Non-specific binding of regulatory proteins to DNA can be an important mechanism for target search and storage. This seems to be the case for the lambda repressor protein (CI), which maintains lysogeny after infection of E. coli. CI binds specifically at two distant regions along the viral genome and induces the formation of a repressive DNA loop. However, single-molecule imaging as well as thermodynamic and kinetic measurements of CI-mediated looping show that CI also binds to DNA non-specifically, and that this mode of binding may play an important role in maintaining lysogeny. This paper presents a robust phenomenological approach using a recently developed method based on the partition function, which allows calculation of the number of proteins bound non-specifically to DNA from measurements of the DNA extension as a function of applied force. This approach was used to analyze several cycles of extension and relaxation of λ-DNA performed at several CI concentrations to measure the dissociation constant for non-specific binding of CI (~100 nM), and to obtain the first measurement of the induced DNA compaction (~10%) by CI.
We have determined the change in the number of proteins bound non-specifically to DNA as a function of applied force using force–extension measurements on tethered DNA. Using magnetic tweezers, single molecules of λ DNA were repeatedly stretched and relaxed in the absence and presence of 170 nM λ repressor protein (CI). CI binds to six specific sites of λ DNA with nanomolar affinity and also binds non-specifically with micromolar affinity. The force versus extension data were analyzed using a recently developed theoretical framework for quantitative determination of protein binding to the DNA. The results indicate that the non-specific binding of CI changes the force–extension relation significantly in comparison to that of naked DNA. The DNA tether used in our experiment would have about 640 bound repressors, if it was completely saturated with bound proteins. We find that as the pulling force on DNA is reduced from 4.81 to 0.13 pN, approximately 138 proteins bind to DNA, which is about 22% of the length of the tethered DNA. Our results show that 0.13 pN is not low enough to cause saturation of DNA by repressor and 4.81 pN is also not high enough to eliminate all the repressors bound to DNA. This demonstrates that the force–extension relation provides an effective approach for estimating the number of proteins bound non-specifically to a DNA molecule.