Assume that you have carried out an anaerobic Saccharomyces cerevisiae fermentation.

Substrates were glucose $($s$)$ and ammonia $(n.$ Metabolic products included carbon dioxide $($c$),$

water $($w$),$ ethanol $($e$)$ and glycerol $($g$).$ The composition of biomass was $C{H}_{1\mathrm{.}61}{O}_{0\mathrm{.}52}{N}_{0\mathrm{.}15}$ and

stoichiometry can be described following:

$-C{H}_{2}O-Y_{ss}N{H}_3+Y_{sx}C{H}_{1\mathrm{.}61}{O}_{0\mathrm{.}52}{N}_{0\mathrm{.}15}+Y_{sc}C{O}_2+$

$Y_{se}CH{H}_3{O}_{0\mathrm{.}5}+Y_{sg}C{H}_{\frac{8}{3}}O+Y_{sw}{H}_{2}O=0$

The fermentation was modeled using a black$-$box model with volumetric yield and consumption

rates $q_s,q_x$ and $q_g$ as measured variables and the rest of the fluxes, i$.$e$.q_c,q_n,q_w$ and $q_e$ as

calculated variables as functions of the measured variables, and solved as follows:

$([q_e],[q_n],[q_w],[q_e])$:$=([-0\mathrm{.}333,-0\mathrm{.}313,-0\mathrm{.}222],[0,-0\mathrm{.}15,0],[0,0\mathrm{.}45,-0\mathrm{.}167],[-0\mathrm{.}667,-0\mathrm{.}687,-0\mathrm{.}778])*([q_s],[q_s],[q_8])$

Calculate the yield coefficients $Y_{sn},Y_{sc},Y_{se}$ and $Y_{sw}$ and $q_c,q_n,q_w$ and $q_e$ for the reaction when

biomass yield from substrate $Y_{sx}=0,128,$ glycerol yield from biomass $Y_{x9}=0,67,$ specific growth rate

was $0,1h^{-1}$ and the biomass concentration was $14\frac{g}{L}.$ Finally, calculate carbon balance and the

reduction balances with the yield coefficients.

a$)$ Suppose that the enzyme pathway follows Michaelis$-$Menten kinetics and $v_{\text{m}\text{a}\text{x}}=50$ and $K_M=$

$0,08mM$ :

$v=\frac{S*v_{\text{m}\text{a}\text{x}}}{S+K_M}$

Nhat is the elasticity of the enzyme to the substrate, when the substrate concentration is $1)0,03$

$nM$ and $2)0,25mM?$

$)$ Citrulline is synthesized in mitochondria with reactions:

$N{H}_4^{+}+HC{O}_3^{-}+2$ATP$$ carbamoylP $+2$ADP$+P_i$

carbamoyl $+$ ornithine $$ citrulline $+P_i$

$$he reaction $1)$ is catalyzed by a carbamoyl phosphate synthase $($CPS$),$ and the reaction $2)$ by

ornithine transcarbamoylase $($OTC$).$ If the elasticity of these two enzymes in relation to carbamoyl

sosphate $($cp$)$ are ${}_{cp}^{CPS}=-0,05$ and ${}_{cp}^{\text{O}\text{T}\text{C}}=0,85,$ what are the values of their relative flux control

:oefficients $C_{CPS}^J$ and $C_{\text{O}\text{T}\text{C}}^J$ and which enzyme has the main flux control?