Author Archives: fingolfn

In a follow up to our posts on Intuiting Enzyme Kinetics and Sequential Biochemical Pathways, we next wanted to consider the kinetic curves branch points in biochemical pathways (or equivalently kinetic competitions). Luckily exact mathematical models exist for competitive first-order processes (see below) and we can use these to develop intuitive rules (figure above) if we consider these pathways to be approximately pseudo-first order (which is often true in the context of biosynthetic pathways).

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In a follow up to our post our post on intuiting enzyme kinetics, we next wanted to consider the kinetic curves for sequential biochemical pathways. Luckily exact mathematical models exist for sequential first-order processes (see below) and we can use these to develop intuitive rules (figure above) if we consider these pathways to be approximately pseudo-first order (which is often true in the context of biosynthetic pathways).

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While many drugs act like agonists and “turn on” their target/receptor (see posts on Hill Equation and Agonist Limits), many more drugs act like antagonists and “turn off” their target/receptor. One of the most common mechanisms by which drugs “turn off” a target receptor (R) is by blocking the binding of its natural ligand (L). This mechanism is called competitive inhibition and the antagonist is known as an inhibitor (I). Here there are two dissociation constants:the K_d which describes the strength of the interaction between R and L and the K_i which describes the strength of the interaction between R and I.

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The Michaelis-Menton Equation has a very similar form to the Hill Equation but the key difference is that it deals with enzyme rates not ligand/receptor or drug/target interactions per se. Basically, it describes how fast an enzyme (E) makes its product (P) as a function of the total concentration of substrate ([S]_t). This rate of production formation (d[P]/dt) is proportional to the k_cat and the amount of complex ([ES]) which is exact what the Michaelis-Menton equation models. The Michaelis-constant (K_m = (k_off+k_cat) / k_on) describes how tightly the substrate binds the enzyme and the k_cat is a rate-constant that describes how quickly the enzyme can make the product. Here,brackets denote concentrations and a t subscript indicates “total concentrations.”

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If you want to understand how drugs work/behave (or just how 2 molecules interact with each other) then you need to understand one of the oldest and most useful theories in biochemistry: the Hill Equation. The Hill Equation mathematically models how Ligands(L)/Drugs interaction with their Receptors(R)/targets and generally assumes that the amount of complex that forms (RL) is proportional to some biological response . Here the K_d represents the “dissociation constant” (which is a measure of the strength of the interaction between R and L) and brackets denote concentrations/dosages (with a t subscript indicating total concentrations).

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