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Abed S, Rashid A, Hasan O. Formal reasoning about synthetic biology using higher-order-logic theorem proving. IET Syst Biol 2020; 14:271-283. [PMID: 33095748 DOI: 10.1049/iet-syb.2020.0026] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Synthetic biology is an interdisciplinary field that uses well-established engineering principles for performing the analysis of the biological systems, such as biological circuits, pathways, controllers and enzymes. Conventionally, the analysis of these biological systems is performed using paper-and-pencil proofs and computer simulation methods. However, these methods cannot ensure accurate results due to their inherent limitations. Higher-order-logic (HOL) theorem proving is proposed and used as a complementary approach for analysing linear biological systems, which is based on developing a mathematical model of the genetic circuits and the bio-controllers used in synthetic biology based on HOL and analysing it using deductive reasoning in an interactive theorem prover. The involvement of the logic, mathematics and the deductive reasoning in this method ensures the accuracy of the analysis. It is proposed to model the continuous dynamics of the genetic circuits and their associated controllers using differential equations and perform their transfer function-based analysis using the Laplace transform in a theorem prover. For illustration, the genetic circuits of activated and repressed expressions and autoactivation of protein, and phase lag and lead controllers, which are widely used in cancer-cell identifiers and multi-input receptors for precise disease detection, are formally analyzed.
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Affiliation(s)
- Sa'ed Abed
- Computer Engineering Department, College of Engineering and Petroleum, Kuwait University, Kuwait.
| | - Adnan Rashid
- School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan
| | - Osman Hasan
- School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan
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Ferreira GR, Nakaya HI, Costa LDF. Gene regulatory and signaling networks exhibit distinct topological distributions of motifs. Phys Rev E 2018; 97:042417. [PMID: 29758668 DOI: 10.1103/physreve.97.042417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2017] [Indexed: 06/08/2023]
Abstract
The biological processes of cellular decision making and differentiation involve a plethora of signaling pathways and gene regulatory circuits. These networks in turn exhibit a multitude of motifs playing crucial parts in regulating network activity. Here we compare the topological placement of motifs in gene regulatory and signaling networks and observe that it suggests different evolutionary strategies in motif distribution for distinct cellular subnetworks.
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Affiliation(s)
| | - Helder Imoto Nakaya
- School of Pharmaceutical Sciences, University of São Paulo, São Paulo, Brazil
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Murrugarra D, Veliz-Cuba A, Aguilar B, Laubenbacher R. Identification of control targets in Boolean molecular network models via computational algebra. BMC SYSTEMS BIOLOGY 2016; 10:94. [PMID: 27662842 PMCID: PMC5035508 DOI: 10.1186/s12918-016-0332-x] [Citation(s) in RCA: 42] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Accepted: 08/23/2016] [Indexed: 11/10/2022]
Abstract
BACKGROUND Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. RESULTS This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg . CONCLUSIONS This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.
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Affiliation(s)
- David Murrugarra
- Department of Mathematics, University of Kentucky, Lexington, 40506-0027, KY, USA.
| | - Alan Veliz-Cuba
- Department of Mathematics, University of Dayton, Dayton, 45469, OH, USA
| | - Boris Aguilar
- Institute for Systems Biology, Seattle, 98109-5263, WA, USA
| | - Reinhard Laubenbacher
- Center for Quantitative Medicine, University of Connecticut Health Center, Farmington, 06030-6033, CT, USA.,Jackson Laboratory for Genomic Medicine, Farmington, 06030, CT, USA
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Montefusco F, Akman OE, Soyer OS, Bates DG. Ultrasensitive Negative Feedback Control: A Natural Approach for the Design of Synthetic Controllers. PLoS One 2016; 11:e0161605. [PMID: 27537373 PMCID: PMC5004582 DOI: 10.1371/journal.pone.0161605] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/20/2016] [Accepted: 08/08/2016] [Indexed: 12/18/2022] Open
Abstract
Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems—the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems.
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Affiliation(s)
- Francesco Montefusco
- Department of Information Engineering, University of Padova, Padova, Italy
- * E-mail:
| | - Ozgur E. Akman
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom
| | - Orkun S. Soyer
- School of Life Sciences, University of Warwick, Coventry, United Kingdom
| | - Declan G. Bates
- School of Engineering, University of Warwick, Coventry, United Kingdom
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Shin YJ. Digital Signal Processing and Control for the Study of Gene Networks. Sci Rep 2016; 6:24733. [PMID: 27102828 PMCID: PMC4840392 DOI: 10.1038/srep24733] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2015] [Accepted: 04/04/2016] [Indexed: 11/09/2022] Open
Abstract
Thanks to the digital revolution, digital signal processing and control has been widely used in many areas of science and engineering today. It provides practical and powerful tools to model, simulate, analyze, design, measure, and control complex and dynamic systems such as robots and aircrafts. Gene networks are also complex dynamic systems which can be studied via digital signal processing and control. Unlike conventional computational methods, this approach is capable of not only modeling but also controlling gene networks since the experimental environment is mostly digital today. The overall aim of this article is to introduce digital signal processing and control as a useful tool for the study of gene networks.
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Affiliation(s)
- Yong-Jun Shin
- Biomedical Engineering Department, University of Connecticut, Storrs, CT 06269, USA
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Harris AWK, Dolan JA, Kelly CL, Anderson J, Papachristodoulou A. Designing Genetic Feedback Controllers. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 2015; 9:475-484. [PMID: 26390502 DOI: 10.1109/tbcas.2015.2458435] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
By incorporating feedback around systems we wish to manipulate, it is possible to improve their performance and robustness properties to meet pre-specified design objectives. For decades control engineers have been successfully implementing feedback controllers for complex mechanical and electrical systems such as aircraft and sports cars. Natural biological systems use feedback extensively for regulation and adaptation but apart from the most basic designs, there is no systematic framework for designing feedback controllers in Synthetic Biology. In this paper we describe how classical approaches from linear control theory can be used to close the loop. This includes the design of genetic circuits using feedback control and the presentation of a biological phase lag controller.
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Shin YJ, Mahrou B. Modeling collective & intelligent decision making of multi-cellular populations. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2015; 2014:334-7. [PMID: 25569965 DOI: 10.1109/embc.2014.6943597] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
In the presence of unpredictable disturbances and uncertainties, cells intelligently achieve their goals by sharing information via cell-cell communication and making collective decisions, which are more reliable compared to individual decisions. Inspired by adaptive sensor network algorithms studied in communication engineering, we propose that a multi-cellular adaptive network can convert unreliable decisions by individual cells into a more reliable cell-population decision. It is demonstrated using the effector T helper (a type of immune cell) population, which plays a critical role in initiating immune reactions in response to invading foreign agents (e.g., viruses, bacteria, etc.). While each individual cell follows a simple adaptation rule, it is the combined coordination among multiple cells that leads to the manifestation of "self-organizing" decision making via cell-cell communication.
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Shin YJ, Chen KY, Sayed AH, Hencey B, Shen X. Post-translational regulation enables robust p53 regulation. BMC SYSTEMS BIOLOGY 2013; 7:83. [PMID: 23992617 PMCID: PMC3844394 DOI: 10.1186/1752-0509-7-83] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/24/2012] [Accepted: 08/23/2013] [Indexed: 12/13/2022]
Abstract
Background The tumor suppressor protein p53 plays important roles in DNA damage repair, cell cycle arrest and apoptosis. Due to its critical functions, the level of p53 is tightly regulated by a negative feedback mechanism to increase its tolerance towards fluctuations and disturbances. Interestingly, the p53 level is controlled by post-translational regulation rather than transcriptional regulation in this feedback mechanism. Results We analyzed the dynamics of this feedback to understand whether post-translational regulation provides any advantages over transcriptional regulation in regard to disturbance rejection. When a disturbance happens, even though negative feedback reduces the steady-state error, it can cause a system to become less stable and transiently overshoots, which may erroneously trigger downstream reactions. Therefore, the system needs to balance the trade-off between steady-state and transient errors. Feedback control and adaptive estimation theories revealed that post-translational regulation achieves a better trade-off than transcriptional regulation, contributing to a more steady level of p53 under the influence of noise and disturbances. Furthermore, post-translational regulation enables cells to respond more promptly to stress conditions with consistent amplitude. However, for better disturbance rejection, the p53- Mdm2 negative feedback has to pay a price of higher stochastic noise. Conclusions Our analyses suggest that the p53-Mdm2 feedback favors regulatory mechanisms that provide the optimal trade-offs for dynamic control.
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Affiliation(s)
- Yong-Jun Shin
- School of Electrical and Computer Engineering, 402 Phillips Hall, Cornell University, Ithaca, NY 14853, USA.
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Shi C, Li H, Zhou T. Architecture-dependent robustness in a class of multiple positive feedback loops. IET Syst Biol 2013; 7:1-10. [PMID: 23848050 PMCID: PMC8687178 DOI: 10.1049/iet-syb.2011.0090] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2011] [Revised: 07/20/2012] [Accepted: 09/13/2012] [Indexed: 04/05/2024] Open
Abstract
Many types of multiple positive feedbacks with each having potentials to generate bistability exist extensively in natural, raising the question of why a particular architecture is present in a cell. In this study, the authors investigate multiple positive feedback loops across three classes: one-loop class, two-loop class and three-loop class, where each class is composed of double positive feedback loop (DPFL) or double negative feedback loop (DNFL) or both. Through large-scale sampling and robustness analysis, the authors find that for a given class, the homogeneous DPFL circuit (i.e. the coupled circuit that is composed of only DPFLs) is more robust than all the other circuits in generating bistable behaviour. In addition, stochastic simulation shows that the low stable state is more robust than the high stable state in homogeneous DPFL whereas the high-stable state is more robust than the low-stable state in homogeneous DNFL circuits. It was argued that this investigation provides insight into the relationship between robustness and network architecture.
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Affiliation(s)
- Changhong Shi
- School of Mathematics and Computational Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat‐Sen UniversityGuangzhou510275People's Republic China
| | - Han‐xiong Li
- Department of Manufacturing Engineering and Engineering ManagementCity University of Hong KongHong KongPeople's Republic China
| | - Tianshou Zhou
- School of Mathematics and Computational Science and Guangdong Province Key Laboratory of Computational Science, Sun Yat‐Sen UniversityGuangzhou510275People's Republic China
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Shin YJ, Hencey B, Lipkin SM, Shen X. Frequency domain analysis reveals external periodic fluctuations can generate sustained p53 oscillation. PLoS One 2011; 6:e22852. [PMID: 21829536 PMCID: PMC3145758 DOI: 10.1371/journal.pone.0022852] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2011] [Accepted: 07/01/2011] [Indexed: 12/23/2022] Open
Abstract
p53 is a well-known tumor suppressor protein that regulates many pathways, such as ones involved in cell cycle and apoptosis. The p53 levels are known to oscillate without damping after DNA damage, which has been a focus of many recent studies. A negative feedback loop involving p53 and MDM2 has been reported to be responsible for this oscillatory behavior, but questions remain as how the dynamics of this loop alter in order to initiate and maintain the sustained or undamped p53 oscillation. Our frequency domain analysis suggests that the sustained p53 oscillation is not completely dictated by the negative feedback loop; instead, it is likely to be also modulated by periodic DNA repair-related fluctuations that are triggered by DNA damage. According to our analysis, the p53-MDM2 feedback mechanism exhibits adaptability in different cellular contexts. It normally filters noise and fluctuations exerted on p53, but upon DNA damage, it stops performing the filtering function so that DNA repair-related oscillatory signals can modulate the p53 oscillation. Furthermore, it is shown that the p53-MDM2 feedback loop increases its damping ratio allowing p53 to oscillate at a frequency more synchronized with the other cellular efforts to repair the damaged DNA, while suppressing its inherent oscillation-generating capability. Our analysis suggests that the overexpression of MDM2, observed in many types of cancer, can disrupt the operation of this adaptive mechanism by making it less responsive to the modulating signals after DNA damage occurs.
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Affiliation(s)
- Yong-Jun Shin
- Electrical and Computer Engineering, Cornell University, Ithaca, New York, United States of America
| | - Brandon Hencey
- Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, United States of America
| | - Steven M. Lipkin
- Department of Medicine, Weill Cornell College of Medicine, New York, New York, United States of America
| | - Xiling Shen
- Electrical and Computer Engineering, Cornell University, Ithaca, New York, United States of America
- * E-mail:
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