Equation 8 · Part 4 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle

Symbol Z

P(a_1,\ldots,a_L) = \frac{1}{Z}\exp\!\left[\sum_{i} h_i(a_i) + \sum_{i<j} e_{ij}(a_i,a_j)\right],

Z

What this part means

Z occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Its job in the formula

Z occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionSymbol ZArticle meaning

The passage around this formula

The fix is to fit a global model that explains the observed column statistics with the smallest number of direct couplings. In the maximum-entropy formulation used in this literature, the probability of a full sequence takes a Potts form, $P(a_1,\ldots,a_L) = \frac{1}{Z}\exp\!\left[\sum_{i} h_i(a_i) + \sum_{i<j} e_{ij}(a_i,a_j)\right]$ . with single-site fields $h_i$ and pair couplings $e_{ij}$ fitted so that the model reproduces the single-column and pairwise frequencies of the alignment. Marks and colleagues reported that the strength of the inferred couplings is a strong predictor of residue proximity in the folded structure, and that the top-scoring couplings are accurate and well-distributed enough to define a three-dimensional fold [ 5 ] . Morcos and colleagues…

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