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Published equation contexts

Nconf=ν L−1N_{\mathrm{conf}} = \nu^{\,L-1}

Why this formula appears here

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: Nconf=ν L−1N_{\mathrm{conf}} = \nu^{\,L-1}. Take a modest three states per residue and a hundred-residue chain. The arithmetic gives 3^{100} ≈\approx 5.2 ×\times 10^{47} configurations; sampling one every 10^{-13} seconds would take about 5 ×\times 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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NconfN_{\mathrm{conf}}

Symbol N_conf

NcN_conf is part of the quantity the equation computes from the expression on the right.

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ν L−1\nu^{\,L-1}

Symbol nu^L-1

nuLu^L-1 is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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Nconf=ν L−1.N_{\mathrm{conf}} = \nu^{\,L-1}.

Equation 1 · Structural Biology

Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle

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

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: Nconf=ν L−1N_{\mathrm{conf}} = \nu^{\,L-1}. Take a modest three states per residue and a hundred-residue chain. The arithmetic gives 3^{100} ≈\approx 5.2 ×\times 10^{47} configurations; sampling one every 10^{-13} seconds would take about 5 ×\times 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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