Transition state theory $20pts.$ The enzyme aspartate aminotransferase catalyzes the formation of tyrosyl$-$tRNA for protein synthesis. In the first step of the reaction, tyrosine and ATP react to form tyrosyl$-$adenylate $($Tyr$-$AMP$).$ For the purposes of this problem, consider the simplified kinetic scheme below $($we will assume ATP is saturating so we can ignore the ATP binding step and start with enzyme bound to ATP$)$:

a$)[5$ pts$]$ Given an enzymatic reaction in which $k_2=38s^{-1},$ calculate the value of $G_E^{}($the barrier between $ES$ and $E{S}^{})$ at $25C.$ Assume the transmission coefficient $=1.$ Give your answer in kca$\frac{l}{m}ol.$

b$)15pts$ Sketch a free energy profile for the enzymatic reaction, showing the three states in the kinetic scheme above Tyr$,E_{\text{A}\text{T}\text{P}}*$ Tyr$,$ and $($:$E*Tyr-$AMP$+P{P}_i\}$ and the transition states between them.

Use $K_S=12M$ to calculate $G_S($using a standard state of $1M-$ in practice this means convert $K_S$ from $M$ to $M$ to calculate $G_s)$

Assume $G_{rxn}$ between $E_{\text{A}\text{T}\text{P}}+$ Tyr and $E*Tyr-$AMP$+P{P}_i$ is $-5$kca$\frac{l}{m}ol.$

You can choose an arbitrary barrier height for the transition from $E_{\text{A}\text{T}\text{P}}+Tyr$ to $E_{\text{A}\text{T}\text{P}}*Tyr.$

Show $G_E^{},G_S,G_{rxn}$ on your plot. Make sure that the relative energy levels and barrier heights reflect these free energy values.