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

Most information transfer in neuronal systems occurs through action potentials.  The first quantitative description of action potential generation was published over 60 years ago [1].  Considering the huge importance of AP generation for the functioning of the nervous system, it came as a large surprise when we realized that the community is to this day far from a quantitative understanding of the AP generation in mammalian neurons.  Biophysically motivated multi-compartment models of neurons fail to reproduce the shape of individual action potentials and fail to reproduce the ability of central neurons to encode frequencies as high as 200 or 300 Hz.  We identified two core problems in the field:  1. Sodium channels activate so rapidly that the 1 to 2 kHz resolution typically used in previous studies significantly distorts the measurements.  2. The surface density of sodium channels at the soma, often used as a reference value in simulations, is ill-determined.  We addressed these problems by precise measurements and analyses, obtaining data at a temporal resolution of 5 kHz from minimally invasive recordings of individual sodium channels in the somatic membrane of pyramidal cells.  We revealed that these sodium channels open much faster than widely used models suggest (e.g. [2]).  Our tightly constrained model provided a quantitative match between predicted somatic action current and measured dV/dt (Fig. 1).  This, together with the direct measurement of single channel current and open probability, led to a lower bound for the surface density of sodium channels of 10 channels per square micro meter at the soma of pyramidal neurons.  Importantly, even this lower bound is three times larger than the widely used estimates obtained from excised patches of somatic membrane [3].  Our results suggest that the arguments about axonal sodium channel densities and the basis of action potential generation ([4], [5]) are in parts based on inaccurate assessments of sodium channel kinetics and somatic surface density.  Our findings cannot however be extended to the description of axonal channels and their control of action potential generation, as even our novel models fail to explain the encoding of high-frequency input.  Studying spike encoding, from fluctuating input currents to fluctuating spike rates, during the maturation of neurons, we found evidence for two separate mechanisms that shape the transfer function (Fig. 2 and caption).  The biophysical basis of these two mechanisms is now being explored using neurons from genetically altered mice and simulations of multi-compartment models.

Fig. 1: Action potential phaseplot and model predictions of somatic sodium action currents.  Our model explains the contribution of somatic sodium channels to the action potential waveform, as the predicted current (orange) parallels dV/dt (black).  Other, frequently used models ([2] blue) fail this test.

 

Fig. 2:  Transfer functions from neurons at different developmental stages.  A sharp cut off above 200 Hz is already in place, when the neurons just started to produce action potentials (orange).  The shallow slope, which dominates the transfer function at lower frequencies, changes during development and is strongly correlated with the effective membrane time constant.

 

[1] A. L. Hodgkin, A. F. Huxley, J. Physiol. 117, 500 (1952)

[2] C. M. Colbert, E. Pan, Nat. Neurosci. 5, 533 (2002)

[3] G. J. Stuart, B. Sakmann, Nature 367, 69-72 (1994)

[4] B. Naundorf, F. Wolf, M. Volgushev, Nature 445, E2-E3 (2007)

[5] D. A. McCormick, Y. Shu, Y. Yu, Nature 45, E1-E2 (2007)


Contact:  Andreas Neef 

Members working within this Project:

 Fred Wolf 
 Andreas Neef 

Selected Publications:

R. Samhaber, M. Schottdorf, A. El Hady, K. Bröking, A. Daus, C. Thielemann, W. Stühmer, and F. Wolf (2016).
Growing neuronal islands on multi-electrode arrays using an accurate positioning-μCP device
J Neurosc Meth 257(1):194-203.

S. Stern , A. Agudelo-Toro, A. Rotem, E. Moses, and A. Neef (2015).
Chronaxie Measurements in Patterned Neuronal Cultures from Rat Hippocampus
PLoS ONE 10(7):e0132577. download file

Y. Yang, T.R. Adowski, B. Ramamurthy, A. Neef, and M.A. Xu-Friedman (2015).
High speed dynamic clamp interface
J Neurophysiol 113(7):2713-2720.

A. Rotem, A. Neef, N.E. Neef, A. Agudelo-Toro, D. Rakhmilevitch, W. Paulus, and E. Moses (2014).
Solving the Orientation Specific Constraints in Transcranial Magnetic Stimulation by Rotating Fields
PLoS ONE 9(2):e86794.

B. Naundorf, F. Wolf, and M. Volgushev (2007).
Hodgkin and Huxley model - still standing?
Nature 445:E2-E3.