4.5.1 Fast onset dynamics
We now have all tools at hand to compare the AP dynamics which is predicted by Hodgkin-Huxley type models with the AP initiation dynamics of cortical neurons. Representative examples of APs recorded in cats’ visual cortices are displayed in Fig. 4.2A,C. These were acquired in vivo and in vitro. In the in vitro recordings, current steps were injected via a patch-pipette. To make sure that only intrinsic, ion channel gated currents through the membrane were involved in the generation of an AP, the amplitude of the injected step current was carefully adjusted to values close to the rheobase of the neuron.
In the MP traces, the dynamics of the AP is characterized by a rapid depolarization with peak poten-tials around+10 mV. The half width at half height (HWHH) is approximately 1 ms in the in vivo recording and a bit larger, approximately 1.5 ms, in the in vitro recording. Fig.4.2E shows, for com-parison, a trace of a simulated AP (Model A). The simulated AP shares characteristic features of the measured APs, i.e. a comparable duration and a sign reversal at peak depolarization. However, sev-eral differences compared to the measured APs are apparent. Firstly, the peak depolarization is larger in the simulation, indicating a different balance between sodium channel activation, inactivation and activation of the delayed potassium rectifier. Secondly, the simulated AP exhibits a pronounced after-hyperpolarization, which is almost missing in the measured APs.
The most striking difference is, however, the AP onset dynamics. While the cortical APs exhibit a kink-like AP initiation, the simulated AP exhibits a very smooth onset behavior. This difference stands out much more clearly in the corresponding phase-plots (Fig.4.2B,D,F). There, the kink-like onset behavior manifests itself as a virtually vertical take-off of V−dV/dt-trajectories at AP onset.
At the start of the AP loops, the velocity increases rapidly from values less than 5 mV/ms to more than 20 mV/ms. This several-fold increase of the velocity occurs within a range of less than 1 mV and takes less than 0.2 ms. This dynamical feature is shared by both in vivo and in vitro recordings. In contrast, the simulated AP exhibits a very smooth onset dynamics, in which a velocity of 20 mV/ms is reached over a voltage range of 7−8 mV after about 1 ms.
In Fig.4.3A-D, phase plots and MP traces of recordings from two neurons with different receptive field types from cat visual cortex are displayed. In both recordings, the neurons were visually stim-ulated with moving gratings of preferred orientation. The first cell exhibits a simple receptive field.
This is reflected by a pronounced modulation of its subthreshold MP and a clearly modulated rate response (Fig.4.3B). The second cell exhibits a complex receptive field. Although it fires at a high rate of approximately 10 Hz, the MP does not lock to the phase of the moving grating (Fig.4.3D). In Fig.4.3A,C, the corresponding phase-plots are displayed. All APs initiate as rapidly as in Fig.4.2B.
In Fig. 4.3E, a simulated trace of a conductance-based model A is shown. To model the in vivo fluctuations of the MP, a fluctuating synaptic input was added to the model equations, where the parameters values were adjusted such that the resulting MP fluctuations match the typical stationary MP fluctuations of a cortical neuron in vivo. As for the cortical neuron with a complex receptive field, APs are emitted irregularly with a stationary rate of approximately 10 Hz. The AP onset behavior is, however, as before, very different from the onset dynamics of the cortical neurons. All APs initiate very slowly over a large voltage range, whereas in both simple and complex cells APs rise vertically out of the cloud of subthreshold fluctuations.
4.5. AP initiation in cortical neurons
Figure 4.2: Dynamics of AP initiation in neocortical neurons and in a Hodgkin-Huxley type conductance-based model of a neocortical neuron. (A) Plot of an AP recorded in cat visual cortex in vivo. The arrow denotes the characteristic kink at the AP onset. (B) Phase plot (dV/dt vs. V) of the same AP as in (A). The big loop corresponds to the AP. Inset: Initial phase of AP at expanded scale. The AP onset manifests itself as an almost vertical take-off. (C,D) AP recorded in vitro (slice of cat visual cortex, 20◦C), in the same representation as in (A,B). Although the AP is broader, and the peak velocity smaller, the AP onset dynamics remains fast, similar as in (A,B). (E,F) Typical shape of an AP from a simulation of a Hodgkin-Huxley type conductance-based model of a neo-cortical neuron. Note the smooth AP onset in (E) in comparison to (A) and (C), which is reflected
Figure 4.3: Different AP initiation in visual cortex neurons recorded in vivo and in a Hodgkin-Huxley type model subject to synaptic fluctuating input. (A) Response of a neuron with a simple receptive field to a moving grating of optimal orientation represented by a phase plot. For better resolution, only the initial phases of the APs together with subthreshold fluctuations (dark grey) are shown in the main panel. The inset shows the complete trace. APs are shown in red, three sample APs are marked by arrows. Green dots mark the data point immediately before crossing the threshold velocity (10 mV/ms). (B) Part of the recording shown in (A) as a voltage trace (APs truncated).
Green bars: AP onset potentials. Inset: Three sample APs marked in (A). Histogram on the right hand side: Distribution of AP onset potentials in the entire 7s recording. Color code as in (A).
(C,D) Response of a neuron with a complex receptive field to a moving grating of optimal orienta-tion. Color code and trace representations as in (A,B). (E,F) Response of a Hodgkin-Huxley type conductance-based model of a neocortical neuron subject to fluctuating synaptic input. Color code and trace representations as in (A,B).
Note the steeper upstroke and larger variability of the onset potentials in the recorded cells com-pared to the simulation.