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Equation 12 · Part 11 · Structure from Sequence: What Protein Folding Prediction Did and Did Not Settle

fraction

p(x)=e−βF(x)∫e−βF(x′) dx′,β=1kBT,p(x) = \frac{e^{-\beta F(x)}}{\displaystyle\int e^{-\beta F(x')}\,dx'}, \qquad \beta = \frac{1}{k_{\mathrm B}T},
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

The passage around this formula

A protein in solution is not a coordinate file. It is a distribution. Under equilibrium conditions the physically meaningful object is a Boltzmann-weighted ensemble over conformations, p(x)=e−βF(x)∫e−βF(x′) dx′,β=1kBTp(x) = \frac{e^{-\beta F(x)}}{\displaystyle\int e^{-\beta F(x')}\,dx'}, \qquad \beta = \frac{1}{k_{\mathrm B}T}. and function frequently depends on the populations and interconversion rates of its modes rather than on the single most populated one. A predicted structure is a point estimate. It carries no populations, no relative free energies, and no exchange kinetics — none of which can be recovered from the file by inspection.

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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