A young researcher studied the relationship between structure and function of an enzyme.

Details:

Molecular weight: The enzyme weighs $18$ kDa and is homologous to other enzymes that catalyze the precursor substance "Smartlogen" to the hormone "Smart by Night."

Conditions tested: Enzyme activity was evaluated in a steady$-$state under hyperbolic kinetics, showing reaction velocity as a function of substrate concentration.

Results: At high substrate levels, $10$ mmol of "Smartlogen" were converted into "Smart by Night" per minute in a reaction volume of $50$L with a substrate concentration of $1$ mM$.$

$1.$ Calculate the turnover number $($kcat$)$:

How many molecules of "Smartlogen" does the enzyme convert to "Smart by Night" per second? Assume conditions with substrate concentrations much higher than Km$.$

$2.$ Calculate specific activity:

Using the data provided, determine the enzyme's specific activity $($pay attention to units$).$

$3.$ Effects of enzyme concentration:

Would the values calculated in parts $(1)$ and $(2)$ change with variations in enzyme concentration? Explain.

$4.$ Gel filtration chromatography principle:

Explain the principle of gel filtration chromatography. How can you monitor the protein quantity in elution? What is the relationship between elution volume and the molecular weight of the protein?

$5.$ Structural implications of findings:

Based on the results, deduce the structure of each enzyme sample.

$6.$ Physiological implications of Poz's influence:

Define the effect of Poz $($a later product in the signaling pathway activated by "Smart by Night"$)$ on the enzyme. Where does it bind? Explain the physiological principle behind its impact.