1. “Can we predict synchrony and asynchrony in networks coupled by multiple dendritic gap junctions?” Frances K. Skinner Toronto Western Research Institute University Health Network and University of Toronto New York University April 13, 2008

2. From Scholarpedia: Mathematical Biology article of Frank Hoppensteadt “highly interdisciplinary nature” “barriers to collaborations between mathematicians and biologists” “a shift from mathematical analysis to computer simulation due mostly to improvements in computer power and accessibility.. With the shift being made possible to include more information in models and still derive useful insights from them.” Especially in neuroscience with all the details being uncovered, increasingly sophisticated techniques etc. these comments are very timely. With increasing specialization and interdisciplinarity and potential moving apart of mathematical and biological sciences (or separation of viewpoints) we organized a Theoretical Neuroscience Minisymposium at 2006 Society for Neuroscience meeting, one of the aims being to help counteract this.

3. Interneuron Heterogeneity Domain-specific innervation of hippocampal interneurons Different types of interneurons containing calcium-binding proteins and neuropeptides purple –laminae where axonal arbor typically extends turquoise indicates that other interneurons rather than principal cells are targets apical basal McBain and Fisahn NRN 2001

4. General challenge – how to best consider various neurobiological details. Specific challenge – understanding the contribution of electrical coupling in different contexts. Outline of Talk: background, discussion of some of our previous work, and then get to question posed for this talk.

5. “Can we predict synchrony and asynchrony in networks coupled by multiple dendritic gap junctions?” Frances K. Skinner Toronto Western Research Institute University Health Network and University of Toronto New York University April 13, 2008

6. Acknowledgements Tariq Zahid Fernanda Saraga, Leo Ng NSERC of Canada Computing support – RIS of UHN

7. The hippocampus (part of medial temporal lobe) is an intensely studied region of the brain because: It is associated with memory and learning (i.e., LTP, LTD), epileptic seizures, and neurogenesis. It exhibits a wide range of population rhythmic activity patterns ( 200 Hz) that are associated with various behavioural states. It is amenable to experiment, retaining its synaptic circuitry and thus population activities in the slice.

8. EEG activities of mouse hippocampus Sharp wave-ripples Electrode location Theta-GammaSPW-ripples

9. Gillis et al., J. Neurosci. Meth. (2005) Spontaneous Rhythmic Field Potentials (SRFPs) (Liang Zhang’s lab; Wu et al. J Physiol 2002, J Neurophysiol 2005)

10. Blockade of field rhythms and pyramidal IPSPs by GABA-A receptor antagonist rhythmic activities also dependent on electrical coupling (gap junctions)

11. Background Electrical coupling (i.e., gap junctions) is present in much of the mammalian brain (e.g., inferior olive, striatum, neocortex, hippocampus, retina, thalamus). In particular, gap junctions occur between inhibitory cells, often of the same type, and can be located at sites quite distant (> 200 μm) from the soma.

12. Interneurons represent 10-20% of the neuronal population but may provide the precise temporal structure necessary for ensembles of neurons to perform specific functions. - Buzsáki and Chrobak, 1995

13. Interneuron Heterogeneity Domain-specific innervation of hippocampal interneurons Different types of interneurons containing calcium-binding proteins and neuropeptides purple –laminae where axonal arbor typically extends turquoise indicates that other interneurons rather than principal cells are targets apical basal McBain and Fisahn NRN 2001

14. Background From Fukuda & Kosaka, J Neurosci 2000 Gap junctions located far from cell bodies, at non-proximal sites (basket cells in hippocampus) Gap junctions can be modulated Inhibitory cells have active dendrites, spikes can be generated in dendrites

15. Dendrodendritic Gap Junctions Fukuda & Kosaka, J Neurosci 2000

16. Model (Hippocampal Basket Cell) 50 mV 100 ms Saraga et al., J Neurophysiol 2006 Morphology from Gulyas et al.(1999) 372-compartment model developed in NEURON Passive dendrites

17. WB used for kinetic model basis, Martina and Jonas (1997), Martina et al (1998) used as conductance value basis and spike characteristics and electrophysiological responses from Morin et al. (1996) and van Hooft et al. (2000).

18. Anatomical distance to soma (  m) Electrotonic distance to soma (L) V in Anatomical distance from soma (  m) Electrotonic distance from soma (L) V out s d d V in =0.25 V out =0.14 “Reduced” 3-compartment model based on matching electrotonic length from soma (Vout) 1003005000 0.04 0.12 0.4 1.2 0100300500

19. PRCs calculated using XPPAUT (Ermentrout, 2002) 0.5% 1.5% 10% 1% 50 mV 10 ms s d d dds Voltage along dendrite (Distal) phase response curves (PRCs) Using the reduced model geometry Phase Phase Shift

20. Predicted Network Dynamics 75 50 25 0 28 26 24 23 20 18 16 14 0.1 1 10 100 % Active Intrinsic Frequency (Hz) % Phase Lag LOW MEDIUM HIGH Phase lags determined from interaction functions calculated using XPPAUT (Ermentrout, 2002) Weakly coupled oscillator theory used to define three different dynamic regions -LOW, MEDIUM, HIGH that refer to PRCs with particular characteristics (e.g., negative PRCs for MEDIUM)

21. Results % Phase Lag g gap Simulations confirm theoretical predictions % Active 0.1 1 10 100 75 50 25 0 % Active Intrinsic Frequency (Hz) % Phase Lag LOW MED HIGH “Weak coupling” is about 10 pS (comparing predicted and simulated) Compare full and reduced model phase lag values to “define” synchronous and asynchronous Synchronous is 10% or less phase lag, asynchronous otherwise

22. Cell 1: 15% basal attenuation, 2% apical attenuation Cell 2: 8% basal attenuation, 8% apical attenuation Cell 3: 6% basal attenuation, 14% apical attenuation CELL 3 basal apical basal

23. Cell 1, apical coupling (multistability)

24. Beyond weak coupling

27. Discussion and Conclusions PRC skewness quantifications can be used to predict whether synchronous or asynchronous modes occur in electrically coupled basket cells. Averaged PRCs can be used to predict modes for coupling at multiple sites. Predictions cannot be made under all circumstances and multistability can occur. Different apical and basal attenuation (due to different channel densities) allow more ‘robust’ asynchrony to occur with coupling on the more attenuated dendritic side. Network couplings that produce asynchrony (as compared to synchrony) with weak coupling encompass more dynamic richness (i.e., range of possible phase lags) with gap junction conductance changes. Thus, gap junction coupling may be able to tune networks in and out of synchronous activities if asynchrony with weak coupling is predicted.

28. the end Thank you!