Figure 4. Clusters of cooperative channels mediate persistent activity at different levels in a model neuron.

(A) Current stimulation with different amplitudes to test the response of clusters to different firing rates. Left: Voltage traces demonstrating stimulated firing at increasing frequencies. Whereas the neuron returns to rest after a low amplitude stimulation, after a stronger drive the neuron continues to spike at a stable frequency $f_{PA}$, which increases with the frequency of the stimulated firing $f_{drive}$. Right: Persistent activity is mediated by the conductance of the clusters, which builds up during high-frequency spiking and remains stable during low-frequency spiking and at rest. (B) A strong hyperpolarizing step closes the clusters and stops persistent firing. (C) Left: The cooperative clusters track the input strength; more clusters open when the cell fires at higher frequencies. Firing below 20 Hz, however, does not open clusters. The number of open clusters can differ across trials (black dots) because of stochastic channel gating. Right: Persistent activity increases with the number of open clusters, thereby allowing the neuron to represent the input strength after the stimulus has ended, for example 3 Hz after 29 Hz firing and 9 Hz after 51 Hz firing. Big dots denote the mean for each stimulation strength, small dots the individual trials. The simulation procedure is described in Materials and methods and parameters are summarized in Table 1.

Figure 4—figure supplement 1. Depending on their reversal potential, clusters of cooperative channels can mediate de- or hyperpolarization-activated persistent activity.

(A) Depolarization-activated persistent activity. After stimulated spiking, the neuron continues to spike, because of the depolarizing current ($E_{coop}$=100 mV) through the persistently open clusters (bottom trace). (B) Hyperpolarization-activated persistent activity. A very distinct mnemonic firing behavior is possible with clusters of cooperative channels that have the same dynamics as the ones in A, but conduct a hyperpolarizing current ($E_{coop}$=-100mV). When such clusters are open initially, they provide a standing leak current that prevents the neuron from firing (bottom trace). A strong hyperpolarizing pulse persistently closes the clusters and thereby activates low-frequency spiking. Strong stimulated spiking reopens the clusters and hence silences the neuron. For a summary of cluster parameters, see Table 1.

Figure 4—figure supplement 2. Clusters are robust against noise in the membrane potential.

(A) A neuron is stimulated for 2 s with a white noise current (middle) to induce membrane potential fluctuations and spontaneous spikes (top). Despite the noisy membrane potential, the clusters remain in their closed state (bottom). Even spontaneous spikes only open a few channels transiently in each cluster and cannot switch a whole cluster persistently to the open state (B) The clusters remain closed after exposure to 5 s of noise stimulation. Only an unphysiologically high noise level leads to the opening a few clusters by spontaneous firing at around 10 Hz (see indicated firing frequencies). For details on the white noise stimulation see Materials and methods. There are 100 clusters of eight cooperative channels each. Further parameters are summarized in Table 1.