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Erschienen in:
Nonautonomous Dynamical Systems in the Life Sciences Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

4. Stimulus-Response Reliability of Biological Networks

verfasst von : Kevin K. Lin

Erschienen in: Nonautonomous Dynamical Systems in the Life Sciences

Verlag: Springer International Publishing

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Abstract

If a network of cells is repeatedly driven by the same sustained, complex signal, will it give the same response each time? A system whose response is reproducible across repeated trials is said to be reliable. Reliability is of interest in, e.g., computational neuroscience because the degree to which a neuronal network is reliable constrains its ability to encode information via precise temporal patterns of spikes. This chapter reviews a body of work aimed at discovering network conditions and dynamical mechanisms that can affect the reliability of a network. A number of results are surveyed here, including a general condition for reliability and studies of specific mechanisms for reliable and unreliable behavior in concrete models. This work relies on qualitative arguments using random dynamical systems theory, in combination with systematic numerical simulations.

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Vorheriges Kapitel Canard Theory and Excitability
Nächstes Kapitel Coupled Nonautonomous Oscillators
Fußnoten
1
Theta neurons can also model neurons operating in an excitable regime. The reliability of excitable theta neuron networks is studied in [22].
 
2
See, e.g., [5], but note that phase truncations can sometimes miss important dynamical effects [30], and their use in biological modeling should be carefully justified.
 
3
The fiber exponent can be defined exactly as in (4.6), but with the tangent vector v chosen to lie in the subspace tangent to each fiber; note these subspaces are invariant due to the skew product structure.
 
4
It is straightforward to show that there is always a unique modular decomposition connected by an acyclic graph that is “maximal” in the sense that it cannot be refined any further without introducing cycles into the quotient graph.
 
5
These results have been extended to certain nonlinear parabolic PDEs [32] and periodically-kicked homoclinic loops [37].
 
6
A rough estimate shows that when A = 2, each kick should be sufficient to drive the oscillator roughly 1/3 of the way around its cycle.
 
Literatur
1.
L. Arnold, Random Dynamical Systems (Springer, New York, 2003)
2.
W. Bair, E. Zohary, W.T. Newsome, Correlated firing in macaque visual area MT: time scales and relationship to behavior. J. Neurosci. 21(5), 1676–1697 (2001)
3.
P.H. Baxendale, Stability and equilibrium properties of stochastic flows of diffeomorphisms, in Progress in Probability, vol. 27 (Birkhauser, Basel, 1992)
4.
M. Berry, D. Warland, M. Meister, The structure and precision of retinal spike trains. Proc. Natl. Acad. Sci. 94, 5411–5416 (1997)CrossRef
5.
E. Brown, P. Holmes, J. Moehlis, Globally coupled oscillator networks, in Problems and Perspectives in Nonlinear Science: A celebratory volume in honor of Lawrence Sirovich, ed. by E. Kaplan, J.E. Marsden, K.R. Sreenivasan (Springer, New York, 2003), pp. 183–215CrossRef
6.
H.L. Bryant, J.P. Segundo, Spike initiation by transmembrane current: a white-noise analysis. J. Physiol. 260, 279–314 (1976)
7.
R. de Reuter van Steveninck, R. Lewen, S. Strong, R. Koberle, W. Bialek, Reproducibility and variability in neuronal spike trains. Science 275, 1805–1808 (1997)CrossRef
8.
R.E.L. Deville, N. Sri Namachchivaya, Z. Rapti, Stability of a stochastic two-dimensional non-Hamiltonian system. SIAM J. Appl. Math. 71, 1458–1475 (2011)CrossRefMATHMathSciNet
9.
A.S. Ecker, P. Berens, G.A. Keliris, M. Bethge, N.K. Logothetis, A.S. Tolias. Decorrelated neuronal firing in cortical microcircuits. Science 327, 584–587 (2010)CrossRef
10.
11.
G.B. Ermentrout, Type I membranes, phase resetting curves and synchrony. Neural Comput. 8, 979–1001 (1996)CrossRef
12.
G.B. Ermentrout, D. Terman, Foundations of Mathematical Neuroscience (Springer, Berlin, 2010)CrossRefMATH
13.
A.A. Faisal, L.P.J. Selen, D.M. Wolpert, Noise in the nervous system. Nat. Rev. Neurosci. 9, 292–303 (2008)CrossRef
14.
J.-M. Fellous, P.H.E. Tiesinga, P.J. Thomas, T.J. Sejnowski, Discovering spike patterns in neuronal responses. J. Neurosci. 24, 2989–3001 (2004)CrossRef
15.
D. Goldobin, A. Pikovsky, Antireliability of noise-driven neurons. Phys. Rev. E 73, 061906-1–061906-4 (2006)
16.
J. Hunter, J. Milton, P. Thomas, J. Cowan, Resonance effect for neural spike time reliability. J.Ñeurophysiol. 80, 1427–1438 (1998)
17.
P. Kara, P. Reinagel, R.C. Reid, Low response variability in simultaneously recorded retinal, thalamic, and cortical neurons. Neuron 27, 636–646 (2000)CrossRef
18.
19.
P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations (Springer, New York, 2011)
20.
E. Kosmidis, K. Pakdaman, Analysis of reliability in the Fitzhugh–Nagumo neuron model. J.C̃omput. Neurosci. 14, 5–22 (2003)
21.
H. Kunita, Stochastic Flows and Stochastic Differential Equations. Cambridge Studies in Advanced Mathematics, vol. 24 (Cambridge University Press, Cambridge, 1990)
22.
G. Lajoie, K.K. Lin, E. Shea-Brown, Chaos and reliability in balanced spiking networks with temporal drive. Phys. Rev. E 87 (2013)
23.
Y. Le Jan. Équilibre statistique pour les produits de difféomorphismes aléatoires indépendants. Ann. Inst. H. Poincaré Probab. Stat. 23(1), 111–120 (1987)MATHMathSciNet
24.
25.
26.
27.
28.
K.K. Lin, E. Shea-Brown, L.-S. Young, Spike-time reliability of layered neural oscillator networks. J. Comput. Neurosci. 27, 135–160 (2009)CrossRefMathSciNet
29.
K.K. Lin, E. Shea-Brown, L.-S. Young, Reliability of layered neural oscillator networks. Commun. Math. Sci. 7, 239–247 (2009)CrossRefMATHMathSciNet
30.
K.K. Lin, K.C.A. Wedgwood, S. Coombes, L.-S. Young, Limitations of perturbative techniques in the analysis of rhythms and oscillations. J. Math. Biol. 66, 139–161 (2013)CrossRefMATHMathSciNet
31.
T. Lu, L. Liang, X. Wang, Temporal and rate representations of time-varying signals in the auditory cortex of awake primates. Nat. Neurosci. 4, 1131–1138 (2001)CrossRef
32.
K. Lu, Q. Wang, L.-S. Young, Strange Attractors for Periodically Forced Parabolic Equations. Memoirs of the AMS, American Mathematical Society, (Providence, Rhode Island, 2013)
33.
Z. Mainen, T. Sejnowski, Reliability of spike timing in neocortical neurons. Science 268, 1503–1506 (1995)CrossRef
34.
G. Murphy, F. Rieke, Network variability limits stimulus-evoked spike timing precision in retinal ganglion cells. Neuron 52, 511–524 (2007)CrossRef
35.
H. Nakao, K. Arai, K. Nagai, Y. Tsubo, Y. Kuramoto. Synchrony of limit-cycle oscillators induced by random external impulses. Phys. Rev. E 72, 026220-1–026220-13 (2005)
36.
D. Nualart, The Malliavin Calculus and Related Topics (Springer, Berlin, 2006)MATH
37.
W. Ott, Q. Wang, Dissipative homoclinic loops of two-dimensional maps and strange attractors with one direction of instability. Commun. Pure Appl. Math. 64, 1439–1496 (2011)MATHMathSciNet
38.
K. Pakdaman, D. Mestivier, External noise synchronizes forced oscillators. Phys. Rev. E 64, 030901–030904 (2001)CrossRef
39.
J. Ritt, Evaluation of entrainment of a nonlinear neural oscillator to white noise. Phys. Rev. E 68, 041915–041921 (2003)CrossRefMathSciNet
40.
J. Teramae, T. Fukai, Reliability of temporal coding on pulse-coupled networks of oscillators. arXiv:0708.0862v1 [nlin.AO] (2007)
41.
J. Teramae, D. Tanaka, Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. Phys. Rev. Lett. 93, 204103–204106 (2004)CrossRef
42.
A. Uchida, R. McAllister, R. Roy, Consistency of nonlinear system response to complex drive signals. Phys. Rev. Lett. 93, 244102 (2004)CrossRef
43.
B.P. Uberuaga, M. Anghel, A.F. Voter, Synchronization of trajectories in canonical molecular-dynamics simulations: observation, explanation, and exploitation. J. Chem. Phys. 120, 6363–6374 (2004)CrossRef
44.
S. Varigonda, T. Kalmar-Nagy, B. LaBarre, I. Mezić, Graph decomposition methods for uncertainty propagation in complex, nonlinear interconnected dynamical systems, in 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas (2004)
45.
46.
47.
Q. Wang, L.-S. Young, Strange attractors in periodically-kicked limit cycles and Hopf bifurcations. Commun. Math. Phys. 240, 509–529 (2003)MATHMathSciNet
48.
49.
50.
L.-S. Young, Ergodic theory of differentiable dynamical systems, in Real and Complex Dynamics, NATO ASI Series (Kluwer, Dordrecht, 1995), pp. 293–336
51.
L.-S. Young, What are SRB measures, and which dynamical systems have them? J. Stat. Phys. 108(5), 733–754 (2002)CrossRefMATH
52.
53.
C. Zhou, J. Kurths, Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons. Chaos 13, 401–409 (2003)
Metadaten
Titel
Stimulus-Response Reliability of Biological Networks
verfasst von
Kevin K. Lin
Copyright-Jahr
2013
Buch
Nonautonomous Dynamical Systems in the Life Sciences

Print ISBN: 978-3-319-03079-1

Electronic ISBN: 978-3-319-03080-7

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-3-319-03080-7_4