Further development of a gap-junction connected mitral cell model representing a single glomerulus

[Simon-at-Ely]

In 2005, Migliore et al published a model in which they showed that asynchronous oscillations in two mitral cells connected by gap-junctions between their apical tufts would rapidly synchronise. In the following years we further developed the Migliore et al (2005) model (O’Connor et al. 2012, Figure 1 and 2) to:

a) incorporate 6 NeuroLucida mitral cell morphology reconstructions. b) include fitted passive parameters from dual patch clamp recordings for each of the mitral cell reconstructions. c) incorporate calcium mechanisms (LCa, KCa, Ca pool) from Bhalla and Bower 1993.

http://www.opensourcebrain.org/attachments/download/92/Mitral_Cell_Model.png

Figure 1 – Olfactory bulb gap-junction connected network model created using neuroConstruct (O’Connor et al. 2012).

http://www.opensourcebrain.org/attachments/download/94/MC_Net_Model_Output.jpg

Figure 2 - Somatic voltage recordings from the O’Connor et al. (2012) olfactory bulb model.

The neuroConstruct generated neuron model that produces Figure 2 can be down loaded from ModelDB here: http://senselab.med.yale.edu/ModelDB/ShowModel.cshtml?model=146030. Various changes were made in the mapping of NeuroML which has changed the output from this model. The main difference is in the way in which the volume of the calcium pool is calculated now includes the length of the compartment instead of just the radius.

The aim of this project is to allow collaboration on the development of the O’Connor et al. (2012) model to better reflect the dynamics and heterogeneity of a group of mitral cells whose apical tufts are found in the same glomerulus. It has been placed on Open Source Brain to allow anybody who wishes to collaborate in the development of this model and the join in the debate about how the model should be developed. If you wish to collaborate in this project and or have data that may be useful for constraining this development, please make contact at simon.oconnor@btinternet.com.

References

Bhalla and Bower 1993 http://www.ncbi.nlm.nih.gov/pubmed/7688798 Migliore et al. 2005 http://www.ncbi.nlm.nih.gov/pubmed/15714267 O’Connor et al. 2012 http://www.frontiersin.org/computational_neuroscience/10.3389/fncom.2012.00075/abstract

[Simon-at-Ely]

Constraints, assumptions and errors

To start the process of deciding how to improve the model, I thought it would be best if I do an appraisal of where we are with the current model:

1.0 Morphology

The model contains six NeuroLucida reconstructions of mitral cells. The reconstructions are of mitral cells in slice preparations that were filled with biocytin at the end of the electrophysiology recordings. Issues/errors

1.1 Producing a slice preparation rips out all lateral dendrites that are not in the plane of the slice and removes the edges of the apical tuft that are either side of the slice plane.

1.2 Fixing the preparation causes shrinkage and distortions in the morphology.

1.3 NeuroLucida reconstructions assume sections of fibres are circular as the cross section is reconstructed from a single diameter at each point along the fibre.

1.4 Successively prepared slices will yield mitral cells from different glomeruli. With current methods it is not possible to produce reconstructions for a good proportion of mitral cells from the same intra glomerular population.

2.0 Passive Parameters

The passive parameters were fitted to dual patch clamp recordings that were obtained from each of the cells that were bathed in a cocktail of blockers for ion channels and synaptic activity. Fitting was carried out using the Multi Run Fitter module in Neuron with the built in Praxis algorithm. I put together the protocol with the help of Arnd Roth, more details can be found in O’Connor et al 2012 (I can also supply the protocol on request).

Issues/errors

2.1 A full discussion of fitting errors for passive parameters can be found in:

Major et al 1994 http://www.ncbi.nlm.nih.gov/pubmed/8046439 Roth and Häusser 2001 http://www.ncbi.nlm.nih.gov/pubmed/11533136 Additions specific to this model are given in O’Connor et al 2010.

2.2 As explained under morphology the six mitral come from different glomeruli from different animals. While the methods used collect a sample of the heterogeneity of passive parameters found in mitral cells, but we would be quite unaware if mitral cells were tuned into a narrow band of passive parameters for each glomeruli. This could be an important error for how the model behaves.

3.0 Gap Junctions

The gap junctions are placed at 100 stochastically chosen locations between each pair of mitral cell apical tufts using a function built in neuroConstruct. A maximum distance is set so the function chooses locations on both mitral cells and then checks that the distance is below the set minimum distance. It repeats this exercise until the set number of locations have been selected. This is repeated for each of the possible pairs (16 pairs for a 6 cell system giving 1600 gap junctions). The conductances of the gap-junctions are adjusted to give a coupling ratio of 0.04 (see O’Connor et al. 2012, Migliore et al 2005 for method). Synchronisation of oscillations was not achieved when one or ten gap junctions between each pair with conductance adjusted upwards to achieve the 0.04 coupling ratio.

The experimental basis for the modelling of the gap-junction is found in:

Kosaka and Kosaka 2004 http://www.ncbi.nlm.nih.gov/pubmed/15236862 Christie et al 2005 http://www.ncbi.nlm.nih.gov/pubmed/?term=christie+bark+hormuzdi Rash et al 2005 http://www.ncbi.nlm.nih.gov/pubmed/16841170 Schoppa and Westbrook 2002 http://www.ncbi.nlm.nih.gov/pubmed/12379859

3.1 The version of the model that was published on ModelDB and described in O’Connor et al 2012 used the Migliore et al 2005 implementation of gap-junctions which used a hoc file rather than a mod file. This implementation is currently not possible in neuroConstruct, I had to generate the code from neuroConstruct then edit all 1600 statements to use the hoc implementation. However when I used the built in mod file implementation it did not affect the oscillatory behaviour. I do have a file containing the edited statements that allow the hoc implementation to be inserted if required.

3.2 While the coupling ratio is constrained by experimental results, the quantity of gap-junctions is not. We do not know how likely it is that there are gap junctions between all pairs of mitral cells. Some effort should be made to find out if there are now estimates of the quantity of gap junction connectivity, or if this will have to wait until a full EM reconstruction of a glomerulus is available.

4.0 Ion Channels

The ion channels are from two sources:

Migliore et al 2005

Na Rat Hippocampal CA1 cells Migliore et al. 1999 http://www.ncbi.nlm.nih.gov/pubmed/10481998 Kdr +KA Rat olfactory bulb mitral cells Wang et al 1996 http://www.ncbi.nlm.nih.gov/pubmed/8745279

Bhalla and Bower 1993

The kinetics of the ion channels were modified by brute force fitting to current clamp recordings from Mori et al 1981, 1982 http://www.ncbi.nlm.nih.gov/pubmed/7310692 http://www.ncbi.nlm.nih.gov/pubmed/6279800

Ca pool Bhalla and Bower 1993

LCa Rat Cerebellar Purkinje Cell Hirano et al. 1989 http://www.ncbi.nlm.nih.gov/pubmed/2544852 KCa This channel is both voltage and [Ca] dependent Bhalla and Bower 1993

4.1 The Migliore et al 2005 ion channels would seem adequate for the current model unless someone is able to use a peeling method to obtain more accurate measurements.

4.2 The Bhalla and Bower 1993 ion channels and pool mechanism have a critical influence on the dynamic behaviour of the model as noted in O’Connor et al 2012. It would therefore be useful to obtain any experimental measurements available to better constrain the kinetics and density distribution on these channels.

4.3 Other ion channel mechanisms have been reported for the mitral cell:

Heterogenous expression of IH Angelo and Margrie 2011 http://www.ncbi.nlm.nih.gov/pubmed/22355569

A sub-threshold oscillation of mitral/tufted cell membrane potential, thought to synchronise spike firing in populations of mitral cells and to be mediated by a non-inactivating sodium current INaP Desmaisons et al 1999 http://www.ncbi.nlm.nih.gov/pubmed/10594056

Spike clustering in mitral/tufted cells which is thought to depend on the interplay between slowly inactivating ID-like K+ channels and a sub-threshold TTX-sensitive Na+ current Balu et al 2004 http://www.ncbi.nlm.nih.gov/pubmed/?term=balu+larimer+strowbridge

Local control of dendritic excitability which is mediated by small conductance calcium activated potassium (SK) channels Maher and Westbrook 2005 http://www.ncbi.nlm.nih.gov/pubmed/16107526

4.4 It may be possible to constrain the dynamics of the mitral cells in the model further by fitting to slice mitral cell recordings in the presence of synaptic current blockers.

[Simon-at-Ely]

Why a community model?

With models of neuronal systems it is important to be able to isolate a part that can be both constrained and examined. This generally limits the complexity of models and prevents an examination of system dynamics and understanding the role of heterogeneity. So it really makes sense that individual research groups are not over ambitious and tackle modelling exercise that are within the limits of the resources they have available and their ability to constrain the variables. However it would be advantageous to all these efforts if a more complex understanding of some components could be developed and used to plug into the individual models. So if we can harness a community wide effort to tackle some of these difficult questions it would help improve all the individual models.

Why s community mitral cell model?

A community model needs to have an achievable goal, so we have to tackle a question that makes sense and not just dump in everything that is known into a single model in the hope that it will lead to some state of enlightenment. Within the olfactory bulb the complexity is staggering and the question becomes where would you start. I think that the projection neurons represent a first level of complexity on which many more layers of complexity are layered on top of. So building an understanding from a complex dynamics and heterogeneity point of view should be more easily achieved from the foundation upwards. Tackling a second order problem like understanding all the variables contributing to the dynamics of a feedback mechanism would be a more difficult exercise. I appreciate that this argument maybe reversed if the feedback mechanism is explored as a phenomenon rather than as the result of a whole family of dynamic mechanisms hence Shepherd and Rall 1968. So if we pick projection neuron’s as a starting point, the only reason for picking ‘classic’ mitral cells as a starting point is they are the sub group that are most easily defined (nucleus in the mitral cell layer). Once progress has been made with the mitral cells, work could be extended to projection neuron diversity.

[Simon-at-Ely]

Somatic membrane potential recordings for 6 mitral cells in the gap junction connected network for the form of the model published as O'Connor et al 2012.

Somatic membrane potential recordings for 6 mitral cells in the gap junction connected network for the form of the model post a NeuroML mappings update that changes the way the Ca pool volume is calculated.

Cell 1 somatic LCa Ca current density and KCa k current density for the post NeuroML update. Compare with http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3459005/figure/F9/ for the original pre-NeuroML update model.

Cell 1 somatic [Ca2+] in ca pool for the post NeuroML update.

[Simon-at-Ely]

The aim of this project is to gain a better understanding of mammalian (concentrating on rat or mouse where genetic manipulation is required) MOB mitral cell dynamics and heterogeneity by the development of a well constrained small gap junction connected model.

Rick Gerkin suggested that a good place to start might be to use NeuroElectro to find a selection of constraining variables. The mitral cell page can be found here: http://www.neuroelectro.org/neuron/129/.

Shawn Burton is the curator for this page and these are the current values:

Input resistance: 130.19 Mohms SD +/- 78.9 n = 17 Resting membrane potential: -58.44 mV SD +/- 5.21 n = 14 Spike threshold: -41.45 mV SD +/- 8.05 n = 2 Spike amplitude: 71.00 mV SD +/- 4.00 n = 2 Spike half width: 1.81 ms SD =+/- 0.17 n = 2 Membrane time constant 24.38 ms SD +/- 10.85 n = 4 Spontaneous firing rate 15.90 Hz n = 1

The passive parameters were individually fitted for each of the six cells in the model using dual patch clamp recordings that came from the reconstructed cell. This should be more accurate than relying on average Input resistance.

The model initiates all the cells at -65 mV and the reversal potential of the leak current is also set to -65 mV. This effectively sets the resting potential to -65 mV at the same time as using the leak current to set the membrane resistance. This value is more hyperpolarised than mean reported value on NeuroElectro, but not outside the range of the reported values. Raising the value produced spontaneous firing with the active properties in the model. So if it was felt desirable to use the mean reported values adjustments would need to be made to ion channels.

The sodium and main potassium channels (Kdr KA are the ones used in Migliore et al 2005. While the origin for the KCa and LCa come from Bhalla and Bower (1993). The reversal potential of sodium is 50 mV, potassium -80 mV and calcium 70 mV. There are two versions the sodium channel the second has a 10 mV shunt over the first.