Question: Here we consider a simplified model of the lac repressor. We assume that the repressor can only s…
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Show transcribed image text Here we consider a simplified model of the lac repressor. We assume that the repressor can only stably bind in the looped state, and the energy shift associated with the looped state is the sum of the energy shift due to binding the repressor to the specific DNA sequences (Delta epsilon_rd) and the energy associated with looping the DNA (Delta F_loop). Otherwise this diagram looks very similar to the one we would draw for a simple repressor, with only 3 states. Here R is the number of RNAP molecules. N_NS is the number of non-specific DNA binding sites, R is the number of repressor molecules, Delta epsilon_pd is the energy shift associated with specific binding by RNAP, and beta = 1/k T. Show that the probability the RNAP is bound can he written as: P_bound (R) = 1/1 + N_NS/P middot F_reg (R) e Delta epsilon_pd/kT Solve for F_reg (R). Estimate the free energy shift associated with looping, Delta F_loop, if the radius of the loop is 31.4 nm given that the persistence length of DNA is 50 nm. Write your answer as a multiple of k_g T. In the limit that P_bound (R)
Here we consider a simplified model of the lac repressor. We assume that the repressor can only stably bind in the looped state, and the energy shift associated with the looped state is the sum of the energy shift due to binding the repressor to the specific DNA sequences (Delta epsilon_rd) and the energy associated with looping the DNA (Delta F_loop). Otherwise this diagram looks very similar to the one we would draw for a simple repressor, with only 3 states. Here R is the number of RNAP molecules. N_NS is the number of non-specific DNA binding sites, R is the number of repressor molecules, Delta epsilon_pd is the energy shift associated with specific binding by RNAP, and beta = 1/k T. Show that the probability the RNAP is bound can he written as: P_bound (R) = 1/1 + N_NS/P middot F_reg (R) e Delta epsilon_pd/kT Solve for F_reg (R). Estimate the free energy shift associated with looping, Delta F_loop, if the radius of the loop is 31.4 nm given that the persistence length of DNA is 50 nm. Write your answer as a multiple of k_g T. In the limit that P_bound (R)
