Dude, where's my 'dudes?

Neurodudes, one of the first neuroscience blogs I ever saw, seems to have gone 404. Hopefully it is just temporary.

Note added 4/14/08: it seems to be back up, with a sleek new look.

Getting intimate with rat whiskers (2): Ritt et al.

In the previous post, I briefly discussed the background and methods behind this paper by Ritt et al.. In this post I summarize and discuss the main results. I just noticed that Neuron added the apt banner, "What the rat's vibrissa tell the rat's brain" to the article.

Ex vivo whiskers
As I discussed in the previous post, the resonance hypothesis is the claim that the resonance frequencies of whiskers provide an ethologically important channel of information about what is going on in the world of the rat. Subsequent papers, however, have argued against the resonance hypothesis, as they were unable to reproduce whisker resonance in a more ethologically realistic preparation in which a whisker is fixed at a base and moved across a fixed surface (this is a little odd, since Hartmann already showed that resonance occurs in whiskers of awake behaving rats).

The first set of experiments in the paper addressed these issues, monitoring whisker movement as a whisker was brushed against a fixed surface at different speeds. They did observe resonance, as expected, but found an interesting twist--resonance wasn't prominent at every speed, but at a relatively narrow range of speeds, a 'hot spot' (see Figure 1B of the paper, shown below, which shows whisker angular velocity traces when the whisker is moved across the same surface at different speeds). This hot spot is thought to be within the range of speeds that whiskers move in ethological contexts, so it could be that rats exploit resonance during certain tasks by moving their whiskers at the appropriate speed.
In situ whiskers
The majority of the paper examined the micromotions of whiskers while rats performed a texture discrimination task. The task was relatively simple: the rat runs into a chamber that contains two different textures along the wall--a rough texture and a smooth texture (think of it as rough and smooth sandpaper). The rats are trained to get reward by running to a door that corresponds to a particular texture (e.g., when the smooth texture is on the right, enjoy a reward when you move to the right).

Their high-resolution monitoring of the whisker motions revealed a very interesting pattern to the movements. A whisker will slip along the surface, and then stick to a particularly abrasive feature, staying in place as the rat continues to move its head. Then, after the tension grows enough, the whisker whips forward (slips) before sticking at another spot further along (for example, see the clip from Figure 3 below: the top panel shows the trace of a whisker during the trial, and the bottom panel shows the angle (red) and position (blue) of the whisker). This is often accompanied by a kind of 'ringing' of the whisker as it sticks in place. Perhaps not surprisingly, this slip-n-stick pattern occurrs more often when it sweeps along the rough surface.
In the frequency domain, the mean frequency of movement of each whisker was inversely proportional to whisker length. This suggests that the elasticity that confers different resonance frequencies upon whiskers of different lengths also influences the frequency of whisker vibrations during the present discrimination task (the figure below, clipped from the paper, shows an example of the likelihood of different frequency components in two whiskers of different length).
While the frequencies of oscillation were consistent with resonance frequencies observed ex vivo, the rats didn't seem to sample the textures with all of their whiskers, which they might do if their goal was to maximize the information about frequency available from whiskers of different lengths (e.g., the "whiskers as cochlea" picture may need to be tweaked). Indeed, the largest two arcs of whiskers rarely touched the textured surface.

Among other things, their analysis also revealed a unique signature of rough-surface contact: a set of high velocity, large amplitude whisker deflections that were not seen in previous studies. Figure 8 of the paper provides a scatter plot that includes the rise time (roughly, time from trough to peak of a whisker movement) and velocity of whisker movements, and those events that were both high velocity and longer in duration (signifying higher amplitude) were much more likely to occur during contact with the rough surface.

Where are we?
This paper, a heroic effort that has established a great method and some intriguing results, is only the beginning. The whisker coding literature is finally catching up to vision when it comes to understanding the inputs to this system. Many more experiments are needed, not just to examine the role of resonance in transmitting information about the world, but to determine the role of different types of whisking patterns the rat employs as it scurries about.

Apropos of the resonance hypothesis, it would be interesting to see how rats fare when their whiskers are cut so they are all the same length. This should decrease the differences in resonance frequencies in different whiskers. Hence, to the extent that resonance is important for a task, we would expect to see their performance compromised (note, though, things are a little more complicated: resonance frequency depends on other factors than length). It will also be crucial to measure which micro-features of whisker movement are tracked neurally in awake behaving rodents.

This paper has opened up possibilities beyond just the resonance hypothesis. It reveals the slippery, sticky, messiness that is present when rats use their wonderful keratinous appendages to explore their world.


Acknowledgments:: Thanks to Jason Ritt for clarifying an important point about the velocity 'hot spot' mentioned in the ex vivo experiments.

Getting intimate with rat whiskers (1): Ritt et al.

This is the first of a two-part post on the recent Neuron paper Embodied information processing: vibrissa mechanics and texture features shape micromotions in actively sensing rats by Jason Ritt and others in Christopher Moore's group. They provide a much-needed high-resolution look at the the movement of whiskers in freely-moving rats as they perform a discrimination task.

Where's the neuroscience?
Before describing the main results, I'd like to discuss why, as neuroscientists, we should care about what whiskers are doing. "Where is the neuroscience?" someone may ask of a paper that just examines whisker movements. To that I would respond, "What is the stimulus?" The first rule of psychophysics and sensory coding is, "Know thy stimulus" (it was EJ Chichilnisky that hammered this into my mind). Students of psychophysics and sensory coding try to quantify the relationship between the stimulus and some other variable (either behavior (psychophysics) or neuronal activity (sensory coding)), so we need to precisely quantify the stimulus on each trial to make sure we have all the relevant information contained in the stimulus.

Because of such concerns, the question we should be asking is why researchers studying coding in the whisker system know so little about what the whiskers are doing, given the importance of understanding the stimulus in sensory coding and psychophysics. In the present paper, Ritt et al. provide a much-needed corrective to this deficit.

The resonance hypothesis
For a few years now, Moore (and Mitra Hartmann at Northwestern) have been pointing out that whiskers are not simple passive detectors of what goes on in the world. Rather, whiskers have interesting intrinsic properties that shape their responses as the rat scurries about palpating the world.

For example, each whisker has a resonance frequency. If you attach a stimulator to the end of a whisker and move it at frequencies, there is a 'hot spot' at which the whisker will vibrate with a significantly higher amplitude. The following figure (Figure 2 from Niemark et al) shows the amplitude of a whisker's movement as a function of stimulation frequency. The breakaway images show data from individual frequencies (gray line: stimulus, black line: whisker movement downstream from the stimulus):


This whisker in the figure has a resonance frequency just under 400 Hz. The resonance frequency of a whisker depends on that whisker's length (longer whiskers have lower resonance frequencies). Interestingly, the length of whiskers increases quite significantly as you move from the front to the back of a rat's face.

As an interesting historical aside, the possiblity that whiskers have resonance frequencies was initially noticed by Niemark while she was still an undergraduate working with John Hopfield. Then the idea was fleshed out experimentally by Niemark, Moore and Mark Andermann (leading to this paper) and by Mitra Hartmann and others at Cal Tech (leading to this paper). The present paper is the latest in a series of papers from Christopher Moore's group exploring the consequences of whisker resonance.

Getting back to the science, what is the significance of all this resonance business? Is it possible that whiskers with different resonant frequencies are induced to resonate by different types of stimuli? This is part of what has become known as the resonance hypothesis (review here). As described in the original paper by Niemark and others, "vibrissa resonance is optimally positioned to increase the range of detection and the specificity of discrimination, and may provide the ability to represent complex stimuli through a compact, somatotopically distributed code" (p 6500).

Many of us think of the resonance hypothesis as the 'whiskers as cochlea hairs' hypothesis. It has been a quite productive idea for experimentalists, and it is interesting to note that it wasn't even on our radar until Neimark asked a simple question: what are the properties of the sensor used by the rat?

Resonant oscillations have been observed in detached whiskers (image above) and in the whiskers of anesthetized rats. It has also been shown that cortical neurons respond differently when a whisker is stimulated at its resonance frequency (see the above review of the resonance hypothesis). But is whisker resonance ethologically important?

Does resonance really matter? Why it is hard to answer this question
A key question is whether resonance is important in the awake freely moving rat performing a discrimination task. One step toward anwering this question is to determine whether resonance is observed in the whiskers in a particular task. If not, then resonance cannot be used so we'd have evidence that resonance is irrelevant for that task.

So, what's the problem? Measure the whiskers in awake freely moving rats and get on with it. Unfortunately, it turns out to be extremely difficult to track tiny whisker movements in a rat that is running around moving its body, head, and whiskers any old place it wants. You need to get the optics just right to see many of these wispy whiskers in focus, use a high-speed camera (the resonance frequencies can be higher than 500 Hz), and then set up a system to automate the tracking of the whiskers (no way you are going to code all that data by hand with the required large fields of view and fast frame rates). It would be a herculean effort.

Mitra Hartmann, presently at Northwestern, chipped away at this problem a bit. She analyzed some interesting video data from the awake freely moving rat in this paper where whisker movements were sampled between 250 and 1000 Hz. She observed that whiskers often exhibit resonant oscillations after contacting an object, but not when the rat is simply whisking in open air.

But what about when a rat is performing a stimulus discrimination task? Could resonant oscillations actually be used to discriminate the features of an object such as its texture? To get at such questions, Ritt et al have pushed things much further. They have developed algorithms to automatically track the entire length of individual whiskers during a texture discrimination task in freely moving rats. They capture images at the impressive frame rate of 3000 Hz. Here's one example from Figure 3 of their paper:
Here they show the results when a single whisker is tracked (it shows the shape of the whisker over multiple frames into the past in red) as the rat moves its head across a surface that changes from rough to smooth texture (you can think of it as moving from rough to smooth sandpaper). To someone interested in sensory coding and psychophysics in the whisker system, this image is simply a symphony.

So what did they observe? To give away the punchline, it seems resonance is present during the task. But there is enough cool stuff in the paper that I'll put off the discussion of the results and interesting open questions to Part 2.

Acknowledgements Many thanks to Mitra Hartmann and Christopher Moore for explaining some of the history of the resonance hypothesis and for clarification of some key points.

Large-scale thamamocortical model

While the Blue Brain folk want to construct an incredibly detailed model of a single cortical column, a recent paper by Izhikevich and Edelman (Large-scale model of mammalian thalamocortical systems) reports on a less detailed model of the entire human thalamocortical system.

Some of the details of their model (roughly from large-scale to lower scale) include:
1. The cortical sheet's geometry was constructed from human MRI data.
2. Projections among cortical regions were modeled using data from diffusion tensor MRI of the human brain (above image is Figure 1 of the paper showing a subset of such connections).
3. Synaptic connectivity patterns among neurons within and between cortical layers are based on detailed studies of cat visual cortex (and iterated to all of cortex).
4. Individual neurons are not modelled using the relatively computationally intensive Hodgkin-Huxely models, but a species of integrate-and-fire neuron that included a variable threshold, short-term synaptic plasticity, and long term spike-timing dependent plasticity.
5. The only subcortical structure included in the model is the thalamus, but the model does include simple simulated neuromodulatory influences (dopamine, acetylcholine).

Their model exhibited some very interesting behavior. First, larger-scale oscillatory activity that we see in real brains emerged in the model (e.g., as you would observe via EEG). Also like real brains, the model exhibited ongoing spontaneous activity in the absence of inputs (note this only occurred after an initial 'setup' period in which they simulated random synaptic release events: the learning rule seemed to take care of the rest and push the brain into a regime in which it would exhibit spontaneous activity). Quite surprisingly, they also found that when a single spike was removed from a single neuron, the state of the entire brain would diverge compared to when that spike was kept in the model. There is a lot more, so if this sounds interesting check out the paper. They also mention in the paper that they are currently examining how things change when they add sensory inputs to the model.

Of course, a great deal of work is yet to be done, a great deal of thinking through the implications (and biological relevance) of some of the model's behavior (especially its global sensitivity to single spikes, which to me sounds biologically dubious). However, I find it quite amazing that by simply stamping the basic cortical template onto a model of the entire cortical sheet, and adding the rough inter-area connections, they observed many of the qualitative features of actual cortical activity. We tend to focus so much on local synaptic connections in our models of cortex, it is easy to miss the fact that the long-range projections could have similarly drastic influences on the global behavior of the system.

This paper is just fun. First, it is a great example of how to write a modeling paper for nonmathematicians. It had enough detail to give the modeler a sense for what they did, but not so much detail that your average systems neuroscientist would instinctively throw it in the trash (as is the case with too many modelling papers). Second, it provides a beautiful example of how people interested in systems-level phenomena can build biology into their model without making the model so computationally expensive that it would take fifty years to simulate ten milliseconds of cortical activity. It will be very interesting in the future as the hyper-realist Blue Brain style models make contact with these middle-level theories. I don't see conflict, but a future of productive theory co-evolution.

Visualizing the SVD

Warning: this post isn't directly about neuroscience, but a mathematical tool that is used quite a bit by researchers.

One of the most important operations in linear algebra is the singular value decomposition (SVD) of a matrix. Gilbert Strang calls the SVD the climax of his linear algebra course, while Andy Long says, "If you understand SVD, you understand linear algebra!" Indeed, it ties about a dozen central concepts from linear algebra into one elegant theorem.

The SVD has many applications, but the point of this message is to examine the SVD itself, to massage intuitions about what is going on mathematically. To help me build intuitions, I wrote a Matlab function to visualize what is happening in each step of the decomposition (svd_visualize.m, which you can click to download). I have found it quite helpful to play around with the function. It takes in two arguments: a 3x3 matrix (A) and a 3xN 'data' matrix in which each of the N columns is a 'data' point in 3-D space. The function returns the three matrices in the SVD of A, but more importantly it generates four plots to visualize what each factor in the SVD is doing.

To refresh your memory, the SVD of an mxn matrix A is a factorization of A into three matrices, U, S, and V' such that:

A=U*S*V'

where * is matrix multiplication and V' means the transpose of V. Generally, A is an mxn matrix, U is mxm, S is mxn, and V' is nxn.

One cool thing about the SVD is that it breaks up the multiplication of a matrix A and a vector x into three simpler matrix transformations which can be easily visualized. To help with this visualization, the function svd_visualize generates four graphs: the first figure plots the original data and the next three plots show how those data are transformed via sequential multiplication by each of the matrices in the SVD.

In what follows, I explore the four plots using a simple example. The matrix A is a 3x3 rank 2 matrix, and the data is a 'cylinder' of points (a small stack of unit circles each in the X-Y plane at different heights). The first plot of svd_visualize simply shows this data in three-space:



In the above figure, the black lines are the standard basis vectors in which the cylinder is initially represented. The green and red lines are the columns of V, which form an orthogonal basis for the same space (more about this anon).

When the first matrix in the SVD (V') is applied to the data, this serves to rotate the data in three-space so that the data is represented relative to the V-basis. Spelling this out a bit, the columns of V form an orthogonal basis for three-space. Multiplying a vector by V' changes the coordinate system in which that vector is represented. The original data is represented in the standard basis, multiplication by V' produces that same vector represented in the V-basis. For example, if we multiply V1 (the first column of V) by V, this rotates V1 so that V1 is represented as the point [1 0 0]' relative to the V-basis. Application of this rotation matrix V' to the above data cylinder yields the following:


As promised, the data is the exact same as in Figure 1, but our cylinder has been rotated in three-space so that the V-basis vectors lie along the main axes of the plot. The two green vectors are the first two columns of V, which now lie along the two horizontal axes in the figure (for aficianados, they span the row space of A, or the set of all linear combinations of the rows of A). The red vertical line is the third column of V (its span is the null space of A, where the null space of A is the set of all vectors x such that Ax=0). So we see that the V' matrix rotates the data into a coordinate system in which the null space and row space of A can be more readily visualized.

The second step in the SVD is to multiply our rotated data by the 'singular matrix' S, which is mxn (in this case 3x3). S is a "diagonal" matrix that contains nonnegative 'singular values' of A sorted in descending order (technically, the singular values are the square roots of the eigenvalues of A'*A that correspond to its eigenvectors, which are the columns of V). In this case, the singular values are 3 and 1, while the third diagonal elment in S is zero.

What does this mean? Generally, multiplying a vector x=(x1,....xn)' by a diagonal matrix with r nonzero elements on the diagonal s1,....sr simply yields b=(s1*x1, s2*x2, .... sr*xr, 0 .. 0). That is, it stretches or contracts the components of x by the magnitude of the the singular values and zeroes out those elements of x that correspond to the zeros on the diagonal. Note that S*V1 (where V1 is the first column of V) would yield b=(s1, 0 0 0 0 0). That is, it yields a vector whose first entry is s1 and the rest zero. Recall this is because S acts on vectors represented in the V-basis, and in the V-basis, V1 is simply (1,0, ..., 0).

Application of our singular matrix to the above data yields the following:



This 3-D space represents the outputs space (range) of the A transformation. In this case, the range happens to be three-space, but if A had been Tx3, the input data in three-space would be sent to a point in a T-dimensional space. The figure shows the columns of the matrix U (in green and red) are aligned with the main axes: so the transform S returns values that are in the range of A, but represented in the orthogonal basis set in U. The green basis vectors are the first two columns of U (and they span the column space of A), while the red vector is the third column of U (which spans the null space of A').

Since the column space of A (for this example) is two dimensional, any point in 3-D space in the input space (the original data) is constrained to be projected onto a plane in the output space.

Notice that the individual circles that made up the cylinder have all turned into ellipses in the column space of A. This is due to the disproportionate stretching action of the singular values: the stretching is maximum for the vectors in the direction of V1. Also note that in the U-basis, S*V1 lies on the same axis as U1 (U1, in the U-basis, is of course (1, 0, 0)), but s1 units along that axis for reasons discussed in the text after Figure 2.

One way to look at S is that it implements the same linear transformation as the matrix A, but with the inputs and outputs represented in different basis sets. The inputs to S are the data represented in the V-basis, while the outputs from S are the data represented in the U-basis. That makes it clear why we first multiply the data by V': this changes the basis of the input space to that which is appropriate for S. As you might guess, the final matrix, U, simply transforms the output of the S transform from a representation in the U-basis back into the standard basis.

Hence, we shouldn't be surprised that the final step in the SVD is to apply the mxm (in this case, 3x3) matrix U to the transformed data represented in the U-basis. Just like V', U is a rotation matrix: it transforms the data from the U-basis (above picture) back to the standard basis. The standard basis vectors are in black in the above picture, and we can see that the U transformation brings them back into alignment with the main axes of the plot:



Pretty cool. The SVD lets you see, fairly transparently, the underlying transformations implicitly lurking in any matrix. Unlike many other decompositions (such as a diagonalization), it doesn't require A to have any special properties (e.g., A doesn't have to be square, symmetric, have linearly independent columns, etc). Any matrix can be decomposed into a change of basis (rotation by V'), a simple scaling (and "flattening") operation (by the singular matrix S), and a final change of basis (rotation by U).

Postscript: I realize this article uses a bit of technical jargon, so I will post a linear algebra primer someday that explains the terminology. For the aficianados, I have left out some details that would have complicated things and made this post too long. In particular, I focused on how the SVD factors act on "data" vectors, but little on the properties of the SVD itself (e.g., how to compute U, S, and V; comparison to orthogonal diagonalization, and tons of other things).

If you have suggestions for improving svd_visualize, please let me know in the comments or email me (thomson ~at~ neuro [dot] duke -dot- edu).

Sensory processing in mouse motor cortex

Over at Nature's neuroscience group, I wrote up a summary and discussion of the excellent paper Spatiotemporal Dynamics of Cortical Sensorimotor Integration in Behaving Mice by by Ferezou et al.. You can find the original paper here, and my summary is here.

Here is the conclusion paragraph of my summary:

Ferezou et al. showed that subthreshold responses to whisker stimulation can be quite broadly distributed, often extending into M1. This suggests that M1 does not have a purely motor function, but serves also to process sensory information. While M1 projects directly to the brain stem and spinal cord to coordinate motor activity, its tight link with S1 opens up interesting questions about its role in sensory processing and sensorimotor transformations. Also, the sensory response in S1 and M1 depends on the behavioral state of the animal, suggesting that sensory processing isn’t a stationary process, but is sensitive to the context in which a stimulus is delivered. So, when someone asks how a mouse’s cortex would respond to a given stimulus, you probably have to ask, “What is the critter doing?”

Frontiers in Neuroscience

A new neuroscience journal, Frontiers in Neuroscience, recently published its inaugural issue. It has a big-name editorial board including Larry Abbot,Henry Markram, and my postdoctoral advisor Miguel Nicolelis.

They are taking a big risk with this journal, as it flouts the traditional business model of the big journals like Nature (expensive, for profit journals with access only to paid subscribers). Just like its successful cousin, PLOS, Frontiers is open access, authors have copyright control and can distribute the article as they see fit. With these guys, you won't be directed to any annoying web pages asking you to pay $50.00 for an article you need.

What makes the Frontiers journals even more interesting is their novel policy for article reviewers. Reviewers are not anonymous, but rather "the Referee remains anonymous only during the review period. After the review, the screen is lifted and the Referees are disclosed and acknowledged on the published paper." No more annoying reviews by lazy referees who obviously haven't read the paper closely.

Also, if you review a paper that is ultimately accepted for publication you will have the option of writing up "a one-page summary of the paper co-authored by all participating Referees. These commentaries are referenced and citable and are major incentive for Referees because the current trend is for readers to read more meta-papers before going to the deeper original studies."

This is a very interesting experiment in publication practices. On one hand, writers are almost guaranteed to get constructive and helpful criticisms rather than half-thought-out potshots. On the other hand, if you are a small fish reviewing the paper of a "big name" lab, you might be tempted to hold your punches so as not to incur the wrath of someone with a lot of power in your subfield. Also, referees might be tempted to accept publications so they can get their summary published, thereby packing their CV.

Time will tell whether this radical experiment in open access journals has legs. The first issue has some very interesting articles. The first four are:
1.Shaul Druckmann, Yoav Banitt, Albert A. Gidon, Felix Schürmann, Henry Markram and Idan Segev A Novel Multiple Objective Optimization Framework for Constraining Conductance-Based Neuron Models by Experimental Data.
2.Alex Thomson and Christophe M. Lamy Functional maps of neocortical local circuitry.
3.Sidarta Ribeiro, Xinwu Shi, Matthew Engelhard, Yi Zhou, Hao Zhang, Damien Gervasoni, Shih-Chieh Lin, Kazuhiro Wada, Nelson A. Lemo and Miguel A. Nicolelis Novel experience induces persistent sleep-dependent plasticity in the cortex but not in the hippocampus.
4.Nestor Parga and Larry Abbott Network model of spontaneous activity exhibiting synchronous transitions between up and down states.