Problem 11 - Biochemistry

Question

Minor species. For an amino acid such as alanine, the major species in solution at \(\mathrm{pH} 7\) is the zwitterionic form. Assume a \(\mathrm{p} K_{\mathrm{a}}\) value of 8 for the amino group and a \(\mathrm{p} K_{2}\) value of 3 for the carboxylic acid. Estimate the ratio of the concentration of the neutral amino acid species (with the carboxylic acid protonated and the amino group neutral) to that of the zwitterionic species at \(\mathrm{pH} 7(\text { see } \mathrm{p} .16)\)

Step-by-Step Solution

Answer

The ratio of neutral species to zwitterionic species is \(10^{-5}\).

Step 1: Identify the Species Involved

Alanine has two main forms in solution: the neutral form (NH2-CH(CH3)-COOH) and the zwitterionic form (NH3+-CH(CH3)-COO−). At different pH levels, protons associate or dissociate, leading to these different species.

Step 2: Apply the Henderson-Hasselbalch Equation to the Carboxylic Group

To estimate the ratio, first consider the carboxylic group with pKa = 3. Use the Henderson-Hasselbalch equation: \[\mathrm{pH} = \mathrm{p}K_a + \log\left(\frac{\text{[base form]}}{[\text{acid form}]\right)}.\]At pH 7, the formula becomes: \[7 = 3 + \log\left(\frac{[\text{COO}^-]}{[\text{COOH}]}\right)\]Solving for the ratio gives: \[\log\left(\frac{[\text{COO}^-]}{[\text{COOH}]\right)} = 4 \implies \frac{[\text{COO}^-]}{[\text{COOH}]} = 10^4.\]

Step 3: Apply the Henderson-Hasselbalch Equation to the Amino Group

Next, consider the amino group with pKa = 8. Using the same equation, \[7 = 8 + \log\left(\frac{[\text{NH}_2]}{[\text{NH}_3^+]}\right)\]Solving for the ratio gives: \[\log\left(\frac{[\text{NH}_2]}{[\text{NH}_3^+]\right) = -1 \implies \frac{[\text{NH}_2]}{[\text{NH}_3^+] = 10^{-1} = 0.1.\]

Step 4: Calculate the Ratio of Neutral to Zwitterionic Species

The neutral species is mainly NH2-CH(CH3)-COOH, and the zwitterionic form is NH3+-CH(CH3)-COO−. The overall ratio is the product of individual group effects:\[\frac{[\text{neutral species}]}{[\text{zwitterionic species}]} = \frac{[\text{NH}_2]}{[\text{NH}_3^+]} \times \frac{[\text{COOH}]}{[\text{COO}^-]} = 0.1 \times 10^{-4} = 10^{-5}.\]

Step 5: Interpret the Result

The result, \(10^{-5}\), indicates that the concentration of the neutral species is much lower compared to the zwitterionic form at pH 7. This aligns with the typical behavior of amino acids, where the zwitterionic form predominates at physiological pH.

Key Concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is central in acid-base chemistry. It provides a way to calculate the pH of a solution by accounting for the ratio of base form to acid form of a particular species. The equation is given as:\[\mathrm{pH} = \mathrm{p}K_a + \log\left(\frac{[\text{base}]}{[\text{acid}]}\right)\]This formula is especially useful when dealing with weak acids or bases like amino and carboxylic groups in amino acids.
The equation allows us to predict how pH influences the balance between different forms of an acid or base. In other words, it helps us understand whether an amino group will be protonated \((\text{NH}_3^+)\) or deprotonated \((\text{NH}_2)\) depending on the surrounding pH levels. To apply this equation, we use it twice: first for the carboxylic group and then for the amino group, which helps in determining the ratio of different species present in solutions of compounds like alanine.

Amino acids

Amino acids are the building blocks of proteins and play numerous roles in biology. Structurally, they consist of a central carbon atom bonded to an amino group \((\text{NH}_2)\), a carboxylic acid group \((\text{COOH})\), a hydrogen atom, and a variable side chain. This structure allows them to exist in different ionic forms depending on the pH of their environment.
Some key characteristics of amino acids include:

• Existence in zwitterionic form at physiological pH, which means they carry both a positive and a negative charge.
• Ability to act as buffers, minimizing pH changes in biological systems.
• Diverse side chains that determine the amino acid's properties and its role in proteins.

Using alanine as an example, at a neutral pH of around 7, it primarily exists in the zwitterionic form \((\text{NH}_3^+-\text{CH(CH}_3\text{)-COO}^-)\), where the amino group gains a proton and the carboxylic group loses one. Each amino acid can transform into various ionic states as the environmental pH shifts, highlighting the importance of understanding these states for biological processes.

Physiological pH

The term "physiological pH" refers to the pH level typically found within the body, generally around 7.4. This pH range is crucial for maintaining the proper function of cells and organs. Many biomolecules, such as amino acids, have different properties and structures that are sensitive to changes in pH.
At physiological pH:

• Amino acids like alanine often exist in their zwitterionic forms, where they carry no net charge.
• Enzymes perform optimally, as the structure and charge of amino acids influence enzyme activity and stability.
• The pH impacts biochemical pathways that are essential for life, ensuring that reactions occur at the correct rates and sequences.

Understanding physiological pH is key to predicting solute behavior in biological systems. It affects how amino acids interact and form proteins, as well as how other biological processes are regulated. Recognizing how different factors like pH influence amino acid structure can aid significantly in fields like biochemistry and pharmacology.