Biomolecules - Formula Sheet
Essential Formulae and Equations
1. Isoelectric Point of Amino Acids
For amino acids with neutral side chains, the isoelectric point (\(pI\)) is calculated as the average of the carboxyl and amino group pKa values:
\(pI = \frac{pK_{a1} + pK_{a2}}{2}\)
Where:
- \(pI\): Isoelectric point (pH at which the molecule carries no net electrical charge).
- \(pK_{a1}\): Negative logarithm of the dissociation constant of the alpha-carboxyl group (-COOH).
- \(pK_{a2}\): Negative logarithm of the dissociation constant of the alpha-amino group (-NH3+).
2. Number of Stereoisomers in Carbohydrates
The total number of optically active stereoisomers (\(N\)) for an open-chain carbohydrate is determined by the number of chiral carbons in the molecule:
\(N = 2^n\)
Where:
- \(N\): Number of stereoisomers.
- \(n\): Number of asymmetric (chiral) carbon atoms in the carbon skeleton.
3. Chargaff's Rules of Base Pairing
In double-stranded DNA, the ratio of purines to pyrimidines is always equal to 1, meaning the concentration of Adenine equals Thymine, and Guanine equals Cytosine:
\(\frac{[A]}{[T]} = \frac{[G]}{[C]} = 1\)
Which can also be expressed as:
\([A] + [G] = [T] + [C]\)
Where:
- \([A]\): Molar concentration of Adenine.
- \([T]\): Molar concentration of Thymine.
- \([G]\): Molar concentration of Guanine.
- \([C]\): Molar concentration of Cytosine.
4. Specific Optical Rotation
The specific rotation (\([\alpha]_D^T\)) of an optically active carbohydrate solution is calculated to standardize observed rotation values:
\([\alpha]_D^T = \frac{\alpha}{l \cdot c}\)
Where:
- \([\alpha]_D^T\): Specific rotation at temperature \(T\) (in degrees Celsius) using the sodium D-line wavelength.
- \(\alpha\): Observed optical rotation in degrees.
- \(l\): Path length of the polarimeter sample tube in decimeters (dm).
- \(c\): Concentration of the optically active solute in grams per milliliter (g/mL).