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Chapter 36: Problem 44

Oxygen sensing is important in biological studies of many systems. The variation in oxygen content of sapwood trees was measured by del Hierro and coworkers \([J . \text { Experimental Biology } 53(2002): 559]\) by monitoring the luminescence intensity of \(\left[\operatorname{Ru}(\operatorname{dpp})_{3}\right]^{2+}\) immobilized in a sol-gel that coats the end of an optical fiber implanted into the tree. As the oxygen content of the tree increases, the luminescence from the ruthenium complex is quenched. The quenching of \(\left[\mathrm{Ru}(\mathrm{dpp})_{3}\right]^{2+}\) by \(\mathrm{O}_{2}\) was measured by Bright and coworkers [Applied Spectroscopy \(52(1998): 750]\) and the following data were obtained: $$\begin{array}{rr} I_{0} / I & \% \mathrm{O}_{2} \\ \hline 3.6 & 12 \\ 4.8 & 20 \\ 7.8 & 47 \\ 12.2 & 100 \end{array}$$ a. Construct a Stern-Volmer plot using the data supplied in the table. For \(\left[\operatorname{Ru}(\operatorname{dpp})_{3}\right]^{2+} k_{r}=1.77 \times 10^{5} \mathrm{s}^{-1},\) what is \(k_{q} ?\) b. Comparison of the Stern-Volmer prediction to the quenching data led the authors to suggest that some of the \(\left[\operatorname{Ru}(\operatorname{dpp})_{3}\right]^{2+}\) molecules are located in sol-gel environments that are not equally accessible to \(\mathrm{O}_{2}\). What led the authors to this suggestion?

Short Answer

Expert verified
In this problem, a Stern-Volmer plot is used to analyze the quenching of a ruthenium complex by oxygen in a tree. The rate constant for the quenched state, \(k_q\), is calculated using the given data and the known rate constant for the unquenched state, \(k_r\). A deviation from the Stern-Volmer plot indicates that the ruthenium complex may be located in sol-gel environments with varying accessibility to oxygen, which could be due to different diffusion rates or sequestered complexes.

Step by step solution

01

Understand the Stern-Volmer Equation

The Stern-Volmer equation is given by \( I_0/I = 1 + k_q\tau_0[\text{Q}] \), where \(I_0\) is the intensity in the unquenched state, \(I\) is the intensity in the quenched state, \(\tau_0\) is the average life time in the absence of quencher and \([\text{Q}]\) the concentration of the quencher. Knowing that for \( [\text{Ru}(\text{dpp})_3]^{2+} \), the rate \(k_r = 1/ \tau_0 = 1.77 \times 10^{5} s^{-1}\), we can rewrite the Stern-Volmer equation as: \(I_0/I = 1 + k_q/k_r[\text{Q}]\).
02

Plot the Stern-Volmer Graph and Calculate \(k_q\)

To create the plot, plot \(\% O_2\) on the x-axis and \(I_0/I\) on the y-axis. The slope of this curve (in the linear range) is equal to \(k_q/k_r\). Determine the slope, and then use it to calculate \(k_q\) by rearranging the equation to solve for \(k_q = k_r \times\) slope.
03

Explaining the Sterna-Volmer Deviation

Some points on the plot may not lie on the calculated straight line, indicating that the Stern-Volmer quenching is not a perfect model for this situation, thus suggesting variation in the accessibility of the ruthenium complex to oxygen in different environments of sol-gel. This could be due to different diffusion rates of \(O_2\) within the sol-gel matrix, or due to some proportion of the ruthenium complex being sequestered in areas of the sol-gel not accessible to the oxygen. This leads to the discrepancy in the Stern-Volmer plot.

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Key Concepts

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

Oxygen Sensing in Biological Studies
Oxygen sensing plays a crucial role in various biological and environmental studies. It helps to monitor and understand the oxygen levels in different systems, such as plants, animals, and ecosystems. In the field of plant biology, particularly in the study of trees, measuring the oxygen content helps researchers understand physiological processes and the health of the trees.
Researchers often use sophisticated tools for oxygen sensing, like optical fibers coated with sensitive materials. These sensors detect changes in luminescence, which correlate with oxygen concentration. As oxygen levels change, the luminescence intensity varies, aiding in accurate oxygen sensing.
Understanding these changes is vital for research in fields like botany and climate science, where oxygen levels influence overall ecosystem functions. The ability to accurately sense oxygen levels can give insight into processes like respiration and photosynthesis.
The Role of Quenching in Luminescence
Quenching is a process where the luminescence of a material is reduced, often by a quencher substance like oxygen. This concept is critical in spectroscopic studies, especially when examining changes in light-emitting materials. Quenching can result from physical interaction between the luminescent substance and the quencher.
In the context of the Stern-Volmer equation, quenching helps us understand the interaction between the ruthenium complex and oxygen. The decrease in luminescence intensity indicates the presence and concentration of oxygen. Understanding quenching can help chemists design better sensors for detecting gases or studying biological samples.
Quenching can occur via multiple pathways, such as collisional quenching or static quenching, and comprehending these mechanisms is essential for interpreting quenching data accurately.
Understanding Luminescence Intensity
Luminescence intensity is the brightness or strength of the light emitted by a luminescent substance. This property is pivotal in investigations that utilize luminescent materials. Measuring variations in luminescence intensity can indicate changes in environmental conditions or molecular interactions.
In a practical scenario, like oxygen sensing with a ruthenium complex, the luminescence intensity decreases as the amount of oxygen increases. The change in intensity helps determine the concentration of oxygen. This principle is exploited in various sensors to provide quantitative data on oxygen levels.
  • High luminescence intensity typically means low quenching and thus lower oxygen levels.
  • Low luminescence intensity suggests higher quenching, indicating more oxygen is present.
Monitoring and analyzing these changes is critical for experiments in chemistry and biology, where the reaction environment can significantly affect the outcome.
Ruthenium Complex in Oxygen Detection
Ruthenium complexes are popular in photophysical studies due to their strong luminescence properties. A specific ruthenium complex, \([\text{Ru}(\text{dpp})_3]^{2+}\), is often used for oxygen detection. This compound is embedded in a sol-gel, enhancing its functionality in an optical fiber-based sensor.
This complex exhibits strong luminescence, which diminishes in the presence of oxygen — a result of oxygen quenching. The reduction in luminescence allows researchers to deduce the concentration of oxygen in a given sample. The effectiveness of ruthenium complexes in oxygen sensing lies in their sensitivity and stability.
Moreover, understanding the behavior of ruthenium complexes aids in developing advanced sensors for various applications. The ability to detect and measure oxygen precisely is vital for both scientific research and industrial applications, making these complexes an invaluable tool in modern chemistry and biology.

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Most popular questions from this chapter

Reciprocal plots provide a relatively straightforward way to determine if an enzyme demonstrates Michaelis-Menten kinetics and to determine the corresponding kinetic parameters. However, the slope determined from these plots can require significant extrapolation to regions corresponding to low substrate concentrations. An alternative to the reciprocal plot is the Eadie- Hofstee plot in which the reaction rate is plotted versus the rate divided by the substrate concentration and the data are fit to a straight line. a. Beginning with the general expression for the reaction rate given by the Michaelis-Menten mechanism: \\[ R_{0}=\frac{R_{\max }[\mathrm{S}]_{0}}{[\mathrm{S}]_{0}+K_{m}} \\] rearrange this equation to construct the following expression, which is the basis for the Eadie-Hofstee plot: \\[ R_{0}=R_{\max }-K_{m}\left(\frac{R_{0}}{[S]_{0}}\right) \\] b. Using an Eadie-Hofstee plot, determine \(R_{\max }\) and \(K_{m}\) for hydrolysis of sugar by the enzyme invertase using the following data: $$\begin{array}{cc} \text { [Sucrose ] }_{\mathbf{0}}(\mathbf{M}) & \mathbf{R}_{\mathbf{0}}\left(\mathbf{M} \mathbf{~ s}^{-\mathbf{1}}\right) \\ \hline 0.029 & 0.182 \\ 0.059 & 0.266 \\ 0.088 & 0.310 \\ 0.117 & 0.330 \\ 0.175 & 0.362 \\ 0.234 & 0.361 \end{array}$$

One can use FRET to follow the hybridization of two complimentary strands of DNA. When the two strands bind to form a double helix, FRET can occur from the donor to the acceptor allowing one to monitor the kinetics of helix formation (for an example of this technique see Biochemistry 34 \((1995): 285) .\) You are designing an experiment using a FRET pair with \(\mathrm{R}_{0}=59.6\) A. For B-form DNA the length of the helix increases \(3.46 \AA\) per residue. If you can accurately measure FRET efficiency down to 0.10 , how many residues is the longest piece of DNA that you can study using this FRET pair?

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The enzyme glycogen synthase kinase \(3 \beta(\operatorname{GSK}-3 \beta)\) plays a central role in Alzheimer's disease. The onset of Alzheimer's disease is accompanied by the production of highly phosphorylated forms of a protein referred to as " \(\tau . " \mathrm{GSK}-3 \beta\) contributes to the hyperphosphorylation of \(\tau\) such that inhibiting the activity of this enzyme represents a pathway for the development of an Alzheimer's drug. A compound known as Ro \(31-8220\) is a competitive inhibitor of GSK-3 \(\beta\). The following data were obtained for the rate of GSK-3 \(\beta\) activity in the presence and absence of Ro \(31-8220[\text { A. Martinez et al., } J .\) Medicinal Chemistry \(45(2002): 1292]:\) $$\begin{array}{ccc} & \mathbf{R}_{0}\left(\boldsymbol{\mu} \mathbf{M} \mathbf{~ s}^{-1} \mathbf{)}\right. \\ {[S](\boldsymbol{\mu} \mathbf{M})} & \mathbf{R}_{0}\left(\boldsymbol{\mu} \mathbf{M} \mathbf{~} \mathbf{s}^{-1}\right),[\boldsymbol{I}]=\mathbf{0} & {[\mathbf{I}]=\mathbf{2} \mathbf{0} \mathbf{0} \boldsymbol{\mu} \mathbf{M}} \\\ \hline 66.7 & 4.17 \times 10^{-8} & 3.33 \times 10^{-8} \\ 40.0 & 3.97 \times 10^{-8} & 2.98 \times 10^{-8} \\ 20.0 & 3.62 \times 10^{-8} & 2.38 \times 10^{-8} \\ 13.3 & 3.27 \times 10^{-8} & 1.81 \times 10^{-8} \\ 10.0 & 2.98 \times 10^{-8} & 1.39 \times 10^{-8} \\ 6.67 & 2.31 \times 10^{-8} & 1.04 \times 10^{-8} \end{array}$$ Determine \(K_{m}\) and \(R_{\max }\) for GSK-3 \(\beta\) and, using the data with the inhibitor, determine \(K_{m}^{*}\) and \(K_{I}\)

In this problem you will investigate the parameters involved in a single- molecule fluorescence experiment. Specifically, the incident photon power needed to see a single molecule with a reasonable signal-to-noise ratio will be determined. a. Rhodamine dye molecules are typically employed in such experiments because their fluorescence quantum yields are large. What is the fluorescence quantum yield for Rhodamine B (a specific rhodamine dye) where \(k_{r}=1 \times 10^{9} \mathrm{s}^{-1}\) and \(k_{i c}=1 \times 10^{8} \mathrm{s}^{-1} ?\) You can ignore intersystem crossing and quenching in deriving this answer. b. If care is taken in selecting the collection optics and detector for the experiment, a detection efficiency of \(10 \%\) can be readily achieved. Furthermore, detector dark noise usually limits these experiments, and dark noise on the order of 10 counts \(s^{-1}\) is typical. If we require a signal- tonoise ratio of \(10: 1,\) then we will need to detect 100 counts \(\mathrm{s}^{-1} .\) Given the detection efficiency, a total emission rate of 1000 fluorescence photons \(s^{-1}\) is required. Using the fluorescence quantum yield and a molar extinction coefficient for Rhodamine \(\mathrm{B}\) of \(\sim 40,000 \mathrm{M}^{-1} \mathrm{cm}^{-1},\) what is the intensity of light needed in this experiment in terms of photons \(\mathrm{cm}^{-2} \mathrm{s}^{-1} ?\) c. The smallest diameter focused spot one can obtain in a microscope using conventional refractive optics is approximately one-half the wavelength of incident light. Studies of Rhodamine B generally employ 532 nm light such that the focused-spot diameter is \(\sim 270 \mathrm{nm}\). Using this diameter, what incident power in watts is required for this experiment? Do not be surprised if this value is relatively modest.
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