Question

The effect of \(\mathrm{pH}\) on the activity of an enzyme was examined. At its active site, the enzyme has an ionizable group that must be negatively charged in order for substrate binding and catalysis to take place. The ionizable group has a \(\mathrm{p} K_{\mathrm{a}}\) of \(6.0 .\) The substrate is positively charged throughout the \(\mathrm{pH}\) range of the experiment. (EQUATION CAN'T COPY) (a) Draw the \(V_{0}\) -versus-pH curve when the substrate concentration is much greater than the \(K_{M}\) of the enzyme. (b) Draw the \(V_{0}\) -versus-pH curve when the substrate concentration is much less than the \(K_{M}\) of the enzyme. (c) At which \(\mathrm{pH}\) will the velocity equal one-half of the maximal velocity attainable under the conditions described in (b)?

Short answer

(a) Enzyme activity increases past pH 6. (b) Activity is similar but lower at low substrate concentration. (c) Velocity is half-maximal at pH 6.0.

Step-by-step solution

Understanding the Enzyme Ionization

The enzyme's activity depends on an ionizable group at the active site that must be negatively charged for proper function. Given the \( \mathrm{p}K_{\mathrm{a}} = 6.0 \), this means that the group will be deprotonated (and thus negatively charged) when \( \mathrm{pH} > 6.0 \) and protonated (neutral) when \( \mathrm{pH} < 6.0 \). This affects how the concentration of the active enzyme varies with \( \mathrm{pH} \).

Drawing the Curve with High Substrate Concentration

When the substrate concentration is much greater than \( K_M \), the reaction is saturated with substrate. The shape of the \( V_0 \)-versus-\( \mathrm{pH} \) curve will rely on the proportion of enzyme that is in the active (deprotonated) form. As \( \mathrm{pH} \) increases past \( 6.0 \), more enzyme becomes active, leading to increased velocity up to a maximal point.

Drawing the Curve with Low Substrate Concentration

When the substrate concentration is much less than \( K_M \), the reaction is not saturated, and \( V_0 \) becomes directly proportional to the active enzyme concentration, itself pH-dependent. The curve will start lower than the high substrate situation and will increase with \( \mathrm{pH} \) as the enzyme becomes deprotonated and active past \( \mathrm{pH} = 6.0 \).

Determining Half-Maximal Velocity Conditions

In the scenario of low substrate concentration, half-maximal velocity is determined when the ionizable group is half deprotonated. This condition occurs at \( \mathrm{pH} = \mathrm{p}K_{\mathrm{a}} \), which is \( \mathrm{pH} = 6.0 \). This is where the concentration of active enzyme is half-maximized under low substrate conditions.

Key concepts

Enzyme Kinetics

Enzyme kinetics is the study of how enzymes influence the rates of chemical reactions in biological systems. Typically, enzymes speed up reactions by lowering the activation energy required. This process is influenced by several factors, including substrate concentration, temperature, and pH.

In enzyme kinetics, Michaelis-Menten kinetics is a common model explaining how enzymes bind to substrates to form a complex, which then produces a product. The model suggests that the reaction rate will depend on the concentration of both the enzyme and the substrate.

• At high substrate concentrations where the active sites on the enzyme are saturated, the reaction reaches its maximum rate, known as the maximum velocity ( V_{max} ).
• The Michaelis constant ( K_M ) is a measure of the substrate concentration at which the reaction velocity is at half V_{max} .

Understanding enzyme kinetics helps in determining the efficiency of an enzyme under different conditions, such as changes in pH.

Enzyme Active Site

The enzyme active site is a specific region on an enzyme where substrates bind. It has a unique shape and chemical properties that allow only certain substrates to fit. This specificity is crucial for the enzyme's catalytic action.

The ionization state of residues in the active site affects binding and catalysis. In the given exercise, the enzyme has an ionizable group that needs to be negatively charged for the substrate to bind effectively. This means that the active site must be in the correct ionization state to enable the catalytic process.

• The active site utilizes various interactions such as hydrogen bonds and ionic bonds, to stabilize the transition state of the reaction.
• Any change, such as pH fluctuations, can alter the charge and structure of the active site, impacting enzyme activity.

Therefore, maintaining an optimum pH is essential to ensure the enzyme's structure and function are unchanged.

pKa

The term \( \text{pKa} \) refers to the pH at which half of an ionizable group is in its acidic form, and half is in its basic form. It is a crucial concept for understanding how enzymes work at varying pH levels because it indicates the pH at which an ionizable group's charge is most balanced.

In the context of the exercise, the \( \text{pKa} \) of 6.0 means that at \( \text{pH} = 6.0 \), the ionizable group on the enzyme’s active site is half deprotonated (negatively charged) and half protonated (neutral). This understanding of \( \text{pKa} \):

• Helps in determining the ideal pH for the fastest enzyme reaction rate.
• Is essential when predicting the enzyme behavior in environments with fluctuating pH.

Knowing the \( \text{pKa} \) value is crucial for adjusting conditions to maximize enzyme activity.

Substrate Concentration

Substrate concentration is a key factor in enzyme-catalyzed reactions. It refers to the amount of substrate available for the enzyme to act upon. Substrates bind to the active site of enzymes, allowing the conversion into products.

The level of substrate concentration influences how quickly a product is formed. When substrate concentration is low, not all enzymes are occupied, and the reaction rate increases with increased substrate. Conversely, at high substrate concentrations, the reaction rate plateaus as all enzyme active sites are occupied, reaching the maximum velocity ( V_{max} ):

• When substrate concentration is much greater than K_M , the enzyme operates at V_{max} , as the enzymes are fully saturated.
• When substrate concentration is much less than K_M , the reaction rate is slow and directly proportional to the available active enzyme concentration.

Understanding substrate concentration effects is essential for controlling biochemical pathways and for maximizing enzyme efficiency in industrial and medical settings.