I’m going to focus on the small scale details. The overall picture you describe is interesting, so don’t take any of this as me disagreeing with you.
It makes sense for bursting to be for attention, but it probably isn’t all-or-nothing. I think of attention as how aware the neurons are of each thing. There are probably some aspects which are sort of all-or-nothing, like switching attention to something for which there was no awareness whatsoever.
Be careful when researching bursting and dendrites. In my experience, it’s very slow to read the articles because each one is pretty different and technical, and the results from different studies are often quite different. Interpreting things in context of the rest of the cortical circuitry (what inputs are on which parts of the cell and what types of synapses they use and the sparsity of those inputs firing) is another nightmare.
Don't trust results based on calcium imaging. They're useful for some things but they're the bane of my existence.
A lot of studies on bursting and apical events use calcium imaging, where they inject a dye that fluoresces in response to calcium. Calcium imaging is not good for showing anything except that there was an increase in calcium. It can’t be used to identify the timing, duration, or magnitude of an event. It can theoretically show those things, but there are all sorts of problems it can cause. The results of these problems are often reported in studies because they seem new and interesting. For example, they can cause signals lasting seconds, possibly because of saturation (I don’t really know what that means), and they can cause repetitive calcium events (e.g. burst frequencies) to produce much larger signals. The usage of calcium imaging varies a lot between studies, like the concentration of the dye in the cell, the sensitivity of the dye, and probably the time scale. I don’t know much about chemistry so I might be totally wrong, but it seems like calcium imaging is very misleading.
Bursting probably isn’t a binary event based on L6 and the thalamus.
In thalamic cells, bursting isn’t an all-or-nothing event in terms of magnitude, although whether or not it happens is all or none. Thalamic bursts are caused by low threshold calcium spikes (different calcium channels than the main ones on the distal apical trunk in cortex), and they only occur if the cell has been hyperpolarized for a bit because that de-inactivates T-type calcium channels. When the cell becomes depolarized by an input, the magnitude of the calcium spike depends on how hyperpolarized the cell was and how long it has been hyperpolarized up to some limits. This can cause single spike bursts.
In L6 cells and presumably in L5, it’s sort of linear. I strongly disagree with the idea of a critical frequency, which for L5 thick tufted cells is generally around 100 hz, both for artificially induced spikes generating large tuft calcium signals and for a spike train to be considered a burst.
ADPs (afterdepolarizing potentials) are recorded at the soma and are what directly trigger bursts. This study measured the amplitude of the ADP triggered by different frequencies of artificially induced firing. Around 40 hz and up to about 80 hz, so practically all firing rates above 40 hz since L6 cells fire slower than L5 cells, the ADP amplitude is basically linear. That’s not the same as a bAP and apical depolarization together triggering a burst. However, in L5 TT cells, 100 hz is the supposed critical frequency for both the artificially induced firing and the burst that results from an apical calcium event, so there’s likely no difference. Also, since it only starts at a fairly high firing frequency, this is almost certainly caused by a calcium event in the apical dendrite, so the calcium event that results from a coincident bAP and dendritic input is probably also not all-or-nothing.
http://www.jneurosci.org/content/30/39/13031.full fig. 6 d, e.
My sources are in google docs linked here: Layer 6 Notes Summary - #2 by Casey. This is mostly based on memory so I might be wrong about some things. Some things might be hard to find so I can give you a list of sources if you want.
Some studies (maybe just one) found that the apical dendrite can produce APs at probably unrealistic levels of input, but also at much lower levels of input increases firing rates evoked by somatic injection, if I recall correctly in a multiplicative manner.
The proximal region of the dendritic arbor causes APs directly. This includes the proximal apical dendrite, something like .2 mm I think. Oblique dendrites are basically ignored so they probably also complicate things.
200 hz is an exaggeration by the researchers. It can happen but probably just because of injecting way more current than is realistic.
The NMDA receptors are on the apical tuft, whereas the distal apical trunk* is the location of the voltage gated calcium channels. They seem to perform localized summation like distal basal dendrites and HTM dendritic segments.
*and possibly the first order branches of the tuft, possibly because L5 TT cells can branch their apical shaft around L4 into effectively two apical shafts
If you haven’t read about them yet and want to, try searching martinotti cells and somatostatin positive cells, although be careful because not all of those are the same. They’re pretty interesting in regards to bursting. They can be inhibited by other interneurons, possibly some which are activated by motor cortex signals to L1.
I haven’t heard of apical dendrites only responding to burst frequency inputs, but this is possible indirectly. Higher order thalamus synapses in primary cortex in L1 and L5a (probably not much on L5 TT cells but perhaps even proximally on L5 slender tufted cells which might modulate L2/3 and L5 TT cells). It activates metabotropic receptors, which might be frequency-sensitive. This mirrors feedback from L6 to primary thalamus, which is thought to be involved in attention.
NMDA receptors can also be frequency-dependent, maybe. This is all pretty complicated though so it’s hard to tell what happens in the brain.
Those interneurons don’t receive input from the thalamus, at least most or all Martinotti cells don’t.