HARRY R. ERWIN (herwin at osf1.gmu.edu) wrote:
: Interim Report/Lessons Learned on a Simulation Model of the Olfactory Bulb
: As a graduate school project during the last quarter, I've been developing
: a computational and compartmental model of a small but biologically
: realistic subset of the olfactory bulb.
: I'm posting this report for anyone who might provide useful critical
: feedback. The simulation consists of a number of small compartmental
: models of sensory, tufted/mitral, periglomerular, and granule cell neurons
Question: what are 1) the free parameters in the anatomical
construction of the model, and 2) what are the free parameters in
the "functional construction"? It appears that you need more
information before you will be able to say anything really
useful. It would help to know the circuit: how well is the
connectivity known?
If you have more than about 5-10 "really" free parameters, it
will be difficult for anyone to understand how the model
operates. Evaluate how large your free space is, in terms of the
number of free parameters. Constrain the parameters any way that
you can. Only then try to test the free space.
: Lessons learned in developing this simulation include the following:
: 1. Errors in the equations for neural dynamics--a number of errors were
: noted in recent papers. My take is that it is unsafe to rely on the
: equations in published papers, and any equations used should be rederived.
You should assume this. Modelers are notorious for changing
equations/results, and papers are sometimes very sloppy.
: 2. Instability in explicit compartmental models--compartmental neural
: models are advective with all the problems associated with such models.
: This becomes clear if one reviews Wilfred Rall's 1989 paper, "Cable theory
: for dendritic neurons," in Koch and Segev, Methods in Neuronal Modeling.
: Since both the shape and strength of the signals between compartments are
: biologically important, the preferred approach would be a high-order
: adaptive scheme using implicit solution techniques. The system of
: equations appears to be stiff, with high long-range connectivity, making
: matrix inversions computationally expensive. My exploratory modeling used
: a low-order explicit code, and so can only be regarded as suggestive.
Look at Mascagni's and also Mike Hines' work on "implicit"
solution methods, also Joyner et al, 1978. Second order implicit
seems to be fastest, because higher orders are too expensive
comutationally. First-order implicit is necessary sometimes
because second- (and higher) order is unstable with fast-changing
stimuli (e.g. voltage-clamps). Also, look at my paper on
"NeuronC", published in: J. Neurosci. Methods (1992) 43:
83-108. If you iterate an explicit solution to the matrix,
plugging in the old solution to get an ever-better new solution,
you compute the "implicit" solution. Stop when the solution
changes less than some criterion. Implicit is the way to go.
: 4. The true role of 'inhibitory' neurotransmitters--GABA and glycine are
: _not_ inverted excitatory neurotransmitters. Instead they serve to
: increase the 'inertia' of the neuron by reducing its sensitivity to
: excitation. The reversal potential for chloride channels is in the
: vicinity of -70 mV, close to the resting potential of the neuron and also
: close to the reversal potential for potassium channels. This means that
: GABA can depolarize as well as hyperpolarize a neuron, depending on the
: chloride gradient. The model for release of GABA at a synapse must take
: that into account.
Yes, there are many possibilities. If you don't know enough
about the physiology, you have to take a guess, and this implies
one or more free parameters. Best to actively search for
different modes of behavior in the circuit by first checking out
"subtractive" GABA behavior, then going to "shunting" behavior.
What do you know about the circuit already that would help with
this?
: Very little work appears to have been done on the mechanism
: by which a depolarization level
: on the presynaptic side results in vesicle release, followed either
: depolarization or buffering against depolarization on the postsynaptic
: side. What appears in most analyses are "all-or-nothing" presynaptic
: spikes and postsynaptic responses, and that does not address the detailed
: dynamics that actually occur. In particular, electrical synapses and
: chemical synapses implementing graded potentials are given short-shrift
: by this model.
Check out recent work of:
Korn and Faber (synaptic psp's, quantal release)
M. Wilson (retinal amacrine cells)
G. Matthews (retinal bipolar cells)
F. Werblin (synaptic physiology)
In general, the literature on the retina is rich with synaptic details.
Although many retinal neurons don't spike, their input properties
are similar to other spiking neurons.
: 6. The crucial role of active tuning in producting the observed EEG
: patterns--to get the observed EEG patterns, the olfactory bulb has to be
: actively tuned in sensitivity. I modeled this by adjusting the trigger
: potential for spiking by active conductances, and over a range of 10 mV, I
: went from fixed point dynamics to completely chaotic dynamics. To
: reproduce the dynamics seen in vivo would thus seem to require sensitive
: tuning in near-real-time.
Very interesting. But to be meaningful you need to constrain
your free parameters.
: 8. The role of granule cells in the system--these appear to force the
: system into a Hopf bifurcation and only work right if the system is
: actively tuned, since they do not appear to be adaptive. Whether they have
: active conductances is a major issue for my model. Active conductances
: appear to overdrive them, since there is no evidence for afferent GABA or
: glycine synapses.
Yes, these kind of issues will make or break your work, and your
audience's patience. But surely your questions will help
physiologists to devise useful experiments. If they can
understand what you've done!
: 9. The role of attention in creating and maintaining neural cellular
: assemblies--see Gary Aston-Jones's work and Gray, Skinner, and Freeman,
: 1986, in Behavioral Neuroscience, 100(4):585-596. Norepinephrine appears
: to have a role in vigilance, by modulating the sensitivity of the
: olfactory bulb. This is much like the modulation by the periglomerular
: neurons, but on a more global scale, adjusting the percentage of the
: existing neural cellular assemblies (NCAs) that respond to afferent
: signals and facilitating NCA assembly, disassembly. I intend to
: investigate this further.
Interesting, but until the circuit and location of receptors is
better known, I would tend to ignore higher-level issues like
this. It's too complicated, with too many degrees of freedom.
: 10. The mechanism of the 'H' synapses in the glomeruli and the reciprocal
: synapses between the tufted/mitral cells and the granule cells remains
: unclear. I suspect they produce some sort of difference signal.
Well this is something that you can explore with a small model.
Just try to make up some hypotheses, and check them out one by
one in a simple model, not worrying at first what the surrounding
circuit does or exactly what the signals represent. If you can
figure out under what circumstances a difference signal is
created by the reciprocal synapses, you will have helped the
field quite a bit.
Are there NMDA synapses involved? Do you need to simulate
calcium flux and diffusion? If so, the model requires calcium
concentration as a state variable, and this would slow it down
quite a bit.
As you can probably imagine by now, I'm working on similar
issuses in the retina. I've learned to keep the models simple
and never have more than 5 or so free parameters. That's the
limit of the human imagination for taking it all in...
Hope this helps,
Rob Smith
