Two-state trajectory

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Figure 1: Two-state trajectories

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.[1]

Two state trajectories in biophysics, and related fields[edit]

Two state trajectories are very common. 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.[22][23][24][25][26][27][28][29][30][31][32] We explain about various relevant systems in what follows.

Ion channels[edit]

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[edit]

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[edit]

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[edit]

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).

See also[edit]

References[edit]

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