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Compensation in Behavioural Timescales

Numerous circadian (daily) rhythms have been documented in a wide range of behavioural and physiological variables.gif For example, they play a role in thermal regulation, sleep, feeding and drinking behaviours, and endocrine, renal and reproductive function. In some cases the rhythm needs to be equivalent to an internal clock of considerable precision, for example it is widely believed that migratory birds use such a clock to correct for the sun's movement across the sky to allow it to be used as a compass. Rhythms on shorter timescales (eg. cardiac and respiratory patterns) and on the longer timescales of seasons and years are also important.

Some biological rhythms are directly derived from environmental cues, but others result from some sort of `endogenous' oscillator in the animal. Such oscillators are capable of free-running in the absence of environmental cues but can also be entrained by multiple `timegivers'gif in the environment such as light-dark cycles, food-availability cycles, temperature cycles, and social and acoustic cues. `Entrainment' means a gradual and ongoing resynchronisation to the environmental timegiver (rather than a sudden resetting). Ongoing interaction with timegivers can result in a different period of oscillation than the free-running period would be in the absence of cues. It has been shown that, apart from entrainment, circadian rhythms are not learnt phenomena, but are genetically specified.

In studies of the circadian rhythms of plants and insects, the tex2html_wrap_inline513 of the free-running period's alteration with temperature has been found to be typically in the range 0.85-1.3, where something in the range 2-3 would be expected from consideration of the Arrhenius equation (see also [11, pp23-27,]). This is in the absence of environmental timegivers, and appears to be the result of active compensation, rather than some inherent insensitivity in the mechanism. There is some evidence that the temperature compensating mechanism may not be an inherent feature of the oscillatory mechanism: certain Neurospora mutants lack temperature compensation in a particular circadian rhythm that is otherwise normal [12].

How can such compensation be achieved? If the oscillation arises from the interaction of two or more processes, each of which is affected by temperature, then the interactions can be arranged so as to give an overall stability in period. For example, the period might depend on the products of a biochemical reaction which increases in rate with temperature; there could be a second reaction which inhibits the first one, and which also increases in rate with temperature. Another possibility is to take the net effect of processes having reciprocal temperature coefficients: this could even be applied to the mutual entrainment of multiple oscillators [13]. Note that even one-celled animals have temperature-independent endogenous rhythms (ibid.). Some progress has been made towards postulating neural bases for circadian rhythms, but this is still far from understood [12].

In an fascinating duality with the solar navigation of birds mentioned above, a prize of £20000 was offered in 1714 for the maker of a time-piece sufficiently accurate to enable longitude to be ascertained at sea. One of the problems was the variation with temperature of the lengths of pendulums and of balance-springs [14]. The solution was to use the net effect of two different metals having different thermal properties: this fits into the general scheme above. Presumably compensation schemes of an analogous nature can be built into electronics, or could arise through evolution given appropriate primitives and a selection pressure.

In evolutionary electronics, the thermal stability of internal timescales could also be achieved through interaction with external timegivers, as in entrainment. For example, if the 1kHz/10kHz discriminator is given a sequence of inputs consisting of both frequencies, then it is constantly being `reminded' of what the two periods are: the inputs are themselves timegivers. The circuit need only say whether the current input corresponds to the higher or lower of the two frequencies it has received in the past. One way of doing this would be to use endogenous entrained oscillators, but other mechanisms are possible.

In applications where the inputs do not implicitly contain appropriate time cues, they could be augmented by an extra input which does. For example, an extra input could be driven by an external crystal oscillator (cheap, accurate, and temperature stable). This is superficially similar to the `clock' used by digital designers to globally synchronise their circuits, with the subcircuits changing in lock-step on the beating of the clock. However, there is a fundamental difference: now the external oscillator is truly a timegiver, to be exploited by evolution in any way, and is not an enforced constraint on the system's dynamical behaviour. Evolution could totally ignore the clock input if it chose, or it could be used as a subtle influence on the circuit's dynamics. In this way, evolution remains free to explore rich architectures and dynamics beyond the scope of human design, but has appropriate resources to evolve thermal stability if there is a selection pressure for it.

I have suggested two mechanisms here (compensation and interaction with external timegivers) which could allow the evolution of temperature-stable circuits. In each case, though, there needs to be a selection pressure for evolution to favour temperature-stability. I propose to arrange for this by evaluating each individual circuit on several different FPGA chips in parallel, each being held at a different temperature (using Peltier-effect heat-pumps -- see §5.1.2 -- and hand-designed thermostatic control). An individual's fitness score will then reflect its ability to perform the desired behaviour in all of these different conditions.


next up previous
Next: Thermal Regulation Up: Temperature Compensation Previous: Cellular and Biochemical Compensation

Adrian Thompson
Thu Oct 2 14:31:53 BST 1997