I recently discussed the role of cell membranes, especially those of glial cells, in performing the complex calculations of the brain, and now I want to take a more detailed look at what sort of things may be going on in these calculations. I'm going to tie this discussion to three recent papers, all of which offer important supporting details in understanding just how "smart" the membranes of neurons and glial cells can be.
First, Fast Subplasma Membrane Ca2+ Transients Control Exo-Endocytosis of Synaptic-Like Microvesicles in Astrocytes (by Julie Marchaland, Corrado Calì, Susan M. Voglmaier, Haiyan Li, Romano Regazzi, Robert H. Edwards, and Paola Bezzi) looks into the both the timing and the micro-structure of vesicle-based release of transmitters by astrocytes, one of the key types of glial cell. Although the potential contributions to overall brain-power of the other key type, the NG2-glia, may be greater, we can tentatively assume that anything astrocytes have been shown to do, NG2-glia and neural dendrites can probably also do, although they may not do so in every region or area (or layer, in the neocortex) of the brain.
The second paper, Mitochondria Modulate Ca2+-Dependent Glutamate Release from Rat Cortical Astrocytes (by Reno C. Reyes and Vladimir Parpura), demonstrates the role of the mitochondria in supporting and modulating the use of calcium in astrocytes as a signal for transmitter release. I've discussed the role of calcium as a signal before, especially the way it ties the cell's energy systems to their information processing systems: calcium is often used as a local signal for some process that's energy-intensive, because the mitochondria both act as a buffer for the calcium itself, and when they absorb that calcium it stimulates them to increase energy production, even before the processes that use that energy get well under weigh.
The third, Modulation of Voltage- and Ca2+-dependent Gating of CaV1.3 L-type Calcium Channels by Alternative Splicing of a C-terminal Regulatory Domain (by Anamika Singh, Mathias Gebhart, Reinhard Fritsch, Martina J. Sinnegger-Brauns, Chiara Poggiani, Jean-Charles Hoda, Jutta Engel, Christoph Romanin, Jörg Striessnig, and Alexandra Koschak), demonstrates the flexibility of one particular type of voltage-gated calcium channel, in terms of modulating properties such as voltage thresholds and inactivation timing through alternative splicing of the RNA that codes for it. Since the activation voltages for these channels are in the same general range as the voltages involved in the calculations that can take place in cell membranes in the absence of action potentials, the demonstration of this flexibility adds support to our ideas of what glia and neural dendrites may be doing as part of the brain's calculations. (A brief introduction to action potentials and membranes may found here.)
The Glial Membrane
What I'm going to do is look at a small section of glial membrane, building a picture based on what these three papers tell us. Then I'm going to try to expand that to a picture of what a huge network of glial and neural membranes can achieve in the way of carrying and integrating huge amounts of transient data, orders of magnitude beyond the amount of information carried by the axons as action potentials. ...
The glial membrane divides the cytoplasm of the cell from the extra-cellular area. There is a great difference in concentrations of many substances between the inside and the out, including sodium, calcium, potassium, chloride, and a wide variety of neuro-active substances, including classic neurotransmitters, ATP and other purines, and hormones and other more generally diffusing substances such as nitric oxide. It is filled with receptors that respond to various substances outside the cell, as well as ion channels subject to control by the voltage across the membrane (voltage-gated) and neurotransmitters (ligand-gated). (Ligand-gated ion channels also count as receptors). Most of these ion channels are subject to modulation in their activity by other substances, and many are quite complex in their behavior, possessing the ability to open in response to one thing (typically voltage), then close after a short period or in response to changing ion concentrations either outside the cell, or inside.
Under the Membrane
Inside the cell, there isn't just a pool of cytoplasm, randomly filled with various molecules and organelles. Rather, the cell has a cytoskeleton made from filaments of actin and microtubules, that among them help to maintain its shape, and provide a scaffolding for the various organelles and large molecules that make up much of the cell's mass. Not far beneath the astrocyte cell membrane are the various structures of the endoplasmic reticulum (ER). These are mostly in the form of fine tubes (called "tubuli") enclosing material of the lumen of the ER, which can vary dramatically from the cytoplasm in its concentrations of many substances.
Figure 1: Spatial relationship between ER tubuli and SLMVs ["synaptic-like microvesicles"] in the submembrane compartment. Click on image to see original caption and enlargeable image. (From Ref 1, Figure 3.)
The cytoplasm right under the cell membrane contains ER tubuli, vesicles containing neurotransmitters, and mitochondria,   at the least. It also contains cytoskeletel elements to which the various others are linked, capable of movement. When calcium concentrations rise in the cytoplasm, the vesicles move to the surface and expel some or all of their contents, a process called exocytosis. As Marchaland et al. show:
We found that the exocytic burst, similar to endocytosis, displayed a bimodal distribution (Fig. 2C), strongly suggesting the existence of two modes of exo-endocytosis. We confirmed this hypothesis with a double transfection approach in that we could directly visualize the fate of SLMVs during exocytosis and retrieval (Fig. 2A,B,D). Indeed, we noticed heterogeneity both in the origin of the SLMVs that underwent exocytosis (Fig. 2D, residents vs newcomers) and in their mode of fusion (kiss-and-run vs full-collapse type of fusion). The rapid phase of the exocytic burst (0–400 ms) was sustained almost exclusively by resident vesicles undergoing kiss-and-run fusion, whereas the slow phase (500 ms–1.6 s) mainly by newcomer vesicles undergoing full-collapse fusion. This duality is reminiscent of observations in neurons in that only readily releasable SVs [synaptic vesicles] are rapidly recycled and reused ([ref]). Our experiments do not clarify whether newcomers and resident vesicles represent distinct population of SLMVs[synaptic-like microvesicles]. The newcomers may indeed represent the same population of resident vesicles that undergo a second round of exocytosis upon rapid recycling.What Marchaland et al. refer to as "synaptic-like microvesicles" are vesicles that look and act very similar to those of the neural synapse, but are present here in astrocytes. They are also almost certainly present in NG2-glia, and may well be present in neural dendrites outside the synapse. I doubt anyone would notice them unless they looked for them, and even if they looked and didn't find them, that would only mean they weren't present in that particular population of nerve cells in that species. (While there may be enough similarity between, say, mice and rats that it could reasonably be assumed that they would be alike, in this respect rodents couldn't possibly be used as a model for humans given 60-90 million years of separate evolution, evolution during which the primates specialized in neural and cognitive enhancements.)
The process by which transmitters are released, then, takes place on a sub-second time scale, and is capable of relatively smooth variation in quantity, at least at the levels of the "kiss-and-run" release. Although this research provides no proof, it seems highly likely that some variation is possible in how much is released, depending on the severity of the rise in calcium levels.
The rise in calcium levels is part of a very complex process, in which surface activity coordinates with release of calcium from the ER tubuli, uptake by mitochondria which helps to buffer and modulate the calcium levels,  and the response by the system which controls exocytosis to the rise in calcium levels. As Marchaland et al. have demonstrated, vesicles and tubuli appear to be closely coordinated in their location, which suggests an ability to localize the release of transmitters to within a few microns, if not much less.
As for calcium signalling, the first thing to understand is that calcium is relatively fast-diffusing, over a micron scale. However, a rise in calcium levels caused by release from tubuli would be buffered by nearby mitochondria, which absorb it, localizing any particular effects.  Why do the tubuli release calcium? As it happens, there is a messenger molecule called IP3 that reacts to receptors on the surface of the ER:
Glutamate-induced Ca2+ oscillations in astrocytes result from the activation of class I metabotropic receptors that induce the phospholipase-dependent accumulation of inositol trisphosphate (IP3) that stimulates the release of Ca2+ from IP3-sensitive internal stores ([ref]). Consequently, by measuring Ca2+ signaling, rather than membrane potential, it was discovered that astrocytes are an excitable system.So basically, what happens is that some condition outside the cell interacts with a receptor, which in turn releases IP3, which in turn causes the ER tubuli to release calcium. If the stimulus is general, so is the response. If the stimulus is localized, so is the response, to a scale of microns or less. And it's kept localized by the quick absorption of the calcium by mitochondria.
Since these initial observations it has been realized that astrocytes express a plethora of metabotropic receptors that can couple to second messenger systems ([refs]). For example, norepinephrine ([refs]), glutamate ([refs]), GABA ([ref]), acetylcholine ([refs]), histamine ([ref]), adenosine ([ref]), and ATP ([ref]) have all been shown to induce Ca2+ elevations in glial cells in brain slice preparations. In culture, the list of metabotropic receptors is extensive. However, because culturing astrocytes can lead to the misexpression of proteins, it is not yet clear whether all of these receptors are normally expressed in astrocytes in vivo.
The Effects of Voltage
Although the voltage across the membrane did not directly stimulate entry of calcium into astrocytes, many of the metabotropic receptors listed above are subject to modulation by membrane voltage. Thus, voltage has an effect on the release of second messengers. Another important point to consider is the specific experiment involved:
Finally, with pharmacological experiments shown in Figure 4D, we confirmed that submembrane Ca2+ events depend exclusively on Ca2+ released from internal stores. Thus, the number of events remained unchanged when we removed Ca2+ from the incubation medium (0 Ca2+ with 5 mM EGTA) or added nifedipine (3 µM), a blocker of L-type voltage-gated Ca2+ channels. In contrast, the number of events increased during the first 15 s of incubation with CPA (approximately by 3.8-fold) (supplemental Fig. 11 SI, available at www.jneurosci.org as supplemental material) and returned to a baseline value between 1 and 7 min (0.76 ± 0.25/s/ROI) and eventually almost completely disappeared in ~10 min (0.095 ± 0.014/s/ROI). After 15 min of incubation with CPA, application of DHPG failed to induce submembrane Ca2+ events (http://www.jneurosci.org/cgi/content-nw/full/28/37/9122/F4D). These results constitute the first evidence of spatially confined, ER-mediated submembrane Ca2+ events occurring in astrocytes on a millisecond time scale.In other words, they got the same results when they disabled the use of external calcium. This certainly doesn't demonstrate that voltage activity couldn't cause similar events, especially in vivo.
This brings up Singh et al., the third paper, which talks about calcium channels and the way their voltage response (and other properties) can be modified by alternative splicing. This is a mechanism by which newly transcribed RNA is edited in different ways depending on a number of factors. Potentially, astrocytes could make use of this to create various populations of receptors, with different voltage responses, on different parts of their membrane. This, in turn, would allow each tiny part of the cell's membrane to respond in its own way to various voltage signals traveling across the surface.
Where does the voltage come from? I discussed this recently, but let me summarize:
[E]very time an action potential arrives at a synapse, the pre-synaptic part of the synapse releases a bunch of neurotransmitters, which cross the synaptic cleft and interact with receptors on the post-synaptic part, usually called the post-synaptic density (PSD).Now, something similar to this will happen to the astrocyte, which has its own synapses from incoming axons. In addition, the various transmitters floating around in the extra-cellular medium will act on various ligand-gated ion channels, creating currents that can, in turn, modify the voltage across the membrane.
Some of these receptors are "ligand gated ion channels", which can allow currents of sodium, chloride, potassium, and calcium in response to neurotransmitters. These currents, in turn, modify the voltage at the synapse, creating a voltage wave that spreads along the cell membrane, that is the membrane of the dendritic arbor. The voltage difference created by any action potential at any synapse decays in the manner described above, even if it never reaches the threshold for an action potential. Similarly, all the other synapses on that post-synaptic cell from that axon (if any) create their local currents, at other points in the arbor. These voltage differences decay in both space and time, the current fading out as the neurotransmitters are taken up or diffuse out of the synapse. While this is happening, other action potentials, in other axons, are adding their own contribution, causing the distribution of voltage across the membrane of the entire arbor to vary in an extremely complex manner. Note that depending on the type of ions involved in the current, it can be depolarizing (tending to lower the voltage towards the threshold) or hyperpolarizing (tending to raise the voltage even farther away from the threshold).
If no action potentials were arriving, the entire membrane might stabilize to constant voltage over time, but even then the voltage might vary from one place to another. With incoming action potentials, you have voltage waves sloshing around, and various ion channels reacting in a non-linear fashion, and various receptors, including ion channels, reacting to the voltage by releasing IP3 and other second messengers, all of which drive the calcium signaling system, producing a pattern of transmitter release that varies over microns in space, and fractions of a second in time. This transmitter release, in turn, drives differences in concentration of various transmitters over similar distances and times in the extra-cellular medium, creating an interactive feedback with the local arbors of axons and dendrites of various nerve cells, as well as NG2-glia.
What's important about this is that the dendrites, and quite possibly the NG2-glia, will respond with their own changes in voltage response, depending on the local concentrations of a variety of transmitters. All of this is happening on a sub-second time scale, over distances measured in microns or less, a small fraction of the size of the cells involved, even astrocytes.
What does this mean for the brain's computing ability? It means that the entire volume of the grey matter is a sort of massive computing machine. Of course, large amounts are given over to supporting material: blood vessels, myelinated axons, cell bodies, etc. The part where computing is concentrated is called neuropil. This is a densely packed mass of cell parts, their cell membranes typically a fraction of a micron apart.
Figure 2: Complete three-dimensional reconstruction of neuropil (2x2x2 µm). Click on image to see original caption. (From Atlas of Ultrastructural Neurocytology by Josef Spacek, MUDr., DrSc.)
The structure of the neuropil is different in different parts of the brain: cortical neuropil, neuropil of the molecular layer of the cerebellar cortex, neuropil characteristic of neocortex between pyramidal cells, neuropil between large dendrites of the Purkinje cells in the molecular layer of the cerebellar cortex, neuropil typical of thalamic nuclei, neuropil from the olfactory bulb (note the dendro-dendritic synaptic contacts), neuropil from the neurohypophysis, Neuropil from anterior horn of spinal cord, Neuropil from external plexiform lamina of the retina, and so on. In most, however, there is a tremendous amount of surface area potentially capable of the detailed electrochemical calculation. An exploration of the Atlas of Ultrastructural Neurocytology by Josef Spacek, MUDr., DrSc. from which these links come (or go to) will discover a number of features whose function is not understood.
In view of recent research, including the three papers discussed here, we have every reason to assume that the brain encompasses far more computing power than is contained in the action potentials, or even the dendritic responses to them. The highest-speed processes, involving action potentials and associated electrical waves in the dendrites, work on a time-frame of milliseconds. The processes I've been describing here work on a slightly longer scale, but still sub-second, and thus appropriate for things like short-term memory, integration of conscious awareness, and so on. Over periods of minutes or longer, cell structures can be modified, allowing the brain to change its behavior, probably part of how our longer-term memory works.
All in all, the brain is potentially a lot more intelligent than we may have thought a decade ago.
Marchaland, J., Cali, C., Voglmaier, S., Li, H., Regazzi, R., Edwards, R., & Bezzi, P. (2008). Fast Subplasma Membrane Ca2+ Transients Control Exo-Endocytosis of Synaptic-Like Microvesicles in Astrocytes Journal of Neuroscience, 28 (37), 9122-9132 DOI: 10.1523/JNEUROSCI.0040-08.2008
Reyes, R., & Parpura, V. (2008). Mitochondria Modulate Ca2+-Dependent Glutamate Release from Rat Cortical Astrocytes Journal of Neuroscience, 28 (39), 9682-9691 DOI: 10.1523/JNEUROSCI.3484-08.2008
Singh, A., Gebhart, M., Fritsch, R., Sinnegger-Brauns, M., Poggiani, C., Hoda, J., Engel, J., Romanin, C., Striessnig, J., & Koschak, A. (2008). Modulation of Voltage- and Ca2+-dependent Gating of CaV1.3 L-type Calcium Channels by Alternative Splicing of a C-terminal Regulatory Domain Journal of Biological Chemistry, 283 (30), 20733-20744 DOI: 10.1074/jbc.M802254200
Links: (I've included only the links referenced in this leader.)
1. Fast Subplasma Membrane Ca2+ Transients Control Exo-Endocytosis of Synaptic-Like Microvesicles in Astrocytes
2. Glutamate-induced Exocytosis of Glutamate from Astrocytes
3. Vesicular release of glutamate mediates bidirectional signaling between astrocytes and neurons
4. Mitochondria Exert a Negative Feedback on the Propagation of Intracellular Ca2+ Waves in Rat Cortical Astrocytes
5. Mitochondria Modulate Ca2+-Dependent Glutamate Release from Rat Cortical Astrocytes
6. Modulation of Voltage- and Ca2+-dependent Gating of CaV1.3 L-type Calcium Channels by Alternative Splicing of a C-terminal Regulatory Domain
7. Changes in dialysate concentrations of glutamate and GABA in the brain: an index of volume transmission mediated actions (Use Figure 1)
8. Nonsynaptic Chemical Transmission Through Nicotinic Acetylcholine Receptors
9. Extrasynaptic and postsynaptic receptors in glycinergic and GABAergic neurotransmission: a division of labor?
10. Glutamate Transporters Regulate Extrasynaptic NMDA Receptor Modulation of Kv2.1 Potassium Channels
11. Neuronal Synchrony Mediated by Astrocytic Glutamate through Activation of Extrasynaptic NMDA Receptors
12. Synapse-Specific Expression of Functional Presynaptic NMDA Receptors in Rat Somatosensory Cortex
13. Tonic activation of NMDA receptors by ambient glutamate of non-synaptic origin in the rat hippocampus
14. The locus coeruleus–noradrenergic system: modulation of behavioral state and state-dependent cognitive processes
15. Mechanisms of Calcium Decay Kinetics in Hippocampal Spines: Role of Spine Calcium Pumps and Calcium Diffusion through the Spine Neck in Biochemical Compartmentalization
16. Astrocyte Control of Synaptic Transmission and Neurovascular Coupling
17. Synaptic transmission onto hippocampal glial cells with hGFAP promoter activity
18. The synaptic organization of the brain by Gordon M. Shepherd