The catalytic activity of a ribozyme (an RNA enzyme) from Tetrahymena thermophila is discu...

The catalytic activity of a ribozyme (an RNA enzyme) from Tetrahymena thermophila is discussed in detail by Herschlag et al. [Biochemistry 29:10,159 (1990)]. The ribozyme uses a guanosine cofactor (G) to cleave a ribo-oligonucleotide substrate. A simplified mechanism for the reaction is:

At 50°C, neutral pH, and 10 mM Mg2+, the following data were obtained. Kinetics of binding of substrate S, E + S → ES and GE + S → GES: k1 = 9 X 107 M-1 min-1; k-1 = 0.20 min-1. Binding of G is fast to equilibrium with dissociation constant, KG = 0.5 mM:

We note that substrate and cofactor bind independently. Chemical step for cleavage of substrate: kc = 350 min-1 Release of product: kp = 0.06 min-1

a. Derive an expression for the steady state concentration of GES in terms of the total concentration of enzyme, [E]0, [S], [G], k1, k-1, kc, and KG. Remember that [E0] = [E] + [ES] + [GE] + [GES].

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b. In the steady state, the rate of formation of product can

be written as

Use your expression from part (a) and the values of rate coefficients and the equilibrium constant to calculate d[P]/dt as a function of [S] for a constant value of [E]0 = 100 μM at three different concentrations of G: [G] = 0.05 mM; [G] = 0.5 mM; [G] = 5 mM. Make an approximate plot of the rate vs. [S] for each value of [G]; use enough values of [S] to be able to see the trends.

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c. Describe the experiments you would need to do to measure k1 and k-1 under different conditions of temperature and solvent.