Protein Engineering Protocols - Mycobacteriology research center

Protein Engineering Protocols - Mycobacteriology research center Protein Engineering Protocols - Mycobacteriology research center

12.07.2015 Views

Combinatorial Protein Design Strategies 13backbone conformations (e.g., T = 300 K). Here, a backbone-dependentrotamer library is used throughout (60). Reference energies are measured withrespect to that of glycine (G), which has no side chain. The energy constrainton the sequences involving interatomic interactions then takes the form:∑E ≈ E = { ε [ α, r ( α)] −γ [ α, β ] w [ α, r ( α)]}c c i k ref ref i ki, α,k+ ∑ εij ,[α, rk(α) ; α′ , rk′( α′)] wi[α, rk (α)] wj[α′ , rk′(α′)]i, j>iα,α′kk , ′2.3.4. Rotamer and Identity ProbabilitiesThe theory maximizes the total conformational entropy, S c, yielding a probabilityw i[α,r(α)] that a particular amino acid is present at site i and is in sidechainconformation k. The amino acid probability, w i(α), can then be determinedusing:Using an analogy to statistical thermodynamics, the Lagrange multiplier thatarises from constraining the conformational energy, β c, may be considered aneffective inverse temperature, 1/β c= T c. The corresponding “heat capacity,” C v,is defined as:EcCv= ∂ 2 2 2= βc ( i−i )∂T∑ ε εc ilocε = ε [ α, r ( α)] w[ α, r ( α)]iα,kilocε [ α, r ( α)] = ε [ α, r ( α)] − γ ( α, β )i∑k i k+w ( α) = ∑ w[ α,r ( α)]i i kk∑j, α′ , k′kwhere ε i is termed a local mean field energy, which denotes the average localfield around a particular amino acid side, i. The effective heat capacity, C v, providesa quantitative measure of the fluctuations in the sequence–rotamer identitiesas values of the constraint conditions, such as the overall energy, aremodulated during a calculation.By way of example, the theory is applied to a particular protein, an SH3domain. The conformational entropy decreases with decreasing the effective temperatureT c(i.e., decreasing E c; Fig. 1). At high energies (high T c,low β c), there aremany unfavorable (high-energy) interactions between residues and a broad distributionof sequence–rotamer states at each site. On average, the number of probablerefikε [ α, r ( α); α′ , r ( α′ )] w [ α′ , ( α′ )]ij , k k′jcr k ′

14 Kono et al.Fig. 1. Sequence–conformation entropy, S c, of the SH3 domain is plotted againsteffective temperature, T c(upper panel). Effective heat capacities per residue C vfor allburied and exposed residues are plotted against effective temperature (lower panel).Temperatures are given in arbitrary units determined by the molecular potential used,here moles per kilocalorie.

14 Kono et al.Fig. 1. Sequence–conformation entropy, S c, of the SH3 domain is plotted againsteffective temperature, T c(upper panel). Effective heat capacities per residue C vfor allburied and exposed residues are plotted against effective temperature (lower panel).Temperatures are given in arbitrary units determined by the molecular potential used,here moles per kilocalorie.

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