Bifurcation structure of the model for values of N KD between 2131 and 10123 while keeping all other parameters constant. Attracting points are represented with color-filled circles, repelling points with circles filled in white, and saddle nodes as blue crosses. Focus points are shown in grey, nodes are shown in blue. The left-most traces correspond to N KD =2131. The trace at the far right corresponds to N KD = 10123.

Contexts in source publication

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... constant), calculate w * and a F (equations (15) and (18) Integration near resting potential and input currents. Now consider the changes in the fixed points as I F increases. The fixed points that have the lowest v * -values (near v NK ) are attractor nodes at first, and may become attracting foci for larger I F before becoming unstable (Fig. 4, transition between blue and gray points in any of the fixed point curves). This transition between attracting nodes and attracting foci is effectively a switch between integration modes in which the first mode the convergence to rest is monotonous (aggregation). In the second mode, the convergence to rest is oscillatory, ...

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... are capable of integrating synaptic input in both, aggregating or resonant modes, depending on the size of the input current ( Destexhe et al., 2003). Increasing the number of Kv2.1 channels increases the values of I F for which attractor nodes become foci and the range for I F in which the attracting foci are present (right-most traces in Fig. 4). That is, increasing the expression of Kv2.1 channels makes neurons more likely to integrate inputs in resonant mode, and increases the range for which input current may cause firing without causing a depolarisation ...

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... let us examine the dynamics two model neurons with Kv2.1 channel expression levels resulting in three and one fixed points for I F = 0, respectively. The idea is to study the transitions between different dynamical regimes for the same neuron, as those induced by increasing the stimulus amplitude during an I-clamp experiment (Fig. 4 and Fig. 5). To interpret our results, we assume that there are no changes in the biological properties of a neuron during the time that an I-clamp experiment is done. That is, we assume no changes in the biophysical properties (parameters) of a model neuron during an I-clamp experiment. As mentioned before, the bifurcation diagrams show that the ...

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... we assume that there are no changes in the biological properties of a neuron during the time that an I-clamp experiment is done. That is, we assume no changes in the biophysical properties (parameters) of a model neuron during an I-clamp experiment. As mentioned before, the bifurcation diagrams show that the rheobase increases with larger N KD (Fig. 4). This means that it takes more input current to obtain repetitive firing when N KD increases, but also, the way in which repetitive firing is generated is more likely to occur in a resonant way because fixed points associated to resting potentials are more likely to be foci if N KD (see also Fig. 5A2 and ...

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... rheobase (Fig. 6). The range for which input current yields repetitive spiking can be loosely identified by finding what values of I F yield repulsive fixed points within a single bifurcation curve. From there, the I F -interval for fixed point repulsivity shifts to the right and becomes larger for larger values of N KD (see right-most traces in Fig. 4, and compare panels in Fig. 5 and Fig. ...

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... complement of transmembrane currents. This approach allows us to establish solid, basic results such as analytical calculation of fixed point types and from there variation of the level of expression of Kv2.1 channels, before extending our models to include other K-currents that may require higher dimensional systems with more parameters. . 4). The lower limit in (A) can be thought of as an approximation to the rheobase current. The upper limit in (B) can be thought of as an approximation to the points where depolarisation blocks occur. The regions where limit cycles occur are pointed to with black arrows in both ...