A two-state trajectory (also termed two-state time trajectory or a trajectory with two states) is a dynamical signal that fluctuates among two distinct values (ON-OFF, opened-closed, plus-minus, etc). In most applications, the signal is stochastic

Stochastic process

In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...

; nevertheless, it can have deterministic ON-OFF components. A completly deterministic two-state trajectory is a square wave

Square wave

A square wave is a kind of non-sinusoidal waveform, most typically encountered in electronics and signal processing. An ideal square wave alternates regularly and instantaneously between two levels...

.

Two state trajectories in biophysics, and related fields

Two-state time trajectories are very common in measurements in chemistry, physics, and the biophysics of individual molecules  (e.g. measurements of protein dynamics and DNA and RNA dynamics

Force spectroscopy

Force spectroscopy is a dynamic analytical technique that allows the study of the mechanical properties of single polymer molecules or proteins, or individual chemical bonds. It is performed by pulling on the system under scrutiny with controlled forces...

, activity of ion channel

Ion channel

Ion channels are pore-forming proteins that help establish and control the small voltage gradient across the plasma membrane of cells by allowing the flow of ions down their electrochemical gradient. They are present in the membranes that surround all biological cells...

s, enzyme activity

Enzyme

Enzymes are proteins that catalyze chemical reactions. In enzymatic reactions, the molecules at the beginning of the process, called substrates, are converted into different molecules, called products. Almost all chemical reactions in a biological cell need enzymes in order to occur at rates...

, quantum dot

Quantum dot

A quantum dot is a portion of matter whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules. They were discovered at the beginning of the 1980s by Alexei...

s ) From these experiments, one aims at finding the correct model. Examples for such experiments are listed in what follows.

Ion channels

Since the ion channel

Ion channel

Ion channels are pore-forming proteins that help establish and control the small voltage gradient across the plasma membrane of cells by allowing the flow of ions down their electrochemical gradient. They are present in the membranes that surround all biological cells...

 is either opened or closed, when recording the number of ions that go through the channel when time elapses, one sees 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 bursts of photons that last for the time period 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 define

Quantum dots

Another system that fluctuates among an on state and an off state is a quantum dot

Quantum dot

A quantum dot is a portion of matter whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules. They were discovered at the beginning of the 1980s by Alexei...

. Here, the fluctuations tell the story of a special state of the molecule that is influenced also from its interactions with the surroundings.

See also

• Single-molecule experiment
• Reduced dimensions form
  Reduced dimensions form
  In biophysics and related fields, reduced dimension forms are unique on-off mechanisms for random walks that generate two-state trajectories...
  
  
• Kinetic scheme
  Kinetic scheme
  In physics and chemistry and related fields, a kinetic scheme is a network of states and connections among the states representing the scheme of a dynamical process. Usually, a kinetic scheme represents a Markovian process, where when the process is not Markovian, the scheme is a generalized...
  
  
• Master equation
  Master equation
  In physics and chemistry and related fields, master equations are used to describe the time-evolution of a system that can be modelled as being in exactly one of countable number of states at any given time, and where switching between states is treated probabilistically...
  
  
• Wave
  Wave
  In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...