1932

Abstract

Feedback is a key element of regulation, as it shapes the sensitivity of a process to its environment. Positive feedback upregulates, and negative feedback downregulates. Many regulatory processes involve a mixture of both, whether in nature or in engineering. This article revisits the mixed-feedback paradigm, with the aim of investigating control across scales. We propose that mixed feedback regulates excitability and that excitability plays a central role in multiscale neuronal signaling. We analyze this role in a multiscale network architecture inspired by neurophysiology. The nodal behavior defines a mesoscale that connects actuation at the microscale to regulation at the macroscale. We show that mixed-feedback nodal control provides regulatory principles at the network scale, with a nodal resolution. In this sense, the mixed-feedback paradigm is a control principle across scales.

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/content/journals/10.1146/annurev-control-053018-023708
2019-05-03
2024-03-29
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Literature Cited

  1. 1.  Olfati-Saber R, Murray RM 2004. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49:1520–33
    [Google Scholar]
  2. 2.  Sepulchre R 2011. Consensus on nonlinear spaces. Annu. Rev. Control 35:56–64
    [Google Scholar]
  3. 3.  Sarlette A, Sepulchre R 2014. Control limitations from distributed sensing: theory and extremely large telescope application. Automatica 50:421–30
    [Google Scholar]
  4. 4.  Tucker G 1972. The history of positive feedback: the oscillating audion, the regenerative receiver, and other applications up to around 1923. Radio Electron. Eng. 42:69–80
    [Google Scholar]
  5. 5.  Black H 1934. Stabilised feedback amplifiers. Bell Labs Tech. J. 13:69–80
    [Google Scholar]
  6. 6.  Thomas R 1981. On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillation. Numerical Methods in the Study of Critical Phenomena J Della Dora, J Demongeot, B Lacolle180–93 Berlin: Springer
    [Google Scholar]
  7. 7.  Tsai TYC, Choi YS, Ma W, Pomerening JR, Tang C, Ferrell JE 2008. Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science 321:126–29
    [Google Scholar]
  8. 8.  Mitrophanov AY, Groisman E 2008. Positive feedback in cellular control systems. BioEssays 30:542–55
    [Google Scholar]
  9. 9.  Smolen P, Baxter D, Byrne J 2001. Modeling circadian oscillations with interlocking positive and negative feedback loops. J. Neurosci. 21:6644–56
    [Google Scholar]
  10. 10.  Åstrom KJ, Murray RM 2008. Feedback Systems: An Introduction for Scientists and Engineers Princeton, NJ: Princeton Univ. Press
  11. 11.  Nyquist H 1932. Regeneration theory. Bell Labs Tech. J. 11:126–47
    [Google Scholar]
  12. 12.  Koch C 2004. Biophysics of Computation: Information Processing in Single Neurons Oxford, UK: Oxford Univ. Press
  13. 13.  Bacaër N 2011. Verhulst and the logistic equation (1838). A Short History of Mathematical Population Dynamics35–39 London: Springer
    [Google Scholar]
  14. 14.  Boyd S, Chua LO 1985. Fading memory and the problem of approximating nonlinear operators with volterra series. IEEE Trans. Circuits Syst. 32:1150–71
    [Google Scholar]
  15. 15.  Hodgkin AL, Huxley AF 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117:500–44
    [Google Scholar]
  16. 16.  Drion G, Franci A, Dethier J, Sepulchre R 2015. Dynamic input conductances shape neuronal spiking. eNeuro 2: https://doi.org/10.1523/ENEURO.0031-14.2015
    [Crossref] [Google Scholar]
  17. 17.  Destexhe A, Mainen ZF, Sejnowski TJ 1998. Kinetic models of synaptic transmission. Methods in Neuronal Modeling: From Ions to Networks C Koch, I Segev1–25 Cambridge, MA: MIT Press. 2nd ed.
    [Google Scholar]
  18. 18.  Sepulchre R, Drion G, Franci A 2018. Excitable behaviors. Emerging Applications of Control and Systems Theory R Tempo, S Yurkovich, P Misra269–80 Cham, Switz.: Springer
    [Google Scholar]
  19. 19.  FitzHugh R 1961. Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1:445–66
    [Google Scholar]
  20. 20.  Nagumo J, Arimoto S, Yoshizawa S 1962. An active pulse transmission line simulating nerve axon. Proc. IRE 50:2061–70
    [Google Scholar]
  21. 21.  Byrne JH, Heidelberger R, Waxham MN 2014. From Molecules to Networks: An Introduction to Cellular and Molecular Neuroscience San Diego, CA: Academic
  22. 22.  Willems J 1972. Dissipative dynamical systems part I: general theory. Arch. Rational Mech. Anal. 45:321–51
    [Google Scholar]
  23. 23.  van der Schaft AJ, Maschke BM 2013. Port-Hamiltonian systems on graphs. SIAM J. Control Optim. 51:906–37
    [Google Scholar]
  24. 24.  Pasqualetti F, Zampieri S, Bullo F 2014. Controllability metrics, limitations and algorithms for complex networks. IEEE Trans. Control Netw. Syst. 1:40–52
    [Google Scholar]
  25. 25.  Wilson HR, Cowan JD 1972. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12:1–24
    [Google Scholar]
  26. 26.  Amari SI 1977. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27:77–87
    [Google Scholar]
  27. 27.  Hopfield JJ 1984. Neurons with graded response have collective computational properties like those of two-state neurons. PNAS 81:3088–92
    [Google Scholar]
  28. 28.  Drion G, O'Leary T, Marder E 2015. Ion channel degeneracy enables robust and tunable neuronal firing rates. PNAS 112:E5361–70
    [Google Scholar]
  29. 29.  Franci A, Drion G, Sepulchre R 2017. Robust and tunable bursting requires slow positive feedback. J. Neurophysiol. 119:1222–34
    [Google Scholar]
  30. 30.  Franci A, Drion G, Sepulchre R 2014. Modeling the modulation of neuronal bursting: a singularity theory approach. SIAM J. Appl. Dyn. Syst. 13:798–829
    [Google Scholar]
  31. 31.  Sherman SM 2001. Tonic and burst firing: dual modes of thalamocortical relay. Trends Neurosci. 24:122–26
    [Google Scholar]
  32. 32.  Krahe R, Gabbiani F 2004. Burst firing in sensory systems. Nat. Rev. Neurosci. 5:13–23
    [Google Scholar]
  33. 33.  Izhikevich EM 2007. Dynamical Systems in Neuroscience Cambridge, MA: MIT Press
  34. 34.  Ermentrout B, Terman DH 2010. Foundations of Mathematical Neuroscience New York: Springer
  35. 35.  Marder E, Calabrese RL 1996. Principles of rhythmic motor pattern generation. Physiol. Rev. 76:687–717
    [Google Scholar]
  36. 36.  Dethier J, Drion G, Franci A, Sepulchre R 2015. A positive feedback at the cellular level promotes robustness and modulation at the circuit level. J. Neurophysiol. 114:2472–84
    [Google Scholar]
  37. 37.  Drion G, Dethier J, Franci A, Sepulchre R 2018. Switchable slow cellular conductances determine robustness and tunability of network states. PLOS Comput. Biol. 14:e1006125
    [Google Scholar]
  38. 38.  Gordon I, Whelan P 2006. Monoaminergic control of cauda-equina-evoked locomotion in the neonatal mouse spinal cord. J Neurophysiol. 96:3122–29
    [Google Scholar]
  39. 39.  Harris-Warrick R, Cohen A 1985. Serotonin modulates the central pattern generator for locomotion in the isolated lamprey spinal cord. J. Exp. Biol. 116:27–46
    [Google Scholar]
  40. 40.  Liu J, Akay T, Hedlund P, Pearson K, Jordan L 2009. Spinal 5-HT7 receptors are critical for alternating activity during locomotion: in vitro neonatal and in vivo adult studies using 5-HT7 receptor knockout mice. J. Neurophysiol. 102:337–48
    [Google Scholar]
  41. 41.  Jordan L, Slawinska U 2011. Modulation of rhythmic movement: control of coordination. Prog. Brain Res. 188:181–95
    [Google Scholar]
  42. 42.  Drion G, Franci A, Sepulchre R 2019. Cellular switches orchestrate rhythmic circuits. Biol. Cybernet. 113:71–82
    [Google Scholar]
  43. 43.  Marder E, Bucher D 2007. Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs. Annu. Rev. Physiol. 69:291–316
    [Google Scholar]
  44. 44.  McCormick DA, Bal T 1997. Sleep and arousal: thalamocortical mechanisms. Annu. Rev. Neurosci. 20:185–215
    [Google Scholar]
  45. 45.  McCormick DA, Nusbaum MP 2014. Editorial overview: neuromodulation: tuning the properties of neurons, networks and behavior. Curr. Opin. Neurobiol. 29:iv–vii
    [Google Scholar]
  46. 46.  Kühn AA, Williams D, Kupsch A, Limousin P, Hariz M et al. 2004. Event-related beta desynchronization in human subthalamic nucleus correlates with motor performance. Brain 137:735–46
    [Google Scholar]
  47. 47.  Sherman SM, Guillery RW 2006. Exploring the Thalamus and Its Role in Cortical Function Cambridge, MA: MIT Press. 2nd ed.
  48. 48.  Sherman SM 2012. Thalamocortical interactions. Curr. Opin. Neurobiol. 22:575–79
    [Google Scholar]
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