An E. coli cell of volume $10^{-12}$ cm³ contains 60 molecules of lac-repressor. The repressor has a binding affinity ($K_a$) of $10^{-8}$ M and $10^{-9}$ M with and without lactose respectively, in the medium.
Calculating Lac-Repressor Molar Concentration
To find the molar concentration of the lac-repressor protein within the E. coli cell, we need to determine the number of moles of repressor and divide it by the cell's volume in liters.
Repressor Molecules and Cell Volume
- Number of lac-repressor molecules = 60
- Cell volume = $10^{-12}$ cm³
Volume Conversion
First, convert the cell volume from cubic centimeters (cm³) to liters (L), knowing that 1 cm³ = 1 mL and 1 mL = $10^{-3}$ L.
Volume in Liters = $10^{-12} \text{ cm}^3 \times \frac{10^{-3} \text{ L}}{1 \text{ cm}^3} = 10^{-15} \text{ L}$
Calculating Moles of Repressor
Next, convert the number of repressor molecules to moles using Avogadro's number ($N_A \approx 6.022 \times 10^{23}$ molecules/mol).
Moles of Repressor = $\frac{60 \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}}$
Moles of Repressor $\approx 9.96 \times 10^{-23}$ mol
Determining Molar Concentration
Calculate the molar concentration (Molarity, M) using the formula: Molarity = Moles / Volume (L).
Molar Concentration = $\frac{9.96 \times 10^{-23} \text{ mol}}{10^{-15} \text{ L}}$
Molar Concentration $\approx 9.96 \times 10^{-8}$ M
Converting to Nanomolar (nM)
Convert the concentration from Molar (M) to Nanomolar (nM). Note that 1 M = $10^9$ nM.
Molar Concentration in nM = $(9.96 \times 10^{-8} \text{ M}) \times (10^9 \text{ nM/M})$
Molar Concentration in nM $\approx 9.96 \times 10^1$ nM
Molar Concentration in nM $\approx 99.6$ nM
This value is approximately 100 nM.
The binding affinity values ($K_a$) provided are not required for this calculation.
Important Questions from Regulation of Gene Expression
- Which of the following conditions induce(s) the expression of $ \beta$-galactosidase gene in the lac operon?
Determine the correctness or otherwise of the following Assertion [a] and the Reason [r].
Assertion [a]: In multicellular organisms, cells of different lineages have different gene expression profiles.
Reason [r]: Alternative splicing is the only mechanism to generate protein diversity.- The event(s) that lead(s) to inactivation of tumor suppressor genes in cancer cells is(are)
- Which of the following statement(s) is(are) CORRECT regarding the $lac$ operon in $E. coli$ when grown in the presence of glucose and lactose?
Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]
Assertion: Ab initio gene finding algorithms that predict protein coding genes in eukaryotic genomes are not completely accurate.
Reason: Eukaryotic splice sites are difficult to predict.
