Equation 1 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle
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Symbol N_conf
onf is part of the quantity the equation computes from the expression on the right.
Symbol nu^L-1
n-1 is one of the signed contributions combined to compute the quantity on the left.
=
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.
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What the article says around this equation
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.
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