The EPFL LATSIS Symposium 2006
Na+ /K+ -ATPase-Specific Spike-Frequency Adaptation Renaud Jolivet∗ and Pierre J. Magistretti∗ Brain Mind Institute, EPFL, 1015, Lausanne, Switzerland
[email protected] [email protected]
Spike-frequency adaptation is exhibited by almost all neurons that generate action potentials. It is a widespread phenomenon present in peripheral and central systems of both vertebrates and invertebrates. Beyond filtering out slow changes in stimulus, it was recently shown to play a specific role in information processing in the weakly electric fish by separating transient signals from background oscillations [1]. On the modelling side, it is a necessary mechanism for quantitative neural models to connect between different stimulation regimes [2, 3]. Spike-frequency adaptation may originate from many different processes most of which are wellknown and having been extensively studied in in vitro preparations as well as in computational models (see e.g. [4]). We wanted to explore more specifically adaptation that may originate from the activity of the electrogenic Na+ /K+ -ATPase pump. Following sustained activation, sodium accumulates in the neuron and can reach a very high level above the resting state (8 − 15 mM), up to 100 mM on some locations [5]. High intracellular sodium concentrations increase the activity of the electrogenic Na+ /K+ -ATPase pump which is responsible for an outward current INaK [6, 7, 8] as well as increased metabolic demand [9]. Using an Hodgkin-Huxley-type model including an mAHP current (ImAHP ) plus an Na+ /K+ -ATPase pump [10, 11], we studied the neuronal response to long sustained tonic stimulation. We found that INaK induces spike-frequency adaptation with a long time scale of the order of a few seconds to a few tens of seconds (Figure 1). This is essentially due to the time scale for sodium extrusion (31.4 s) that allows to integrate the output down to a very low critical frequency of ∼ 0.03 Hz. However, this is not the sole reason. The effective late adaptation time constant is the result of a complex interaction between the mAHP current and the electrogenic pump (Figure 1C). Interestingly, this interaction takes place even below frequencies where calcium accumulates with consecutive spikes. Overall, the resulting pattern of instantaneous frequency that is generated is very similar to what is observed in in vitro recordings. For weak stimulations, INaK induces phasic spiking.
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Figure 1: INaK induces spike-frequency adaptation. A. From top to bottom, applied current (Istim = 1 µA/cm2 ) and voltage response. B. Intracellular Na+ (top) and Ca2+ concentrations (bottom). In A and B, arrowheads indicate the baseline level. C. Instantaneous frequency during stimulation (symbols) and fitted double exponentials for the complete model (solid line) and when ImAHP is blocked (dashed line). The longest apparent adaptation time constant τadaptation is highly dependent on the time constant for Ca2+ extrusion τCa (inset). The dependence is plotted for increasing stimulation intensities: Istim = 1 µA/cm2 (solid line), Istim = 2 µA/cm2 (short dots) and Istim = 5 µA/cm2 (dots).
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Dynamical principles for neuroscience and intelligent biomimetic devices
a potential role for the Na+ /K+ -ATPase pump in signal processing at frequencies accessible in vivo.
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References
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[1] J. Benda, A. Longtin and L. Maler “Spike-frequency adaptation separates transient communication signals from background oscillations” Journal of Neuroscience, Vol. 25, pp. 2312–2321, 2005.
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[2] A. Rauch, G. La Camera, H.-R. L¨uscher, W. Senn and S. Fusi “Neocortical Pyramidal Cells Respond as Integrateand-Fire Neurons to In Vivo-Like Input Currents” Journal of Neurophysiology, Vol. 90, pp. 1598–1612, 2003.
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[3] R. Jolivet, A. Rauch, H.-R. L¨uscher and W. Gerstner “Predicting spike timing of neocortical pyramidal neurons by simple threshold models” To appear in the Journal of Computational Neuroscience, 2006.
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[4] J. Benda and A. Herz “A Universal Model for SpikeFrequency Adaptation” Neural Computation, Vol. 15, pp. 2523–2564, 2003.
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[5] C. Rose and A. Konnerth “NMDA receptor-mediated Na+ signals in spines and dendrites” Journal of Neuroscience, Vol. 21, pp. 4207–4214, 2001.
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[6] P. Sokolove and I. Cooke “Inhibition of impulse activity in a sensory neuron by an electrogenic pump” Journal of General Physiology, Vol. 57, pp. 125–163, 1971.
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Figure 2: INaK induces phasic spiking for weak stimulations. A. From top to bottom, applied current (Istim = 0.8 µA/cm2 ) and voltage response. B. Intracellular Na+ (top) and Ca2+ concentrations (bottom). In A and B, arrowheads indicate the baseline level. C. The number of spikes produced in the phasic spiking regime is plotted versus the applied current Istim for the complete model (solid line) and when ImAHP is blocked (dashed line). For currents ≥ 0.83 µA/cm2 , the neuron fires steadily with a continuous gain function, i.e. the steady-state frequency fss is a continuous function of the applied current Istim , like in a type I neuron (inset) [12].
[7] A. French “Ouabain selectively affects the slow component of sensory adaptation in an insect mechanoreceptor” Brain Research, Vol. 504, pp. 112–114, 1989. [8] D. Parker, R. Hill and S. Grillner “Electrogenic pump and a Ca2+ -dependent K+ conductance contribute to a posttetanic hyperpolarization in lamprey sensory neurons” Journal of Neurophysiology, Vol. 76, pp. 540–553, 1996. [9] L. Pellerin and P. J. Magistretti “Glutamate Uptake into Astrocytes Stimulates Aerobic Glycolysis - a Mechanism Coupling Neuronal-Activity to GlucoseUtilization” PNAS, Vol. 91, pp. 10625–10629, 1994. [10] R. Heinrich and S. Schuster, The Regulation of Cellular Systems, Chapman & Hall, 1996.
Spiking stops after a few seconds even though the stimulation is maintained (Figure 2) [6]. Interestingly, this type of behavior cannot be obtained with the mAHP current alone. While calcium entry is entirely dependent on spiking, sodium continues to flow in the neuron through voltage-gated channels even after spiking has stopped if the membrane is sufficiently depolarized. This process approximately linearly converts the stimulus amplitude in a finite number of spikes (Figure 2C). For stronger stimulations, the model behaves as a type I neuron.
[11] X. Wang “Calcium coding and adaptive temporal computation in cortical pyramidal neurons” Journal of Neurophysiology, Vol. 79, pp. 1549–1566, 1998. [12] A. Hodgkin “The local electric changes associated with repetitive action in a non-medullated axon” Journal of Physiology, Vol. 107, pp. 165–181, 1948.
These results illustrate the importance of sodium as a messenger for long-term signal integration and point to
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