Simulation and analysis of FRET in the study of membrane proteins

Modeling is an essential part of all kinds of scientific studies of real-world objects. Being complex and many-sided, real objects cannot be investigated in all their manifestations; therefore we are forced to limit ourselves to study only a part of their properties. It means that from the very beginning of the study, a researcher builds in his mind a model of the object, which contains only its essential and interesting properties.

A model, associated with the studied object or system, can be a physical prototype (as in the case of physical modeling) or a formal system of concepts and relations (mathematical modeling), describing the object and its behavior with the required level of details.

Mathematical models can be divided into groups, based on the following criteria (Low and Kelton, 2000):

• Method of formal description (one can distinguish analytical and simulation models);
• Usage of time concept (static and dynamic models);
• Presence of stochastic components and relations (deterministic and stochastic models);
• Continuity (continuous and discrete models).
  

If the relations, which form a mathematical model, are rather simple and can be described using mathematical analytical expressions, analytical modeling can be used. The advantages of analytical modeling are its universality (in relation to the tasks of its application) and high precision. Unfortunately, the use of analytical models is not always possible. Systems of high complexity are currently studied in many science disciplines (informatics, electronics, astrophysics, biology, chemistry, economy). These systems contain a significant number of interacting components (which can be systems as well), diversity of interconnections, have a non-linear behavior, and, as a result, they are difficult to describe and predict. Usually an analytical prediction of such a system is concerned with a number of approximations and simplifications, resulting in rather rough estimations.