Enzymes are catalysts for living organisms. They have evolved to enable specific chemical reactions — Physical Chemistry — Kinetics Chemistry Question
Transition state in enzymatic reactions
Enzymes are catalysts for living organisms. They have evolved to enable specific chemical reactions necessary for life to thrive more efficiently. In the active site of an enzyme, amino acid residues including side chains have evolved to provide space for the transition state (TS) of the chemical transformation to exist with conformational and electrostatic match.
Thus, the binding affinity of this TS to the enzyme is expected to be very high (if one can calculate), stabilizing the energy of the transition state through an enzyme–TS complex. This lowers the activation energy of the reaction and creates rate acceleration. If one can calculate the binding constant owing to the complex formation, one could readily deduce how efficient the enzyme is by calculating kcat / kuncat.
Man–made enzymes are holy grails for some chemists, because they can give insight about the behavior of natural enzymes and can be used as useful synthetic and therapeutic tools. Catalytic antibodies can be one of these kinds of artificial enzymes. Antibodies have antigen–binding sites, in which the target antigen binds with high affinity (KD = 10–9 – 10–11) and with great specificity. These properties can be exploited as active sites in artificial enzymes. Antigen–binding sites may serve to specifically recognize substrates and perform certain chemical reactions.
Since these catalytic antibodies need to accommodate transition state (TS) structures in chemical transformations, an antigen that triggers the production of the catalytic antibody must be designed and synthesized just like the TS structure. However, chemists cannot prepare a transition state structure because it is transient. Instead, one can synthesize a stable compound that resembles the structure of the transition state. This newly designed compound is called a transition state analogue (TSA). Once a TSA is made, it can be injected into mice to generate antibodies. The half–life of the TSA should be longer than 2 weeks at physiological conditions to obtain an adequate immune response.
After generating as many antibodies as possible, the most tightly binding and specific antibodies are selected as candidates for antibody catalysts.
If one of the selected antibodies has KD = 1×10–13 against the TSA, comparing with normal antibody (KD = 1×10–6) how much stabilization energy can the TSA gain from the binding to this specific antibody?
Model Answer
The reduced energy of the transition state can be calculated by comparing ∆G° (∆G° = – RT ln Keq) values between KD of selected antibody and normal antibody.
∆G° = (–RT ln KD, selected) – (–RT ln KD, normal) = –RT (ln KD, selected – ln KD, normal)
= –8.314 J mol–1 K–1 × 310 K × ln (10–13/10–6) = 41.6 kJ mol–1
Let us assume that the TSA can be considered as the real transition state (TS). Then, how much rate enhancement will be obtained when we will use this catalytic antibody for the intended chemical transformation? Describe this enhancement by kcat / kuncat.
Model Answer
kcat / kuncat = exp(Euncat – Ecat / RT) by Arrhenius equation (k = A exp(–Ea / RT))
kcat / kuncat = exp (41,600 J mol–1 / 8.314 J mol–1 K–1 × 310 K) ≈ 1×107; (reciprocal value of KD)
Most scientists are interested in the specific hydrolysis of the pathogenic proteins or peptides such as β–amyloid as the intended chemical reaction by catalytic antibodies. Assuming that the following reaction is the intended reaction by catalytic antibody, TS of the hydrolysis of the amide bond should be considered to make a plausible TSA.
[VISUAL]
What is the transition state or reactive intermediate of the above amide bond hydrolysis?
Model Answer
The transition state (or reactive intermediate) of the amide bond hydrolysis is a tetrahedral intermediate formed by the nucleophilic addition of water (or hydroxide) to the carbonyl carbon of the amide group. This intermediate has a tetrahedral geometry around the carbon atom, with a negatively charged oxygen atom (an oxyanion) and a newly formed C-O bond from the water molecule:
[VISUAL]
Design a stable TSA suitable for replacing the TS. Remember that the TSA should be stable and structurally close to the TS.
Model Answer
To mimic the tetrahedral transition state, a stable phosphorus-based analogue such as a phosphonamidate or phosphonate is designed. These compounds contain a tetrahedral phosphorus atom which is stable under physiological conditions and structurally resembles the tetrahedral carbon in the transition state:
[VISUAL]