Biomolecules Formula Sheet

Last-minute revision sheet for Biomolecules. Since this is a largely descriptive chapter, this sheet front-loads the few genuine formulas (peptide-count, pI, Chargaff, enzyme catalysis) and then packs the rest as high-yield reactions, structural facts, and reference tables. Everything here is drawn straight from the chapter pages.

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Core Formulas & Relations

These are the only true formulas in the chapter — memorise them cold.

Quantity	Formula	Notes
Number of peptides	$n^m$	$n$ = different amino acids, $m$ = peptide length
Isoelectric point	$\text{pI} = \dfrac{\text{pK}_1 + \text{pK}_2}{2}$	For amino acids without ionizable R group
Holoenzyme	Apoenzyme + Cofactor	Apoenzyme alone is inactive
Enzyme catalysis	$\text{E} + \text{S} \leftrightarrow \text{ES} \rightarrow \text{E} + \text{P}$	Enzyme regenerated

$$\boxed{\text{Number of peptides} = n^m}$$$$\boxed{\text{pI} = \frac{\text{pK}_1 + \text{pK}_2}{2}}$$$$\boxed{\text{Apoenzyme} + \text{Cofactor} = \text{Holoenzyme (active)}}$$$$\boxed{\text{E} + \text{S} \leftrightarrow \text{ES} \rightarrow \text{E} + \text{P}}$$

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Carbohydrates

General Formulas

$$\boxed{\text{C}_n(\text{H}_2\text{O})_m}$$

Class	Formula	Examples
Monosaccharide (hexose)	$\text{C}_6\text{H}_{12}\text{O}_6$	Glucose, fructose, galactose
Disaccharide	$\text{C}_{12}\text{H}_{22}\text{O}_{11}$	Sucrose, maltose, lactose
Polysaccharide	$(\text{C}_6\text{H}_{10}\text{O}_5)_n$	Starch, cellulose, glycogen

Glucose — Key Structural Facts

• Aldohexose ($\text{C}_6\text{H}_{12}\text{O}_6$), 4 chiral centres (C2, C3, C4, C5).
• D-configuration: OH on C5 is on the right (Fischer).
• Exists ~99% in cyclic (pyranose) form via intramolecular hemiacetal (C5-OH attacks C1=O).

Anomer	OH at C1 (Haworth)	% at equilibrium	Specific rotation
α-D-glucose	Down (axial)	36%	+112°
β-D-glucose	Up (equatorial)	64%	+19°

Mutarotation: equilibrium specific rotation $= 0.36(+112°) + 0.64(+19°) = +52.5°$. β is more stable (equatorial OH).

Reactions of Glucose

$$\text{Glucose} \xrightarrow{[\text{O}],\ \text{Br}_2/\text{H}_2\text{O}} \text{Gluconic acid} \quad(\text{C1 oxidised})$$$$\text{Glucose} \xrightarrow{\text{conc. HNO}_3} \text{Glucaric (saccharic) acid} \quad(\text{C1 \& C6 oxidised})$$$$\text{Glucose} \xrightarrow{\text{NaBH}_4\ \text{or}\ \text{H}_2/\text{Ni}} \text{Sorbitol (glucitol)}$$$$\text{Glucose} + 5(\text{CH}_3\text{CO})_2\text{O} \rightarrow \text{Glucose pentaacetate} \quad(\text{proves 5 OH groups})$$$$\text{Glucose} + \text{CH}_3\text{OH} \xrightarrow{\text{HCl}} \text{Methyl glucoside} + \text{H}_2\text{O}$$$$\text{Glucose} \xrightarrow{\text{Fehling's}} \text{red ppt of Cu}_2\text{O} \quad(\text{reducing-sugar test})$$

• Prolonged HI on glucose → n-hexane (proves straight chain of 6 carbons).

Fructose

• Ketohexose ($\text{C}_6\text{H}_{12}\text{O}_6$), ketone at C2, 3 chiral centres (C3, C4, C5 — one less than glucose).
• Forms 5-membered furanose ring; reducing sugar; sweetest natural sugar.

Disaccharides

Sugar	Units	Glycosidic linkage	Reducing?
Sucrose	Glucose + Fructose	α(1→2)	No (both anomeric C tied)
Maltose	Glucose + Glucose	α(1→4)	Yes
Lactose	Galactose + Glucose	β(1→4)	Yes

$$\text{Sucrose} + \text{H}_2\text{O} \xrightarrow{\text{H}^+\ \text{or invertase}} \text{Glucose} + \text{Fructose} \quad(\text{invert sugar})$$$$\text{Maltose} + \text{H}_2\text{O} \xrightarrow{\text{maltase}} 2\ \text{Glucose}$$$$\text{Lactose} + \text{H}_2\text{O} \xrightarrow{\text{lactase}} \text{Glucose} + \text{Galactose}$$

Polysaccharides

Polysaccharide	Monomer	Linkage	Key point
Amylose (starch, 20–30%)	α-D-glucose	α(1→4)	Linear, blue with iodine
Amylopectin (starch, 70–80%)	α-D-glucose	α(1→4) + α(1→6)	Branched
Cellulose	β-D-glucose	β(1→4)	Indigestible (no cellulase)
Glycogen	α-D-glucose	α(1→4) + α(1→6)	“Animal starch,” highly branched

$$\text{Starch} \xrightarrow{\text{diastase}} \text{Maltose} \xrightarrow{\text{maltase}} \text{Glucose}$$

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Proteins & Amino Acids

Structure & Zwitterion

$$\boxed{\text{H}_2\text{N–CHR–COOH}} \qquad \text{Zwitterion: } {}^{+}\text{H}_3\text{N–CHR–COO}^{-}$$

• α-amino acid: -NH₂ and -COOH on same (α) carbon; chiral except glycine (R = H).
• 20 common amino acids, all L-form.
• Zwitterion (dominant at neutral pH) explains: high melting point (e.g. glycine MP 232°C), water-soluble / non-polar-insoluble, amphoteric.

pH region	Net charge	Form
pH < pI	Positive	Cation
pH = pI	Zero	Zwitterion
pH > pI	Negative	Anion

Essential amino acids mnemonic: “PVT TIM HALL” (Phe, Val, Thr, Trp, Ile, Met, His, Arg, Leu, Lys).

Peptide Bond

$$\text{–COOH} + \text{H}_2\text{N–} \rightarrow \text{–CO–NH–} + \text{H}_2\text{O}$$

• -CO-NH- amide linkage; resonance-stabilised, partial double-bond character.
• C–N bond length 132 pm (between single 147 pm and double 127 pm) → planar, restricted rotation, usually trans.
• Named N-terminus → C-terminus (e.g. Gly-Ala-Ser).

Protein Structure Levels

Level	What	Bonds	Example
Primary (1°)	Amino-acid sequence	Peptide bonds	Gly-Ala-Val…
Secondary (2°)	Local folding (α-helix, β-sheet)	H-bonds (backbone)	α-keratin, silk fibroin
Tertiary (3°)	Overall 3D shape	All interactions (H-bond, ionic, S-S, hydrophobic)	Enzyme active site
Quaternary (4°)	Multiple subunits	Same as 3°	Hemoglobin (2α + 2β)

• α-helix: right-handed, 3.6 amino acids/turn, H-bond between C=O of residue n and N-H of residue (n+4).
• β-pleated sheet: extended zigzag, H-bonds between adjacent chains (parallel/antiparallel).

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Nucleic Acids

Building Block

$$\boxed{\text{Nucleotide} = \text{Sugar} + \text{Base} + \text{Phosphate}}$$$$\text{Nucleoside} = \text{Sugar} + \text{Base} \quad(\text{no phosphate})$$

Component	DNA	RNA
Sugar	2-Deoxyribose (no OH at C2′)	Ribose (OH at C2′)
Bases	A, G, C, T	A, G, C, U
Strands	Double helix (antiparallel)	Usually single
Stability	More stable	Less stable

• Purines (double ring): Adenine, Guanine — “PURe As Gold.”
• Pyrimidines (single ring): Cytosine, Thymine, Uracil — “CUT the PY.”
• Backbone = sugar–phosphate via phosphodiester linkage; 5′→3′ direction.

Base Pairing & Chargaff’s Rules

$$A = T \ (2\ \text{H-bonds}) \qquad G \equiv C \ (3\ \text{H-bonds})$$$$\boxed{[\text{A}] = [\text{T}], \quad [\text{G}] = [\text{C}]}$$$$[\text{A}] + [\text{G}] = [\text{T}] + [\text{C}] \quad(\%\text{purines} = \%\text{pyrimidines})$$

• DNA double helix (Watson-Crick, 1953): right-handed, diameter 2 nm, one turn 3.4 nm = 10 base pairs.
• Melting temperature: $T_m \propto \%\text{GC content}$ (G≡C has 3 H-bonds, stronger).

Central Dogma

$$\text{DNA} \xrightarrow{\text{Replication}} \text{DNA} \xrightarrow{\text{Transcription}} \text{RNA} \xrightarrow{\text{Translation}} \text{Protein}$$

• Codon = triplet of bases; $4^3 = 64$ codons for 20 amino acids → degenerate code.
• Start: AUG (methionine). Stop: UAA, UAG, UGA.

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Vitamins

Classification

$$\boxed{\text{Fat-soluble: A, D, E, K (``ADEK'')} \qquad \text{Water-soluble: B-complex \& C}}$$

• Fat-soluble (ADEK): stored in liver/adipose, toxic in excess (hypervitaminosis), no daily intake needed.
• Water-soluble (B, C): not stored (excreted in urine), no toxicity, need regular intake.

Vitamin → Chemical Name → Deficiency

Vitamin	Chemical name	Type	Deficiency disease
A	Retinol	Fat	Night blindness, Xerophthalmia
D	Calciferol (D₂ ergocalciferol, D₃ cholecalciferol)	Fat	Rickets, Osteomalacia
E	α-Tocopherol	Fat	Rare (hemolytic anemia)
K	Phylloquinone (K₁), Menaquinone (K₂)	Fat	Hemorrhage
B₁	Thiamine	Water	Beriberi
B₂	Riboflavin	Water	Ariboflavinosis (cheilosis)
B₃	Niacin	Water	Pellagra (3D: dermatitis, diarrhea, dementia)
B₆	Pyridoxine	Water	Anemia, dermatitis
B₉	Folic acid	Water	Megaloblastic anemia
B₁₂	Cobalamin	Water	Pernicious anemia
C	L-Ascorbic acid	Water	Scurvy

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Enzymes

Specificity Types

Type	Acts on	Example
Absolute	One substrate only	Urease (urea only)
Group	Specific functional group	Alcohol dehydrogenase
Linkage	Specific bond type	Proteases (peptide), lipases (ester), amylases (α-1,4)
Stereochemical	Distinguishes stereoisomers	L-amino acid oxidase; maltase (α not β)

Models & Energetics

• Lock-and-key (Fischer, 1894): rigid, exact fit.
• Induced fit (Koshland, 1958): flexible, active site molds to substrate — modern, accepted model.
• Enzyme lowers activation energy (Eₐ) but does NOT change ΔG (affects rate, not equilibrium).

Factors Affecting Activity

Factor	Effect
Temperature	Optimum ~37°C; Q₁₀ ≈ 2 (rate doubles per 10°C); high temp → denaturation
pH	Each enzyme has optimum (pepsin 1.5–2.0, salivary amylase 6.7–7.0, trypsin 7.5–8.5, arginase 9.5–10.0)
[S]	Low [S]: rate ∝ [S] (1st order); high [S]: rate = Vmax (zero order)
[E]	Rate ∝ [E] at constant [S]

• Km (Michaelis constant): [S] at which $V = V_{max}/2$; low Km = high affinity, high Km = low affinity.

Enzyme Inhibition (master this table)

Type	Binding site	Reversible?	Vmax	Km	Overcome by ↑[S]?
Competitive	Active site	Yes	Unchanged	Increases	Yes
Non-competitive	Allosteric site	Yes	Decreases	Unchanged	No
Irreversible	Active site (covalent)	No	Decreases	Variable	No

• Competitive example: malonate vs succinate dehydrogenase.
• Non-competitive example: heavy metals (Hg²⁺, Pb²⁺) on -SH groups.
• Irreversible example: nerve gases (DFP, Sarin) on acetylcholinesterase; penicillin on cell-wall synthesis.

Vitamin-Derived Coenzymes

Vitamin	Coenzyme	Role
B₁ (Thiamine)	TPP	Decarboxylation
B₂ (Riboflavin)	FAD, FMN	Redox
B₃ (Niacin)	NAD⁺, NADP⁺	Redox
B₅ (Pantothenic acid)	Coenzyme A	Acyl transfer
B₆ (Pyridoxine)	PLP	Amino-acid metabolism

Enzyme Classes (IUPAC)

Oxidoreductases (redox) · Transferases (group transfer) · Hydrolases (hydrolysis) · Lyases (add/remove to form double bonds) · Isomerases (rearrangement) · Ligases (join using ATP).

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One-Glance Summary Map

graph TD
    A[Biomolecules] --> B[Carbohydrates]
    A --> C[Proteins]
    A --> D[Nucleic Acids]
    A --> E[Vitamins]
    A --> F[Enzymes]
    B --> B1["Reducing test: free anomeric C"]
    B --> B2["α vs β linkage = digestibility"]
    C --> C1["Zwitterion, pI = (pK1+pK2)/2"]
    C --> C2["1°→2°→3°→4° structure"]
    D --> D1["A=T (2HB), G≡C (3HB)"]
    D --> D2["Chargaff: %A=%T, %G=%C"]
    E --> E1["Fat ADEK vs Water B,C"]
    F --> F1["Competitive Km↑ / Non-comp Vmax↓"]

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Related Pages

• Carbohydrates
• Proteins
• Nucleic Acids
• Vitamins
• Enzymes