> See also: > - [[Enzymes]] > - [[Binding Curves and Hill Plots]] > - [[Reaction Kinetics]] > - [[Chemical Equilibria]] # Enzyme Kinetics Some enzymes $E+S \xleftrightharpoons[k_{-1}]{k_1}ES\xrightarrow{k_2}P+E$ There is always a way to determine the initial concentrations: - $[E]_o=[E]_t+[ES]_t$ - $[S]_o=[S]_t+[ES]_t$ ## Slope/Rate of Reactions > See also: [[Differentiation|Differentiation]] The reaction velocity: $v=\frac{d[P]}{dt}=k_2[ES]_t$ - In layman’s terms, the velocity (rate) of the reaction at any given time ($t$) is equal to the rate constant --- **The Turnover Number** $K_{\text{cat}}$ Number of substrate molecules converted into product per active site per second --- Rate Enhancement is a ratio of the rates of the catalyze and uncatalyzed reactions ## Michaelis-Menten Equation Despite this diversity, *all enzymes can be analyzed such that their reaction rate/overall efficiency can be quantified.* To do this, we use the **Michaelis-Menten Equation**: $v_o=\frac{v_{\max}[S]_o}{[S]_o+K_M}$ ### Assump The Lump (waaa^2) There are several assumptions that must be made before we can utilize the ### Assumption of Steady State The Michaelis-Menten Equation assumes that the enzyme-substrate (ES) complex maintains a **steady state** - Not to be confused with the *standard state* (of [[chemical thermodynamics]]) ![[Pasted image 20231121132535.png|300]] --- Assumes that as soon as the reaction begins, *the rate at which the enzyme-substrate complex is consumed is equal to the rate at which it is formed*. $\frac{d[ES]}{dt}=k_1[E]_t[S]_t-k_{-1}[ES]_t-k_2[ES]_t$ This equations lets us determine the concentration of the enzyme-substrate complex at any given time by considering the rate laws for its formation and breakdown. Instead of all the junk above, we set it equal to 0: $\frac{d[ES]}{dt}=0$ --- **Assumption of Equilibrium** The physiologically common condition that substrate is *in great excess* over enzyme ($[S] \gg [E]$) ES maintains a steady state and $[ES]$ and $K_M=\frac{k_{-1}+k_2}{k_1}$ > [!warning] **What About Non-Steady States?** > While we assume that --- My initial thoughts on this content are: “how is this equation even useful if we have to make so many assumptions about the conditions” I can see how it could be useful in experimental setups but can’t even begin to imagine how you would translate that information into a biological system while maintiaing any level of accuracy ### Effects of Inhibitors ## Lineweaver-Burk Plots