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Equation 1 · Part 5 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle

subscript

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

What this part means

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.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

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