Study Guide - Protein Physics & Bioenergetics Course
A single-page review of core concepts, vocabulary, equations, and quick-reference tables for exams and problem sets.
Reinforce with the Bioenergetics Game.
| Term | Definition |
|---|---|
| Gibbs free energy (G) | Thermodynamic potential that combines enthalpy and entropy; at constant T and P, the direction of spontaneous change follows delta G for a defined process. |
| Enthalpy (H) | Heat content at constant pressure; bond making and breaking contributions appear in delta H for a reaction. |
| Entropy (S) | Measure of dispersal of energy and positional disorder; contributes -T delta S to delta G. |
| Exergonic | A process with negative delta G under stated conditions (spontaneous in the thermodynamic sense). |
| Endergonic | A process with positive delta G under stated conditions (requires coupling or driving input). |
| Standard transformed free energy (delta G°') | Standard free energy referenced to biochemical standard states (often 1 M total concentrations, pH 7 for biochemistry problems unless stated otherwise). |
| Equilibrium constant (Keq) | Ratio of product to reactant activities at equilibrium; relates to delta G°' by delta G°' = -RT ln Keq. |
| ATP | Adenosine 5'-triphosphate; central carrier of phosphoryl-group transfer potential in metabolism. |
| Phosphoryl transfer potential | Tendency of a phosphorylated compound to transfer phosphate to a suitable acceptor; higher means more negative delta G of hydrolysis under comparable conditions. |
| Phosphoenolpyruvate (PEP) | High-energy intermediate in glycolysis/gluconeogenesis with very high phosphoryl transfer potential. |
| Zwitterion | Dipolar form of an amino acid with a protonated cationic group and deprotonated anionic group near neutral pH. |
| pKa | Negative log of the acid dissociation constant; the pH at which half the species is protonated for a simple acid-base pair in ideal dilute solutions. |
| pI (isoelectric point) | pH at which the net charge of an amino acid or protein is zero (zwitterionic for simple amino acids). |
| Henderson-Hasselbalch equation | pH = pKa + log([A-]/[HA]) for a conjugate acid-base pair; links pH, ratio of species, and pKa. |
| Peptide bond | Amide linkage between amino acids; partial double-bond character restricts rotation and favors planarity. |
| Phi angle (phi) | Backbone dihedral about the N-Cα bond; one axis of the Ramachandran plot. |
| Psi angle (psi) | Backbone dihedral about the Cα-C bond; paired with phi on the Ramachandran plot. |
| Alpha-helix | Right-handed helical secondary structure stabilized by i to i+4 backbone hydrogen bonds along the helix axis. |
| Beta-sheet | Extended strands paired by hydrogen bonds, arranged parallel or antiparallel. |
| Ramachandran plot | Plot of phi versus psi showing sterically allowed backbone conformations and clusters for secondary structure. |
| Levinthal's paradox | Observation that random search over all backbone conformations cannot explain observed folding times; folding must be directed on an energy landscape. |
| Molten globule | Partially folded intermediate with native-like secondary structure but incomplete tertiary packing and increased hydrodynamic size. |
| Folding funnel | Free-energy landscape picture in which many unfolded states converge through downhill paths toward a narrow native ensemble. |
Non-standard conditions
delta G = delta G°′ + RT ln Q
Equilibrium
delta G°′ = -RT ln Keq
At 25 °C, RT ln(10) ~ 5.708 kJ/mol when using log10: delta G°′ (kJ/mol) ~ -5.708 log10 Keq.
Henderson-Hasselbalch
pH = pKa + log([A-]/[HA])
Isoelectric point (simple diprotic amino acid)
pI = (pKa1 + pKa2) / 2
Use the two pKa values that bracket the neutral zwitterion. For acidic side chains (Asp, Glu), average the two lowest pKa values that flank the neutral form; for basic side chains (Lys, Arg, His), average the appropriate pair for the zwitterionic species.
Approximate ranking by hydrolysis driving force under biochemical standard-state conventions (more negative delta G°′ of hydrolysis ~ higher transfer potential). Exact numbers vary slightly by source and ionic conditions.
| Compound | Notes |
|---|---|
| Phosphoenolpyruvate (PEP) | Among the highest in glycolysis; drives ATP synthesis via pyruvate kinase. |
| 1,3-Bisphosphoglycerate | Mixed anhydride; substrate-level phosphorylation to ATP. |
| Creatine phosphate | Rapid phosphate reservoir in muscle and brain. |
| ATP | Central hub; hydrolysis to ADP + Pi or to AMP + PPi couples many cellular processes. |
| Glucose 6-phosphate | Lower transfer potential than ATP; phosphorylated hexose pool. |
| Glycerol 3-phosphate | Lower still; not used to resynthesize ATP directly in this manner. |
Typical textbook values at ~25 °C in dilute aqueous solution; proteins shift apparent pKa with microenvironment.
| Group | Representative pKa | Comments |
|---|---|---|
| Alpha-carboxyl (-COOH) | ~2.0-2.5 | First to lose a proton on titration from acidic pH. |
| Side-chain carboxyl (Asp, Glu) | ~3.9-4.5 | Negative charge dominates above ~pH 4-5. |
| Imidazole (His) | ~6.0 | Often protonated near physiological pH; key in catalysis and buffering. |
| Alpha-amino (-NH3+) | ~9.0-9.5 | Deprotonates at high pH. |
| Side-chain sulfhydryl (Cys) | ~8.3 | Ionization relevant for disulfide chemistry and metal binding. |
| Phenolic OH (Tyr) | ~10.1 | Often still protonated at pH 7 unless environment lowers pKa. |
| Side-chain amino (Lys) | ~10.5 | Typically +1 at pH 7. |
| Guanidinium (Arg) | ~12.5 | Remains protonated across physiological pH. |
| Feature | Alpha-helix | Beta-sheet | Beta-turn |
|---|---|---|---|
| Backbone H-bonds | i to i+4 carbonyl-amide pairs along the helix | Between adjacent strands (parallel or antiparallel) | Often stabilizes chain reversal (3-10 or type I/II turns) |
| Phi / psi (typical) | Near -60°, -45° (Ramachandran cluster) | Extended near -120°, +120° (varies) | One or more residues adopt less common combinations |
| Rise per residue | ~1.5 A along the helix axis | Strand spacing ~3.3-3.5 A between paired strands | Reverses direction over a few residues |
| Side-chain packing | Outward from helix axis | Alternating above/below sheet plane | Often Gly/Pro enriched at tight positions |
Q1.Starting from delta G°' = -RT ln Keq, derive how a 10-fold change in Keq at 298 K alters delta G°' when using log10.
Using ln Keq = ln(10) log10 Keq, delta G°' = -(RT ln(10)) log10 Keq. At 298 K, RT ln(10) ~ 5.71 kJ/mol, so each 10-fold increase in Keq makes delta G°' about -5.71 kJ/mol more favorable (more negative). A 10-fold decrease in Keq shifts delta G°' by about +5.71 kJ/mol.
Q2.Why is ATP hydrolysis a reliable biochemical 'motor' even though its delta G under cellular conditions differs from delta G°'?
delta G°' ranks relative phosphoryl transfer potential versus a standard state, while actual delta G depends on concentrations through delta G = delta G°' + RT ln Q. Cells maintain high ATP/ADP ratios and rapidly consume Pi sinks in coupled pathways, so ATP hydrolysis often remains strongly exergonic in vivo. Coupling to endergonic steps is achieved when Q for the coupled network favors product formation.
Q3.Explain how the Ramachandran plot rationalizes proline and glycine outliers in quality checks of crystal structures.
Most residues cluster in allowed regions because of steric exclusion. Glycine lacks a beta carbon, so its map is unusually permissive and glycines can occupy Ramachandran regions forbidden for other amino acids. Proline constrains phi and often appears in turns; unusual combinations may be real but warrant scrutiny. Outliers can indicate model error, alternative conformations, or true exceptions.
Q4.A protein intermediate shows native-like CD spectra, increased ANS fluorescence, and a larger Stokes radius than the native state. What state is this consistent with, and why?
This pattern matches a molten globule or other compact non-native intermediate: CD implies secondary structure, ANS reports solvent-exposed hydrophobic clusters not yet buried as in the native fold, and increased hydrodynamic radius indicates incomplete packing relative to the native globule.
Q5.Calculate the pH of a buffer containing 0.02 M acetic acid and 0.08 M acetate if pKa = 4.76.
Apply Henderson-Hasselbalch: pH = 4.76 + log([A-]/[HA]) = 4.76 + log(0.08/0.02) = 4.76 + log(4) ~ 4.76 + 0.60 = 5.36.
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