Editing Protein design (section)

====Belief propagation====

In [[belief propagation]] for protein design, the algorithm exchanges messages that describe the ''belief'' that each residue has about the probability of each rotamer in neighboring residues. The algorithm updates messages on every iteration and iterates until convergence or until a fixed number of iterations. Convergence is not guaranteed in protein design. The message <var>m</var><sub><var>i&rarr; j</var></sub><var>(r<sub>j</sub></var> that a residue <var>i</var> sends to every rotamer <var>(r<sub>j</sub></var> at neighboring residue <var>j</var> is defined as:

: <math>m_{i\to j}(r_j) = \max_{r_i} \Big(e^{\frac{-E_i(r_i)-E_{ij}(r_i,r_j)}{T}}\Big) \prod_{k \in N(i)\backslash j} m_{k\to i (r_i)}</math>

Both max-product and sum-product belief propagation have been used to optimize protein design.