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Tuesday, August 01, 2006
I read this review article by Marder and Goaillard today. It starts off pretending to be a relatively bland discussion of ion channel densities and ends up in some important theoretical territory. The gist of the article is that there is a parameter space underlying neural activity that can vary greatly while preserving cellular and network properites. At the cellular level, multiple configurations of different ion channels (some excitatory, some inhibitory, with varying conductances and activation requirements) are capable of producing almost identical cellular action potential firing (bursting) patterns. This variability in the means for achieving the cellular target activity level can be observed in the Purkinje cells of the cerebellum and other model systems, and long-lasting perturbations of one of the ion channel levels result in compensatory changes in other parameters to return to the activity level. At the network level, multiple configurations of synaptic weights can lead to the same network properties. Synaptic strengths in an oscillatory network of heart interneurons in the leech and in a rhythmic network in the lobster can vary widely (~3-fold) and yet display the same network rhythms. The point is that many means can be used to achieve the same end, and if you block one path the system will just take a detour. This reminded me of Gerald Edelman's discussion of degeneracy in biological systems. He takes the idea that there are several solutions to a given biological problem and runs it up and down the scale. His table is reproduced below the fold:
| | Table 1. Degeneracy at different levels of biological organization |
| | 1. Genetic code (many different nucleotide sequences encode a polypeptide) | | 2. Protein fold (different polypeptides can fold to be structurally and functionally equivalent) | | 3. Units of transcription (degenerate initiation, termination, and splicing sites give rise to functionally equivalent mRNA molecules) | | 4. Genes (functionally equivalent alleles, duplications, paralogs, etc., all exist) | | 5. Gene regulatory sequences (there are degenerate gene elements in promoters, enhancers, silencers, etc.) | | 6. Gene control elements (degenerate sets of transcription factors can generate similar patterns of gene expression) | | 7. Posttranscriptional processing (degenerate mechanisms occur in mRNA processing, translocation, translation, and degradation) | | 8. Protein functions (overlapping binding functions and similar catalytic specificities are seen, and "moonlighting" occurs) | | 9. Metabolism (multiple, parallel biosynthetic and catabolic pathways exist) | | 10. Food sources and end products (an enormous variety of diets are nutritionally equivalent) | | 11. Subcellular localization (degenerate mechanisms transport cell constituents and anchor them to appropriate compartments) | | 12. Subcellular organelles (there is a heterogeneous population of mitochondria, ribosomes, and other organelles in every cell) | | 13. Cells within tissues (no individual differentiated cell is uniquely indispensable) | | 14. Intra- and intercellular signaling (parallel and converging pathways of various hormones, growth factors, second messengers, etc., transmit degenerate signals) | | 15. Pathways of organismal development (development often can occur normally in the absence of usual cells, substrates, or signaling molecules) | | 16. Immune responses (populations of antibodies and other antigen-recognition molecules are degenerate) | | 17. Connectivity in neural networks (there is enormous degeneracy in local circuitry, long-range connections, and neural dynamics) | | 18. Mechanisms of synaptic plasticity (changes in anatomy, presynaptic, or postsynaptic properties, etc., are all degenerate) | | 19. Sensory modalities (information obtained by any one modality often overlaps that obtained by others) | | 20. Body movements (many different patterns of muscle contraction yield equivalent outcomes) | | 21. Behavioral repertoires (many steps in stereotypic feeding, mating, or other social behaviors are either dispensable or substitutable) | | 22. Interanimal communication (there are large and sometimes nearly infinite numbers of ways to transmit the same message, a situation most obvious in language) |
Neuroanatomy is also degenerate, and Edelman is not the only one to have noticed this. The interesting thing about having a degenerate rather than a redundant system is that when the system compenates for a perturbation, it does so imperfectly. You can drive on a spare tire and the network properties of your car seem all the same until you push it too far on speed or grip. This brings us to an important issue for behavioral neuroscience today. The literature is chock-full of lesion studies. The most famous cases in neuroscience, H.M. and Phineas Gage, are both lesion studies. More recently, transgenic mice with this or that gene knocked-out have flooded into the literature. In almost every instance the time following perturbation is more than long enough for compensation to occur. Lesion studies that produce no effect do not mean that the lesioned component isn't involved in a behavior in a normal brain. Perhaps more commonly overlooked is the fact that lesion studies that do produce effects do not necessarily mean that the missing component is involved either. Faulty compensation or overcompensation could lead to deficits that have nothing to do with the perturbation. Potentially poor analogy coming off the top of my head: If all the busboys went on strike, the waitstaff would have to do their job, and I wouldn't get my Dr. Pepper as fast, but this doesn't mean that busboys are usually responsible for bringing me my drinks.
Noppeney, Friston, and Price have suggested a framework for dealing with degeneracy in neuroanatomy, and I won't go all the way into it, but one of the approaches is to stop throwing away intra- and inter- subject variability in fMRI studies. Degeneracy reveals itself in this noise. This same point comes up in the Marder and Goaillard review:
For years, the limitations of their experimental tools have so concerned most reductionist biologists that they have assumed that much variation in measurements from cell to cell, day to day, and animal to animal are an outcome of measurement error, although, of course, we know that individuals differ in almost any property we can describe. Improvements in computational power and imaging methods now offer new ways to look at the complex correlations that will allow us to understand the mechanisms by which compensations in complex networks occur.
Several of these authors agree that degeneracy is generally a good thing because it makes the system robust. For instance, you can't have natural selection without a diverse population to choose from. In another interesting case pointed out by Marder and Goaillard, degeneracy in the network might prevent high network synchrony that could be maladaptive if it leads to epilepsy. One last irresponsible conjecture. When I started thinking about this in terms of evolution I was reminded about gene duplication. I don't know the literature that well, but I know that some believe that after gene duplication the gene is under less pressure to toe the line, so it can start experimenting with new sequences. This is supposed to be a driving force for invention of new protein activities as an enzyme with a particular activity develops a taste for some new substrate. I wonder if the nervous system on a larger scale ever works like that. Is there network duplication followed by release from selection constraint? The energy cost of a network duplication would be much higher than that for a gene duplication, but degeneracy is a big plus. This is easy to imagine for neocortical columns attaining new functions, but I wonder about older brain regions.
So stop throwing away all your variable data, reintepret all your lesion studies, and learn multivariate statistics, you degenerates!
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