1. Bursting Neurons (Lecture 10) Harry R. Erwin, PhD COMM2E University of Sunderland

2. Resources Bower and Beeman, 1998, The Book of Genesis, second edition, TELOS, ISBN: 0-387-94938-0 Rieke et al, 1999, Spikes: Exploring the Neural Code, Bradford Books. Shepherd, G., ed., 2004, The Synaptic Organization of the Brain, 5th edition, Oxford University Press. Nicholls et al. Kandel et al. Koch, 2004, Biophysics of Computation, OUP. Koch and Segev, 1998, Methods in Neuronal Modelling, 2nd edition, MIT Press. Churchland and Sejnowski, 1994, The Computational Brain, Bradford Books.

3. The Platonic neuron Consists of a soma, one or more dendrites, and an axon Any of these elements may be missing You can also have binary neurons where a dendrite is axon-like. These can signal bi- or unidirectionally Apical Dendrite Basal Dendrite Soma Axon and Axon Collateral

4. More complex biologically relevant neurons Characterised by wide variation in firing patterns Often make use of active conductances in the dendritic tree, which serve to amplify PSPs generated there and send them over longer electrotonic distances. Many different ion channel types The HH model found in the squid is particularly simple, serving to conduct regular neural impulses rapidly.

5. Physiological behaviour of the neuron Determined by the types of conductances found in its membranes and its topological structure. These experiments will address how periodic bursts of action potentials can be generated. This behaviour is found in molluscan pacemaker neurons and in the CA3 pyramidal neurons of the mammalian hippocampus.

6. Molluscan neurons 1.R3 beater neuron 2.R15 regular burster 3.L10 irregular burster (from Kandel via Bower and Beeman)

7. Periodicity Often entirely endogenous to a neuron, persisting when the soma is isolated. These are termed pacemakers, responsible for controlling highly regular behaviour that is only moderately regulated. Other neurons generate a periodic signal in response to input—conditional bursters. In the cortex, dopamine and GABA seem to be able to turn this on and off.

8. Control of periodicity Uses channels qualitatively similar to the Na + and K + channels in the HH model. Shape and firing patterns influenced by other channels and their interactions. 1.Conductances for Ca ++ and Cl - exist. 2.Activation and inactivation is more complex than for the HH model. 3.Voltage and ligand-sensitive channels are also important. 4.Finally, time constants vary greatly

9. Dance of the ions

10. Ionic conductances Nominal resting potential of -40 mV Reaches 0 mV during the action potential The model molluscan neuron includes: –Fast Na + currents –Delayed K + currents –High-threshold Ca ++ currents –Slow inward “B-current” (Na + /Ca ++ ) –Calcium dependent K + “C-current” –Transient K + “A-current”

11. Details Fast Na + currents, associated with AP generation. Do not inactivate for hyperpolarisation. Delayed K + currents, associated with APs and repolarisation. “Delayed rectifier current.” High-threshold Ca ++ currents, activated by APs. These channels trigger transmitter release. Slow inward “B-current” (Na + /Ca ++ ). Produces a sustained depolarisation. “Burst current”. Creates the burst region. Calcium dependent K + “C-current”. Produces a slow hyperpolarisation and an inward Ca ++ current. Ends the burst. In mammals shifted lower (and called the “T-current”). Transient K + “A-current”, maintaining hyperpolarisation and delaying the next AP in pacemaker neurons. Primitive.

12. Adrift in parameter space Experiments are often insufficient to provide all the parameters needed. Approach: –Build a correct compartmental model –Add passive membrane properties –Incorporate active channels based on experimental evidence –Search parameter space for solutions, taking advantage of the different time scales for subsystems.

13. Research opportunities I have been funded by EPSRC for a large-scale computational model of the inferior colliculus, a part of the auditory system We have opportunities for MSc-level projects associated with elements of the modelling. This will involve work similar to that described here, and also with exploiting those results in robotics and linguistics applications. Interested?