Biochemistry: Structural and Mathematical Overview

Biochemistry Overview

• Biochemistry can be divided into mathematical and theoretical sections.
• Mathematical questions often come from hardcore chemistry.
• Theoretical aspects divided into structural biochemistry and metabolism.
• Metabolism focuses on carbohydrate metabolism.

Structural Biochemistry

• Key topics include DNA/RNA structures, Ramachandran plot, hydropathy plot, protein structures, hemoglobin oxygen saturation curve, protein domains, and protein motifs.
• Questions are often application-based, such as predicting peptide fragment generation after enzyme treatment (e.g., trypsin).
• Avoid reading in-depth from textbooks like Lehninger or White and Voet due to time constraints.
• Focus on practicing mathematical problems and understanding key theoretical topics.
• Study metabolism from Lehninger and structural biochemistry from White and Voet.
• Carbohydrate metabolism is a primary source of questions.

Enzymes

• Mathematical questions about enzymes involve calculating turnover number.
• Focus on understanding enzyme inhibition types and their properties for theoretical questions.

Enzyme Function

• Enzymes lower the activation energy required for a reaction to occur.
• Enzymes facilitate reactions by forming an enzyme-substrate complex.
• The enzyme-substrate complex properly positions substrates and brings them closer together for faster reactions.
• Enzymes, as catalysts, accelerate the process of converting substrates into products.

Turnover Number (kcat)

• Turnover number (kcat) is the maximum number of substrate molecules converted to product per second by each active site of the enzyme.
• Its unit is substrate inverse.
• Catalytic efficiency is kcat/Km, representing the affinity of the substrate towards the enzyme.
• High catalytic efficiency is associated with a high turnover number and high affinity (low Km).
• kcat can be calculated as Vmax / [total enzyme concentration].

Catalytic Efficiency

• Catalytic efficiency is determined by dividing the turnover number (kcat) by the Michaelis constant (Km).
• The less Km, the higher the affinity and catalytic efficiency.
• The higher the turnover number, the higher the catalytic efficiency.
• Catalytic efficiency can be represented as Vmax / (Et * Km).

Substrate Conversion Time

• Reversing the kcat value (1/kcat) gives the time required for the enzyme to convert one substrate molecule into the product.
• kcat is the number of substrate molecules converted to the product per second per active site.
• 1/kcat is the time it takes for the enzyme to convert one substrate molecule.

Km and Vmax

• Km (Michaelis constant) is the substrate concentration at which the reaction rate is half of Vmax.
• Km measures the affinity of an enzyme towards its substrate.
• High Km indicates lower affinity, while low Km indicates higher affinity.

Enzyme Inhibition

• In competitive inhibition, the inhibitor binds to the active site.
• In non-competitive inhibition, the inhibitor can bind with the enzyme or enzyme-substrate complex.
• In uncompetitive inhibition, the inhibitor binds with the enzyme-substrate complex.

Effects of Inhibition

• Competitive inhibition: Vmax remains the same; Km increases.
• Non-competitive inhibition: Vmax decreases; Km is unaffected.
• Uncompetitive inhibition: Vmax decreases; Km decreases.

Enzyme Structures

• Primary Structure: Amino acid sequence.
• Secondary Structure: Interactions between amino acids, mainly through hydrogen bonding, forming alpha helices and beta sheets.
• Tertiary Structure: Three-dimensional folding of secondary structures, primarily maintained by hydrophobic interactions.
• Quaternary Structure: Combination of multiple tertiary structure subunits, such as hemoglobin with two alpha and two beta units.

Alpha Helix

• Alpha helix is a secondary structure resembling a telephone cord.
• Hydrogen bonds form between the oxygen of a carbonyl carbon and the hydrogen of an amino group (NH) four residues later (i to i+4).
• Formation produces a spiral structure.

Beta Sheet

• Beta Sheet: Secondary structure where the oxygen from a carbonyl carbon and NH groups interact side by side.
• It is also known as an intramolecular hydrogen bond.
• Interactions occur between distant amino acids (e.g., amino acid #1 with #25 or #30).

Amino Acid Chain and Protein Backbone

• Amino acids are arranged linearly to form a polypeptide chain.
• The protein backbone consists of repeating units of N-Cα-C.
• The peptide bond formation involves a C=O and N-H interaction.

Phi and Psi Bonds

• Rotation is possible around the bonds connecting N, Cα, and C atoms.
• The bond between N and Cα is the phi (Φ) bond.
• The bond between Cα and C is the psi (Ψ) bond.
• The bond between C and N is the omega (Ω) bond.
• The size of the R group on Cα affects the rotation around phi and psi bonds.
• The carbonyl group (C=O) interacts with the hydrogen of the NH group in neighboring amino acids, influencing psi bond rotation.
• Knowing phi and psi angles helps in predicting polypeptide chain structure.
• Combinations of phi and psi angles favor the formation of alpha helices or beta sheets.

Ramachandran Plot

• The Ramachandran plot was created by G.N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan.
• It visualizes energetically allowed regions for phi and psi angles in a polypeptide chain backbone.
• The plot helps predict whether a polypeptide chain will form an alpha helix or a beta sheet based on phi and psi values.
• The Ramachandran plot is a quadrant analysis with psi on the y-axis and phi on the x-axis, ranging from -180 to +180 degrees.
• Positive psi and negative phi values favor beta sheets.
• Negative psi and phi values favor right-handed alpha helices.
• Positive phi and psi values represent left-handed alpha helices.
• The Ramachandran plot can help determine the relative frequency of amino acids in alpha helices or beta sheets.
• Glutamic acid and leucine are frequently found in alpha helices.
• Threonine is more common in beta sheets than in alpha helices.

Hierarchy of Protein Structure

• Primary structure leads to secondary structure (alpha helix and beta sheets).
• Secondary structures combine to form supersecondary structures or domains.
• Arrangements of domains form motifs, which define the 3D structure of the protein.
• The quaternary structure involves the arrangement of multiple protein subunits.

Protein Domains and Motifs

• Two alpha helices or two beta sheets can form a supersecondary structure.
• Beta-alpha-beta or alpha-beta-alpha arrangements can also form supersecondary structures.
• Domains are stretches of supersecondary structures linked together.
• Motifs are functional units formed by the arrangement of domains.
• An example of a motif is the greek key motif, formed by the specific arrangement of four beta strands, common in immunoglobulin proteins.
• Motifs describe how a structure is arranged, determining its function.

Fibrous vs. Globular Proteins

• There are two main types of proteins: fibrous and globular.
• Fibrous proteins are long and thin molecules (e.g., keratin in hair, collagen in skin and bone).
• Globular proteins have spherical 3D shapes (e.g., hemoglobin, insulin, enzymes).
• Fibrous proteins are insoluble in water and primarily serve structural roles.
• Globular proteins are soluble and perform various physical functions.

Collagen Structure

• Collagen formation involves the production of mRNA from DNA.
• mRNA is translated into protein products, forming different primary structures.
• Polypeptide chains link with each other at terminal sites to form procollagen.
• Trimerization of primary sequences occurs, forming trimers of domains.
• Procollagen forms collagen fibrils through interactions.
• Collagen consists of three identical left-handed helices.
• The repeating sequence in collagen is glycine-X-Y, where X is often proline and Y is often hydroxyproline.
• Glycine makes up approximately 33% of collagen, proline 30%, and hydroxyproline 30%.
• Glycine's small R group allows for close packing without steric hindrance.

Amino Acid Distribution in Globular Proteins

• Valine, leucine, isoleucine, methionine, and phenylalanine are mostly found in the protein's interior, being hydrophobic.
• Arginine, histidine, lysine, aspartic acid, and glutamic acid are located on the surface, interacting with hydrophilic regions.
• Serine, threonine, asparagine, glutamine, and tyrosine are found on both the surface and interior, participating in hydrogen bonding.

Hydrophobicity and Hydrophilicity

• Hydrophobicity plots help determine protein structure.
• Highly hydrophobic amino acids include isoleucine, valine, and leucine.
• Highly hydrophilic amino acids include arginine, lysine, aspartic acid, and glutamic acid.
• Mildly hydrophobic amino acids include tyrosine and tryptophan.
• Mildly hydrophilic amino acids include histidine, glutamate, and serine.

Amino Acid Properties

• Basic amino acids (positively charged): glycine, arginine, histidine.
• Acidic amino acids (negatively charged): aspartic acid, glutamic acid.
• Polar amino acids (hydrophilic): glycine, serine, threonine.
• Non-polar amino acids (hydrophobic): alanine, valine, leucine, isoleucine.
• Knowing the three-letter and single-letter codes for amino acids is important.
• Hydrophilicity plots help predict whether a protein is globular or a membrane protein.
• These plots use hydrophobic residues find the structure of a protein.