Wednesday, 20 January 2016

Thoughts on William Bialek's "Perspectives on theory

In modelling almost anything in biology the complexity of the process leads almost inevitably to an explosion of free parameters whose tuning may give very different results.While this is often explained away as inevitable due to the rich diversity of the natural world, for a physicist there is something unsettling about a profusion of parameters, coupled with a hope that they could be obtained instead by resorting to some underlying principle. The question is: what principle (or principles) might be at work here? A recent post on the arXiV by Professor William Bialek at Princeton and CUNY summarises a discussion on this topic at the Simons Foundation 2014 Theory in Biology workshop.

The main goal of this paper is to explore possible guiding principles that allow us to recover the correct spot in parameter space, or render precise tuning of parameters unnecessary. A second topic is a pointed but valid critique of how theory (whether implicit or in an explicit mathematical form) is currently considered in the biological community, which I won't discuss here - if you're interested look in sections II - IV and IX of the paper. The three classes of principles explored in the paper are: functional behaviours emerging as 'robust' properties of biological systems without precise tuning (section VI), optimality arguments based on evolution (section VII), and emergent phenomena from large interacting systems (section VIII). In the interests of remaining concise I'll miss out a lot of the interesting examples from the paper and concentrate instead on one or two of the main examples in each section - the paper itself is well worth a look for these alone.

In Section VI the main emphasis is on robust behaviours - properties where entire regions of parameter space will produce similar results. In this case the main example is spike train production in neurons. Varying the copy number of protein channels in neurons produces neurons with qualitatively different spike train characteristics including silence, single, double, and triple spike bursts and rapid repeated spiking. This resolves a continuous parameter space into a set of distinct objects which can be combined to form a functional system; by adjusting the copy numbers of any particular neuron in a network it can be robustly changed from one type to another. This suggests a view of neurons as more like building blocks than objects for individual investigation (although this insight would of course have been impossible without such prior study!), and leads to questions of what can be done with networks of neurons, and what naturally emerges. The ability to maintain a continuum of fixed points is not generic and requires tuning parameters, so how does it emerge? The suggested answer is through feedback, which provides a signal for how well the network is doing, and thus allows for further tuning of parameters towards the desired behaviour, which is illustrated by a surprising and elegant experiment involving confused goldfish!

Section VII broadly discusses biological measurement processes (like vision or chemical sensing) and their nearness to optimality. If operation near biological limits is the rule, then this provides a guide to selection of parameters - choose the parameter set which is as close as the system allows to the physical limits imposed upon it. Again neuronal networks provide a good example here, for instance the ability of flies to avoid being swatted. The combination of their fast movement speed and low-resolution eyes leads to a requirement for the fly brain to carry out near-exact motion estimation. This is a nice idea - it arises from a clear biological principle but can be formalised precisely in terms of information-theoretic concepts. It also ties in nicely to the principle in the previous section; information generates feedback, which helps with the precise tuning of a system to achieve the desired effect. From a thermodynamic perspective, however, more accurate measurement can often be carried out at an increasing energy cost (for example the Berg and Purcell work on cellular sensing). This implies a tradeoff: the organism can balance expenditure with increased information gain and it's not clear where this balance should be set. In non-sensing organs it's not clear what design principles could be at work - although information makes a lot of these ideas easy to quantify, it also limits their range of application.

Section VIII talks mainly about statistical physics-type models involving emergent behaviour from a large number of relatively simple agents. The main example here is the highly successful model of flocking in birds. This was revolutionised by the ability to take large-scale measurements of many (>1,000) individual birds simultaneously, which was used to build a maximum entropy flocking model. Local interactions are present, however long-range correlations emerge in the flock through Goldstone modes (in the case of direction) and tuning to a critical point in velocity. Further experiments show that criticality, rather than symmetry breaking, is the most common mechanism for the emergence of long-range correlations.

Although Section VIII is claimed to be a separate guiding principle earlier in the paper, the re-emergence of criticality as a central player suggests that really this is more an exploration of the consequences of the principle discussed in Section VII. Because of this it seems that there's really one principle at work here - emergent behaviour through tuning to criticality where the tuning occurs due to the flow of information in the system, which we expect to be as close to physical limits as possible. This seems like a fruitful avenue for the creation of characteristic models which capture these ideas together while remaining as simple as possible, and I'd be very interested to learn of any such models currently in existence.

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