Question

I created a simulation which approximates molecule concentrations in a cell. One part of it are enzymes that can catalyze pre-defined reactions, e.g. A↽−−⇀B.

I based the kinetics for these reactions on Michaelis-Menten kinetics, so every enzyme has a Vₘₐₓ and K_M, and has velocity v = Vₘₐₓ x / K_M+x at a given time point, where x is the concentration of substrates. I use the Reaction Quotient Q at any point in time to determine in which direction a reaction would proceed. E.g. would (net/overall) A be converted to B or vice versa. Each reaction is defined with a reaction energy which is used to calculate Equilibrium constant Ke.
Here is my question
My understanding is that Miachelis-Menten kinetics only describe the case in which Q≪Ke. What happens if Q→Ke? Intuitively I would assume that the overall reaction velocity slows down as Q approaches Ke. Is there a term that I can add to the Michaelis-Menten equation which would describe this decreasing v?

Answer 1

The Michaelis-Menten equation predicts an hyperbola when v is plotted against [S]. If the reaction quotient, Q, approaches the equilibrium constant, Ke, the reaction velocity, v, slows down. Other equations or models, such as the Briggs-Haldane equation, can be used to better describe this decreasing v as Q approaches Ke.

Step-by-step explanation:

Michaelis and Menten defined Vmax and Km as key kinetic factors in enzymatic reactions. In the generic example of substrate conversion to product, we saw that increasing [S] results in a higher rate of product formation because a higher rate of encounters of enzyme and substrate molecules. At some point however, increasing [S] does not increase the initial reaction rate any further.

Instead, v, asymptotically approaches a theoretical maximum for the reaction, defined as Vmax, the maximum initial rate. As we have already seen, Vmax occurs when all available enzyme active sites are saturated (occupied by substrate). At this point, the intrinsic catalytic rate determines the turnover rate of the enzyme.

The substrate concentration at which the reaction rate has reached 1/2Vmax is defined as KM (the Michaelis-Menten constant). The Km is a ratio of rate constants remaining after rewriting the rate equations for the catalyzed reaction.

The Michaelis-Menten equation predicts an hyperbola when v is plotted against [S]. This plot approaches a constant v at high [S]. However, if the reaction quotient, Q, approaches the equilibrium constant, Ke, the reaction velocity, v, slows down. There is no term that can be added to the Michaelis-Menten equation to directly describe this decreasing v as Q approaches Ke.

The Michaelis-Menten equation describes the case in which Q << Ke, so its applicability becomes less accurate as Q approaches Ke. To account for this, other equations or models, such as the Briggs-Haldane equation, can be used.