S, Akutsu T. Finding and analysing the minimum set of driver nodes required to control multilayer networks. Sci Rep 2019; 9:576. [PMID: 30679639 PMCID: PMC6345816 DOI: 10.1038/s41598-018-37046-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2018] [Accepted: 11/30/2018] [Indexed: 02/07/2023] Open
Abstract
It is difficult to control multilayer networks in situations with real-world complexity. Here, we first define the multilayer control problem in terms of the minimum dominating set (MDS) controllability framework and mathematically demonstrate that simple formulas can be used to estimate the size of the minimum dominating set in multilayer (MDSM) complex networks. Second, we develop a new algorithm that efficiently identifies the MDSM in up to 6 layers, with several thousand nodes in each layer network. Interestingly, the findings reveal that the MDSM size for similar networks does not significantly differ from that required to control a single network. This result opens future directions for controlling, for example, multiple species by identifying a common set of enzymes or proteins for drug targeting. We apply our methods to 70 genome-wide metabolic networks across major plant lineages, unveiling some relationships between controllability in multilayer networks and metabolic functions at the genome scale.
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Affiliation(s)
- Jose C Nacher
- Department of Information Science, Toho University, Funabashi, Chiba, 274-8510, Japan.
| | - Masayuki Ishitsuka
- Department of Information Science, Toho University, Funabashi, Chiba, 274-8510, Japan
| | - Shuichi Miyazaki
- Academic Center for Computing Media Studies, Kyoto University, Kyoto, 606-8501, Japan
| | - Tatsuya Akutsu
- Bioinformatics Center, Institute for Chemical Research, Kyoto University, Uji, 611-0011, Japan.
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106
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Hou W, Ruan P, Ching WK, Akutsu T. On the number of driver nodes for controlling a Boolean network when the targets are restricted to attractors. J Theor Biol 2018; 463:1-11. [PMID: 30543810 DOI: 10.1016/j.jtbi.2018.12.012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Revised: 12/01/2018] [Accepted: 12/10/2018] [Indexed: 01/28/2023]
Abstract
It is known that many driver nodes are required to control complex biological networks. Previous studies imply that O(N) driver nodes are required in both linear complex network and Boolean network models with N nodes if an arbitrary state is specified as the target. In order to cope with this intrinsic difficulty, we consider a special case of the control problem in which the targets are restricted to attractors. For this special case, we mathematically prove under the uniform distribution of states in basins that the expected number of driver nodes is only O(log2N+log2M) for controlling Boolean networks, where M is the number of attractors. Since it is expected that M is not very large in many practical networks, the new model requires a much smaller number of driver nodes. This result is based on discovery of novel relationships between control problems on Boolean networks and the coupon collector's problem, a well-known concept in combinatorics. We also provide lower bounds of the number of driver nodes as well as simulation results using artificial and realistic network data, which support our theoretical findings.
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Affiliation(s)
- Wenpin Hou
- Department of Computer Science, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD, 21218-2608, USA; Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong.
| | - Peiying Ruan
- Deep Learning Solution Architect, NVIDIA, Tokyo, Japan.
| | - Wai-Ki Ching
- Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong; Hughes Hall, Wollaston Road, Cambridge, UK; School of Economics and Management, Beijing University of Chemical Technology, North Third Ring Road, Beijing, China.
| | - Tatsuya Akutsu
- Bioinformatics Center, Institute for Chemical Research, Kyoto University, Kyoto, Japan.
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107
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Rozum JC, Albert R. Identifying (un)controllable dynamical behavior in complex networks. PLoS Comput Biol 2018; 14:e1006630. [PMID: 30532150 PMCID: PMC6301693 DOI: 10.1371/journal.pcbi.1006630] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2018] [Revised: 12/20/2018] [Accepted: 11/11/2018] [Indexed: 12/13/2022] Open
Abstract
We present a technique applicable in any dynamical framework to identify control-robust subsets of an interacting system. These robust subsystems, which we call stable modules, are characterized by constraints on the variables that make up the subsystem. They are robust in the sense that if the defining constraints are satisfied at a given time, they remain satisfied for all later times, regardless of what happens in the rest of the system, and can only be broken if the constrained variables are externally manipulated. We identify stable modules as graph structures in an expanded network, which represents causal links between variable constraints. A stable module represents a system "decision point", or trap subspace. Using the expanded network, small stable modules can be composed sequentially to form larger stable modules that describe dynamics on the system level. Collections of large, mutually exclusive stable modules describe the system's repertoire of long-term behaviors. We implement this technique in a broad class of dynamical systems and illustrate its practical utility via examples and algorithmic analysis of two published biological network models. In the segment polarity gene network of Drosophila melanogaster, we obtain a state-space visualization that reproduces by novel means the four possible cell fates and predicts the outcome of cell transplant experiments. In the T-cell signaling network, we identify six signaling elements that determine the high-signal response and show that control of an element connected to them cannot disrupt this response.
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Affiliation(s)
- Jordan C Rozum
- Department of Physics, The Pennsylvania State University, University Park, PA, USA
| | - Réka Albert
- Department of Physics, The Pennsylvania State University, University Park, PA, USA
- Department of Biology, The Pennsylvania State University, University Park, PA, USA
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108
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Luo M, Jiao J, Wang R. Impulsive control of a nonlinear dynamical network and its application to biological networks. J Biol Phys 2018; 45:31-44. [PMID: 30377881 DOI: 10.1007/s10867-018-9513-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2018] [Accepted: 09/12/2018] [Indexed: 10/28/2022] Open
Abstract
The control of nonlinear dynamical systems is always a notable problem in science. According to control theory, suitable inputs for a controllable dynamical system are critical. Previous studies have shown some principles to determine control nodes and design control function. In this work, we propose a new control strategy of nonlinear systems by constructing impulsive control functions, i.e., we can realize the transition from an undesired state to a desired one by controlling appropriately chosen nodes in a discrete manner. In order to demonstrate the effectiveness of the strategy, we apply it to two biological networks: the epithelial-mesenchymal transition (EMT) network and the Notch1-Dll1-Jag1 signaling pathway. The strategy can not only be used to guide pharmacological design in a more feasible form but can also be applied into the fields of biological, medical and other multistable dynamical systems.
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Affiliation(s)
- Min Luo
- Department of Mathematics, Shanghai University, Shanghai, China
| | - Jianfeng Jiao
- Department of Mathematics, Shanghai University, Shanghai, China
| | - Ruiqi Wang
- Department of Mathematics, Shanghai University, Shanghai, China.
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109
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Gan X, Albert R. General method to find the attractors of discrete dynamic models of biological systems. Phys Rev E 2018; 97:042308. [PMID: 29758614 DOI: 10.1103/physreve.97.042308] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2017] [Indexed: 12/31/2022]
Abstract
Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.
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Affiliation(s)
- Xiao Gan
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Réka Albert
- Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
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110
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Li M, Gao H, Wang J, Wu FX. Control principles for complex biological networks. Brief Bioinform 2018; 20:2253-2266. [DOI: 10.1093/bib/bby088] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2018] [Revised: 08/16/2018] [Accepted: 08/18/2018] [Indexed: 11/13/2022] Open
Abstract
Abstract
Networks have been widely used to model the structure of various biological systems. Currently, a series of approaches have been developed to construct reliable biological networks. However, the ultimate understanding of a biological system is to steer its states to the desired ones by imposing signals. The control process is dominated by the intrinsic structure and the dynamic propagation. To understand the underlying mechanisms behind the life process, the control theory can be applied to biological networks with specific target requirements. In this article, we first introduce the structural controllability of complex networks and discuss its advantages and disadvantages. Then, we review the effective control to meet the specific requirements for complex biological networks. Moreover, we summarize the existing methods for finding the unique minimum set of driver nodes via the optimal control for complex networks. Finally, we discuss the relationships between biological networks and structural controllability, effective control and optimal control. Moreover, potential applications of general control principles are pointed out.
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Affiliation(s)
- Min Li
- School of Information Science and Engineering, Central South University, Changsha, Hunan, China
| | - Hao Gao
- School of Information Science and Engineering, Central South University, Changsha, Hunan, China
| | - Jianxin Wang
- School of Information Science and Engineering, Central South University, Changsha, Hunan, China
| | - Fang-Xiang Wu
- School of Information Science and Engineering, Central South University, Changsha, Hunan, China
- Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, Canada
- Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada
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111
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Yang JM, Lee CK, Cho KH. Global Stabilization of Boolean Networks to Control the Heterogeneity of Cellular Responses. Front Physiol 2018; 9:774. [PMID: 30072906 PMCID: PMC6060448 DOI: 10.3389/fphys.2018.00774] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Accepted: 06/04/2018] [Indexed: 12/13/2022] Open
Abstract
Boolean networks (BNs) have been widely used as a useful model for molecular regulatory networks in systems biology. In the state space of BNs, attractors represent particular cell phenotypes. For targeted therapy of cancer, there is a pressing need to control the heterogeneity of cellular responses to the targeted drug by reducing the number of attractors associated with the ill phenotypes of cancer cells. Here, we present a novel control scheme for global stabilization of BNs to a unique fixed point. Using a sufficient condition of global stabilization with respect to the adjacency matrix, we can determine a set of constant controls so that the controlled BN is steered toward an unspecified fixed point which can then be further transformed to a desired attractor by subsequent control. Our method is efficient in that it has polynomial complexity with respect to the number of state variables, while having exponential complexity with respect to in-degree of BNs. To demonstrate the applicability of the proposed control scheme, we conduct simulation studies using a regulation influence network describing the metastatic process of cells and the Mitogen-activated protein kinase (MAPK) signaling network that is crucial in cancer cell fate determination.
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Affiliation(s)
- Jung-Min Yang
- School of Electronics Engineering, Kyungpook National University, Daegu, South Korea
| | - Chun-Kyung Lee
- School of Electronics Engineering, Kyungpook National University, Daegu, South Korea
| | - Kwang-Hyun Cho
- Laboratory for Systems Biology and Bio-inspired Engineering, Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea
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112
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Kobayashi K, Maeda K, Tokuoka M, Mochizuki A, Satou Y. Controlling Cell Fate Specification System by Key Genes Determined from Network Structure. iScience 2018; 4:281-293. [PMID: 30240747 PMCID: PMC6147236 DOI: 10.1016/j.isci.2018.05.004] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2018] [Revised: 04/19/2018] [Accepted: 05/07/2018] [Indexed: 11/25/2022] Open
Abstract
Network structures describing regulation between biomolecules have been determined in many biological systems. Dynamics of molecular activities based on such networks are considered to be the origin of many biological functions. Recently, it has been proved mathematically that key nodes for controlling dynamics in networks are identified from network structure alone. Here, we applied this theory to a gene regulatory network for the cell fate specification of seven tissues in the ascidian embryo and found that this network, which consisted of 92 factors, had five key molecules. By controlling the activities of these key molecules, the specific gene expression of six of seven tissues observed in the embryo was successfully reproduced. Since this method is applicable to all nonlinear dynamic systems, we propose this method as a tool for controlling gene regulatory networks and reprogramming cell fates.
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Affiliation(s)
- Kenji Kobayashi
- Department of Zoology, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan; CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - Kazuki Maeda
- CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan; Department of Mathematical Sciences, School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda, Hyogo 669-1337, Japan
| | - Miki Tokuoka
- Department of Zoology, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan; CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
| | - Atsushi Mochizuki
- CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan; Theoretical Biology Laboratory, RIKEN, Wako, Saitama 351-0198, Japan; Institute for Frontier Life and Medical Sciences, Kyoto University, Sakyo, Kyoto 606-8507, Japan.
| | - Yutaka Satou
- Department of Zoology, Graduate School of Science, Kyoto University, Sakyo, Kyoto 606-8502, Japan; CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan.
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113
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G T Zañudo J, Steinway SN, Albert R. Discrete dynamic network modeling of oncogenic signaling: Mechanistic insights for personalized treatment of cancer. ACTA ACUST UNITED AC 2018; 9:1-10. [PMID: 32954058 PMCID: PMC7487767 DOI: 10.1016/j.coisb.2018.02.002] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Targeted drugs disrupting proteins that are dysregulated in cancer have emerged as promising treatments because of their specificity to cancer cell aberrations and thus their improved side effect profile. However, their success remains limited, largely due to existing or emergent therapy resistance. We suggest that this is due to limited understanding of the entire relevant cellular landscape. A class of mathematical models called discrete dynamic network models can be used to understand the integrated effect of an individual tumor's aberrations. We review the recent literature on discrete dynamic models of cancer and highlight their predicted therapeutic strategies. We believe dynamic network modeling can be used to drive treatment decision-making in a personalized manner to direct improved treatments in cancer. Cancer is rooted in incorrect cellular decisions caused by genetic alterations. Dynamic models of signaling networks can map the relevant repertoire of alterations. Discrete dynamic network models can predict therapeutic interventions. Progress in personalized medicine needs integration of multiple data and model types.
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Affiliation(s)
- Jorge G T Zañudo
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA.,Department of Medical Oncology, Dana-Farber Cancer Institute and Broad Institute of Harvard and MIT, Boston MA, USA
| | - Steven N Steinway
- Department of Medicine, Johns Hopkins University School of Medicine, Baltimore, MD 21287, USA
| | - Réka Albert
- Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA.,Department of Biology, The Pennsylvania State University, University Park, PA 16802, USA
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114
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Yang G, Gómez Tejeda Zañudo J, Albert R. Target Control in Logical Models Using the Domain of Influence of Nodes. Front Physiol 2018; 9:454. [PMID: 29867523 PMCID: PMC5951947 DOI: 10.3389/fphys.2018.00454] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2018] [Accepted: 04/13/2018] [Indexed: 11/13/2022] Open
Abstract
Dynamical models of biomolecular networks are successfully used to understand the mechanisms underlying complex diseases and to design therapeutic strategies. Network control and its special case of target control, is a promising avenue toward developing disease therapies. In target control it is assumed that a small subset of nodes is most relevant to the system's state and the goal is to drive the target nodes into their desired states. An example of target control would be driving a cell to commit to apoptosis (programmed cell death). From the experimental perspective, gene knockout, pharmacological inhibition of proteins, and providing sustained external signals are among practical intervention techniques. We identify methodologies to use the stabilizing effect of sustained interventions for target control in Boolean network models of biomolecular networks. Specifically, we define the domain of influence (DOI) of a node (in a certain state) to be the nodes (and their corresponding states) that will be ultimately stabilized by the sustained state of this node regardless of the initial state of the system. We also define the related concept of the logical domain of influence (LDOI) of a node, and develop an algorithm for its identification using an auxiliary network that incorporates the regulatory logic. This way a solution to the target control problem is a set of nodes whose DOI can cover the desired target node states. We perform greedy randomized adaptive search in node state space to find such solutions. We apply our strategy to in silico biological network models of real systems to demonstrate its effectiveness.
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Affiliation(s)
- Gang Yang
- Department of Physics, Pennsylvania State University, University Park, PA, United States
| | - Jorge Gómez Tejeda Zañudo
- Department of Physics, Pennsylvania State University, University Park, PA, United States.,Department of Medical Oncology, Dana-Farber Cancer Institute, Boston, MA, United States.,Eli and Edythe L. Broad Institute of MIT and Harvard, Cambridge, MA, United States
| | - Réka Albert
- Department of Physics, Pennsylvania State University, University Park, PA, United States.,Department of Biology, Pennsylvania State University, University Park, PA, United States
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115
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Manos T, Zeitler M, Tass PA. Short-Term Dosage Regimen for Stimulation-Induced Long-Lasting Desynchronization. Front Physiol 2018; 9:376. [PMID: 29706900 PMCID: PMC5906576 DOI: 10.3389/fphys.2018.00376] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Accepted: 03/27/2018] [Indexed: 11/23/2022] Open
Abstract
In this paper, we computationally generate hypotheses for dose-finding studies in the context of desynchronizing neuromodulation techniques. Abnormally strong neuronal synchronization is a hallmark of several brain disorders. Coordinated Reset (CR) stimulation is a spatio-temporally patterned stimulation technique that specifically aims at disrupting abnormal neuronal synchrony. In networks with spike-timing-dependent plasticity CR stimulation may ultimately cause an anti-kindling, i.e., an unlearning of abnormal synaptic connectivity and neuronal synchrony. This long-lasting desynchronization was theoretically predicted and verified in several pre-clinical and clinical studies. We have shown that CR stimulation with rapidly varying sequences (RVS) robustly induces an anti-kindling at low intensities e.g., if the CR stimulation frequency (i.e., stimulus pattern repetition rate) is in the range of the frequency of the neuronal oscillation. In contrast, CR stimulation with slowly varying sequences (SVS) turned out to induce an anti-kindling more strongly, but less robustly with respect to variations of the CR stimulation frequency. Motivated by clinical constraints and inspired by the spacing principle of learning theory, in this computational study we propose a short-term dosage regimen that enables a robust anti-kindling effect of both RVS and SVS CR stimulation, also for those parameter values where RVS and SVS CR stimulation previously turned out to be ineffective. Intriguingly, for the vast majority of parameter values tested, spaced multishot CR stimulation with demand-controlled variation of stimulation frequency and intensity caused a robust and pronounced anti-kindling. In contrast, spaced CR stimulation with fixed stimulation parameters as well as singleshot CR stimulation of equal integral duration failed to improve the stimulation outcome. In the model network under consideration, our short-term dosage regimen enables to robustly induce long-term desynchronization at comparably short stimulation duration and low integral stimulation duration. Currently, clinical proof of concept is available for deep brain CR stimulation for Parkinson's therapy and acoustic CR stimulation for tinnitus therapy. Promising first in human data is available for vibrotactile CR stimulation for Parkinson's treatment. For the clinical development of these treatments it is mandatory to perform dose-finding studies to reveal optimal stimulation parameters and dosage regimens. Our findings can straightforwardly be tested in human dose-finding studies.
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Affiliation(s)
- Thanos Manos
- Institute of Neuroscience and Medicine (INM-7), Research Centre Jülich, Jülich, Germany
- Institute of Systems Neuroscience, Medical Faculty, Heinrich Heine University Düsseldorf, Düsseldorf, Germany
| | - Magteld Zeitler
- Institute of Neuroscience and Medicine (INM-7), Research Centre Jülich, Jülich, Germany
| | - Peter A. Tass
- Department of Neurosurgery, Stanford University, Stanford, CA, United States
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Bonneau H, Hassid A, Biham O, Kühn R, Katzav E. Distribution of shortest cycle lengths in random networks. Phys Rev E 2018; 96:062307. [PMID: 29347364 DOI: 10.1103/physreve.96.062307] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2017] [Indexed: 11/07/2022]
Abstract
We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to configuration model networks, for which analytical results for the DSPL were obtained before. We first calculate the fraction of nodes in the network which reside on at least one cycle. Conditioning on being on a cycle, we provide the DSCL over ensembles of configuration model networks with degree distributions which follow a Poisson distribution (Erdős-Rényi network), degenerate distribution (random regular graph), and a power-law distribution (scale-free network). The mean and variance of the DSCL are calculated. The analytical results are found to be in very good agreement with the results of computer simulations.
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Affiliation(s)
- Haggai Bonneau
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Aviv Hassid
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Ofer Biham
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
| | - Reimer Kühn
- Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom
| | - Eytan Katzav
- Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
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117
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Klickstein I, Shirin A, Sorrentino F. Locally Optimal Control of Complex Networks. PHYSICAL REVIEW LETTERS 2017; 119:268301. [PMID: 29328728 DOI: 10.1103/physrevlett.119.268301] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Indexed: 06/07/2023]
Abstract
It has recently been shown that the minimum energy solution of the control problem for a linear system produces a control trajectory that is nonlocal. An issue then arises when the dynamics represents a linearization of the underlying nonlinear dynamics of the system where the linearization is only valid in a local region of the state space. Here we provide a solution to the problem of optimally controlling a linearized system by deriving a time-varying set that represents all possible control trajectories parametrized by time and energy. As long as the control action terminus is defined within this set, the control trajectory is guaranteed to be local. If the desired terminus of the control action is far from the initial state, a series of local control actions can be performed in series, relinearizing the dynamics at each new position.
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Affiliation(s)
- Isaac Klickstein
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Afroza Shirin
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Francesco Sorrentino
- Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA
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118
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Xiong W, Wang C, Zhang X, Yang Q, Shao R, Lai J, Du C. Highly interwoven communities of a gene regulatory network unveil topologically important genes for maize seed development. THE PLANT JOURNAL : FOR CELL AND MOLECULAR BIOLOGY 2017; 92:1143-1156. [PMID: 29072883 DOI: 10.1111/tpj.13750] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/02/2017] [Revised: 10/10/2017] [Accepted: 10/17/2017] [Indexed: 06/07/2023]
Abstract
The complex interactions between transcription factors (TFs) and their target genes in a spatially and temporally specific manner are crucial to all cellular processes. Reconstruction of gene regulatory networks (GRNs) from gene expression profiles can help to decipher TF-gene regulations in a variety of contexts; however, the inevitable prediction errors of GRNs hinder optimal data mining of RNA-Seq transcriptome profiles. Here we perform an integrative study of Zea mays (maize) seed development in order to identify key genes in a complex developmental process. First, we reverse engineered a GRN from 78 maize seed transcriptome profiles. Then, we studied collective gene interaction patterns and uncovered highly interwoven network communities as the building blocks of the GRN. One community, composed of mostly unknown genes interacting with opaque2, brittle endosperm1 and shrunken2, contributes to seed phenotypes. Another community, composed mostly of genes expressed in the basal endosperm transfer layer, is responsible for nutrient transport. We further integrated our inferred GRN with gene expression patterns in different seed compartments and at various developmental stages and pathways. The integration facilitated a biological interpretation of the GRN. Our yeast one-hybrid assays verified six out of eight TF-promoter bindings in the reconstructed GRN. This study identified topologically important genes in interwoven network communities that may be crucial to maize seed development.
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Affiliation(s)
- Wenwei Xiong
- College of Agronomy, Henan Agricultural University, Zhengzhou, 450002, China
- Department of Biology, Montclair State University, Montclair, NJ, 07043, USA
| | - Chunlei Wang
- National Maize Improvement Center, China Agricultural University, Beijing, 100083, China
| | - Xiangbo Zhang
- National Maize Improvement Center, China Agricultural University, Beijing, 100083, China
| | - Qinghua Yang
- College of Agronomy, Henan Agricultural University, Zhengzhou, 450002, China
| | - Ruixin Shao
- College of Agronomy, Henan Agricultural University, Zhengzhou, 450002, China
| | - Jinsheng Lai
- National Maize Improvement Center, China Agricultural University, Beijing, 100083, China
| | - Chunguang Du
- College of Agronomy, Henan Agricultural University, Zhengzhou, 450002, China
- Department of Biology, Montclair State University, Montclair, NJ, 07043, USA
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119
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Csermely P. The Wisdom of Networks: A General Adaptation and Learning Mechanism of Complex Systems: The Network Core Triggers Fast Responses to Known Stimuli; Innovations Require the Slow Network Periphery and Are Encoded by Core-Remodeling. Bioessays 2017; 40. [PMID: 29168203 DOI: 10.1002/bies.201700150] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Revised: 10/12/2017] [Indexed: 12/30/2022]
Abstract
I hypothesize that re-occurring prior experience of complex systems mobilizes a fast response, whose attractor is encoded by their strongly connected network core. In contrast, responses to novel stimuli are often slow and require the weakly connected network periphery. Upon repeated stimulus, peripheral network nodes remodel the network core that encodes the attractor of the new response. This "core-periphery learning" theory reviews and generalizes the heretofore fragmented knowledge on attractor formation by neural networks, periphery-driven innovation, and a number of recent reports on the adaptation of protein, neuronal, and social networks. The core-periphery learning theory may increase our understanding of signaling, memory formation, information encoding and decision-making processes. Moreover, the power of network periphery-related "wisdom of crowds" inventing creative, novel responses indicates that deliberative democracy is a slow yet efficient learning strategy developed as the success of a billion-year evolution. Also see the video abstract here: https://youtu.be/IIjP7zWGjVE.
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Affiliation(s)
- Peter Csermely
- Department of Medical Chemistry, Semmelweis University, Budapest, Hungary
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120
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Sun YZ, Leng SY, Lai YC, Grebogi C, Lin W. Closed-Loop Control of Complex Networks: A Trade-Off between Time and Energy. PHYSICAL REVIEW LETTERS 2017; 119:198301. [PMID: 29219507 DOI: 10.1103/physrevlett.119.198301] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2017] [Indexed: 05/07/2023]
Abstract
Controlling complex nonlinear networks is largely an unsolved problem at the present. Existing works focus either on open-loop control strategies and their energy consumptions or on closed-loop control schemes with an infinite-time duration. We articulate a finite-time, closed-loop controller with an eye toward the physical and mathematical underpinnings of the trade-off between the control time and energy as well as their dependence on the network parameters and structure. The closed-loop controller is tested on a large number of real systems including stem cell differentiation, food webs, random ecosystems, and spiking neuronal networks. Our results represent a step forward in developing a rigorous and general framework to control nonlinear dynamical networks with a complex topology.
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Affiliation(s)
- Yong-Zheng Sun
- Center for Computational Systems Biology of ISTBI, Fudan University, Shanghai 200433, China
- School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
| | - Si-Yang Leng
- Center for Computational Systems Biology of ISTBI, Fudan University, Shanghai 200433, China
- School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China
- Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706, USA
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - Wei Lin
- Center for Computational Systems Biology of ISTBI, Fudan University, Shanghai 200433, China
- School of Mathematical Sciences and LMNS, Fudan University, Shanghai 200433, China
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121
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Abstract
A challenging problem in network science is to control complex networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. However, if we implement actual control by imposing input signals on the minimum set of driver nodes, an unexpected phenomenon arises: due to computational or experimental error there is a great probability that convergence to the final state cannot be achieved. In fact, the associated control cost can become unbearably large, effectively preventing actual control from being realized physically. The difficulty is particularly severe when the network is deemed controllable with a small number of drivers. Here we develop a physical controllability framework based on the probability of achieving actual control. Using a recently identified fundamental chain structure underlying the control energy, we offer strategies to turn physically uncontrollable networks into physically controllable ones by imposing slightly augmented set of input signals on properly chosen nodes. Our findings indicate that, although full control can be theoretically guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control cost to achieve physical control.
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