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Turbulent Relationships – Single Cell Dynamics and the Decay of Information in Balanced
Neuronal Circuits
Neuronal circuits in the central nervous system process information by the collective
dynamics of large recurrently connected networks of nerve cells interacting with each other
by sending and receiving electrical impulses called action potentials (APs). Interacting
exclusively by APs implies that the cellular process of action potential initiation constitutes a
fundamental bottleneck for information flow within neuronal circuits. Theoretical analyzes
over the past decade have established circuit models in which dynamical properties can be
comprehensively analyzed taking account of each and every AP.
In this presentation, I will use such models to examine the relationship of single neuron AP
initiation dynamics and a fundamental feature of information flow in spiking neuron
networks, the flow of information from past into future states as quantified by dynamical
(Kolmogorov-Sinai) entropy production rate. In contradistinction to many statistical
properties of AP patterns, dynamical entropy production turns out to be extremely sensitive
to minute details of the AP initiation dynamics. Increasing the instability of single neuron AP
initiation - perhaps somewhat paradoxically – renders the collective dynamics more stable
and can reduce dynamical entropy production by orders of magnitude. Very “crisp” action
potential generators can even lead to a temporally irregular circuit dynamics that is not
chaotic but stable.
This phenomenon can be understood from the bandwidth of population encoding in an
ensemble of uncoupled noise-driven neurons. At fixed rate of AP firing, spike trains
generated by model neurons become more and more informative about high frequency
components in their input when the instability of action potential initiation is increased. As a
consequence, recurrent circuits of neurons collectively generating fluctuating inputs can
maintain information about their past state for longer periods of time corresponding to a
reduced rate of entropy production. Cell physiological experiments on noise-driven AP firing
in neocortical neurons confirm the prediction of AP onset-dependent bandwidth and
demonstrate that the bandwidth of mammalian neurons is in fact surprisingly high. We
examine the detailed structure of phase space underlying stable irregular dynamics and find
that it is organized by an intertwined system of basins of attraction, which we call
“dynamical flux tubes”. I will conclude with a discussion of the potential utility of these
structures for stimulus categorization.
Related publications:
Monteforte, M., & Wolf, F. (2010). Dynamical Entropy Production in Spiking Neuron Networks in the Balanced
State. Physical Review Letters, 105(26), 1–4.
Tchumatchenko, T., Malyshev, A., Geisel, T., Volgushev, M., & Wolf, F. (2010). Correlations and synchrony in
threshold neuron models. Physical Review Letters, 104(5), 58102.
Wei, W., & Wolf, F. (2011). Spike onset dynamics and response speed in neuronal populations. Physical Review
Letters, 106(8), 88102.
Tchumatchenko, T., & Wolf, F. (2011). Representation of dynamical stimuli in populations of threshold neurons.
PLoS Computational Biology, 7(10), e1002239.
Tchumatchenko, T., Malyshev, A., Wolf, F., & Volgushev, M. (2011). Ultrafast population encoding by cortical
neurons. The Journal of Neuroscience, 31(34), 12171–12179.
Monteforte, M., & Wolf, F. (2012). Dynamic Flux Tubes Form Reservoirs of Stability in Neuronal Circuits.
Physical Review X, 2(4), 041007.
Ilin, V., Malyshev, A., Wolf, F., & Volgushev, M. (2013). Fast computations in cortical ensembles require rapid
initiation of action potentials. The Journal of Neuroscience, 33(6), 2281–2292.