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As we suggested in Robotic Motion Planning and Protein Motion , the main difference between modeling a macroscopic robot arm and a protein chain is that the protein is subject to forces resulting from differences in free energy between its states. The protein's conformation space does not consist only of colliding and non-colliding structures, but of structures on a continuum of free energy values. In this module, we will provide a very brief overview of free energy as it relates to protein structures, and then give some examples of how path planning techniques have been applied to solving problems in structural biology.
In other modules, we have introduced the concept of a
native conformation for any given protein, that is, the conformation of the protein that is observed, or expected to be observed, under physiological conditions of temperature, pH, and ion balance. What distinguishes this structure from other structures is that it has the minimum
free energy of all accessible conformations. There are several different definitions of free energy depending on how the system is defined (for example, whether it is allowed to change in temperature, volume, and/or pressure). One common definition, applicable when temperature and volume are constant, is the Helmholtz Free Energy:
In practice, because entropy is very difficult to approximate computationally, potential energy is often used instead of free energy in molecular simulations and docking procedures. When the process is driven by potential energy, this is a reasonable approximation. Some processes are entropically driven, and results are usually poor when trying to model these processes using only potential energy.
Potential functions are functions used to evaluate the feasibility of a particular structure of a molecule. Ideally, this would be done with quantum mechanics, in which case the energy function could report the true energy of a particular structure. In practice, quantum mechanical analysis of molecules the size of proteins is wildly intractable. As a compromise, biophysicists have developed artificial functions based on classical physics to approximate the true energy of molecular systems. Sometimes called potential functions or molecular force fields , these functions generally accept as input a molecular conformation, in the form of Cartesian coordinates for all atoms, and output an energy value. These energy values are generally only meaningful in relative terms: They provide information on what conformations of the molecule are more or less probable than others. The lower the energy value, then the more likely the conformation is to be observed. Most molecular potential functions have the form:
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