The rate of chemical reactions increases with temperature. This is described by the Arrhenius relationship, which can be written in the form:
where 
and 
are the absolute temperatures
corresponding to reaction
velocities 
and 
, R is the gas constant, and 
is the
critical thermal increment: a constant characterising the particular
reaction. When this relationship holds, a more friendly measure can be
calculated: 
,
where 
is the rate at temperature t, and 
is the rate at
C
higher. So 
simply tells us by what factor a rate increases for a
C rise in temperature.
In biochemical processes, often composed of a complex pathway of many
intermediate reactions, is only a constant over a limited temperature
range, which might be smaller than that of the phenomenon under study. A
change in temperature can change which of the steps in the pathway is the
rate-limiting one, resulting in a sharp change in (and ) at
particular temperatures. In practice, the interaction of several potentially
rate-limiting processes (physical as well as chemical) can lead to gradual,
rather than sharp, changes in and with temperature. Even for a
single biochemical reaction, the rate increase with temperature
falls off as temperature increases,
presumably because of the destruction of enzymes on which they depend
[5]. Nevertheless, the Arrhenius relationship holds for many
biological phenomena under temperature ranges of interest, and is even
reflected in behaviours such as the rate of creeping of ants, the
chirping of crickets, the flashing of fireflies, the beating of cilia, and
some respiratory and cardiac rhythms. `The slope of the linear relationship
between the log of the rate of most biological reactions and the reciprocal of
absolute temperature is the Arrhenius divided by approximately 4.6,
with defined by the limiting step.' [6, Chap. 37,]. For
thermochemical (enzymatic) reactions, in typically somewhere
between 2 and 3 : they often go about
twice as fast for every C rise in temperature.
The temperature dependencies of neural systems also arise from
physical, as well as chemical, origins; in semiconductors the processes are
entirely physical. In general, the values associated with physical
processes (such as for diffusion or conductivity), and also of
those associated with
photochemical reactions, are less than 1.5. The operation of both neurons and
semiconductor devices is to a large extent based upon the movement of
charge-carriers in an electric field (at a speed proportional to their
mobility) and the interplay between this and the diffusion of those particles
(at a speed proportional to their diffusion constant) in the
concentration-gradient which is influenced by that movement. In neurons and
semiconductors, the charge-carriers are different, and the processes
establishing electric fields and concentration gradients are different, but
the link between diffusion and the electric field is fundamental to both.
The Einstein relationship is crucial to this link: the diffusion constant is proportional to the mobility multiplied by the absolute temperature, so temperature appears in many of the fundamental equations of neurons and semiconductors (eg. the Nernst equation for equilibrium potentials at neuron membranes, and -- via the Boltzmann distribution -- basic equations in semiconductor physics) [7, 8]. The rest of this section will now give some examples of how these temperature dependencies are manifested in neural and electronic systems.
The refractory period for nerve impulses increases for lower temperatures
[5]. Mammals (which have nerves capable of propagating impulses at
speeds ranging all the way from 
to 
) have a
for the speed of nerve impulse propagation of around 1.7, with a lower bound
of 
C
below which propagation ceases. In fact, the is higher at low
temperatures: at high temperatures cell-membrane permeability changes become
so fast that discharging of the cell membrane capacitance by fully activated
permeability mechanisms begins to be rate-limiting. Conduction velocity in
cold-blooded animals is less temperature-sensitive than in mammals. Conduction
velocity can also change with acclimation
and seasons
[7, Chap. 4,] -- see the next section.
As well as affecting the rate of action potential propagation, temperature influences the rate of neuron firing: `The changes of action potential frequencies with temperature are associated, although not in a simple manner, with changes in resting potentials. Cooling reduces the resting potential (depolarization) and this leads to a rise in action potential frequencies; but certain nerve cells show a frequency increase when temperature is raised.' [9]
A similarly changeable situation prevails in VLSI chips such as the FPGAs used
in evolutionary electronics. These devices are made in complementary
metal-oxide semiconductor (CMOS) technology, where the rate-limiting factor is
the time taken for a field-effect transistor's `ON' resistance to charge or
discharge the gate capacitances of the transistors connected to it and
the parasitic capacitance of the interconnections. The overall outcome is that
delays increase by about 0.3% per 
C,
which translates to a of
1.03. This sounds very good compared to the biological case, until we remember
that electronic circuits are commonly expected to work with no
observable change in performance over a very wide range of ambient
temperatures -- typically 
C
to 
C or even 
C.
Clearly, both biological evolution and evolutionary electronics has a challenging task in producing systems with adequate thermal stability. How does nature do it? The rest of the paper addresses this question, attempting to apply the findings to evolutionary electronics along the way, before finally commenting on the implications for ALife modelling studies. There are two complementary possibilities: the first is to produce a system that works even when the temperature changes, which I will call compensation. The second is to produce a system that regulates its internal temperature to be within limits it can cope with. Many animals do both.
