Derive the rate expressions for non-competitive competitive

Question

1. Derive the rate expressions for non-competitive, competitive, un-competitive and substrate inhibition based on the Michaelis-Menten rate equation.

2. Simulate the Michaelis-Menten equation in the absence and presence of the non-competitive inhibition using v_max = 1 d^-1, K_m = 50 M, K_I = 500 M and S_I = 200 M. Subsequently, using the three linearization techniques, estimate v_max, K_m and K_I.

3. Describe the principal differences between the Michaelis-Menten and Monod rate equations? Give mathematical relations if possible.