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Published equation contexts

RMSD=1N∑i=1N∥xi−x^i∥2\text{RMSD} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \lVert x_i - \hat{x}_i \rVert^2}

Why this formula appears here

AlphaFold2 was assessed in CASP14, the blind, independently organized structure-prediction assessment in which competing methods predict structures for proteins whose experimentally solved coordinates are not yet public, and are scored by assessors with no stake in any team’s outcome. Against that standard, AlphaFold2’s median backbone accuracy was 0.96 angstroms of Cα root-mean-square deviation from the experimental structure, against 2.8 angstroms for the next-best method, and its median all-atom accuracy was 1.5 angstroms against 3.5 angstroms for the next-best method [ 9 ] . What that root-mean-square-deviation figure actually measures is worth stating explicitly, because the number is…

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ii

Symbol i

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

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xix_i

Symbol x_i

the coordinate of atom i in the experimentally solved structure, x^i\hat{x}_i is the corresponding coordinate in the predicted structure after optimal superposition of the two.

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x^i\hat{x}_i

Symbol hatx_i

the corresponding coordinate in the predicted structure after optimal superposition of the two.

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i=1i=1

Starting index or lower bound: i=1

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.

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NN

Ending index or upper bound: N

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

A symbol can carry a different meaning in another article. Each occurrence keeps its own guide and term definitions.

RMSD=1N∑i=1N∥xi−x^i∥2\text{RMSD} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \lVert x_i - \hat{x}_i \rVert^2}

Equation 5 · AI for Science

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

AlphaFold2 was assessed in CASP14, the blind, independently organized structure-prediction assessment in which competing methods predict structures for proteins whose experimentally solved coordinates are not yet public, and are scored by assessors with no stake in any team’s outcome. Against that standard, AlphaFold2’s median backbone accuracy was 0.96 angstroms of Cα root-mean-square deviation from the experimental structure, against 2.8 angstroms for the next-best method, and its median all-atom accuracy was 1.5 angstroms against 3.5 angstroms for the next-best method [ 9 ] . What that root-mean-square-deviation figure actually measures is worth stating explicitly, because the number is…

Meanings in this article

  • NN: the number of atoms compared.
  • xix_i: the coordinate of atom i in the experimentally solved structure, x^i\hat{x}_i is the corresponding coordinate in the predicted structure after optimal superposition of the two.
  • x^i\hat{x}_i: the corresponding coordinate in the predicted structure after optimal superposition of the two.
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