Equation 5 · Comparing the Main Approaches to AI for Science and Medicine
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol i
i appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.
Symbol x_i
the coordinate of atom i in the experimentally solved structure, is the corresponding coordinate in the predicted structure after optimal superposition of the two.
Symbol hatx_i
the corresponding coordinate in the predicted structure after optimal superposition of the two.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subtraction
Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.
subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
See an illustrated explanation →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.
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.
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.
What the article says around this equation
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…
Read the full surrounding passage
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 often quoted without the definition it depends on: . where is the coordinate of atom i in the experimentally solved structure, is the corresponding coordinate in the predicted structure after optimal superposition of the two, and N is the number of atoms compared. This is a statement about the average positional deviation of one predicted, static conformation from one experimentally solved, static conformation. It is not, by construction, a statement about how the molecule moves, how quickly it interconverts between conformations, or what its folding pathway looks like — and that distinction is the entire content of what comes next.
Sources cited in the surrounding passage
These citations give research context. Read each source to check which claims it supports.
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