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Plasticity in the intrinsic excitability of cortical pyramidal neurons

Nature Neuroscience volume 2, pages 515–520 (1999)Cite this article

Abstract

During learning and development, the level of synaptic input received by cortical neurons may change dramatically. Given a limited range of possible firing rates, how do neurons maintain responsiveness to both small and large synaptic inputs? We demonstrate that in response to changes in activity, cultured cortical pyramidal neurons regulate intrinsic excitability to promote stability in firing. Depriving pyramidal neurons of activity for two days increased sensitivity to current injection by selectively regulating voltage-dependent conductances. This suggests that one mechanism by which neurons maintain sensitivity to different levels of synaptic input is by altering the function relating current to firing rate.

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Figure 1: Chronic activity blockade increased the firing frequency and lowered the spike threshold of pyramidal neurons.
Figure 2: The amplitude of INa was increased by activity deprivation, but the voltage dependence was unaltered.
Figure 3: Cell-attached patch recordings of sodium currents confirmed that activity deprivation increases their amplitude.
Figure 4: Calcium currents were unaffected by activity blockade.
Figure 5: Persistent outward currents were reduced by activity blockade, but inactivating currents were unaltered.
Figure 6: Current densities were differentially regulated by activity.

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Acknowledgements

We thank Sacha B. Nelson and Xiao-Jing Wang for discussions and Mark van Rossum for reading the manuscript. This work was supported by NIH grants K02 NS01893 and RO1 NS36853. N.S.D. was supported by a postdoctoral fellowship from the Sloan Center for Theoretical Neurobiology at Brandeis University and by an individual NRSA. G.G.T. is an Alfred P. Sloan Fellow.

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Authors and Affiliations

  1. Department of Biology and Center for Complex Systems, Brandeis University, 415 South Street, Waltham , 02454-9110, Massachusetts, USA

    Niraj S. Desai, Lana C. Rutherford & Gina G. Turrigiano

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  1. Niraj S. Desai
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  3. Gina G. Turrigiano
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Correspondence to Gina G. Turrigiano.

Supplementary Information

The number or strengths of a neuron's synapses may vary dramatically during development and learning, raising the question of how neurons maintain their responsiveness to input at such times of intense synaptic change. Our experiments1 demonstrated that one mechanism available to cortical pyramidal neurons to address this problem is to regulate their intrinsic excitability in an activity-dependent manner. In particular, we found that depriving neurons of activity for two days lowered spike threshold and increased firing rate in response to injected current. Furthermore, voltage clamp experiments suggested that the increase in excitability was mediated by a selective regulation of voltage-gated currents: activity blockade increased the density of sodium currents by 33 ± 15%, decreased that of persistent potassium currents by 37 ± 11% and left calcium and transient potassium currents unaltered.

To determine whether these measured changes in the amplitudes of sodium and persistent potassium currents were sufficient to account for the measured increase in excitability, we constructed a conductance-based model neuron based upon our physiological data. Our intention was not to match the biological neurons exactly, but rather to determine whether a simple model with minimal assumptions could reproduce experimentally observed changes in neuronal excitability. The model was composed of two compartments, one to represent the soma and initial axon segment and the other to represent the dendrites, and contained the full range of voltage-gated currents. Maximal conductances and reversal potentials were chosen to match the voltage clamp data. When the maximal conductances were set to the values measured from neurons grown under conditions of normal activity, somatic current injection produced patterns of action potentials similar to those seen experimentally (Fig. 1a). The firing rates were higher, but the basic features were reproduced correctly.

Figure 1

(GIF 13.8 KB)

Altering current densities in a model neuron reproduced the increased excitability observed in biological neurons. (a) Response of somatic potential to current injection in two model neurons, one with current densities equal to the experimental averages measured in control neurons, the other with current densities equal to those measured in activity-deprived neurons. (b) f-I curves for model neurons with control and activity-deprived current densities. The initial firing rate is plotted against current amplitude. To simulate the variability between cells present in the experimental data, the relative size of the somatic and dendritic compartments was varied; the results were then averaged.

To simulate the effects of activity blockade, we increased the sodium-current density and reduced the delayed-rectifier density by the percentages specified by the experimental data. This had a pronounced effect on the excitability of the model neuron (Fig. 1). The threshold current for firing was substantially reduced (from 45 to 30 pA), and both the firing rate and the height of the first spike were increased. All of these effects are compatible with the physiological results. They remained true even if the initial maximal conductances were changed individually by as much as 40% (that is, by as much as the variability in the experimental data).

Because averaging experimental data from a population of cells produces an f-I curve more linear than that of any single cell, comparisons with experimental average f-I curves required taking variability between cells into account in our model. We introduced variability by varying the relative size of the somatic and dendritic compartments (Fig. 1b) or by varying the input resistance. The result was that the f-I curve for model neurons with an 'activity-deprived' balance of conductances was shifted upward with respect to that for neurons with a 'control' conductance profile by percentages similar to those seen in the physiological data. While factors other than those measured in the voltage-clamp experiments may contribute to the increased excitability, these results suggest that changes in the magnitudes of the sodium and persistent potassium currents are sufficient to account for the effect.

Methods

The model neuron was very similar to the one described in ref. 2; equations for currents not included that model were taken from other published sources3,4. The model contained two compartments, one to represent the soma and initial axon segment, the other to represent the dendrites. The currents in the somatic compartment consisted of leak (IL), sodium (INa), delayed rectifier potassium (IDR), A-type potassium (IA), high- and low-voltage-activated calcium (ICa) currents, coupling with the other compartment, as well as a term representing the somatic current injection (Iinj):

CmdVs/dt = -IL-INa-IDR-IA-ICa-(gC/p)(Vs-Vd)+Iinj(1)

Here, Cm is the membrane capacitance, Vs is the somatic membrane potential, gC is a coupling parameter between the two compartments, and p is the ratio of the somatic area to the total area. The dendritic compartment, with a potential given by Vd, contained a leak current, a calcium current, and a coupling term:

CmdVd/dt = -IL-ICa-[gC/(1-p)](Vd-Vs) (2)

All of the voltage-gated currents were described by the standard Hodgkin-Huxley formalism, IX = gXmphq(V-EX), where gX is the maximal conductance, m and h are gating variables with exponents p and q, and EX is the reversal potential. The gating variables all obeyed first-order kinetics. Equations for the rate constants were identical to those in the cited literature, with one exception: both the activation and inactivation curves for sodium were shifted by +5 mV to obtain better fits to our sodium I-V curves. Also, unlike the model in ref. 2, our model was not simplified by setting the sodium activation gating variable to its steady-state value. Maximal conductances and reversal potentials were chosen to produce currents in response to simulated voltage steps that matched those measured in the voltage-clamp experiments. For control cells, they were given (in mS per cm2 or mV) by:

gL = 0.1, gNa = 6, gDR = 3, gA = 3, gCa = 0.3, EL = -60, ENa = 55, EDR = EA = -100, ECa = 120.

To mimic the effects of TTX treatment, gNa was set to 8 and gDR to 2. The coupling parameters gC and p were adjusted to give patterns of action potentials in response to somatic current injections that resembled those of the experimental data (gC = 0.2-0.4 mS per cm2 and p = 0.2-0.5); choosing coupling parameters outside these ranges resulted in firing patterns that were not observed experimentally (for example, firing rates above 100 Hz, afterhyperpolarizations 10 mV or more below rest). In modeling inter-cell variability, p was varied uniformly between 0.2 and 0.5; or gL was varied between 0.05 mS per cm2 and 0.15 mS per cm2, so as to match the variance of input resistance measurements. The membrane capacitance was set to 20 pF, close to the average measured capacitance of 23 pF.

REFERENCES in Supplementary Information

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    Wang, X.-J. Calcium coding and adaptive temporal computation in cortical pyramidal neurons. J. Neurophysiol. 79, 1549-1566 (1998).

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    Traub, R.K.S., Wong, R., Miles, R. & Michelson, H. A model of a CA3 hippocampal pyramidal neuron. J. Neurophysiol. 66, 635-650 (1991).

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    Wang, X.-J., Rinzel, J. & Rogawski, M. A. A model of the T-type calcium current and the low threshold spike in thalamic neurons. J. Neurophysiol. 66, 839-850 (1991).

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Desai, N., Rutherford, L. & Turrigiano, G. Plasticity in the intrinsic excitability of cortical pyramidal neurons . Nat Neurosci 2, 515–520 (1999). https://doi.org/10.1038/9165

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