/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 Rubisco catalyzes both a carboxy... [FREE SOLUTION] | 91Ó°ÊÓ

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Rubisco catalyzes both a carboxylation reaction and a wasteful oxygenase reaction. Below are the kinetic parameters for the two reactions. $$\begin{array}{cccc}\hline K_{\mathrm{M}}^{\mathrm{CO}_{2}}(\mu \mathrm{M}) & K_{\mathrm{M}}^{\mathrm{O}_{2}}(\mu \mathrm{M}) & K_{\mathrm{cat}}^{\mathrm{CO}_{2}}\left(\mathrm{s}^{-1}\right) &K_{\mathrm{cat}}^{\mathrm{O}_{2}}\left(\mathrm{s}^{-1}\right) \\\10 & 500 & 3 & 2 \\\\\hline\end{array}$$ (a) Determine the values of \(k_{\text {cat }}^{\text {CO }_{2} / K_{M}^{\text {CO }_{2}} \text { and } k_{\text {cat }}^{\mathbf{O}_{2}} / K_{M}^{\mathbf{O}_{2}}}\) as \(s^{-1} M^{-1}\).

Short Answer

Expert verified
The catalytic efficiencies are \(3.0 \times 10^5 \, s^{-1} M^{-1}\) for CO2 and \(4.0 \times 10^3 \, s^{-1} M^{-1}\) for O2.

Step by step solution

01

Understand the Kinetic Parameters

Identify the given parameters: \(K_{M}^{CO_2} = 10 \, \mu M\), \(K_{M}^{O_2} = 500 \, \mu M\), \(k_{cat}^{CO_2} = 3 \, s^{-1}\), and \(k_{cat}^{O_2} = 2 \, s^{-1}\). These values are crucial for calculating the catalytic efficiency.
02

Convert Units for Kinetic Parameters

Convert \(K_{M}\) values from \(\mu M\) to \(M\) by multiplying by \(10^{-6}\). Thus, \(K_{M}^{CO_2} = 10 \, x \, 10^{-6} \, M = 1.0 \times 10^{-5} \, M\) and \(K_{M}^{O_2} = 500 \, x \, 10^{-6} \, M = 5.0 \times 10^{-4} \, M\).
03

Calculate Catalytic Efficiency for CO2

Use the formula for catalytic efficiency: \(\frac{k_{cat}}{K_M}\). Substituting the values for CO2: \[\frac{k_{cat}^{CO_2}}{K_M^{CO_2}} = \frac{3 \, s^{-1}}{1.0 \times 10^{-5} \, M} = 3.0 \times 10^5 \, s^{-1} M^{-1}\].
04

Calculate Catalytic Efficiency for O2

Similarly, use the formula for catalytic efficiency for O2: \(\frac{k_{cat}^{O_2}}{K_M^{O_2}}\). Substituting the known values: \[\frac{k_{cat}^{O_2}}{K_M^{O_2}} = \frac{2 \, s^{-1}}{5.0 \times 10^{-4} \, M} = 4.0 \times 10^3 \, s^{-1} M^{-1}\].
05

Summarize the Results

The values for catalytic efficiencies are \(3.0 \times 10^5 \, s^{-1} M^{-1}\) for CO2 and \(4.0 \times 10^3 \, s^{-1} M^{-1}\) for O2.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rubisco
Rubisco, short for Ribulose-1,5-bisphosphate carboxylase-oxygenase, is an enzyme found in the chloroplasts of plant cells. It is one of the most abundant proteins on Earth. Rubisco plays a crucial role in the process of photosynthesis, specifically during the fixation of atmospheric carbon dioxide into organic compounds. This process is a part of the Calvin cycle, where Rubisco catalyzes the first major step.

The enzyme is unique because it possesses dual functionality:
  • Carboxylation: This is where Rubisco adds carbon dioxide to a molecule, leading to the formation of organic molecules.
  • Oxygenation: This involves the addition of oxygen, resulting in a process known as photorespiration, which can be seen as wasteful since it leads to a loss of fixed carbon.
Understanding Rubisco's preference for either reaction is key to improving plant efficiency, especially in agricultural contexts where maximizing carbon fixation is desired.
Catalytic Efficiency
Catalytic efficiency is a measure of how effectively an enzyme converts a substrate into a product. For Rubisco, this concept is critical because it determines how well the enzyme can facilitate the conversion of its substrates, carbon dioxide, and sometimes oxygen. Catalytic efficiency is described mathematically as the ratio of the rate constant for catalysis ( $ k_{cat} $ ) to the Michaelis constant ( $ K_M $ ) for a given reaction. This ratio, expressed in units of $ s^{-1} M^{-1} $ , captures both the enzyme's speed in processing a substrate and its affinity for that substrate.

Some factors influencing catalytic efficiency include:
  • The concentration of substrates (like CO2 or O2 in this case).
  • The structure of the enzyme and how it interacts with its substrate.
  • The environmental conditions, such as temperature and pH.
In the case of Rubisco, comparing the catalytic efficiencies for carboxylation versus oxygenation highlights the enzyme's efficiency in performing its evolved function and its limitations in ensuring desirable plant growth outcomes.
Carboxylation Reaction
The carboxylation reaction facilitated by Rubisco is an essential process in the photosynthetic pathway of plants. This reaction involves the incorporation of carbon dioxide into an organic molecule, effectively turning inorganic carbon into a form that can be used by the plant. The reaction typically involves the substrate ribulose-1,5-bisphosphate (RuBP) and results in the formation of two 3-phosphoglycerate molecules, which are then used in the Calvin cycle to produce glucose.

Characteristics of the carboxylation reaction include:
  • The necessity for carbon dioxide, aligning with Rubisco's primary function.
  • Contribution to the global carbon cycle by removing CO2 from the atmosphere.
  • Mediated by the enzyme Rubisco, which acts as a catalyst to facilitate the transformation without being consumed in the process.
The efficiency and prevalence of the carboxylation reaction over the oxygenation reaction are critical for plant productivity and agricultural yield, making research into enhancing Rubisco's carboxylation efficiency a significant area of interest.

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Most popular questions from this chapter

Use the following information to estimate the efficiency of photosynthesis. The \(\Delta G^{\text {o\prime }}\) for the reduction of \(\mathrm{CO}_{2}\) to the level of hexose is \(+477 \mathrm{kJ} \mathrm{mol}^{-1}\left(+114 \mathrm{kcal} \mathrm{mol}^{-1}\right)\)' A mole of 600 -nm photons has an energy content of \(199 \mathrm{kJ}(47.6 \mathrm{kcal})\) Assume that the proton gradient generated in producing the required NADPH is sufficient to drive the synthesis of the required ATP.

Glyceraldehyde 3 -phosphate dehydrogenase in chloroplasts uses NADPH to participate in the synthesis of glucose. In gluconeogenesis in the cytoplasm, the isozyme of the dehydrogenase uses NADH. Why is the use of NADPH by the chloroplast enzyme advantageous?

\(\mathrm{C}_{3}\) plants are most common in higher latitudes and become less common at latitudes near the equator. The reverse is true of \(\mathrm{C}_{4}\) plants. How might global warming affect this distribution?

An illuminated suspension of Chlorella is actively carrying out photosynthesis in the presence of \(1 \%\) \(\mathrm{CO}_{2} .\) The concentration of \(\mathrm{CO}_{2}\) is abruptly reduced to \(0.003 \% .\) What effect will this reduction have on the levels of 3-phosphoglycerate and ribulose \(1,5-\) bisphosphate in the next minute?

Light and dark talk. Rubisco requires a molecule of \(\mathrm{CO}_{2}\) covalently bound to lysine 201 for catalytic activity. The carboxylation of rubisco is favored by high \(\mathrm{pH}\) and high \(\mathrm{Mg}^{2+}\) concentration in the stroma. Why does it make good physiological sense for these conditions to favor rubisco carboxylation?

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