Polymerase binding to the promoter revisited The probability of promoter occupancy can be computed using both statistical mechanics and thermodynamics (that is, using equilibrium constants). These two perspectives were already exploited for simple ligand-receptor binding in Sections 6.1 .1 and 6.4 .1 (a) Write an expression for the probability of finding RNA polymerase bound to the promoter as a function of the equilibrium constants for specific and nonspecific binding. (b) In vitro, the dissociation constant of RNA polymerase binding to nonspecific DNA is approximately $10 \mu \mathrm{M}$ and the dissociation constants of RNA polymerase to the lac $P 1$ and T7A1 promoters are $550 \mathrm{nM}$ and $3 \mathrm{nM}$, respectively. Use these constants and the results from (a) to estimate the in vivo binding energies of RNA polymerase to $\operatorname{lac} P 1$ and $\mathrm{T} 7 \mathrm{Al}$ promoters.
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The equilibrium constant for specific binding (Ks) is the ratio of the rate of binding to the rate of unbinding, and similarly for nonspecific binding (Kn). The probability (P) can be expressed as: P = [Ks/(Ks + Kn)] * [Polymerase]/([Polymerase] + Show more…
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DNA polymerase I (Pol I) of E. coli consists of three functional parts (domains): an N-terminal domain with 5' to 3' exonuclease activities required for removal of the RNA primer, a central domain responsible for 3' to 5' exonuclease proofreading, and a C-terminal domain with polymerase activity. Pol I is thought to simultaneously remove RNA primers and fill in the gaps that result. A group of proteins known as RNase H also have 5' to 3' exonuclease activity and can thus remove RNA primers. However, they lack the other two functions observed for Pol I. Predict the ability of the following mutants to replicate DNA: (1) a strain with a mutant gene encoding Pol I such that it no longer has polymerase activity (but retains both types of nuclease activities); (2) a strain without RNase H proteins; (3) a strain with a mutant gene encoding Pol I such that it no longer has 5' to 3' exonuclease activities (but retains 3' to 5' nuclease and polymerase activities); (4) a strain with the mutant Pol I described in (3) and a strain lacking all RNase H proteins.
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RNA polymerase and ribosomes (a) If RNA polymerase subunits $\beta$ and $\beta^{\prime}$ together constitute approximately $0.5 \%$ of the total mass of protein in an $E .$ coli cell, how many RNA polymerase molecules are there per cell, assuming each $\beta$ and $\beta^{\prime}$ subunit within the cell is found in a complete RNA polymerase molecule? The subunits have a mass of 150 kDa each. (Adapted from Problem 4.1 of Schleif, $1993 .$ (b) Rifampin is an antibiotic used to treat Mycobacterium infections such as tuberculosis. It inhibits the initiation of transcription, but not the elongation of RNA transcripts. The time evolution of an $E .$ coli ribosomal RNA (rRNA) operon after addition of rifampin is shown in Figures $3.36(\mathrm{A})-(\mathrm{C})$ An operon is a collection of genes transcribed as a single unit. Use the figure to estimate the rate of transcript elongation. Use the beginning of the "Christmas-tree" morphology on the left of Figure $3.36(\mathrm{A})$ as the starting point for transcription. (c) Using the calculated elongation rate, estimate the frequency of initiation off of the rRNA operon. These genes are among the most transcribed in $E .$ coli. (d) As we saw in the chapter, a typical $E$. coli cell with a division time of 3000 s contains roughly 20,000 ribosomes. Assuming there is no ribosome degradation, how many RNA polymerase molecules must be synthesizing rRNA at any instant? What percentage of the RNA polymerase molecules in $E .$ coli are involved in transcribing rRNA genes?
The polymerase chain reaction (PCR) has revolutionized biology and medicine, by allowing small regions of DNA to be amplified up to a billion-fold in a few hours. Each cycle involves heating the DNA to 95°C to separate the two strands, cooling the sample to allow primers to bind, and raising the temperature to the optimum for the DNA polymerase to replicate the DNA. This process uses the DNA polymerase from a species of bacteria isolated from hot springs, Thermus aquaticus, which grows at 70°C. Human body temperature is 37°C. What would you predict about the DNA polymerase from T. aquaticus compared with DNA polymerases from human cells? Check All That Apply The DNA polymerase from T. aquaticus would have a lower optimal temperature compared with a DNA polymerase from human cells. The DNA polymerase from T. aquaticus would function normally if placed inside a human cell. The DNA polymerase from T. aquaticus would denature at 70°C. The DNA polymerase from T. aquaticus would have a higher optimal temperature than a DNA polymerase from human cells. A DNA polymerase from human cells would work best for PCR. A DNA polymerase from human cells would likely denature under these conditions.
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