Biochem Sept. 11th
Ionizable side chains and charge calculations
Histidine example: the side chain can be protonated or deprotonated depending on pH relative to its pKa (around 6). In the deprotonated form the side chain is neutral; when protonated it carries a +1 charge.
At pH = 4 (pH is 2 units below pKa): the side chain is protonated; side-chain charge = $+1$, so the whole histidine has net charge +1 (ignoring the fixed charges of the amino and carboxyl groups already discussed in class).
At pH = 5 (pH is 1 unit below pKa): ~90% protonated, ~10% deprotonated; side-chain charge ≈ +0.9; net histidine charge ≈ +0.9.
At pH = 6 (pH ≈ pKa): ~50% protonated, ~50% deprotonated; side-chain charge ≈ +0.5; net histidine charge ≈ +0.5.
At pH higher than pKa by 2 units (e.g., pH ≈ 8): deprotonated form dominates and the side chain is neutral; net charge ≈ 0.
General procedure for calculating charge of ionizable side chains:
Identify protonated (positive) and deprotonated (neutral or negative) forms and their charges.
Use the pKa and pH to determine the fraction in each form (when appropriate). A useful relation for acids is:
f{ ext{protonated}} = \frac{1}{1+10^{\,pH - pKa}}Then assign charges and sum for the full amino acid.
Examples with other ionizable groups:
Glutamic acid: side chain contains a carboxyl group; deprotonated form carries a -1 charge.
Cysteine: side chain is –SH; protonated form is neutral; deprotonated form is –S⁻ with charge -1.
For context, consider a scenario where the side-chain pKa is 8 and pH = 7: f{ ext{protonated}} = \frac{1}{1+10^{7-8}} = \frac{1}{1+0.1} \approx 0.91,
so about 91% protonated (neutral on the side chain for cysteine, if it behaves as a typical thiol), and about 9% deprotonated (–S⁻, charge -1) contributing roughly a -0.09 charge from that side chain.
Practical note: in textbooks you can encounter more complex questions (e.g., for a tripeptide) where you must compute charges for the N-terminus amino group, the C-terminus carboxyl group, and all ionizable side chains. In most midterms you’ll likely encounter simpler versions focusing on a single amino acid or a single ionizable group.
Takeaway: protonation state and charge of ionizable side chains depend on pH relative to pKa; use the protonated/deprotonated forms and their charges to compute the net charge of the residue or peptide.
From amino acids to polypeptides: linking concepts
Building blocks: amino acids join via peptide bonds to form polypeptides.
Peptide bond characteristics:
Formed by a condensation reaction between the amine of one amino acid and the carboxyl of the next.
The peptide bond has partial double-bond character (~40%), due to resonance, which restricts rotation around the bond.
As a result, the bond is planar and all the peptide units tend to lie in a plane (peptide planes).
The N–Cα and Cα–C' bonds can rotate, allowing the chain to adopt different conformations (torsion angles).
Orientation and terminology:
N-terminus = amino terminus; C-terminus = carboxyl terminus.
In a sequence read from N-terminus to C-terminus, you consider the amino group at the N-terminus and the carboxyl group at the C-terminus when counting charges for a short peptide.
Planarity and rotations in detail:
Peptide bond: fixed plane due to partial double-bond character; cannot rotate.
N–Cα and Cα–C' bonds: can rotate; their rotation is described by phi (ϕ) and psi (ψ) torsion angles, which change the overall conformatTellion.
Conceptual model of folding:
A polypeptide chain can be visualized as a series of planar peptide groups connected by rotatable bonds; rotations change the overall 3D shape.
The final fold results from the interplay of local interactions (secondary structure formation) and long-range interactions between distant residues.
A computer-based folding simulation often starts from an extended chain and allows rotation around ϕ and ψ to approach a low-energy, stable structure.
Analogy used in teaching: the snake cube toy illustrates how rotating joints can yield many conformations from a common chain.
Structural representations used in practice:
Backbone-only models: show the connection pattern without side chains.
Ribbon (or Rope/Ribbon) diagrams: emphasize secondary structure elements (helices, sheets).
Wire models: show side-chain orientations.
Space-filling models: emphasize overall shape and surface.
Electrostatic surface maps:
Visualize charge distribution on protein surfaces using electrostatic potential maps (e.g., negative vs. positive regions).
Useful for understanding protein–protein interactions and binding surfaces.
Levels of protein structure
Primary structure:
Definition: the linear sequence of amino acid residues in a protein.
Key point: Knowing the sequence alone does not reveal the 3D structure.
There are 20 standard amino acids; proteins vary in length and composition.
Secondary structure:
Local spatial arrangement of the backbone of the polypeptide.
Two major types:
Alpha helix: a right-handed helix stabilized by backbone hydrogen bonds.
Beta sheet: extended strands stabilized by hydrogen bonds between backbone atoms of adjacent strands.
Other minor forms (turns, etc.) exist but are not the main focus here.
Stabilization: backbone hydrogen bonds (between amide N-H and carbonyl C=O) stabilize helices and sheets; side chains are not required for these backbone interactions.
Tertiary structure:
The overall 3D arrangement of a single polypeptide chain, including how its side chains interact with each other and with the backbone.
Describes the compact folding of the entire chain into a unique 3D shape, including long-range interactions between distant residues.
Quaternary structure:
Spatial arrangement of multiple polypeptide chains (subunits) in a protein that contains more than one chain.
Subunits may assemble independently and then come together to form the functional protein.
Example mentioned: hemoglobin, which has multiple subunits with distinct behaviors.
Secondary structures in detail
Alpha helix:
Cylindrical, rigid structure with side chains projecting outward.
Typical geometry: about 3.6 residues per turn and rise of about 5.4\;\text{Å} per turn.
Hydrogen bonds form between backbone N–H and C=O groups four residues apart (i to i+4).
Side chains extend outward, enabling inter-helix interactions (e.g., ionic interactions between opposing charges on neighboring helices).
Beta sheet:
Made of beta strands aligned side-by-side and connected by hydrogen bonds between backbone atoms.
Strands can be parallel (same N→C termini direction) or antiparallel (opposite directions).
Hydrogen bonds are between backbone atoms of adjacent strands; not involving side chains.
In the sheet, side chains project alternately above and below the plane (ridges alternate).
Antiparallel beta sheets tend to have more linear (stronger) hydrogen bonds because the donor, hydrogen, and acceptor lie on a straight line.
General points about hydrogen bonding in secondary structures:
Stabilizes the structure but is relatively weak compared to covalent bonds; about a small fraction of strength of a covalent bond in water, but many such hydrogen bonds cumulatively stabilize the structure.
The strength of a hydrogen bond depends on geometry (straight line more favorable) and orientation of donor/acceptor.
Beyond secondary structure: stability and interactions
Forces stabilizing protein structure (in aqueous environments):
Covalent bonds (e.g., disulfide bridges) are the strongest stabilizing interactions.
Ionic (salt-bridge) interactions between oppositely charged residues (e.g., Lys/Arg with Asp/Glu) can be strong but are weakened in water.
Hydrogen bonds (backbone and side-chain) contribute significantly to stability, especially in secondary structures.
Van der Waals interactions also contribute to overall stability and packing.
Environment matters:
In aqueous solution, ionic interactions are weaker than in vacuum because water stabilizes separated ions.
Disulfide bonds form only under oxidizing conditions; in reducing environments they do not form.
Common charged residues and interactions:
Positive residues: Lysine (Lys), Arginine (Arg).
Negative residues: Glutamate (Glu), Aspartate (Asp).
Ionic interactions (salt bridges) can occur between, for example, Lys/Asp or Arg/Glu when in close spatial proximity.
Special case: cysteine and disulfide bonds:
Two cysteines can form a disulfide bond (–S–S–) under oxidizing conditions, covalently linking parts of a single chain or different chains.
This bond is a major stabilizing feature for some extracellular proteins, but it is sensitive to the redox environment.
Practical implication for exams and problem-solving:
You may be asked to determine whether residues will be charged as a function of pH, or to assess how a particular environment would affect ionic bonds or disulfide formation.
Be prepared to analyze how the secondary structure elements interact with one another in tertiary structure or how multiple subunits come together in quaternary structure.
Quick practice and exam strategies referenced in the lecture
A common exam question type involves determining the charge of a peptide or small protein at a given pH by considering:
The N-terminus amino group
The C-terminus carboxyl group
Ionizable side chains (e.g., histidine, lysine, arginine; aspartate, glutamate; cysteine, tyrosine, etc.)
Remember: the charge of a residue depends on its protonation state, which is dictated by its pKa and the ambient pH.
Conceptual distinctions you should be able to articulate:
Primary structure vs. secondary structure vs. tertiary structure vs. quaternary structure.
The difference between intra-chain interactions (tertiary) and inter-chain interactions (quaternary).
Notable exam takeaway from the section:
The statement: "Tertiary structure refers to the interaction within the same polypeptide chain, while quaternary structure involves interactions between different polypeptide chains" is a common exam point; this is typically the true statement about tertiary vs. quaternary structure.
Summary connections to core principles
Protein structure emerges from the chemistry of the peptide bond, hydrogen bonding, and side-chain interactions.
Local (secondary) structures are stabilized by backbone hydrogen bonds and define the geometry of the backbone; global (tertiary) structure arises from side-chain interactions and long-range contacts.
Quaternary structure reflects how multiple polypeptide chains assemble and cooperate to form a functional protein complex.
Understanding how pH affects protonation states and how this translates to charge is essential for predicting protein behavior in different environments and for anticipating interactions (e.g., salt bridges, disulfide bonds).
The various representations (backbone models, ribbon models, wire models, space-filling models, electrostatic maps) provide complementary views that emphasize different aspects of protein structure and function.