Compendium of Analyses, Part I: Single Cells

In thinking about data analysis, I realized that I don't have a clear idea of what analyses are possible, their advantages and shortcomings. So I'll just list them all, in two parts, single cell and ensemble techniques. As I continue reading, I will hopefully add more esoteric methods.

PSTH / PETH


The simplest of all analyses is the peri-stimulus time histogram (or for non-stimulated responses, peri-event time histogram).  You record from a neuron while repeating a stimulus, and sum the spikes following a trigger into bins.

Response of neurons in gustatory cortex to different tastants; the triggering event is a lick.
From Katz et al, 2001. My review.

PSTHs are quick, dirty, and reveal the obvious, but have significant limitations. First, PSTHs are highly sensitive to bin size.  In the figure above, in each time bin, the neurons respond to different tastants. Bin size can drastically change how neurons are characterized: before Katz's paper, people guessed that only 10% of gustatory cortical neurons encoded taste; using 500ms time bins, Katz estimated 30-40% of neurons were taste sensitive.

PSTHs also ignore the context surrounding an event.  For example, simple PSTHs are inappropriate if stimuli are presented on an oscillating background, unless you otherwise compensate for oscillations. Furthermore, the identity of triggering events may not be obvious for rapidly changing stimuli.  To look at those, reverse-correlation is a better technique.

Spike phase

For neurons that function in an oscillating context, spike timing matters less than spike phase.  The example below is a recording from the olfactory bulb following an odor presentation.  In the PSTH on the left, there is an obvious tonic response to the odor.  On the right is a phase plot, where the breathing cycle was transmuted from seconds into degrees, with inhalation at zero degrees.  From the phase plot, you can see that the preferred spike phase changed over the course of the response. What is especially interesting are cells that maintain the same firing rate over moderate bin sizes (~300ms), but change their phase.

Left: PSTH of OB neuron spiking following an odor. Right: Spike phase of this neuron.  0 degrees = start of inhalation (see breathing plot on left). The neuron's preferred phase of the breathing cycle changes between breathing cycles.
From Bathelier et al 2008.

Phase plots are obviously only useful in oscillating contexts, although these contexts can vary.  In the hippocampus, Buzsaki has found that there is phase precession around the theta oscillations. In olfaction, the phase is usually defined around the breathing cycle. In gustation, it is the licking cycle.

"Receptive fields"

Once you have many PSTHs or phase diagrams for a neuron, the next step is to organize the PSTHs. In other words, you have to identify which stimuli cause the neuron to respond, given some definition of "response." The set of all stimuli that a neuron responds to are its "receptive field."

The term "receptive field" comes from the visual system.  Retinal or visual cortical neurons are excited by stimuli in one location, and inhibited by stimuli in other locations.  You can similarly plot their orientation and direction selectivity.  For the hippocampus, the receptive field is location.

Receptive fields of V1 neurons. Excitatory regions shown in red, inhibitory in blue. You can see orientation selectivity in panels A-C.
From Tanaka and Ohzawa, 2009.

For olfactory or gustatory neurons, the "receptive field" is simply the set of odorants or tastants that elicit responses (which unfortunately is harder to visualize than a nice center-surround). In the olfactory bulb, there is a lot of disagreement as to how sparse or dense mitral cells' receptive fields are, in part due to the semantics of a "response."  In the anesthetized state, mitral cells respond with large firing rate changes, while in the awake animal, these are less pronounced.  However, there do seem to remain phase changes in the awake state.


Stimulus (de-)composition

In thinking about these analyses, I remembered the Lin and Katz paper where they used gas chromatograpy to deconstruct a natural odorant into its components. While this is not an analysis technique per se, I think it's important to consider how stimuli are combined in the brain.  For example, do the component odorants in a natural odorant combine linearly or non-linearly? How do odorant receptor neurons and mitral cells respond to mixtures of odorants? While people have made stabs at answering these questions, the answer remains elusive. In the visual system, retinal and visual cortical neurons have been found to have highly non-linear receptive fields.

A. Gas chromatography of cloves. B. Intrinsic imaging of OB during gas chromatography. The clove response (C), is more than just a sum of B. D&E. An artificial mixture of clove components elicits a map similar to the clove map.
From Lin and Katz, 2006.

Reverse correlation techniques


As mentioned before, PSTHs are not good at detecting responses to rapidly changing stimuli.  In the visual cortex, this has been addressed via reverse correlation techniques.  Rather than look at the spike following an event, reverse correlation looks at which stimuli precede a spike.

This is most useful in visual cortex, where it is possible to present movies, record neurons' responses, and then use reverse correlation to decode their spatiotemporal receptive field.  That is, besides the spatial information of the receptive field, you also gain information on how the receptive field changes; for example, whether a certain area is both inhibitory and excitatory at different times.

This technique is obviously less useful in olfaction and gustation, where stimuli vary less rapidly. And it is impossible to record natural stimuli for playback to an animal.

That's it for the single cell analyses.  The point on the single cell level is to identify which stimuli make a neuron spike, or stop spiking (ignoring subthreshold effects).  Things get more complicated on the population level, where spike timing becomes more important. (I did not mention spike timing separately here, although it can be very precise, both in vision and audition. I would be surprised if spike timing on the 1-5ms scale mattered for chemosensation.)

References

Bathellier, B., Buhl, D. L., Accolla, R., and Carleton, A. (2008). Dynamic ensemble odor coding in the mammalian olfactory bulb: sensory information at different timescales. Neuron 57, 586-98.

Katz, D. B., Simon, S. A., and Nicolelis, M. A. L. (2001). Dynamic and multimodal responses of gustatory cortical neurons in awake rats. The Journal of neuroscience 21, 4478-89.

Lin, D. Y., Shea, S. D., and Katz, L. C. (2006). Representation of natural stimuli in the rodent main olfactory bulb. Neuron 50, 937-49.

Tanaka, H., and Ohzawa, I. (2009). Surround suppression of V1 neurons mediates orientation-based representation of high-order visual features. Journal of neurophysiology 101, 1444-62.

I Don't Think the Ethics Committee Would Approve That

"But no matter. I had my little revenge in due time. A man from Pasadena told me one day that Mrs. Maximovich née Zborovski had died in childbirth around 1945; the couple had somehow got over to California and had been used there, for an excellent salary, in a year-long experiment conducted by a distinguished American ethnologist. The experiment dealt with human and racial reactions to a diet of bananas and dates in a constant position on all fours. My informant, a doctor, swore he had seen with his own eyes obese Valechka and her colonel, by then gray-haired and also quite corpulent, diligently crawling about the well-swept floors of a brightly lit set of rooms (fruit in one, water in another, mats in a third and so on) in the company of several other hired quadrupeds, selected from indigent and helpless groups. I tried to find the results of these tests in the Review of Anthropology; but they appear not to have been published yet. These scientific products take of course some time to fructuate. I hope they will be illustrated with photographs when they do get printed, although it is not very likely that a prison library will harbor such erudite works."

-Lolita, Chapter 6

Walk Along the Paper Trail: Satiating Trail Mix

In the last trek we took, I wrote about two seminal papers that describe taste coding in gustatory cortex.  Today I'm going to cover a followup paper which described satiety's effects on gustatory coding.

Let me fill you up


The neural systems involved in satiety, food intake, and body weight are incredibly intricate.  First, there are endocrine responses: after food intake, leptin and insulin are released, blood sugar increases, and cannabinoid levels drop.  Then, as you get hungry again, leptin, insulin, and blood glucose levels drop while endocannabinoid increases.

These endocrine molecules bind to a variety of receptors on the tongue, and throughout the brain, including the hypothalamus.  On the tongue, leptin receptors are expressed on sweet taste bud cells, and leptin binding causes a decrease in firing, presumably decreasing perceived sweetness.  In contrast, cannabinoid receptors on taste bud cells can sensitize the taste response, increasing perceived sweetness.

The other well described pathway for endocrine signaling is via the hypothalamus.  I'll probably delve into this later, but in brief, the hypothalamus has multiple cell populations which express endocrine receptors, and can directly regulate feeding behaviour.  For example, Aponte and Sternson recently showed that if you stimulate AGRP-expressing neurons in the hypothalamus, you can induce feeding behaviour; while stimulation of POMC-expressing neurons over 24h reduces food intake.

Given all these ways that satiety can be regulated, what happens in gustatory cortex?

CNS coding of taste


To see how satiety influences the CNS, you first need to establish a metric for satiety.  de Araujo and colleagues chronically implanted rats with electrodes, and then gave them limited access to a sucrose solution.  The sucrose was behind a gate that would only stay open for five seconds after a lick.  Two seconds after closing, the gate would reopen, allowing the rat to lick again.  They then measured the inter-trial-interval (ITI) to quantify how motivated the rats were to get some sugar (panel A).

ITI reflects mouse satiety. A. Schematic of licking paradigm, and ITI definition. B. Example ITI for a rat going through hunger-satiety-hunger cycle. C. Population ITI. D. Measured blood glucose in these three phases. E. Measured insulin in the three phases.
From de Araujo et al, 2006.

In 16/19 animals they found distinct hunger and satiety phases, with ITIs of 18s during hunger1, 180s during satiety, and 35s during "hunger2."  On Saturday, I wrote a mini-review on mouse licking, and showed that mice lick in bouts with a regular frequency.  Here they also analyzed the microstructure of the licking bouts during hunger and satiety, and found the rats licked at ~6.5 Hz in both phases.

Once they categorized well-defined hunger and satiety phases, they then characterized the neural response in four brain areas: orbitofrontal cortex (OFC), gustatory cortex (INS; insular cortex), the lateral hypothalamus (LH), and the amygdala (AM). As you may remember from last time, 30-40% of neurons in gustatory cortex encode taste information; I'm not well read on taste responses in other areas, but I think the percentage is similar. Since they are applying a single tastant, sucrose, one might expect the percentage to be lower here.

Of the 625 neurons recorded in all the areas, they found 101 (16%) were licking related, while 152 (24%) responded to taste delivery.  179 (29%) neurons had firing changes related to satiety, but none of these were licking-related cells (panel F).  Of these, most (104/179) responded simply by changing their baseline firing rate (panels D & E).  For the other 75, their responses to sucrose were altered, with both increases and decreases in firing (panel A-C). Satiety-related responses were found in all four brain areas measured,  but some had more responsive neurons than others.  (LH > AM > INS > OFC).

Examples of cells modulated by satiety. Event rasters are shown above peri-event time histograms. Satiety border shown as dashed blue line. A. This cell lost its sucrose response during satiety. B. This cell lost its anticipatory response. C. This cell gained an anticipatory response. D&E. Changes in baseline firing rate. F. Licking related neurons do not change firing.
From de Araujo et al, 2006.

So far I have described the single cell response, but what about the population response? They looked at this by calculating the mean population firing rate, and found that for 12/19 sessions, mean firing rate decreased during satiety (panel A, below).  However, this seems fairly dirty, given that they were able to calculate individual cells' changes in firing rate.  They continued this analysis for the next two figures, looking at the population's performance vs individual cells, but to be honest, I don't find it compelling.

Population firing during satiety. A. The population firing rate decreases during satiety. B. ITI showing satiety. C-E. Example cells from the population. Only cell E is bimodal.
From de Araujo et al, 2006.

I have a few issues with this paper.  First, the temporal analysis is rather shallow: when they characterized cells responsiveness, they simply binned the 500ms before and after a lick.  However, five years earlier, they showed that taste responses could have complex temporal profiles, including periods of inhibition and excitation in the same response. Second, I wish they had used more than one tastant, given that there are leptin receptors on sucrose taste bud cells.  Using other tastants would help differentiate between endocrine effects on the tongue versus effects via the hypothalamus or other areas.  Finally, I would have liked to have seen a more sophisticated population analysis, even just looking at cross-correlation within ensembles.

Given those caveats, there are a lot of interesting results.  First, there is the most common modulation, changes in baseline firing rate.  This could influence coding in a few different ways, changing the gain or dynamic range of firing, or changing the potential for synchrony between neurons.  That there are more modulations of baseline firing than taste responses seems significant.

Second, the changes in firing rates of these neurons are quite long (see panels C&D in the last figure), and can continue beyond the end of satiated behaviour.  Satiety is a long-term process, changing gradually over hours, so it make sense that neurons' behaviour would also be long term.  Perhaps mice's perception of hunger and satiety are faster given their metabolism.

Finally, it was interesting to see there were satiety changes in all areas (it would have been nice to see a table with a complete breakdown).  The changes in hypothalamus make sense given its involvement in feeding, and orbitofrontal cortex makes sense given its executive function.  But there were also changes in the amygdala and gustatory cortex.  This could be due to common processes influencing all areas (e.g. reduction in taste receptor sensitivity), or could simply be indicative of how complicated body weight and food intake regulation is.

de Araujo IE, Gutierrez R, Oliveira-Maia AJ, Pereira A Jr, Nicolelis MA, & Simon SA (2006). Neural ensemble coding of satiety states. Neuron, 51 (4), 483-94 PMID: 16908413

Paper Trail Day Trip: Mouse Lick Throughs

Last week at lab meeting, I found myself having the absurd discussion of how to best train a mouse to lick a water spout.  Mice don't have many ways to talk to us dumb humans, and head-fixed mice have even less.  The best way we have is licking.

After lab meeting, I did some Google Scholaring, and found a great little article that quantified mouse lick rates.  In two mouse strains! Comparative mouse licking ethology!  It doesn't merit a full blog post, but I wanted to highlight the main findings for all you other mouse lickers out there.

They used a lickometer (pardon the technical jargon) to measure how often C57 and DBA/2J mice licked.  They found mice licked in bouts of 1-20s, about once a minute.

Mouse licking. A. Mice lick in bursts. B. Individual bursts have regular licking. C. Inter-lick-interval during bursts.
From Boughter et al 2010.

As you can see in the inter-lick interval (ILI) histogram above (panel c), licking is highly regular, but mice occasionally miss a lick, either due to lickometer error, or actual pauses in licking.  There is a much smaller third harmonic. During the bouts, C57 mice lick at 8Hz, while DBA mice lick at 10Hz.

C57/B6 mice have more licking bouts than DBA/2J mice, but lick more slowly during them.
From Boughter et. al. 2010.

Since C57 mice lick at a slower rate than DBA mice, they compensate by having more licking bursts (compare black and white bars).  The average lick volume for both strains was 1.2uL.

I love that papers like this exist, because their kinda handy, and kinda absurd.  Another paper along these lines is, "Distribution of serotonin immunoreactivity int he main olfactory bulb of the Mongolian gerbil." Just don't tell Sarah Palin.

Boughter Jr, J., Baird, J. P., Bryant, J., St John, S., and Heck, D. (2007). C57BL/6J and DBA/2J mice vary in lick rate and ingestive microstructure. Genes, Brain and Behavior 6, 619–627.

Spines Only Grow Once

Continuing my series of publishing extra data from my graduate work (probably only 1-2 more posts left), today I'm going to talk about my favourite experiment I ever did.

Spine size is a proxy for memory


The standard cellular model for learning and memory is that memories are stored in the synapses between neurons, and that learning changes the strength of these synapses.  While this model makes sense, no one has actually been able to measure the strength of a synapse while an animal learns.  However, you can use spine size as a proxy for synaptic strength: among other things, bigger spines have more AMPA receptors and stronger synaptic currents. If you image spines while animals are learning you can see all sorts of changes in spine number, and watch spines be created and destroyed.

Since spine size is correlated with synaptic strength, and synaptic strengths change, Haruo Kasai theorized that a spine's size actually represents the stimulation history of a synapse.  That is, a small spine represents a synapse that is either newly formed, or has been depotentiated; and a large spine represents a synapse that has been repeatedly potentiated.  There are lots of cool questions you can ask if this is true, like whether there are a discrete number of spine sizes, or if spine size is graded; and whether there is a continuous, random process of spine shrinkage that allows us to form new memories.

Double uncaging, OMG

If a spine's size can represent its stimulus history, this implies that a spine/synapse can repeatedly change size. Some people have tried to test this using a minimal stimulation technique, but because they could not identify the synapse they were recording, the results are not 100% conclusive.  Another group used glutamate uncaging and found that synaptic strength changed in a step-wise fashion, but did not stimulate twice.

Two-photon glutamate uncaging allows you to address this question.  You can measure a spine's size (i.e. synaptic strength), and stimulate it with glutamate to cause an increase in spine size.

Stimulating a spine increases spine volume.  Neurons are transfected with fluorophores so you can see them. Before stimulation (top row), spine are relatively small; one minute after stimulation, they are much larger; 30 minutes later, their size has relaxed, but is still larger than originally.
From Patterson et. al. 2010.

This allows one to answer the question: what happens if you stimulate the same spine twice?   I started by stimulating the same spine twice, at intervals of 15 min. (standard Yasuda lab uncaging protocol: 4mM MNI glutamate, 6mW power, 6ms pulses, 30x stim, 0.5 Hz).  Following the first stimulation, the spine grew to +310% of its original volume, and decayed to +100% fifteen minutes following stimulation (panel A). I then repeated the same stimulation protocol.  After the second stimulation, the peak spine volume was +360%, with a volume at 15 min. of +135%. (Figure saved at FigShare.)

Stimulating the same spine twice does not cause growth beyond the first stimulation. A. Double stimulation at 15 min. interval. n=11 spines, 10 cells. B. Paired spine structural plasticity. n=5 pairs. C. Double stimulation at 60 min. interval. n=8 spines, 7 cells.
Unpublished data!

There is a lot of variability in the transient phase of structural plasticity (<5 min), so it's best to look at structural plasticity after 30 min.  To do this, I uncaged on nearby "control" spines (panel B).  If you compare the structural plasticity for the two spines at 30 min., you can see they're basically the same.

So that's at 15 minutes, what about longer time intervals?  I repeated the experiment with a 60 minute interval, and saw the same basic result: following the second stimulation, there was no obvious increase in structural plasticity, for both the transient and sustained phases (panel C).

So how do I interpret these results?  First, I think this shows that structural plasticity has a refractory period; that is, once a synapse changes strength, it is stable, and cannot be changed again for a while.  How long this refractory period lasts is a great question, and could be a limiting factor in memory formation.  I tried stimulating twice with an interval of 24 hours, but the slices got contaminated by bacteria.

A second interpretation is that structural plasticity is saturable.  That is, the capacity for change has a limit at any given time point.  Note that this does not really address the question of whether spine sizes are distributed over a continuous space, or discrete sizes.

What I really love about this experiment is how simple it is, and how many different directions you can go from here.  And it was all enabled by new technology.