Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Dynamics of cortical action potential initiation

In all neurons of the cerebral cortex, the results of single neuron computations are encoded into action potential sequences. The dynamics of cortical action potential generators thus determines how much and which information is transmitted to other cells in the brain and conversely which aspects of intracellular activity are not communicated to the receiving neuron. The reduction of information by action potential encoding in neocortical neurons is in fact tremendous. It was recently shown that of the 1000 bits per second that are contained in the ongoing membrane potential fluctuations of a typical cortical neuron only roughly 30 bits are encoded into its output sequence of action potentials [1]. In our research on action potential initiation dynamics in cortical neurons, we are using an approach integrating biophysical modelling, dynamical systems theory, in vivo recording of the behaviour of action potential initiation in the intact brain, and neurophysiological and biophysical in vitro experiments to unravel the computational rules and biophysical mechanisms of this key step of neuronal computation.


Anomalous action potential dynamics in cortical neurons

Although actively studied for more than three decades by biological and medical researchers, the precise laws of that determine generation of action potential by neurons of the mammalian brain surprisingly are neither well characterized nor mechanistically understood. For instance, it is widely assumed that the initiation of action potentials can be modelled as a threshold crossing process: When the membrane potential of a neuron is driven beyond a fixed threshold voltage, value sodium channels are activated that mediate a strongly depolarizing current that causes the membrane potential to rapidly increase. Surprisingly, we recently found that during the operation of cortical neurons in the intact brain there is no fixed threshold potential underlying the initiation of action potential [2]. Instead, action potentials are obviously initiated over a very wide range of potentials and most importantly even the largest AP initiation potentials can be reached without inducing action potential firing (Fig.1a,b). In addition, the rapidness of action potential initiation, the inverse voltage range over which high rates of membrane potential change are reached during the initial phase of an AP, is much higher than predicted by the universally accepted Hodgkin-Huxley theory. Based on these findings, we suggested that cortical action potential generators might be tailored beyond the range that can be successfully described by the canonical Hodgkin-Huxley theory, indicating that fundamental aspects of the biophysics of action potential initiation in cortical neurons remain unidentified. These results initiated a lively debate on and an ongoing re-evaluation of the universal validity of the classical Hodgkin-Huxley theory of action potential initiation (see e.g. [3-7]).


The cooperative sodium channel activation hypothesis

The abrupt increase of depolarization speed during the initial phase of cortical action potentials that we described suggests that many sodium channels in the neuronal membrane are synchronously activated. This may indicate that the assumption of statistically independence of sodium channel activation that is a basic ingredient of the Hodgkin-Huxley theory is violated in neuronal membranes. We thus considered the hypothesis that neuronal sodium channels may undergo cooperative activation such that activation of one channel can directly induce neighbouring channels to also activate. Intriguingly, quantitative models of membrane potential dynamics based on such a cooperative sodium channel activation kinetics, can faithfully reproduce all key features of action potential initiation as observed in cortical neurons in the intact brain (Fig.1c,d)[2]. Further support for the cooperative sodium channel activation hypothesis comes from in vitro experiments which tested one of its key predictions. If inter-channel interactions are assumed distance-dependent in neuronal membranes, then the cooperative sodium channel activation hypothesis predicts that reducing the effective density of channels should weaken cooperativity, and eventually lead to a action potentials onset dynamics conforming with the assumption of statistically independent gating and Hodgkin-Huxley theory. We tested this prediction in vitro, recording action potentials while reducing the density of available sodium channels by the application of tetrodotoxin (TTX). As predicted, TTX application in fact led to substantial reduction in the onset rapidness of action potentials in all tested cortical neurons [2]. Subsequent experiments revealed that a similar transformation of action potential waveform can also be achieved by reducing the extracellular sodium concentration suggesting that sodium ions might be the mediators of interchannel interactions (Wolf et al. in prep.).

Direct evidence for cooperative ion channel activation
Although prominent neurophysiologists consider the hypothesis of cooperative ion channel activation “exotic” [5,7], the ability of ion channels to exhibit cooperative activation, that we theoretically predicted, was immediately confirmed by an independent experimental study that appeared less than three months after publication of our initial report [8]. In this study, Molina et al. described the activation kinetics of KcsA channels, a minimal model ion channel isolated from bacteria. Their single channel resolution recordings directly demonstrated that channels may either gate statistically independently as conventionally assumed or in a highly cooperative fashion. In addition, ensemble of channels showed transitions between statistically independent and cooperative gating modes that apparently dependent on the degree of channel clustering in the membrane. While it is currently unknown whether neuronal sodium channels do exhibit a similar degree of inter- channel cooperativity, the closely related sodium channels underlying action potential generation and propagation in the heart, have also been shown to be capable of highly synchronized gating (Fig.1e)[9]. Efforts are under way to further characterize sodium channel cooperativity and the underlying molecular mechanisms in cardiomyocytes in collaboration with the groups of Bodenschatz and Luther, and to probe for this phenomenon in cortical neurons in collaboration with Fleidervish and Gutnick at the Hebrew University of Jerusalem [10].

Functional consequences of rapid onset action potential initiation

Our previous theoretical analyses predict that the very rapid onset of action potentials enhances the ability of neurons to lock the firing times of their action potentials to high frequency components of their synaptic inputs (Fig.2a). We are currently testing this important functional consequence in in vitro neurophysiological experiments. In these experiments the intense synaptic bombardment that a cortical neuron experiences in vivo is emulated by the injection of a randomly fluctuating dynamical current superimposed with a weak periodic test signal(Fig.2b). Quantifying the amplitude of spike frequency modulation observed in such experiments, as a function of test stimulus frequency, we find that cortical neurons indeed exhibit very high cut-off frequencies on the order of 200Hz, even when firing at average impulse rates below 10Hz. In contradistinction, previous theoretical studies consistently found that Hodgkin-Huxley type action potential generators typically exhibit cut off frequencies on the order of their mean firing rate [11,12]. Confirming our theoretical predictions [6,12], these preliminary results indeed suggest that the cut-off frequencies of cortical action potential generators are more than one order of magnitude higher than predicted by the classical Hodgkin-Huxley theory. To further corroborate these results our current efforts are concentrating on developing efficient and quantitatively controlled methods for the estimation of frequency response functions and cut off frequencies from neuronal noise injection experiments.

Members working within this Project:

 Andreas Neef 

Former Members:

 Pinar Öz 
 Michael Monteforte 

Selected Publications:

M. Puelma Touzel, and F. Wolf (2015).
Complete Firing-Rate Response of Neurons with Complex Intrinsic Dynamics
PLoS Comput Biol 11(12).

M. Monteforte (2011).
Chaotic Dynamics in Networks of Spiking Neurons in the Balanced State
Phd thesis, Georg-August-University Goettingen. download file

W. Wei, and F. Wolf (2011).
Spike Onset Dynamics and Response Speed in Neuronal Populations
Phys. Rev. Lett. 106(8):088102. download file

M. Monteforte, and F. Wolf (2010).
Dynamical Entropy Production in Spiking Neuron Networks in the Balanced State
Phys. Rev. Lett. 105(26):268104. download file

T. Tchumatchenko, A. Malyshev, T. Geisel, M. Volgushev, and F. Wolf (2010).
Correlations and synchrony in threshold neuron models
Phys. Rev. Lett. 104(5). download file

B. Naundorf, T. Geisel, and F. Wolf (2005).
Action potential onset dynamics and the response speed of neuronal populations
Journal of Computational Neuroscience 18(3):297-309.

B. Naundorf, T. Geisel, and F. Wolf (2005).
Dynamical response properties of a canonical model for type-I membranes
Neurocomputing 65:421-428.