Equation 8 · Part 16 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle

Starting index or lower bound: i

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],

i

What this part means

This label says where the repeated addition, multiplication, or accumulation starts. Read its value or condition together with the article’s description of the index.

Its job in the formula

i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

Full expressionStarting index or lower bound: iArticle 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…

Read this part in the article →

Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

Open the illustrated sums and products: repeat an operation over an index guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.