Functional Symmetry

I am intrigued with conservation and symmetry and general optimization properties as they pertain to biological systems. Well, perhaps simplicity also comes into play, in considerations of general aesthetics.

But there’s something profoundly beautiful about observations of the old biology tenet, “form follows function.” In an investigation of ion channels in biological membranes, particularly of neurons, one often notices a few things. First, a cell’s membrane is rather impermeable to ionic “stuff.” So in order for transport of ions, for instance, across a membrane, there have to be holes in the membrane.

As it turns out, there are many types of holes, including these ion channels, which are often selective for a particular ion. By and large, only that ion can go through its channel, and there are various ways of regulating this. Within the inside of the channels, called the pore (center of figure above), there are at least two factors involved in selectivity of ions – on one hand there is the physical size of the pore, and there is also what’s called a selectivity filter. A selectivity filter is essentially a binding site for the ion that enables it to continue along its pathway from one side of the membrane to the other. (There’s generally some sort of weak hydrogen-type bonding that occurs at that site, I think.)

So consider this – let’s say the ion, say a K⁺, is moving from the inside to the outside of the cell across a membrane. The selectivity would be such that you’d only want K⁺ leaving through the channel and not Ca²⁺ or Na⁺. But in the reverse direction – from out to in – the selectivity ought to be equally efficient.

This implies that the observed transverse symmetry in the protein channel is necessary for the bidirectional selectivity either by size of the ion or using a chemical segment as a filter! Quite fascinating, if you ask me!

“Magnetic Resonance Spectroscopy Identifies Neural Progenitor Cells in the Live Human Brain”

Using widely available techniques, Manganas et al. have been able to characterize a marker to quantify the presence of neural progenitor cells (NPCs) in rodent and human brains, in vivo. They are actually utilizing much of the same technique that takes two distinct functional forms; at the end of the day it’s all nuclear magnetic resonance imaging, but the commonly used NMR in organic chemistry is employed for characterizing chemicals, while the more familiar (to the neurosciences) magnetic resonance imaging (MRI) is utilized for visualization of the brains in vivo. According to Manganas et al., “Our findings thus open the possibility of investigating the role of NPCs and neurogenesis in a wide variety of human brain disorders.”

In regard to the plasticity of adult brains, though known for several years now, it often takes a long time for dogma in sciences to change. It certainly does not occur on the scale of developmental processes, and it’s largely a coping mechanism to compensate for various injuries. However, the evidence for dynamism within the adult brain is clear — it’s actually hard to imagine proper neural function within our daily lives without it, as every new “thing” we learn has got to have a neural correlate.

The article appears in this week’s issue of Science Magazine.

Arbitrary Version Numbering

So with all software, no matter how small, it seems like it’s a good idea to have version numbers. Mine are pretty arbitrary. I try and keep whole numbers as milestones. Like when the code is running in a more or less feature complete form, it’ll be a 1.0. There’s a lot of 1.0s running around.

The primary benefit of this is that, when you look back at your working directory, you’ll be able to have some semblance of the MESS of files that are lying around, all with the same names from copying and modifying files.

Another useful tip is revision numbers in the beginning comments. I can’t understate the importance of this! Otherwise you’ll go nuts later. A simple header like the following is so useful:

function fData = frequency(input1,input2)

% FDATA = FREQUENCY(INPUT1,INPUT2)

% will return the frequency of firing for

% a given input1 and input2 blah blah, etc.

%

% Version 0.9

% Rev. 2007-08-25

Simple and you’ll thank yourself in 6 months when you’re writing your paper and revisiting your code, trying to figure out what on earth you had done!

Another useful tool in determining file differences (UNIX/Linux/Mac folks) is diff. If you have two files for comparison that are the same name (!), then you can use diff to figure out line by line differences. The program is pretty smart and quite simple to use:

diff ~/origdir/frequency.m ~/someotherdir/frequency.m

will give a simple output to the screen with < and > lines marked to note file differences. < means that the line was included in the left file (in origdir) and missing in the right file, and vice versa with >.

Brainbow imaging

Admittedly, molecular biology reads somewhat like the Post-Modern Prometheus, complete with green glowing rabbits and the like. The power to manipulate genetics has been harnessed in many ways in the last couple of decades to give tremendous insight into the complex world of biology. Recently, the Lichtman lab at Harvard University published their results regarding yet another new technology that may just live up to the promise.

The method harnesses a well known Cre/lox strategy of genetic recombination with a clever alteration, which enables the system to naturally create a large variety of permutations that are manifested as distinct fluorescent colors. Thus each cell will express its own color and can be viewed much more distinctly in the absolute mess of cells that constitutes this organ.

Where modern cellular imaging methods, such as fluorescence or electron microscopy, and “ancient” (but still employed) techniques of Golgi silver staining and Nissl staining are often plagued by either problems of sparseness or completeness in their ability to help visualize neurons, by the very nature of this technique, cells can be followed and more or less uniquely identified.

The article can be found in the journal Nature.

Synfire chains, supersynapses, and STDP

An idea proposed in the early 80s called synfire chains proposes that self-assembling networks of neurons can form in which small clusters or groups of neurons communicate with each other, possibly in a sequential linear fashion, more than other neurons. This concept is somewhat interesting if it can play a role in explaining how small networks of neurons spontaneously choose to communicate selectively with each other and possibly form cortical ensembles.

In a paper entitled “Development of Neural Circuitry for Precise Temporal Sequences through Spontaneous Activity, Axon Remodeling, and Synaptic Plasticity” by Jun and Jin, they explore the formation of these synfire chains with a computational model that utilizes leaky integrate and fire neurons along with two activity dependent learning rules. The more well known of these rules is the Hebbian type spike timing dependent plasticity (STDP), a phenomenological model that takes into account the relative timing between pre- and postsynaptic pairs of spikes.

Additionally, employing various thresholds of synaptic potentiation, the second rule they employ caps the number and strength of axonal remodeling — that is to say that when their neurons make strong connections with certain synapses (so-called supersynapses), they prune away other, weaker connections. It is this additional contribution that allows their model to spontaneously exhibit the synfire chain like behavior.

The article appeared in Aug. 2007 online issue of PLoS One, which is a progressive online journal offering free access. You can grab the article at http://www.plosone.org/.

Linux in a production environment

So the tools of the trade include some kind of reasonably modern computing device. I’ve been a Mac OS X user since its inception, after having been a Certifiable Mac Hater for years and years prior to that. To think how adamantly I defended Windows 3.1 and then Win98 back in the day ….

Anyhow, I’ve been a Debian user for a few misguided years of self torture in performing otherwise pedestrian tasks — such was the state of Linux just a few short years ago, especially for PPC architecture. I chose Debian at the time though because of its (arguably) superior package handling system apt-get, which I still use today in the form of Fink and now with Ubuntu.

The beauty of Ubuntu lies in its large user base and support resources. It is the first modern operating system I’ve seen even approach challenging Mac OS X, which continues to be the standard as far as I’m concerned regarding security, interface, and software programming technologies. Anyway, Ubuntu’s user base is large enough on my Intel Mac hardware to have plenty of people interested in solving each and every problem I have encountered. Help has been a quick search away in every instance, with probably 80 – 90% of the functionality of its Mac OS X counterpart.

The benefits above Mac OS X include the speed with which I can write, process, and run MATLAB code, primarily, though MATLAB for Mac Intel is catching up quickly and Terminal.app is going to be THE killer Leopard feature on the front end, at least for me.

Today was my first full day using Ubuntu in my current production environment, and by and large it was seamless, fast, and I didn’t feel like I was missing anything. Quite a long way Linux has come — not bad at all.

General Mechanism for Regulating Current?

Neurons communicate with each other at synapses, and it’s largely a chemical signal, though electrical signals (gap junctions) do exist and are important in their own rite. Now one model of learning and memory involves the dynamic change of these synapses due to activity. These so-called activity-dependent changes — plasticity — require that something physically changes at the synapse. That is to say, somehow, the neurons are communicating more or more effectively.

One way neurons do this post-synaptically is becoming clear. AMPA receptors, the major non-NMDA type of glutamate receptor, have been observed and subsequently modeled to be actively trafficked into and out of the membrane at a synapse. Since these AMPA receptors are also implicated in forms of plasticity such as long term potentiation (LTP), this AMPA receptor trafficking provides at least one piece of the mechanism by which activity dependent changes might occur.

While the details of the AMPA receptor trafficking mechanism become more and more clear, it is interesting to ask whether or not there might be a more generalizable mechanism by which the surface expression of ANY receptors might be similarly regulated. It would make a lot of sense if the method was the same with different details. This idea is kind of extrapolated from the abstract of this article.

Norepinepherine Neuromodulatory System’s Role in Mediating Uncertainty

Peter Dayan of Theoretical Neuroscience fame gave a talk today at Harvard University that I was fortunate enough to attend. One of the great things about Boston/Cambridge area is the sheer pull of our collective universities in bringing top neuroscientists to the area. Anyway, some of his newer work that he was presenting today was entitled, “Norepinepherine and Neural Interrupts.”

There are about four main neuromodulatory systems that each use a particular neurotransmitter as its chemical of action. They seem to have wide ranging connections that span large neural surfaces, and they include dopamine (DA), acetylcholine (ACh), serotonin (5-HT), and norepinepherine (NE). As much as brain chemistry is certainly important, the effects of these particular neuromodulators on the systems that they innervate is incredibly complex, as they make millions of synapses on a what seems to be a wide variety of neurons. Dayan was presenting an interesting viewpoint on the role of NE involved in uncertainty states. The essential idea is that uncertainty must be a top-down mediated process, which starts either with an expectation or no expectation at all. Both of these states are uncertain states, which can be restated as either an expected uncertainty or an unexpected uncertainty. In either case, the brain’s environment must be favorable to a learning condition.

Consider your walk through your school or office. Let’s say that you know that they have been remodeling your wing of the office, so as soon as you turn the last corner, you have an expectation that things will look different. You know already that uncertainty exists. This situation may be neurobiologically different from if you had no idea that they painted the walls pink with green dots, so when you turn the corner, there is (certainly!) an unexpected uncertainty.

Presumably, ACh mediates the former – that is, the expected uncertainty, where NE may modulate the unexpected uncertainty. The experimental evidence seems to come primary from non-human primate studies that measure levels of NE modulation during a target-response visual task that shows a spike in NE pathway activation after the salient target is presented, and no change from baseline levels of activation with the presence of a distractor.

Dayan’s model was a simple state dependent modulation between either the target and distractor that included probabilities of NE activation due to being presented with the two stimuli. He had a pretty simple error predictor that was pointed out did not account for motor type errors, which presumably should be averaged and removed across task difficulty – that is, as task difficulty increases, the number of motor specific mistakes may stay relatively constant. I think this is a reasonable assumption for present purposes.

However good the model was at reproducing the qualitative features of the experimental evidence – and it was, more or less – it was very difficult not to call into question several possible shortcomings. The model set an arbitrary threshold for activation, at 95% probability required for activation, but there did not seem to be any physiological reason for such a threshold. There were also some unexplained qualitative microfeatures of the model’s output that also seemed curious. Additionally, the model included some features such as the random resetting after a certain number of trials that did not seem to have an immediate physiological basis, though I may well just not understand the particulars of the system.

For being a model that simply takes into account the states of NE pathway activation based on the evidence of target presentation, there seemed to emerge some interesting features. However, I think that the next step might be to suggest a mechanism by which this system is acting.

To address this particular question, Dayan suggested a top-down neural interrupt hypothesis presumably governed by the prefrontal cortex and the anterior cingulate cortex. Thus control over the NE neuromodulatory pathway via locus coeruleus may have the ability to globally set the system up for learning in the cases of unexpected uncertainty.

Clearly, many questions remain concerning this proposal, especially considering the lack of a biophysical mechanism, as well as the basic understanding of cortical specificity.

However the idea is certainly interesting nonetheless, in the sense that yet another neuromodulatory system may have a tangible role in a complex behavior such as uncertainty mediation.

A slightly more complex knot problem (for advanced boy scouts)

I heard a pretty great talk today by Jennifer Mann from Baylor College of Medicine. Her talk was on a natural phenomenon of the long DNA strands called knotting. It is well known that DNA must be compacted in order to avoid taking up an unreasonable amount of space within the nucleus of a cell. However one can envision that this compaction process is not without its intricacies.

Imagine taking a long string of some sort, not unlike your headphone cord. When you hastily throw your headphones into your pocket, there’s a good chance that when you pull them out later on, they are in a headache of a knot. It’s somewhat of a mystery how the cord ended up in such a tangled configuration, and every once in awhile, this happens in the compacting process of DNA, which is a long strand of nucleic acids strung together that eventually give rise to the amino acids that make proteins, which are largely the stuff of life. (Forgive my really rudimentary biological descriptions.)

Several interesting properties arise, and one can describe the topology of the resultant knots, if they do form, within the DNA, as pictured here. Though there are an infinite number of minor changes within a given conformational structure, the topology can still be quite similar and thus create tractable problems. This was termed “knot invariant.”

Well, without getting into what amounted to some heavy an fanciful biology, one can imagine a multitude of ways to untangle the knot of DNA, which is quite a problem for a cell to undertake naturally. Essentially, Mann was providing evidence that the cell’s mechanism to untangle the DNA knot was via the easiest (read: lowest energy) change that would then allow the entire molecule to relax.

The computational approaches that such a system presents are vast. For one, there is undoubtedly a conformational strain on the natural configuration of the twisted, knotted DNA strand, and those changes are likely to have some energy stored in them, not unlike a spring, that is eager to be released into a lower energy “rest” configuration.

From a dynamical systems perspective there might be many such stable states of relaxation, and small perturbations from the knotted conformation (i.e. untangling) might allow one to predict – based on optimized bond length and energy parameters – to what stable fixed point the molecule might end up.

Among the several other interesting questions that exist, minimization of energy is among my favorite. But from a biological point of view, it would be nice to be able to selectively target a site at which just one small change (a cut in the loop, twist, and rejoin) can greatly reduce or eliminate the knotting.

For more information, see Z. Liu, J. Mann, E. Zechiedrich, and H. Chan. Topological Information Embodied in Local Juxtaposition Geometry Provides a Statistical Mechanical Basis for Unknotting by Type-2 DNA Topoisomerases. J Mol Biol, 2006.

Convergence of reality

While I think there are several good points floating around concerning the unique roles of science v. other explorations of truth, I am all but convinced that there has got to be a continuity that demands that they are consistent. Essentially, I am not saying that God cannot break the physical law in which we live; rather I tend to believe that God would not choose to. (I tend to think God has the choices that we think we have – there’s another whole volume of discussion, I am afraid.)

I have no basis for believing this except that, like Nathan mentioned, I favor consistency (and symmetry and simplicity, in case you’re curious) and believe consistency to be one of the tenets by which the natural world in which we live operates.

So coming from a physics background, we talk a lot about grand unified (physical) theories. If Lincoln is correct in there being multiple authorities, what happens at their interface?

And I have yet to see overwhelming inconsistencies ……. (please note that I am as wary of saying that as you are reading it)

At the end of the day, there’s more than a non-zero probability that exists that we’re all wrong, anyhow. Fun conversation.