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Equation 1 · Part 3 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle

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

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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: 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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the article section

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