Equation 1 · Part 6 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle
superscript
superscript
What this part means
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.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→Article meaning
The passage around this formula
The standard framing of why search cannot be the mechanism is combinatorial. Treat each residue as having some small number of accessible backbone conformations, and the number of chain configurations is exponential in length: . Take a modest three states per residue and a hundred-residue chain. The arithmetic gives 3^{100} 5.2 10^{47} configurations; sampling one every 10^{-13} seconds would take about 5 10^{34} seconds, on the order of 10^{27} years. Real proteins of that size fold in microseconds to seconds. The gap is not a factor to be tightened by better bookkeeping; it is dozens of orders of magnitude.
Learn the underlying idea
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
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Sources cited in the article section
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