Tris·HCl (pH 7.5 at 25°C), 250 mM KCl, and 0.1 mM EDTA (26). Values of ΔGu and m were obtained by fitting denaturation data to a two-state model by nonlinear least squares methods (26). Effective concentrations were calculated by using the equation Ceff=exp[(m2●ΔG1/m1–ΔG2)/RT], where m1 and ΔG1 are values for the single-chain protein, and m2 and ΔG2 are values for wild-type Arc (1.48 kcal/mol●M and 10.3 kcal/mol, respectively) (26). Stopped-flow kinetic experiments of protein folding and unfolding were monitored by changes in fluorescence at protein concentrations between 1 and 10 μM in the buffer used for stability measurements (26). Unfolding was initiated by urea-jump experiments (mixing ratio 1:10) to yield a final urea concentration of 7 or 9.1 M. Refolding was initiated by mixing protein denatured in 6.0–9.6 M urea with low urea buffer (1:5 ratio) to yield final urea concentrations between 1.0 and 4.5 M. Rate constants were obtained by fitting the kinetic data to single exponentials. In all cases, the residuals of the fits were distributed randomly. For ease of comparison among each library of variants, rates were either measured at a single urea concentration or measured at a series of urea concentrations and extrapolated to this reference concentration by using linear regression of ln(k) vs. [urea] plots (R>0.99).
Variation of Linker Length. A library of single-chain arc genes with linkers composed of Gly, Ser, and Thr and lengths varying from 3 to 59 aa was constructed (Fig. 3A). The fraction of Gly in different linkers ranges from 66 to 80%. The linkers and corresponding proteins are named LLX and Arc-LLX-Arc (Length Library, X=number of residues), respectively. No intracellular expression of the Arc-LL8-Arc protein was detected. Arc-LL3-Arc expressed to high levels but monomers, dimers, and higher-order oligomers were observed following SDS electrophoresis and Western analysis. This behavior may indicate “cross-folding” as has been observed with single-chain antibodies that have very short linkers (27, 28). The remaining 13 proteins in this library were all expressed at high levels and electrophoresed as monomers. The Arc-LLX-Arc variants were tested for repression of transcription of the Pant promoter in E.coli strain UA2F, using resistance to streptomycin as an assay of biological activity (24). Arc-LLX-Arc proteins with linkers containing 13 or more residues had wild-type activities. Arc-LL11-Arc was partially active; single-chain molecules with the LL3, LL8, and LL9 linkers were inactive. Modeling studies show that connecting the Arc subunits with linkers shorter than 13 residues would either require the linker to cross the DNA-binding surface of the protein and/or require distortion of the structure.
Single-chain Arcs with linkers LL9–LL59 were purified for biophysical characterization. All of these single-chain proteins had CD and fluorescence spectra similar to wild-type Arc. Arc-LL11-Arc, Arc-LL19-Arc, and Arc-LL31-Arc were analyzed by analytical ultracentrifugation and found to be monomeric at concentrations between 10 and 100 μM (data not shown). Proteins containing the three longest linkers (LL47, LL51. and UL59) tended to precipitate at concentrations >100 μM, possibly because of aggregation caused by cross-folding of the Arc subunits.
The thermodynamic stabilities of Arc-LLX-Arc proteins with linkers from 9 to 57 residues were determined by urea denaturation studies, revealing that the 19-residue linker provides maximal stability. As shown in Fig. 2 for a subset of these proteins, there are large changes in the concentration of urea required for denaturation of proteins with different linker lengths, but the curves are roughly parallel indicating that the denaturant m-values (variation of ΔGu with urea) are similar. Fig. 3B shows the variations of ΔGu and Ceff with linker length. For linkers from 9 to 19 residues, stability of the single-chain protein increased with length. Arc-L9-Arc was the least stable (ΔGu≈3 kcal/mol; Ceff≈6 μM) and Arc-LL19-Arc was the most stable (ΔGu=8.4 kcal/mol; Ceff=80mM) of the proteins examined. Increases in linker length past 19 residues resulted in decreasing stability until a plateau was reached at ≈4.5 kcal/mol (Ceff ≈150 μM) for linkers between 47 and 59 residues.
The linker-dependent changes in stability arise from changes in both the folding and unfolding rates, as measured in urea-jump, stopped-flow, kinetic experiments. Fig. 3 C and D show that both the folding and unfolding rate constants vary significantly as the linker length is changed. In 7 M urea, Arc-LL9-Arc unfolds with a rate constant (ku) of ≈3,000 s–1. As the linker length is increased from 9 to 19, there is a roughly exponential decrease in ku that spans 3–4 orders of magnitude and reaches a value of ≈1s–1 for Arc-LL19-Arc. Changes in linker length between 19 and 59 residues do not change ku appreciably. Thus, linkers shorter than 19 residues reduce the