Phase oscillators

What is a biological clock?

Certain cells in our body acts as simple oscillators, setting important rhythms for the rest of the body. Of these, some of the most important are in brain, controlling heart beat, breathing and the most well-known biological oscillation of all: the circadian rhythm. Since the behaviour of these cells is repetitive, we can treat it is a biological clock. The phase of an oscillation tells us how far along it we are.

How can we change the time?

Left to their own device, the biological clocks will simply follow their usual rhythms. However, if external factors are present, they can speed up or slow down their usual rhythms, thus changing the cell's 'time'.

How can we quantify the change?

Suppose we have a clock which is very sensitive to being shaken. When you shake the clock, the time changes. Shaking the clock at certain times (or phases) advances the minute hand, shaking it at different times (phases) will move the minute hand back. We can clearly measure how far the minute hand has moved each time we shake the clock. How it moves dependent on what time (phase) you shake it is known as the phase response. Biological clocks behave in similar ways, except the shaking arises due to interactions with other cells.

Why is this important?

Once we know how external factors affect the timing of events in certain cells, we can understand how groups of cells interact with each other to provide clear responses. An important phenomenon is synchronisation, in which cells start behaving in an identical fashion. Synchronisation is observed in many parts of nature, from the cellular level to entire organisms. One of the most striking eexamples of which can be seen in fireflies.

Male fireflies illuminate themselves at night to attract mates. On its own, a single firefly cannot generate a powerful enough signal to attract mates. In large populations, however, the signal can be incredibly powerful, strong enough to be seen at great distances and even by the human eye. In order for this signal to be clearest, the fireflies have to synchronise their illumination. Groups of cells in the body take advantage of the same phenomenon. The strongest signals come from synchronised cells. Understanding how specific cells synchronise and desynchronise is key to understanding the origin of biological rhythms.

What are we doing in our research?

Our research is focussed on two key themes. Firstly, to find better ways to construct phase response curves for large external perturbations and secondly to understand how these can be used to understand synchronisation phenomena in a variety of contexts.