Biomolecular implementation of nonlinear system theoretic operators

Mathias Foo, Rucha Sawlekar, Jongmin Kim, Declan G. Bates, Guy Bart Stan, Vishwesh Kulkarni

Research output: Research - peer-reviewChapter

Abstract

— Synthesis of biomolecular circuits for controlling molecular-scale processes is an important goal of synthetic biology with a wide range of in vitro and in vivo applications, including biomass maximization, nanoscale drug delivery, and many others. In this paper, we present new results on how abstract chemical reactions can be used to implement com-monly used system theoretic operators such as the polynomial functions, rational functions and Hill-type nonlinearity. We first describe how idealised versions of multi-molecular reactions, catalysis, annihilation, and degradation can be combined to implement these operators. We then show how such chemical reactions can be implemented using enzyme-free, entropy-driven DNA reactions. Our results are illustrated through three applications: (1) implementation of a Stan-Sepulchre oscillator, (2) the computation of the ratio of two signals, and (3) a PI+antiwindup controller for regulating the output of a static nonlinear plant.
LanguageEnglish
Title of host publication2016 European Control Conference, ECC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1824-1831
Number of pages8
ISBN (Electronic)978-1-5090-2591-6, 978-1-5090-2590-9
ISBN (Print)978-1-5090-2592-3
DOIs
StatePublished - 6 Jan 2017

Publication series

Name2016 European Control Conference, ECC 2016

Fingerprint

Nonlinear systems
Chemical reactions
Rational functions
Drug delivery
Catalysis
Mathematical operators
Biomass
Entropy
Enzymes
Polynomials
Controllers
Networks (circuits)
Synthetic Biology

Keywords

  • Chemicals
  • DNA
  • Steady-state
  • Degradation
  • Synthetic biology
  • Oscillators

Cite this

Foo, M., Sawlekar, R., Kim, J., Bates, D. G., Stan, G. B., & Kulkarni, V. (2017). Biomolecular implementation of nonlinear system theoretic operators. In 2016 European Control Conference, ECC 2016 (pp. 1824-1831). (2016 European Control Conference, ECC 2016). Institute of Electrical and Electronics Engineers Inc.. DOI: 10.1109/ECC.2016.7810556

Biomolecular implementation of nonlinear system theoretic operators. / Foo, Mathias; Sawlekar, Rucha; Kim, Jongmin; Bates, Declan G.; Stan, Guy Bart; Kulkarni, Vishwesh.

2016 European Control Conference, ECC 2016. Institute of Electrical and Electronics Engineers Inc., 2017. p. 1824-1831 (2016 European Control Conference, ECC 2016).

Research output: Research - peer-reviewChapter

Foo, M, Sawlekar, R, Kim, J, Bates, DG, Stan, GB & Kulkarni, V 2017, Biomolecular implementation of nonlinear system theoretic operators. in 2016 European Control Conference, ECC 2016. 2016 European Control Conference, ECC 2016, Institute of Electrical and Electronics Engineers Inc., pp. 1824-1831. DOI: 10.1109/ECC.2016.7810556
Foo M, Sawlekar R, Kim J, Bates DG, Stan GB, Kulkarni V. Biomolecular implementation of nonlinear system theoretic operators. In 2016 European Control Conference, ECC 2016. Institute of Electrical and Electronics Engineers Inc.2017. p. 1824-1831. (2016 European Control Conference, ECC 2016). Available from, DOI: 10.1109/ECC.2016.7810556
Foo, Mathias ; Sawlekar, Rucha ; Kim, Jongmin ; Bates, Declan G. ; Stan, Guy Bart ; Kulkarni, Vishwesh. / Biomolecular implementation of nonlinear system theoretic operators. 2016 European Control Conference, ECC 2016. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 1824-1831 (2016 European Control Conference, ECC 2016).
@inbook{3d066dab41eb435c88207b90c4ee067a,
title = "Biomolecular implementation of nonlinear system theoretic operators",
abstract = "— Synthesis of biomolecular circuits for controlling molecular-scale processes is an important goal of synthetic biology with a wide range of in vitro and in vivo applications, including biomass maximization, nanoscale drug delivery, and many others. In this paper, we present new results on how abstract chemical reactions can be used to implement com-monly used system theoretic operators such as the polynomial functions, rational functions and Hill-type nonlinearity. We first describe how idealised versions of multi-molecular reactions, catalysis, annihilation, and degradation can be combined to implement these operators. We then show how such chemical reactions can be implemented using enzyme-free, entropy-driven DNA reactions. Our results are illustrated through three applications: (1) implementation of a Stan-Sepulchre oscillator, (2) the computation of the ratio of two signals, and (3) a PI+antiwindup controller for regulating the output of a static nonlinear plant.",
keywords = "Chemicals, DNA, Steady-state, Degradation, Synthetic biology, Oscillators",
author = "Mathias Foo and Rucha Sawlekar and Jongmin Kim and Bates, {Declan G.} and Stan, {Guy Bart} and Vishwesh Kulkarni",
year = "2017",
month = "1",
doi = "10.1109/ECC.2016.7810556",
isbn = "978-1-5090-2592-3",
series = "2016 European Control Conference, ECC 2016",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "1824--1831",
booktitle = "2016 European Control Conference, ECC 2016",
address = "United States",

}

TY - CHAP

T1 - Biomolecular implementation of nonlinear system theoretic operators

AU - Foo,Mathias

AU - Sawlekar,Rucha

AU - Kim,Jongmin

AU - Bates,Declan G.

AU - Stan,Guy Bart

AU - Kulkarni,Vishwesh

PY - 2017/1/6

Y1 - 2017/1/6

N2 - — Synthesis of biomolecular circuits for controlling molecular-scale processes is an important goal of synthetic biology with a wide range of in vitro and in vivo applications, including biomass maximization, nanoscale drug delivery, and many others. In this paper, we present new results on how abstract chemical reactions can be used to implement com-monly used system theoretic operators such as the polynomial functions, rational functions and Hill-type nonlinearity. We first describe how idealised versions of multi-molecular reactions, catalysis, annihilation, and degradation can be combined to implement these operators. We then show how such chemical reactions can be implemented using enzyme-free, entropy-driven DNA reactions. Our results are illustrated through three applications: (1) implementation of a Stan-Sepulchre oscillator, (2) the computation of the ratio of two signals, and (3) a PI+antiwindup controller for regulating the output of a static nonlinear plant.

AB - — Synthesis of biomolecular circuits for controlling molecular-scale processes is an important goal of synthetic biology with a wide range of in vitro and in vivo applications, including biomass maximization, nanoscale drug delivery, and many others. In this paper, we present new results on how abstract chemical reactions can be used to implement com-monly used system theoretic operators such as the polynomial functions, rational functions and Hill-type nonlinearity. We first describe how idealised versions of multi-molecular reactions, catalysis, annihilation, and degradation can be combined to implement these operators. We then show how such chemical reactions can be implemented using enzyme-free, entropy-driven DNA reactions. Our results are illustrated through three applications: (1) implementation of a Stan-Sepulchre oscillator, (2) the computation of the ratio of two signals, and (3) a PI+antiwindup controller for regulating the output of a static nonlinear plant.

KW - Chemicals

KW - DNA

KW - Steady-state

KW - Degradation

KW - Synthetic biology

KW - Oscillators

U2 - 10.1109/ECC.2016.7810556

DO - 10.1109/ECC.2016.7810556

M3 - Chapter

SN - 978-1-5090-2592-3

T3 - 2016 European Control Conference, ECC 2016

SP - 1824

EP - 1831

BT - 2016 European Control Conference, ECC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -