two-state trajectory
A two-state trajectory (also termed two-state time trajectory or a trajectory with two states) is a dynamical signal that fluctuates between two distinct values: ON and OFF, open and closed, , etc. Mathematically, the signal has, for every either the value or .
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.
A stochastic two-state trajectory is among the simplest stochastic processes. Extensions include: three-state trajectories, higher discrete state trajectories, and continuous trajectories in any dimension.{{cite book | author= Erhan Cinlar | title=Introduction to Stochastic Processes | publisher=Prentice Hall Inc, New Jersey |year=1975 |isbn=978-0-486-49797-6}}
=Ion channels=
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.
=Enzymes=
Here, there are several possible experiments on the activity of individual enzymes with a two-state signal. For example, one can create substrate that only upon the enzymatic activity shines light when activated (with a laser pulse). So, each time the enzyme acts, we see a burst of photons during the time period that the product molecule is in the laser area.
=Dynamics of biological molecules=
Structural changes of molecules are viewed in various experiments' type. Förster resonance energy transfer is an example.
In many cases one sees a time trajectory that fluctuates among several cleared defined states.
=Quantum dots=
Another system that fluctuates among an on state and an off state is a quantum dot. Here, the fluctuations are since the molecule is either in a state that emits photons or in a dark state that does not emit photons (the dynamics among the states are influenced also from its interactions with the surroundings).