Question

Sketch a titration curve for the amino acid cysteine, and indicate the \(\mathrm{p} K_{\mathrm{a}}\) values for all titratable groups. Also indicate the pH at which this amino acid has no net charge.

Short answer

The titration curve of cysteine shows \( pK_{a} \) values at 2.0, 8.3, and 10.7. The isoelectric point is at pH 5.15.

Step-by-step solution

- Identify Titratable Groups in Cysteine

Cysteine has three titratable groups: the carboxyl group (-COOH), the amino group (-NH₂), and the thiol group (-SH). We need to determine the \( \text{p}K_{a} \) values for these groups to sketch the titration curve accurately.

- Determine \( \text{p}K_{a} \) Values

The \( \text{p}K_{a} \) values for cysteine are approximately as follows: - Carboxyl group (\text{-COOH}): \( pK_{a_1} \) ≈ 2.0 - Thiol group (\text{-SH}): \( pK_{a_2} \) ≈ 8.3 - Amino group (\text{-NH₃^+}): \( pK_{a_3} \) ≈ 10.7

- Sketch Titration Curve

Draw the titration curve with pH on the x-axis and the fraction of deprotonated species (or equivalents of OH-) on the y-axis. Start with the fully protonated form of cysteine and plot the regions where each group loses a proton. - At low pH (< 2.0): The carboxyl group is protonated (COOH), the thiol group is protonated (SH), and the amino group is protonated (NH₃^+).- pH 2.0: Deprotonation of the carboxyl group occurs (COO⁻).- pH 8.3: Deprotonation of the thiol group occurs (S⁻).- pH 10.7: Deprotonation of the amino group occurs (NH₂).

- Determine the Isoelectric Point (pI)

The isoelectric point (pI) is the pH at which cysteine has no net charge. This can be found by averaging the pKₐ values of the groups that result in a neutral species. For cysteine, this involves the carboxyl and thiol groups. Calculate the pI: \( pI = \frac{pK_{a_1} + pK_{a_2}}{2} = \frac{2.0 + 8.3}{2} = 5.15 \).

- Indicate Key Points on the Curve

Indicate the \( pK_{a} \) values on the titration curve where the groups deprotonate (2.0, 8.3, 10.7) and mark the pI at 5.15 where cysteine has no net charge. Label the regions with the forms of cysteine present at different pH ranges.

Key concepts

cysteine titration

Understanding the titration curve for cysteine begins with recognizing its titratable groups. Cysteine, an amino acid, has three groups that can lose protons during titration: the carboxyl group (-COOH), the thiol group (-SH), and the amino group (-NH₂). The goal is to map out how cysteine responds to changes in pH by identifying where each of these groups loses a proton.
To sketch the titration curve:

• Start by fully protonating cysteine: at low pH, all groups are protonated.
• Draw the curve with pH on the x-axis and the fraction of deprotonated species on the y-axis.
• Plot the key pH points where each group deprotonates:
• Carboxyl group (pKₐ ≈ 2.0) deprotonates first: COOH → COO⁻
• Thiol group (pKₐ ≈ 8.3) deprotonates next: SH → S⁻
• Amino group (pKₐ ≈ 10.7) deprotonates last: NH₃⁺ → NH₂

These deprotonation events create inflection points on the titration curve, indicating where acidic and basic forms of cysteine transition. Identifying the pH at which these changes occur helps you understand cysteine’s behavior in different environments.

pKa values

The pKa value of a titratable group indicates the pH at which that group loses a proton. Lower pKa values mean the group gives up protons more easily (is more acidic), while higher pKa values mean it holds onto protons more tightly (is more basic). For cysteine:

• The carboxyl group’s pKa is around 2.0, meaning it deprotonates at a very low pH.
• The thiol group’s pKa is about 8.3, indicating deprotonation occurs at a moderately high pH.
• The amino group has a pKa of approximately 10.7, so deprotonation happens at an even higher pH.

These values are critical to sketching the titration curve accurately. They help predict which form of cysteine predominates at a given pH. When titrating cysteine, adding a base increases the pH, and you will observe each group losing a proton sequentially at its respective pKa value. By knowing these values, you can understand when each group transitions and how cysteine's net charge changes along the titration.

isoelectric point

The isoelectric point (pI) of an amino acid is the pH at which it has no net charge. For cysteine, this means determining where the overall positive and negative charges balance out. To find the pI, average the pKa values of the titratable groups resulting in a neutral species:
The carboxyl (-COOH) and thiol (-SH) groups mainly contribute to the charge state, as their deprotonation occurs within the pH range where the amino acid switches between different charge forms.
Using the provided pKa values:

• Carboxyl group: pKa ≈ 2.0
• Thiol group: pKa ≈ 8.3

Calculate the pI with the formula:

\text\rightarrow\[ pI = \frac{pKa_1 + pKa_2}{2} \rightarrow pI = \frac{2.0 + 8.3}{2} = 5.15\text\]

At a pH of 5.15, cysteine has an equal number of positive and negative charges, resulting in no net charge. Knowing the isoelectric point is essential for understanding cysteine’s behavior in various pH environments, whether during biological processes or in lab settings.