...conformation

The ground state of a protein is the minimum energy conformation in which the protein spends the greatest time at equilibrium. The native state is the most occupied conformation on the time scale of the functional life of the protein. If this time is less than that necessary for the protein to reach equilibrium from its denatured state, the native and ground states may differ. However, it is believed in Nature that these two conformations are generally equivalent. Unless otherwise stated, we use the two terms interchangeably.

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...landscape

Our energy landscape schematics may be misleading. Real protein landscapes are 2N-dimensional and contain many features not found in one dimension, such as saddles, moats, cul-de-sacs and other structures not expressible in low dimensions. Especially important is the significantly greater number of ways of getting from one point on the landscape to another. Accordingly, landscape schematics shown here should be thought of as slices through more realistic high-dimensional landscapes.

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...conformations,

When the context is clear, we use the terms protein, sequence, conformation, etc., to refer to their respective biological or lattice counterparts.

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...trained

We refer to the selection of a sequence on its apparent ability to fold to a specified target conformation as training.

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...unknown

Interestingly, the correlation of non-native conformations to the target configuration could be used to provide an estimate of the width of the corresponding funnel.

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...saturation

This assumes that the number of patterns stored does not scale more quickly than N, which we find below is reasonable.

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...potential

Bringing the 193#193 from () into the sum over bonds index accounts for frustration.

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...that

This estimation is consistent with our use of the central limit theorem provided 207#207, that is, 208#208.

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...nats

A nat is the base e unit of information analogous to bits for base 2.

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...below.

A more general treatment of optimisation of a system in which the cost function is a random variable is provided in Chapter . We summarise the case for proteins here.

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...combinatoric

By combinatoric we mean that the number of enumerable solutions scales exponentially or more rapidly with the size of the problem.

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...problems

The same phrase is used in [28] to describe probabilistic combinatoric optimisation.

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...reward

We use the terms reward and cost interchangeably, with the understanding that one is the negative of the other.

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...408#408.

Because design 39#39 must previously have been tested, against others which it superceded, we could in principle seek to use also that earlier information about its cost in estimating 48#48. In the present discussion we will ignore this possibility, with the advantage that this makes acceptance decisions statistically independent of each other.

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...length

Jaillet derived a closed form expression for computing the exact expected length of an a priori tour over all realisations of the city probabilities [27]. This allows comparison of conventional optimisation techniques with probabilistic methods, such as the one introduced here.

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...activity.

It is important to distinguish between the tree of nodes, shown in Figure , from the corresponding tree of decisions (cf. 435#435 Figure ); in particular, the decision tree is much more highly branched, the decision at each level being the total number of nodes to purchase.

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...value

The definition of value presented here is not identical to the definition provided in Chapter (this chapter was published earlier). We address the difference in definitions and its implication in Appendix .

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...lattice.

This chapter is the result of work done in collaboration with Yong Mao [32, 33]; the text included here was written by the author.

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...deformed,

The diagrammatic manipulations associated with continuous deformation of a knot are called the Reidemeister moves; see [36].

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...it.

While all of the diagrams in Figure are topologically equivalent to the first, only the first diagram, with terminal sequence intact, corresponds to a tie knot sequence.

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...econophysics

Coined by H. Eugene Stanley.

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