The self-consistent mean field (SCMF) method is an adaptation of mean field theory used in protein structure prediction to determine the optimal amino acid side chain packing given a fixed protein backbone[1]. It is faster but less accurate than dead-end elimination and is generally used in situations where the protein of interest is too large for the problem to be tractable by DEE[2].
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General principles
Like dead-end elimination, the SCMF method explores conformational space by discretizing the dihedral angles of each side chain into a set of rotamers for each position in the protein sequence. The method iteratively develops a probabilistic description of the relative population of each possible rotamer at each position, and the probability of a given structure is defined as a function of the probabilities of its individual rotamer components.
The basic requirements for an effective SCMF implementation are:
- A well-defined finite set of discrete independent variables
- A precomputed numerical value (considered the "energy") associated with each element in the set of variables, and associated with each binary element pair
- An initial probability distribution describing the starting population of each individual rotamer
- A way of updating rotamer energies and probabilities as a function of the mean-field energy
The process is generally initialized with a uniform probability distribution over the rotamers — that is, if there are
Mean-field energies
The energy of an individual rotamer
These mean-field energies are used to update the probabilities through the Boltzmann law:
where
Energy of the system
Although computing the system energy is not required in carrying out the SCMF method, it is useful to know the overall energies of the converged results. The system energy
where the addends are defined as:
Convergence
Perfect convergence for the SCMF method would result in a probability of 1 for exactly one rotamer at each position
Accuracy
Unlike dead-end elimination, SCMF is not guaranteed to converge on the optimal solution. However, it is deterministic (as in, it will converge to the same solution every time given the same initial conditions), unlike alternatives that rely on Monte Carlo analysis. By comparison to DEE, which is guaranteed to find the optimal solution, SCMF is faster but less accurate overall; it is significantly better at identifying correct side chain conformations in the protein's core than it is on identifying correct surface conformations[3]. Geometric packing constraints are less restrictive on the surface and thus provide fewer boundaries to the conformational search.