Protein Folding, Purification, Structure Determination, and Regulation

Amino Acid Structure, Properties, and Classification

• General Formula of an Amino Acid:

  • Every amino acid consists of a central asymmetric ̑\alpha-carbon atom ($\mathrm{C_\alpha}$) covalently bonded to four groups:

    1. An amino group ($-\mathrm{NH_2}$ / $\mathrm{-NH_3^+}$).

    2. A carboxyl group ($-\mathrm{COOH}$ / $\mathrm{-COO^-}$).

    3. A hydrogen atom ($-\mathrm{H}$).

    4. A distinctive side chain ($-\mathrm{R}$).

  • There are $20$ natural side chains ($\mathrm{R}$ groups) commonly found in proteins.

• Ionization State at Physiological pH:

  • At $pH\,7$, both the amino group and the carboxyl group exist in their ionized states ($\mathrm{-NH_3^+}$ and $\mathrm{-COO^-}$).

• Optical Isomerism (Stereoisomerism):

  • Because the $\alpha$-carbon atom is asymmetric, amino acids exist as two mirror-image optical isomers (stereoisomers): the $L$--isomer and the $D$--isomer.

  • Proteins are composed exclusively of $L$--amino acids.

• Classification and Side Chain Functionality:

  • The functionality of an amino acid is conferred by its specific side chain ($\mathrm{R}$ group).

  • A side chain categorized as nonpolar is still capable of forming hydrogen bonds; however, the hydrogen bonds it forms are intrinsically weak.

Water Structure, Dynamics, and Solute Interactions

• Geometric Definition of Water Hydrogen Bonds:

  • A hydrogen bond between two water molecules is defined geometrically by two parameters:

    • Distance ($d$): d < 3.5\,\text{™}.

    • Angle ($\theta$): \theta < 30^\circ.

  • The bond strength of a water-water hydrogen bond is approximately $5\text{--}10\,\mathrm{kcal\,mol^{-1}}$, which is roughly $1/20\text{th}$ the strength of a standard covalent bond.

• Bulk Water Structure and Dynamic Timescales:

  • Short Timescale (< 1\,\mathrm{ps}): Bulk water behaves as a gel composed of a continuous, unbroken hydrogen-bonded network.

  • Longer Timescale ($\mathrm{ps\text{--}ns}$): Molecular rotations and thermal motions cause individual hydrogen bonds to break and re-form in new configurations. This creates continuously shifting local discontinuities whose magnitude and influence depend on temperature and pressure.

• Classification of Hydrogen Bonds:

  • Strong Hydrogen Bonds ($5\text{--}10\,\mathrm{kcal\,mol^{-1}}$): The hydrogen-bond donor is a strong polar covalent bond.

    • Examples: $\mathrm{H_2O \cdots H-O-}$, $\mathrm{-C=O \cdots H-O-}$, $\mathrm{-C=O \cdots H-N-}$.

  • Weak Hydrogen Bonds ($1\text{--}2\,\mathrm{kcal\,mol^{-1}}$): The hydrogen-bond donor is a weak polar covalent bond.

    • Examples: $\mathrm{H_2O \cdots H-C-}$, $\mathrm{-C=O \cdots H-C-}$.

• Solute-Water Interactions:

  • Adding a solute (small molecule or macromolecule) to water disrupts native water-water packing and hydrogen bonding, incurring an energetic cost.

  • Hydrophilic Solutes (Polar): Dissolve in water because the loss of water-water interactions is energetically compensated by the formation of favorable solute-water hydrogen bonds.

  • Hydrophobic Solutes (Non-polar): Do not dissolve in water because they fail to compensate for the lost water-water interaction energy.

Amino Acid Side Chain Ionization States

• Determinants of Charge State:

  • The charge state of a polar side chain depends on:

    1. The environmental $pH$

    2. The acid dissociation constant ($pKa$) of the side chain.

  • The $pKa$ value of a polar side chain is not fixed; it varies based on its local microenvironment.

• Ionization States in Bulk Water at Physiological $pH\,7.4$:

  • Aspartate (Asp) and Glutamate (Glu): Negatively charged ($pKa \approx 4$).

  • Arginine (Arg) and Lysine (Lys): Positively charged ($pKa \approx 10.5$).

  • Histidine (His): Uncharged / neutral ($pKa \approx 6$). In a neutral histidine side chain, only one of the two ring nitrogens is bonded to a hydrogen atom.

Peptide Bond Formation and Polypeptides

• Dehydration Condensation Reaction:

  • Proteins are formed through dehydration reactions, a subset of condensation reactions, in which the carboxyl group of one amino acid reacts with the amino group of another, eliminating a molecule of water ($\mathrm{H_2O}$).

  • The reverse process, which breaks down the peptide backbone using water, is hydrolysis.

• Peptide Bond:

  • The resulting covalent linkage connecting the adjacent amino acid residues is termed a peptide bond.

Thermodynamics and Forces of Protein Folding

• Principles of Folding:

  • The secondary and tertiary structure of a protein is dictated by its primary amino acid sequence and its local environment.

  • A protein adopts a conformation that minimizes the total free energy ($G$) of the entire system (protein + environment), rather than just the free energy of the protein alone.

• Thermodynamic State Variables:

  • Gibbs Free Energy Equation:         ̑G = H - TS         where $H$ is enthalpy, $T$ is absolute temperature in Kelvin, and $S$ is entropy.

  • Enthalpy Equation:         ̑H = U + PV         where $U$ represents internal energy (the average sum of all atomic interaction energies), $P$ represents pressure, and $V$ represents volume. The $PV$ term equals zero if experimental pressure is not actively maintained.

  • Entropy ($S$): A state variable measuring system disorder and state multiplicity.

• Thermodynamic Balance of Protein Folding:

  • For an unfolding/folding equilibrium reaction $\mathrm{Y_{unfolded} \rightleftharpoons Y_{folded}}$, the free energy change is:         ̑\Delta G = G_f - G_u = (H_f - H_u) - T(S_f - S_u) = \Delta H - T\Delta S

  • Protein folding restricts conformational mobility, resulting in a negative change in entropy (\Delta S < 0), which makes the entropic term positive (-T\Delta S > 0).

  • For protein folding to be thermodynamically favorable (\Delta G < 0), the enthalpy change must be negative (\Delta H < 0, meaning H_f < H_u). The gain in favorable intramolecular and solute-solvent non-covalent interactions in the folded state must energetically outweigh the loss in conformational entropy.

• Fundamental Physical Forces:

  1. Strong Force: Short-ranged between sub-atomic particles.

  2. Weak Force: Short-ranged between sub-atomic particles.

  3. Gravitational Force: Long-ranged between mass particles; negligible at the atomic level.

  4. Electromagnetic Force: Long-ranged force between charged and/or magnetic particles.

• Relevant Biological Electromagnetic Forces:

  • Electrostatic Forces:

    • Charge-charge interactions (e.g., salt bridges between acids and bases).

    • Charge-dipole interactions (e.g., Arginine side chains interacting with water).

    • Dipole-dipole interactions (e.g., hydrogen bonds between backbone/side chains and water).

    • Charge-induced dipole and dipole-induced dipole interactions.

  • Electrodynamic Forces:

    • van der Waals forces, occurring as attractions between transient, fluctuating dipoles in all closely packed atoms.

• Hydrophobic Core Formation:

  • In aqueous environments, soluble globular proteins fold into compact shapes to sequester nonpolar and hydrophobic side chains inside an internal core, away from solvent water, while exposing polar hydrophilic residues to the exterior.

Hierarchical Levels of Protein Structure

• Primary Structure: The linear covalent sequence of amino acids linked by peptide bonds.

• Secondary Structure: Local structural conformations formed by hydrogen bonding between peptide backbone atoms (carbonyl oxygens and amide hydrogens), independent of side chain atoms.

  • ̑\alpha-Helix:

    • Backbone carbonyl oxygen of residue $i$ forms a hydrogen bond with the backbone amide nitrogen of residue $i+4$

    • Completes $1$ full turn every $4$ amino acid residues.

  • ̑\beta-Sheet:

    • Adjacent polypeptide strands linked side-by-side by backbone hydrogen bonds, adopting either a parallel or antiparallel arrangement.

  • Ramachandran Plot:

    • Maps permitted polypeptide backbone dihedral angles $\phi$ (phi) and $\psi$ (psi).

    • Common allowed conformations: Right-handed $\alpha$-helix and $\beta$-sheets.

    • Rare conformation: Left-handed $\alpha$-helix.

    • Sterically disfavored regions exist where non-bonded atomic overlap occurs (such as $\phi = 90^\circ, \psi = -90^\circ$).

  • Secondary Structure Breakers:

    • Glycine: Lacks a side chain ($\mathrm{R = H}$), granting it exceptional dihedral angle flexibility.

    • Proline: Ring structure lacks a backbone amide hydrogen (preventing backbone H-bonding) and rigidly constrains backbone $\phi$ and $\psi$ angles.

• Tertiary Structure: The overall 3D shape of a single polypeptide chain containing one or more secondary structures.

  • Stabilized by non-covalent interactions (salt bridges, charge-dipole, van der Waals interactions) and covalent disulfide bridges formed between cysteine residues.

• Quaternary Structure: The 3D arrangement of a protein complex composed of more than one polypeptide chain (subunits).

  • Example: Hemoglobin, which exists as a heterotetramer.

• Protein Domains:

  • A modular unit within a polypeptide chain that folds independently and maintains a self-stabilizing structure.

  • Typically linked to specific biological functions (e.g., Src protein kinase contains three domains dedicated to regulation and catalysis).

  • Domain shuffling during evolution has combined functional domains across different protein families:

    • Calcium-binding domains.

    • "Kringle" domains containing $3$ internal disulfide bonds.

    • Epidermal growth factor (EGF) domains found in proteases.

Disordered Regions and Protein Denaturation

• Intrinsically Disordered Proteins (IDPs):

  • Proteins that contain extended unstructured segments that do not adopt a fixed 3D structure in solution, remaining as random coils.

  • Less than $30\%$ of structured proteins possess zero disorder; disorder exists along a spectrum from level $0$ to level $7$

  • Biological Functions: Essential for scaffolding, cellular signaling, and gene regulation.

  • Structural Flexibility: IDPs can adopt distinct 3D structures depending on which specific protein partner they bind (e.g., p53 binds diverse partners including Cyclin A2, S100̑\beta\beta, CBP, Sirtuin, Set9, tGcn5, Rpa70, Mdm2, Tfb1, and p53 itself).

• Methods of Protein Denaturation (Unfolding):

  • Altering amino acid sequence composition.

  • Increasing temperature.

  • Changing solvent properties or ionic strength.

  • Altering environmental $pH$

  • Adding chemical denaturants:

    • Urea ($8\,\mathrm{M}$): Denatures proteins by binding more strongly to the polypeptide backbone than water does, and by engaging nonpolar groups through van der Waals interactions.

    • Sodium Dodecyl Sulphate (SDS): Dissociates in water into $\mathrm{Na^+}$ and dodecyl sulphate ions. The hydrophobic tail coats nonpolar amino acid residues, unfolding the protein and imparting a uniform negative charge-to-mass ratio. SDS cannot unfold membrane proteins because their exterior surfaces are inherently hydrophobic.

    • ̑\beta-Mercaptoethanol: Cleaves covalent disulfide bridges between cysteine residues via reduction.

Chaperones and Biological Protein Folding

• Chaperone Function:

  • Specialized helper proteins that assist in folding newly synthesized polypeptides as they emerge from the ribosome.

  • Many chaperones are classified as Heat Shock Proteins (HSPs) because their transcription is induced by elevated temperatures.

• Mechanism of Action:

  1. A newly synthesized, partially folded polypeptide is sequestered within the isolated central chamber of the chaperone complex.

  2. A cap binds to the chamber, isolating the polypeptide to allow correct folding without risk of aggregation with other proteins.

  3. Dissociation of the cap releases the correctly folded protein into the cytosol.

Protein Purification: Lysis, Fractionation, and Separation

• Model Systems for Protein Source:

  • Tissue Culture: Inexpensive, accessible, allows large-scale cell harvesting, human cell compatible.

  • Yeast: Inexpensive, rapidly yields high cell volume.

  • C. elegans: Transparent body structure enables direct imaging; short life cycle.

  • Drosophila melanogaster: Simple breeding, established genetic phenotypes.

  • Mouse: Shares $99\%$ of human genes; model for complex physiology.

  • Arabidopsis thaliana: Smallest known plant genome; distinct developmental phenotypes.

• Step 1: Cell Lysis (Homogenization Methods):

  1. Sonication: Disrupts plasma membranes using high-frequency sound (ultrasound).

  2. Detergent Permeabilization: Uses mild detergents to create holes in the plasma membrane.

  3. High-Pressure Extrusion: Forces cell suspensions through a narrow orifice under high pressure.

  4. Mechanical Shearing: Shears cells between a close-fitting rotating plunger and the thick glass wall of a vessel.

• Step 2: Fractionation via Centrifugation:

  • Ultracentrifuge Parameters: Rotational speeds up to $100,000\,\mathrm{rpm}$ producing gravitational forces up to $600,000 \times g$. Requires armored plating, vacuum systems, and refrigeration to counteract air friction heating.

  • Rotor Types:

    • Fixed-angle rotors: Hold larger liquid volumes, but produce an uneven pellet along the tube side.

    • Swinging-arm rotors: Swing out horizontally during rotation, yielding an even pellet at the bottom of the tube.

  • Differential Centrifugation Protocol:

    • Low-speed centrifugation: Pellets whole cells, nuclei, and cytoskeletons (Pellet 1).

    • Medium-speed centrifugation: Pellets mitochondria, lysosomes, and peroxisomes (Pellet 2).

    • High-speed centrifugation: Pellets closed endoplasmic reticulum fragments and small vesicles (Pellet 3).

    • Very high-speed centrifugation: Pellets ribosomes, viruses, and large macromolecules (Pellet 4).

• Step 3: Protein Separation Techniques:

  • Polyacrylamide Gel Electrophoresis (PAGE): Polyacrylamide forms a cross-linked matrix with uniform, controllable pore sizes capable of resolving proteins from $5\,\mathrm{kDa}$ to $2,000\,\mathrm{kDa}$.

    • Native PAGE: Separates proteins based on combined native shape and net charge. Compact or highly charged negative proteins move fastest.

    • Non-native PAGE: Denatures proteins prior to running (using heat, urea, or $\beta$-mercaptoethanol). Separates proteins based on polypeptide chain length/mass and net charge.

    • SDS-PAGE: SDS coats denatured proteins to provide a uniform negative charge per unit length. Because all proteins assume an equivalent charge-to-mass ratio, migration speed depends strictly on molecular weight/length. Provides a rough estimate of peptide mass.

    • Isoelectric Focusing (IEF) PAGE: Separates proteins along a stationary pH gradient based on their Isoelectric Point ($pI$)—the pH at which a protein carries a net zero charge. Migration stops at $pH = pI$ because the electric field exerts no force on a charge-neutral molecule.

    • Two-Dimensional (2-D) PAGE: Combines IEF in the first dimension (separating solely by $pI$) with SDS-PAGE in the second dimension (separating solely by mass).

  • Column Chromatography:

    • Gel-Filtration Chromatography: Separates by size using porous beads. Small molecules enter bead pores and are retarded; large molecules are excluded and elute rapidly.

    • Ion-Exchange Chromatography: Separates by charge using positively or negatively charged beads to bind oppositely charged proteins.

    • Affinity Chromatography: Separates by binding specificity using beads coupled to a specific substrate or ligand, selectively retaining target enzymes while non-binding proteins flow through.

Methods for Structural Determination

• X-ray Diffraction:

  • Directs an X-ray beam at a crystal; scattered X-rays reflect off atomic electron density to produce diffraction patterns.

  • Requirements & Features: Requires protein crystallization; no upper protein size limit; captures a static picture; susceptible to crystal packing artifacts.

• Nuclear Magnetic Resonance (NMR) Spectroscopy:

  • Measures structural positioning based on the intrinsic magnetic moments of atomic nuclei (e.g., hydrogen).

  • Requirements & Features: Requires soluble protein; limited to small proteins (< 50\,\mathrm{kDa}); captures dynamic solution states; free from crystal packing artifacts.

• Cryogenic Electron Microscopy (Cryo-EM):

  • Passes an electron beam through a frozen sample to record thousands of 2D projection images, which are computationally reconstructed into a 3D structure.

  • Requirements & Features: Does not require protein crystals; captures dynamic functional movements; suitable for small proteins as well as large macromolecular complexes.

• Computer Simulations & AI:

  • Utilizes Molecular Dynamics (MD) simulations and machine learning algorithms.

  • Example: DeepMind’s AlphaFold predicts structures where $76\%$ of residue positions show structural deviations under $3\,\text{<span data-name="tm" data-type="emoji">™</span>}$ compared to empirical experiment.

Regulation of Protein Activity and Post-Translational Modifications

• Levels of Regulation: Protein activity is regulated at the transcriptional, translational, and post-translational levels.

• Regulation via Reversible Non-Covalent Interactions:

  • Ligand Binding: Activity is modulated by non-covalent binding of metal ions, small organic/inorganic molecules, nucleotides, or other proteins.

  • Example (Protein Kinase A): Cyclic AMP (cAMP) binds reversibly to the repressor ($\mathrm{R}$) subunit of PKA, releasing active PKA kinase.

  • Protein Interactomes: Physical interaction networks between proteins within a cell.

• Quantitative Thermodynamics of Binding Affinity:

  • For a reversible binding reaction $\mathrm{A + B \rightleftharpoons AB}$, the rates of association and dissociation are:         ̑R_{on} = k_{on}[\mathrm{A}][\mathrm{B}]         ̑R_{off} = k_{off}[\mathrm{AB}]

  • At equilibrium ($R_{on} = R_{off}$):         ̑k_{on}[\mathrm{A}][\mathrm{B}] = k_{off}[\mathrm{AB}]

  • The Dissociation Constant ($K_d$) and Association Constant ($K_a$) are defined as:         ̑K_d = \frac{k_{off}}{k_{on}} = \frac{[\mathrm{A}][\mathrm{B}]}{[\mathrm{AB}]}         ̑K_a = \frac{1}{K_d}

  • Affinity Interpretation: A smaller $K_d$ value indicates a higher binding affinity.

    • Sample Calculation 1: Initial $\mathrm{[MyProtein] = 1\,M}$, $\mathrm{[A] = 1\,M}$. At equilibrium, $\mathrm{[MyProtein] = 0.001\,M}$, $\mathrm{[A] = 0.001\,M}$, $\mathrm{[MyProtein\cdot A] = 0.999\,M}$.             ̑K_d = \frac{(0.001)(0.001)}{0.999}\,\mathrm{M} \approx 10^{-6}\,\mathrm{M} = 1\,\mu\mathrm{M}

    • Sample Calculation 2: Initial $\mathrm{[MyProtein] = 1\,M}$, $\mathrm{[B] = 1\,M}$. At equilibrium, $\mathrm{[MyProtein] = 0.5\,M}$, $\mathrm{[B] = 0.5\,M}$, $\mathrm{[MyProtein\cdot B] = 0.5\,M}$.             ̑K_d = \frac{(0.5)(0.5)}{0.5}\,\mathrm{M} = 0.5\,\mathrm{M}

  • Binding Specificity: Determined by comparing relative $K_d$ values of a protein for different competing ligands.

• Regulation via Covalent Modifications (Post-Translational Modifications - PTMs):

  1. Phosphorylation: Covalent addition of a phosphate group to Serine, Threonine, or Tyrosine residues; adds negative charge.

  2. Methylation: Addition of methyl groups to Lysine or Arginine by methyltransferases (removed by demethylases). Occurs as unmethylated ($\mathrm{Me0}$), monomethylated ($\mathrm{Me1}$), dimethylated ($\mathrm{Me2}$), or trimethylated ($\mathrm{Me3}$) states. Increases side chain hydrophobicity without changing its positive charge.

  3. Palmitoylation: Covalent attachment of a palmityl fatty acid chain to a Cysteine residue. Targets and anchors the protein to lipid bilayer membranes; depalmitoylation releases it into the cytosol.

  4. Acetylation: Attachment of an acetyl group to Lysine residues by Lysine Acetyltransferases (KATs) and removed by Lysine Deacetylases (KDACs). Neutralizes the positive charge on Lysine.

  5. Ubiquitination: Covalent linkage of the C-terminus of Ubiquitin to a Lysine residue on a target substrate:

     • Mono-ubiquitination: Regulates endocytosis, protein transport, DNA repair, and histone function.

     • Multi-ubiquitination: Regulates endocytosis.

     • Poly-ubiquitination (Lysine 63 / K63 linkage): Mediates endocytosis, DNA repair, and signaling.

     • Poly-ubiquitination (Lysine 48 / K48 linkage): Targets the protein for proteasomal degradation.

• Multimodal Integration of Activity (Src Kinase Example):

  • Src kinase fully activates only when three simultaneous conditions are met:

    1. Removal of an inhibitory phosphate from its C-terminal tyrosine.

    2. Binding of an activating ligand to its SH3 domain, loosening the inactive tertiary structure.

    3. Autophosphorylation of a specific active-site tyrosine residue.

• Allosteric vs. Non-Allosteric Regulation:

  • Allosteric Regulation: Occurs when a regulatory molecule binds to an allosteric site physically distinct from the catalytic active site, inducing a conformational change that alters active site function.