Protein Engineering Protocols - Mycobacteriology research center

Combinatorial Protein Design Strategies 11sequences sharing common energetic properties, we assume that the fluctuationin E cabout its mean value caused by variation of sequence is small. We can thenwrite:E ≈ E =∑ ε [α, r ( α )] w [α, r ( α)]c c i ki, α,kAs another constraint, an environmental energy, E envis introduced to accountfor the hydrophobic effect in a way that is efficient within the statistical theory(59). This potential takes into account the surface-exposure preferences of theamino acids. Regarding E c, we can write E envusing amino acid probabilities as:E ≈ E =∑ ε [α, r ( α)] w[ α, r ( α)]env env env ki, α,kwhere ε envis a local environmental energy defined in Subheading 2.3.2. Notethat this energy contains no two-body interactions and is dependent only on theamino acid and rotamer state at each position.2.3.2. Solvation and Hydrophobic EnergyAn important input to any protein design method is some means of quantifyingthe hydrophobic effect and other solvation properties. Explicit representationof solvent is impractical for calculations that examine large variation insequence, and even calculating solvent-accessible surface areas—which oftencorrelate well with hydrophobic tendencies—can be computationally intensive.In an effort to consider solvation effects in a practical manner consistent withthe statistical calculations, an environmental energy has been introduced that isa function of the density ρ of C βatoms in the vicinity of each side chain (59).On average, hydrophobic residues tend to be located in buried regions of proteins,whereas hydrophilic residues tend to be located at the surface. Thus,hydrophobic residues are likely to have a higher C βdensity than hydrophilicones. Using 500 different globular proteins of known structure (the trainingset), we derived effective potentials for the amino acids using the usual equationfor “statistical” potentials:εenvip( αρ , )( α, ρ) =−Telnp( α) p( ρ)where p(α,ρ) is the fraction of times a local C βdensity of ρ is observed for aminoacid α; p(α) is the fraction of times amino acid α is observed in the training set;k+ ∑ εij ,[α, rk( α) α′ , rk′( α′ )] wi[α, rk( α )] wj[α′ , rk′( α′ )];i, j>iαα′kk , , ′ik