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Next: Calcium dynamics and IK-AHP Up: Voltage gated channels Previous: An aside on experimental

Some common currents in cortical and thalamic neurons

There are many different currents in the cortex and thalamus. I only touch on a few of them.

Figure 2: The four different types of gated channels. (1) The passive gate lets ions through a a rate proportional to the voltage drop, (2) The persistent gate requires the ``m'' activating gate to be open, (3) the transient gate requires both the activating gate and the inactivating gate to be open, (4) the anomalous requires the inactivating gate to be open. The functions $m_\infty$ and $h_\infty$are shown in the figure
name ion type speed Rev. Pot threshold
INa Fast Sodium [Na] act/inact very fast 45 mV -50 mV
INap Persistent Sodium [Na] act/inact(slow) fast 45 mV -65 mV
IK Delayed rectifier [K] act fast -100 mV -40 mV
IA A-current [K] act/inact fast -100 mV -60 mV
IAHP Ca-dependent K [K] act (Ca-dep) moderate-slow -100 mV -
IM Slow potassium [K] act slow -100 mV -35 mV
IK2 Slow potassium [K] act/inact slow -100 mV -40 mV
IT Transient Ca [Ca] act/inact slow 150 mV -60 mV
IL High thresh. Ca [Ca] act fast 150 mV -10 mV
Ih Sag current [Ca]&[Na] inact slow 0-40 mV -
Ileak Leak [Cl],[K], [Na] passive - -60 mV -

Given the above table and the form for the kinetic parameters, $\alpha,\beta$ one can easily put together models for active membranes. This can be regarded as a kind of mix and match affair which results in a huge variety of models. In spite of this, there are virtually no differences between the fundamental models of cardiac, smooth muscle, squid axon, thalamic relay cells, etc. Each can be written as (2) where the Ik each satisfy  
 I_k= \bar{g} m^ph^q(V-E)\end{displaymath} (4)
and m,h satisfy equations like (3). In many cases, the calcium current is handled slightly different than the linear conductance model and instead, the constant field equation is used:

I_{Ca} = P m^ph^q \frac{(zFV)^2}{RT}

Here instead of conductance, the permeability is used.

The best known examples of these models are the Hodgkin-Huxley equations which have 3 currents, (i) passive leak, (ii) fast sodium, and (iii) delayed rectifier.

Figure 3: The three different functional forms for the gating rates. Only the increasing ones are shown; decreasing ones are just mirror images. All are chosen to pass through 0.5 at 0.
\psfig {,height=2.5in,angle=270}

All of the currents mentioned in the table above have been found in cortical or thalamic neurons. These currents are responsible for the intrinsic firing properties of neurons which include three different types: (i) regular spiking neurons (ii) fast spike neurons (iii) bursting neurons.

Recall that the typical channel gate satisfies

\frac{dx}{dt}= \alpha(V)(1-x)-\beta(V)\end{displaymath}

The functions $\alpha,\beta$ are generally of three different forms (see Figure 3)

\alpha(v) = C_1 e^{(V-V_T)/V_s}\end{displaymath}


\alpha(v) = C_1 (V-V_T)/(1-e^{(V-V_T)/V_s})\end{displaymath}


\alpha(v) = C_1/(1+e^{-(V-V_T)/V_s})\end{displaymath}

All three are defined by 3 parameters, the magnitude, C1, the ``threshold'', VT and the slope at threshold, Vs.

next up previous
Next: Calcium dynamics and IK-AHP Up: Voltage gated channels Previous: An aside on experimental
G. Bard Ermentrout