Two-state trajectory

In most applications, the signal is stochastic; nevertheless, it can have deterministic ON-OFF components.

A completely deterministic two-state trajectory is a square wave.

There are many ways one can create a two-state signal, e.g. flipping a coin repeatedly.

Here, we focus on relevant trajectories in scientific experiments: these are seen in measurements in chemistry, physics, and the biophysics of individual molecules[2][3] (e.g. measurements of protein dynamics and DNA and RNA dynamics,[4][5][6][7][8] activity of ion channels,[9][10] enzyme activity,[11][12][13][14][15] quantum dots[16][17][18][19][20][21]).

From these experiments, one aims at finding the correct model explaining the measured process.

Since the ion channel is either opened or closed, when recording the number of ions that go through the channel when time elapses, observed is a two-state trajectory of the current versus time.

Here, there are several possible experiments on the activity of individual enzymes with a two-state signal.

In many cases one sees a time trajectory that fluctuates among several cleared defined states.