Clas Blomberg - Physics of life-Elsevier Science (2007)

Chapter 26. What does non-linearity do? 271
26A
Non-linearity in cells: oscillations, pulses and waves
Non-linear effects appear at many instances in living organisms, and we here take up some
of the most conspicuous examples, which also are among the most studied ones. As in most
of this book, we focus the discussion on basic properties that are relevant for the organisms.
There is no place here for going further with problems, for instance occurring in ecology or
concerning spreading of diseases. Some important problems concern occurrence of nonuniform
structures, but we will put the main emphasis on special time effects. There, we have
possibilities of generating pulses, or sustained oscillations, and also to provide changing
spatial structures, in particular in the form of waves.
Regular oscillations are important for providing a kind of clock in the cells, to provide a regular
rhythm. Certainly, there are such mechanisms in all cells, and they are also important for
synchronisation of certain reactions. Oscillations and pulses are also important as first steps
in signal generation. Often signals can be provided by the production of certain substances that
are produced by a special reaction, move in the cell and get to some complex where its presence
can give rise to some response, which in this way can be regarded as triggered by the first
reaction. Non-linear signals proceed at longer distances and provide a better ordered process.
The most typical signalling processes, and the most studied ones, concern the nerve signals.
The generation of nerve signals is rather clear. By energy-driven processes ions are transported
against their concentration differences in what is called active transport (also discussed at
other places), non-equilibrium distributions of ions are put up at different sides of a cell
membrane. This provides considerable concentration differences and by that also an appreciable
electric potential over the membrane. (This is also discussed at other places. The voltage
over a membrane of width a few nanometres is about a tenth of a volt, which leads to very
high electric field strengths, of the order of 10 7 V/m.) By a weak leak current through the
membrane and a continuous active transport to keep the ion non-equilibrium concentrations,
this provides a stable, stationary balanced situation. The most relevant, positive ions, sodium,
potassium, calcium can cross the membrane in channels formed by particular protein complexes
through the membranes, what are called ion channels, which are specific for the particular
ions. In the balanced situation, these are almost closed, allowing small ion currents
that retain the stationarity. Then, as a response to some disturbance (and there are many
possibilities for this, ion channels can open, the balance is broken, and there will be considerable
ion currents through the ion channels, which provide slightly different dynamics for
different ions, leading primarily to a pulse (action potential) where the voltage over the
membrane may be reversed for some instant, and then restored. The system can go back to
the original state or the process can be continued by providing regular oscillations. This also
triggers oscillating ion currents along the nerve threads. There is, also for moving charges,
a damping force, but the oscillating or pulsed behaviour can be reset by the ion channels
mechanisms, and provide a stable wave going along the nerve cell. For general accounts of
these questions, see Nicolis and Prigogine (1977), Haken (1983, 1987) and Bar Yam (2003).
We discuss this process in more detail in a later chapter. An interesting signalling process
has been studied for a kind of primitive organisms, certain kinds of what are called slime
molds, Dictyostelium. These are basically unicellular organisms that live on the ground of
forests. If they have organic nutrients available in the vicinity, these organisms live independently
of each other. If, however, there are less nutrient concentrations to be found, the cells