Enzymes & Bioenergetics Basics

Question 1 (10 marks)

(a) (3)

• First Law: Energy cannot be created or destroyed, only transformed; total energy of cell + surroundings is constant. (1)
• Second Law: Every energy transfer increases the total entropy (disorder) of the universe; no transfer is 100% efficient — some energy is lost as heat. (2)

(b) (3)

• $\Delta G = \Delta H - T\Delta S$. (1)
• Spontaneous (exergonic) when $\Delta G < 0$. (1)
• Thus spontaneity favored when $\Delta H < 0$ (energy released) and/or $\Delta S > 0$ (entropy increase); the $T\Delta S$ term makes entropy more decisive at high $T$. (1)

(c) (4)

• The cell is an open system; the Second Law applies to the total (system + surroundings), not the system alone. (1)
• The cell builds order internally ($\Delta S_{cell} < 0$)… (1)
• …by releasing heat and disordered waste products to surroundings, so $\Delta S_{surroundings} > 0$. (1)
• Net $\Delta S_{universe} > 0$; order is "paid for" by greater disorder released outside. (1)

Question 2 (12 marks)

(a) (2) A is exergonic ($\Delta G < 0$); B is endergonic ($\Delta G > 0$). Criterion: sign of $\Delta G$. (2)

(b) (4)

• Coupled: $\Delta G_{total} = \Delta G_A + \Delta G_B = -30.5 + 13.8 = -16.7$ kJ/mol. (2)
• Since $\Delta G_{total} < 0$, the coupled reaction is spontaneous. (2)

(c) (4)

• Mere summation is a bookkeeping trick; real coupling requires a shared intermediate. (1)
• ATP transfers its terminal phosphate directly to glucose, forming glucose-6-phosphate + ADP in one enzyme-catalyzed step (phosphoryl transfer). (2)
• The energy is passed via a covalent phosphorylated intermediate, not by heat, so it can do useful chemical work. (1)

(d) (2) ATP stores readily releasable free energy in its phosphoanhydride bonds; hydrolysis/transfer drives endergonic reactions, making it the universal energy currency. (2)

Question 3 (10 marks)

(a) (4)

• $E_a$: minimum energy input needed for reactants to reach the transition state so the reaction can proceed. (2)
• Diagram: reactants high-ish → energy hump (transition state) → products lower (exergonic). Enzyme curve shows a lower hump; same start/end points. (2)

(b) (4)

• From $k = A e^{-E_a/RT}$, decreasing $E_a$ increases the exponent (less negative), so $k$ increases exponentially. (1)
• Fold-change = $e^{(\Delta E_a)/(RT)} = e^{20000/(8.314 \times 310)}$. (1)
• Exponent $= 20000/2577.3 = 7.760$. (1)
• Fold-change $= e^{7.76} \approx 2.35 \times 10^{3}$ (~2350×). (1)

(c) (2) Enzyme does not change $\Delta G$; it only lowers $E_a$ (both forward and reverse). $\Delta G$ depends solely on the energy states of reactants and products. (2)

Question 4 (10 marks)

(a) (4)

• Lock-and-key: rigid, pre-shaped active site complementary to a specific substrate; substrate fits like a key. (2)
• Induced-fit: active site is flexible; substrate binding induces a conformational change that molds the site around it. (2)

(b) (4)

• (i) A flexible site can adjust to accommodate related substrates, explaining broader (but limited) specificity — a rigid lock cannot. (2)
• (ii) The conformational change places strain/stress on substrate bonds, distorting it toward the transition state and thus lowering $E_a$ — explaining catalysis, not just binding. (2)

(c) (2) Active site = region where substrate binds and catalysis occurs. Specificity arises from complementary shape/charge of the active site to a particular substrate. (2)

Question 5 (12 marks)

(a) (4)

• Temperature: activity rises with $T$ (more kinetic energy/collisions) to an optimum, then falls sharply as heat denatures the enzyme (H-bonds break, shape lost). (2)
• $[S]$: activity rises then plateaus at $V_{max}$; plateau = all active sites saturated, so enzyme concentration becomes rate-limiting. (2)

(b) (4)

• Competitive: inhibitor resembles substrate, binds active site; raising $[S]$ outcompetes the inhibitor → activity/$V_{max}$ restored. (2)
• Non-competitive: inhibitor binds elsewhere (allosteric), altering active-site shape; raising $[S]$ does not relieve inhibition → $V_{max}$ stays lowered. (2)

(c) (4)

• Feedback inhibition: end product $D$ inhibits an early enzyme ($E_1$) in its own pathway, preventing overproduction — self-regulating economy. (2)
• Allosteric regulation: $D$ binds $E_1$ at an allosteric site (not the active site), changing its conformation and reducing activity; reversible on/off switch. (2)

Question 6 (6 marks)

(a) (3) Cofactor = non-protein helper needed for enzyme activity; can be inorganic (metal ions e.g. Mg²⁺, Zn²⁺). Coenzyme = an organic cofactor (often vitamin-derived, e.g. NAD⁺, FAD). Distinction: coenzymes are organic; cofactors is the broader term including inorganic ions. (3)

(b) (3) NAD⁺ picks up electrons/H (becomes NADH) in one reaction (e.g. glycolysis) and delivers them to a distant reaction (e.g. electron transport). It shuttles reducing power between spatially/temporally separate reactions, coupling catabolism to energy production. (3)

[
  {"claim":"Coupled reaction Q2b delta G = -16.7 kJ/mol and spontaneous","code":"dGa=-30.5; dGb=13.8; total=dGa+dGb; result=(abs(total-(-16.7))<1e-9) and (total<0)"},
  {"claim":"Q3b Arrhenius exponent = 20000/(R*T)","code":"R=8.314; T=310; expo=20000/(R*T); result=abs(expo-7.760)<0.01"},
  {"claim":"Q3b fold-change ~2350x","code":"import sympy as sp; R=8.314; T=310; fc=sp.exp(sp.Rational(20000)/(R*T)); result=abs(float(fc)-2350)<60"},
  {"claim":"Q2b spontaneity requires negative total","code":"total=-30.5+13.8; result=(total<0)"}
]