Conductance-based principles of neuronal firing and excitability

The brain is an electrical organ whose activity is determined by the flow of ions across cell membranes. As such, the conductances that control the ion flux is a key to our understanding of the nervous system.

Neurons process information by their ability to rapidly depolarize and fire action potentials. With the help of dynamical systems theory we have analysed the mechanisms behind this excitability. Specifically, we have used bifurcations theory to characterize the different dynamical pathways that lead to repetitive action potentials, or in terms of dynamical systems, to the emergence of limit cycles. We have demonstrated how downand up-regulation of various conductances (e.g., potassium current) lead to altered firing patterns and altered threshold dynamics. Crudely, electrical activity in nerve cells can be classified in two main classes: resonators and integrators. It was previously believed that certain channels were needed for the different types, but we have shown that in many cases it is sufficient to change the native conductances to alter class. Using the dynamic clamp technique we have also tested this hypothesis in-vivo. By artificially increasing the potassium conductance in pyramidal cells in rat cortex we were able to demonstrate a shift in dynamical type.

Moreover, we have analysed synapse conductances between interneurons in neocortex. In particular, we have investigated fast-spiking interneurons, which recently were shown to be responsible for the generation of gamma oscillation (30-80 Hz). These neurons are interconnected by a combined chemical-electrical synapse. To understand how these synaptic interactions control synchronous firing, artificial synaptic conductances were injected into fast-spiking cells. Using standard techniques from synchronization theory, such as the phase response curve, we showed how this combined synapse is especially suited for entrainment over a wide gamma frequency band, whose upper and lower frequency limits are given by the electrical component and the inhibitory chemical component, respectively.

Conductances can also be studied at an ion channel level. We examined how local anesthetics block ion channel conductance by binding to the ion channel in an open state. This state-dependent block was analysing in terms of Markov-chains and mathematical formulae for the open probability under voltage-clamp were derived. This knowledge might be valuable for developing new principles for pharmacological treatment. Theories must be tested against reality. The so-called dynamic-clamp technique allows mathematical models to be directly integrated using a real-time interface with living cells - a hybrid circuit is created between a computer and a nerve cell. The equations for the currents that one wishes to examine are simulated in a computer. The membrane potential is sampled and the current that would be passed through these artificial channels is injected into the cell, whereupon the voltage change and the current is calculated and injected again. The time scales are so short that this cycle must be performed within tens of microseconds. One problem with the dynamic clamp protocol has been the integration method used. We solved this issue by introducing a stable implicit Runge-Kutta method suited for stiff equations.

Understanding the inherent dynamics of different neuron types and their interplay with network activity is essential for understanding complex processes such as altered awareness levels caused by general anesthesia and psychopharmacological interventions. It is the hope that the findings in this thesis may add a small piece to the puzzle of understanding normal as well as pathological brain function.

List of scientific papers

I. Zeberg H, Blomberg C, Århem P. Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons. PLoS Comput Biol. 2010;6(4)
https://doi.org/10.1371/journal.pcbi.1000753

II. Gouwens N, Zeberg H, Tsumoto K, Tateno T, Aihara K, Robinson HPC. Synchronization of Firing in Cortical Fast-Spiking Interneurons at Gamma Frequencies: A Phase-Resetting Analysis. PLoS Comput Biol. 2010;6(9).
https://doi.org/10.1371/journal.pcbi.1000951

III. Zeberg H, Robinson HPC, Århem P. Density of voltage-gated potassium channels is a bifurcation parameter in pyramidal neurons. J Neurophysiol. 2015;113(2): 537-549
https://doi.org/10.1152/jn.00907.2013

IV. Zeberg H, Wolk A, Århem P, Robinson HPC. A stable implicit integration method for injecting synthetic active conductances in excitable cells. [Manuscript]

V. Zeberg H, Nilsson J, Århem P. The Importanceof the Dissociation Rate in Ion Channel Blocking. [Manuscript]