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Equation 8 · Part 13 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle

addition

P(a1,…,aL)=1Zexp⁡ ⁣[∑ihi(ai)+∑i<jeij(ai,aj)],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],
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

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(a1,…,aL)=1Zexp⁡ ⁣[∑ihi(ai)+∑i<jeij(ai,aj)]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 hih_i and pair couplings eije_{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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Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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