1-3 The Physical Foundations

A cell exchanges both matter and energy with its surroundings; constancy of concentration is maintained by continuous flow.

• Open system — the cell exchanges matter and energy with its surroundings; the membrane is a selective boundary, not an absolute wall
• Energy input — harvested from carbohydrates and lipids or from light; partly spent on ATP synthesis, transport, motility and biosynthesis
• Output — heat and waste matter are released back to the surroundings
• Steady state ≠ equilibrium — in a steady state concentrations barely change while reactions and transport continue; at equilibrium the net driving force ΔG is zero
• Material balance — d[C]/dt = J_in − J_out + v_production − v_consumption
• Key point — d[C]/dt = 0 does not mean each flux or rate is zero
• Worked example — ATP production 8 and consumption 8 mmol·L⁻¹·min⁻¹ gives d[ATP]/dt = 0; if consumption rises to 11, the pool falls at 3 mmol·L⁻¹·min⁻¹ until regulation raises production

Catabolism releases energy and reducing power; anabolism spends them to build cell components.

• Metabolism — the network of enzyme-catalysed reactions inside the cell
• Catabolism — breaks nutrients into smaller molecules, passes electrons to reduced carriers, and yields energy for ATP synthesis
• Anabolism (biosynthesis) — builds amino acids, nucleotides and lipids into cell components, usually consuming ATP and NADPH
• First law — energy is neither created nor destroyed, only converted: ΔU = q + w for a closed system
• Three kinds of work — chemical (synthesis of protein and DNA), transport (ions moved against a gradient), mechanical (muscle contraction, motor proteins)
• Caveat — living systems are open, so the real energy balance includes energy carried by matter crossing the boundary

Oxidation and reduction are the currency; carriers split a large free-energy drop into manageable steps.

• Oxidation — loss of electrons; reduction — gain of electrons. The donor is oxidised, the acceptor reduced
• Carriers — NAD⁺/NADH, FAD/FADH₂, quinones, iron–sulfur proteins, cytochromes; electrons rarely travel free
• Electron transport chain — electrons pass through inner-membrane complexes to oxygen, forming water; some complexes pump H⁺ across the membrane
• Proton-motive force — the H⁺ concentration difference plus membrane potential drives ATP synthase
• Reduction potential — electrons flow favourably from a more negative to a more positive E°′
• Worked example — NAD⁺/NADH E°′ ≈ −0.32 V and O₂/H₂O E°′ ≈ +0.82 V give ΔE°′ = +1.14 V, so ΔG°′ = −2 × 96.485 × 1.14 ≈ −220 kJ/mol per NADH
• Caution — this is a theoretical standard value; the cell does not convert all of it into ATP

Entropy counts the microscopic arrangements consistent with a macroscopic state — not simply "tidiness".

• Boltzmann relation — S = k_B ln Ω links entropy to the number of microstates
• What changes entropy — heat flow, mixing, concentration change, and changes in molecular degrees of freedom
• Second law — ΔS_total = ΔS_system + ΔS_surroundings ≥ 0 for a spontaneous process in an isolated whole
• Why cells do not violate it — a cell maintains internal order by consuming nutrients and releasing heat and waste, which raises the entropy of the surroundings
• Common error — concluding "order increased, therefore impossible". Spontaneity is judged by ΔS_total, or by ΔG at constant temperature and pressure
• Thought experiment — separating a mixed solution generally requires work; selective membrane transport is how the cell sustains such gradients

ΔG combines enthalpy and entropy into a single criterion for direction at constant temperature and pressure.

• Definition — G = H − TS, so at constant T, ΔG = ΔH − TΔS
• Reading the sign — ΔG < 0 favours the forward reaction, ΔG > 0 favours the reverse, ΔG = 0 means equilibrium
• Exothermic ≠ spontaneous — a reaction with ΔH < 0 can be non-spontaneous if the entropy term is unfavourable
• Worked example — ΔH = +20 kJ/mol with ΔS = +0.10 kJ·mol⁻¹·K⁻¹ gives ΔG = 20 − 29.8 ≈ −9.8 kJ/mol at 298 K: endothermic yet favourable
• Temperature dependence — the −TΔS term grows with T, so the direction can change with temperature

An unfavourable reaction proceeds only when it shares a reaction pathway with a favourable one.

• Coupling — a common intermediate or a shared structural change connects the two reactions
• Additivity — for reactions that form one pathway, ΔG_overall = ΔG₁ + ΔG₂
• Not additivity by proximity — two reactions merely occurring in the same tube do not drive each other
• Glucose phosphorylation — hexokinase transfers the γ-phosphate of ATP to glucose, making the overall path favourable
• ATP hydrolysis — ΔG°′ ≈ −30.5 kJ/mol is commonly quoted at about 25 °C; the real value depends on pH, Mg²⁺ and ionic strength
• Misconception — "breaking a bond releases energy" is inaccurate: the net free-energy change comes from resonance stabilisation, hydration, ionisation and entropy of the products
• Other currencies — the H⁺ electrochemical gradient, NADPH reducing power, and Na⁺ or H⁺ symport/antiport

Standard conditions give ΔG°′; actual conditions give ΔG. Only ΔG answers "which way, now".

• Biochemical standard state — pH fixed at 7, so H⁺ activity is held constant; other solutes use their own reference states
• Reaction quotient Q′ — dimensionless combination of product and reactant activities at the current composition
• Relation — ΔG = ΔG°′ + RT ln Q′; at equilibrium ΔG = 0 and Q′ = K′eq, so ΔG°′ = −RT ln K′eq
• Constants — R = 8.314 J·mol⁻¹·K⁻¹; at 25 °C, RT ≈ 2.479 kJ/mol and RT ln 10 ≈ 5.708 kJ/mol
• Direction — Q′ < K′eq gives ΔG < 0 (forward favoured); Q′ > K′eq favours the reverse
• Worked example — K′eq = 100 gives ΔG°′ = −2.479 × 4.605 ≈ −11.42 kJ/mol; ΔG°′ = +5.71 kJ/mol gives K′eq ≈ 0.100
• Worked example — ΔG°′ = +5.71 kJ/mol with Q′ = 0.010 gives ΔG = 5.71 − 11.42 ≈ −5.71 kJ/mol: an unfavourable standard reaction running forward because products are scarce

Enzymes lower the activation barrier; they do not change ΔG or the equilibrium constant.

• Mechanism — stabilise the transition state or provide an alternative pathway, lowering ΔG‡
• Both directions — forward and reverse rates are accelerated equally, so K′eq is unchanged
• Active site — binds substrate and positions catalytic groups; uses electrostatics, hydrogen bonding, acid–base, covalent and metal-ion catalysis
• Induced fit — enzyme and substrate structures can change on binding; not every enzyme uses the same mechanism
• Michaelis–Menten — v₀ = V_max[S] / (K_m + [S]) for initial rates with negligible reverse reaction
• K_m — the substrate concentration giving v₀ = V_max/2; only under special conditions does it approximate a dissociation constant
• Pathways and bottlenecks — flux through A → B → C depends on each enzyme, substrate supply and product removal; do not assume the first enzyme is always rate-limiting

Regulation changes flux through pathways, not the equilibrium of individual reactions.

• Why regulation — overproduction wastes precursors and ATP; underproduction limits growth and function
• Negative feedback — the end product inhibits an earlier enzyme, lowering further production
• Allosteric control — binding at a site other than the active site changes enzyme structure or kinetics
• Timescales — allosteric control acts in seconds, covalent modification in minutes, changes in enzyme amount in hours to days
• Recovery — after a nutrient pulse, increased enzyme activity or use of alternative routes brings production and consumption back toward balance
• Signal ratios — ATP/ADP/AMP report energy status, NAD⁺/NADH reports redox tendency, NADPH/NADP⁺ supports reductive biosynthesis and antioxidant defence
• Reality — regulation is a network of integrated signals, not a single switch; delays and oscillations occur