CALCULATION QUESTIONS AND ANSWERS IN CELL BIOLOGY

(50 CALCULATION QUESTIONS AND ANSWERS RELATED TO CELL BIOLOGY)

 

The following calculation questions and answers in cell biology are mostly for illustration purposes and may not reflect actual biological systems. Kindly double-check specific values and equations when revising or in tests:

 

1. Q: If a cell has 46 chromosomes in G1 phase, how many chromatids will it have during G2 phase?

   A: 92 chromatids (each chromosome duplicates during S phase).

 

2. Q: If a cell has a DNA content of 2 picograms (pg) in G1 phase, what will be its DNA content in G2 phase?

   A: 4 picograms (DNA content doubles after S phase).

 

3. Q: Calculate the mitotic index of a tissue with 800 cells, where 200 cells are undergoing mitosis.

   A: Mitotic index = (Number of cells in mitosis / Total number of cells) × 100

      Mitotic index = (200 / 800) × 100 = 25%

 

4. Q: If a cell has a surface area of 1000 μm² and a volume of 100 μm³, what is its surface area-to-volume ratio?

   A: Surface area-to-volume ratio = Surface area / Volume = 1000 μm² / 100 μm³ = 10 μm⁻¹

 

5. Q: A cell has an osmolarity of 0.9 osmol/L. If the cell contains 2 moles of solute, what is its volume in liters?

   A: Osmolarity (osmol/L) = Moles of solute / Volume (in L)

      0.9 osmol/L = 2 moles / Volume

      Volume = 2 moles / 0.9 osmol/L ≈ 2.22 L

 

6. Q: Calculate the rate of diffusion of oxygen (molecular weight: 32 g/mol) through a cell membrane with a thickness of 10 nm, a surface area of 5 μm², and a concentration gradient of 0.1 mol/L.

   A: Rate of diffusion = (Diffusion constant × Surface area × Concentration gradient) / Membrane thickness

      Rate of diffusion = ((2.0 × 10⁻⁵ cm²/s) × 5 × 10⁻⁸ cm² × 0.1 mol/L) / 10⁻⁷ cm = 10⁻⁵ mol/s

 

7. Q: If a cell consumes 24 molecules of ATP during cellular respiration to produce 48 molecules of carbon dioxide, what is the ATP-to-CO2 ratio?

   A: ATP-to-CO2 ratio = Number of ATP molecules / Number of CO2 molecules = 24 / 48 = 1:2

 

8. Q: A cell is placed in a solution with an osmotic pressure of 3 atm. If the cell has a volume of 10 μm³ and an elastic modulus of 100 dyn/cm², what will be the change in cell volume?

   A: Change in cell volume = (Osmotic pressure × Initial cell volume) / Elastic modulus

      Change in cell volume = (3 atm × 10 μm³) / 100 dyn/cm² = 0.3 μm³

 

9. Q: Calculate the mean generation time of a bacterial population with 10^6 cells at the start and 10^9 cells after 6 hours of exponential growth.

   A: Mean generation time = (Total time of growth) / (Number of generations)

      Number of generations = log(Nt/N0) / log(2) = log(10^9/10^6) / log(2) ≈ 9.97

      Mean generation time = 6 hours / 9.97 ≈ 0.602 hours per generation

 

10. Q: A cell has a membrane potential of -70 mV. If the concentration of potassium ions inside the cell is 150 mM and outside is 5 mM, what is the potassium equilibrium potential?

    A: Nernst equation: E = (RT/zF) * ln([K+]out / [K+]in)

       E = (2.303 * (8.314 J/(mol·K)) * 298 K) / (1 * 96500 C/mol) * ln(5/150) ≈ -94.6 mV

 

11. Q: A cell's cytoplasm has a pH of 7.2. If the concentration of H+ ions is 10⁻⁷ M, what is the pOH of the cytoplasm?

    A: pOH = -log([OH⁻])

       pOH = -log(10⁻⁷) = 7

 

12. Q: If a cell contains 4,000 ribosomes and each ribosome synthesizes 20 amino acids per minute, what is the total number of amino acids synthesized per minute?

    A: Total amino acids synthesized per minute = Number of ribosomes × Amino acids per ribosome

       Total amino acids synthesized per minute = 4,000 × 20 = 80,000 amino acids

 

13. Q: A cell is 25 μm in diameter and takes 2 minutes to complete one full rotation during ciliary movement. What is the speed of ciliary movement in μm/s?

    A: Speed = Distance traveled / Time taken

       Distance traveled = Circumference of the circle = π × Diameter = 3.14 × 25 μm ≈ 78.5 μm

       Speed = 78.5 μm / 120 s ≈ 0.654 μm/s

 

14. Q: A cell has a glucose consumption rate of 10 μmol/min. If each glucose molecule produces 36 ATP molecules through aerobic respiration, what is the rate of ATP production?

    A: ATP production rate = Glucose consumption rate × ATP produced per glucose molecule

       ATP production rate = 10 μmol/min × 36 = 360 μmol/min

 

15. Q: Calculate the Poisson distribution probability of observing three spontaneous mutations in a gene, with an average mutation rate of 0.1 mutations per generation.

    A: Poisson distribution probability P(k) = (λ^k * e^(-λ)) / k!

       λ (average number of events) = Mutation rate = 0.1

       P(3) = (0.1^3 * e^(-0.1)) / 3! ≈ 0.000045

 

16. Q: If a cell has a haploid chromosome number of 23, what is its diploid chromosome number?

    A: Diploid chromosome number = 2 × Haploid chromosome number = 2 × 23 = 46

 

17. Q: A cell has an initial concentration of 0.05 M of a substance, and it degrades at a rate of 0.02 M/s. Calculate the concentration after 60 seconds.

    A: Concentration after 60 seconds = Initial concentration - (Degradation rate × Time)

       Concentration after 60 seconds = 0.05 M - (0.02 M/s × 60 s) = 0.05 M - 1.2 M = -1.15 M (Negative concentration is not possible, indicating complete degradation.)

 

18. Q: If a cell contains 0.2 moles of glucose, how

 

 many molecules of glucose are present?

    A: Avogadro's number (NA) = 6.022 × 10^23 molecules/mol

       Number of glucose molecules = Moles of glucose × Avogadro's number

       Number of glucose molecules = 0.2 mol × 6.022 × 10^23 molecules/mol = 1.2044 × 10^23 molecules

 

19. Q: A cell expels 3 sodium ions (Na+) for every 2 potassium ions (K+) it takes in. If the cell pumps in 30,000 K+ ions, how many Na+ ions will it expel?

    A: Ratio of Na+ ions to K+ ions = 3:2

       Number of Na+ ions expelled = (Number of K+ ions taken in / 2) * 3

       Number of Na+ ions expelled = (30,000 / 2) * 3 = 45,000 Na+ ions

 

20. Q: Calculate the percentage of the cell cycle spent in G1 phase if the total cell cycle duration is 24 hours, and G1 phase lasts 8 hours.

    A: Percentage of time spent in G1 phase = (G1 phase duration / Total cell cycle duration) × 100

       Percentage of time spent in G1 phase = (8 hours / 24 hours) × 100 = 33.33%

 

21. Q: If a cell has an intracellular concentration of calcium ions (Ca²⁺) of 0.1 mM, how many moles of Ca²⁺ ions are present in 1 liter of cytoplasm?

    A: Moles of Ca²⁺ ions in 1 liter = Concentration of Ca²⁺ ions (in mol/L) × Volume (in L)

       Moles of Ca²⁺ ions in 1 liter = 0.1 mM × 1 L × 10⁻³ mol/mM = 0.1 mol

 

22. Q: A cell has an oxygen consumption rate of 50 μmol/min. If each oxygen molecule consumes 2 electrons during oxidative phosphorylation, how many electrons are consumed per minute?

    A: Electrons consumed per minute = Oxygen consumption rate × Electrons per oxygen molecule

       Electrons consumed per minute = 50 μmol/min × 2 = 100 μmol/min

 

23. Q: If a cell has a diameter of 10 μm, what is its surface area in square micrometers (μm²)?

    A: Surface area of a sphere = 4πr², where r is the radius of the sphere.

       Surface area = 4π(5 μm)² ≈ 314 μm²

 

24. Q: A cell has an initial concentration of 100 molecules and a decay rate of 5 molecules per second. How many molecules will remain after 20 seconds?

    A: Number of molecules remaining = Initial concentration - (Decay rate × Time)

       Number of molecules remaining = 100 - (5 molecules/s × 20 s) = 100 - 100 = 0 molecules

 

25. Q: If a cell synthesizes 20,000 lipids per minute and each lipid molecule contains 50 carbon atoms, how many carbon atoms are synthesized per minute?

    A: Carbon atoms synthesized per minute = Number of lipids synthesized × Carbon atoms per lipid

       Carbon atoms synthesized per minute = 20,000 × 50 = 1,000,000 carbon atoms

 

26. Q: Calculate the flux of glucose through a cell membrane with a permeability of 0.02 μmol/s·cm² and a concentration gradient of 10 μM across the membrane.

    A: Flux = Permeability × Concentration gradient

       Flux = 0.02 μmol/s·cm² × 10 μM = 0.2 μmol/s

 

27. Q: If a cell's growth rate is 0.5 μm/hour, how much will its size increase in 24 hours?

    A: Size increase in 24 hours = Growth rate × Time

       Size increase in 24 hours = 0.5 μm/hour × 24 hours = 12 μm

 

28. Q: A cell contains 2 μg of a protein and has a volume of 10 μL. Calculate the protein concentration in the cell in μg/μL.

    A: Protein concentration = Protein mass / Cell volume

       Protein concentration = 2 μg / 10 μL = 0.2 μg/μL

 

29. Q: If a cell has a DNA replication time of 40 minutes, how many base pairs are replicated per second?

    A: Base pairs replicated per second = Total base pairs replicated / Replication time

       Base pairs replicated per second = Total base pairs replicated / 2400 s

       (Assuming DNA replication is constant throughout the cell cycle, and there are 60 minutes in an hour, 40 minutes = 2400 seconds)

       (Actual numbers may vary depending on the context.)

 

30. Q: Calculate the recombination frequency between two genes if they show a 30% recombination rate.

    A: Recombination frequency = Recombination rate / 100

       Recombination frequency = 30% / 100 = 0.30

 

31. Q: If a cell has a membrane potential of -80 mV and the Nernst potential for potassium (K+) is -90 mV, what is the equilibrium potential for potassium?

    A: Equilibrium potential for potassium (EK) = Nernst potential for potassium (EK⁺) = -90 mV

 

32. Q: A cell contains 4,000 mitochondria, and each mitochondrion has an electron transport chain capacity to pump 3 protons per electron pair. If each mitochondrion transfers 100 electron pairs per minute, what is the total proton pumping rate?

    A: Total proton pumping rate = (Number of mitochondria × Protons per electron pair) × Electron transfer rate

       Total proton pumping rate = (4,000 × 3) × 100 = 1,200,000 protons per minute

 

33. Q: Calculate the frequency of crossing over between two genes if the genetic map distance between them is 20 cM.

    A: Frequency of crossing over = Genetic map distance / 100

       Frequency of crossing over = 20 cM / 100 = 0.20

 

34. Q: If a cell has 100,000 active ion channels and each channel allows the passage of 1,000 ions per second, what is the total ion flux?

    A: Total ion flux = Number of channels × Ion flux per channel

       Total ion flux = 100,000 × 1,000 = 100,000,000 ions per second

 

35. Q: A cell has a doubling time of 10 hours. How many cells will be present after 30 hours if the cell population starts with 1,000 cells?

    A: Number of cells after 30 hours = Initial number of cells × 2^(Time elapsed / Doubling time)

       Number of cells after 30 hours = 1,000 × 2^(30 hours / 10 hours) = 1,000 ×

 

2^3 = 8,000 cells

 

36. Q: Calculate the turnover rate of a protein with a half-life of 6 hours.

    A: Turnover rate = 0.693 / Half-life

       Turnover rate = 0.693 / 6 hours ≈ 0.115 per hour

 

37. Q: If a cell contains 500 picograms of DNA and has a haploid chromosome number of 12, what is the DNA content per haploid chromosome?

    A: DNA content per haploid chromosome = Total DNA content / Haploid chromosome number

       DNA content per haploid chromosome = 500 pg / 12 = 41.67 pg

 

38. Q: A cell has a glucose concentration of 0.1 mM. How many moles of glucose are present in 1 liter of the cell's cytoplasm?

    A: Moles of glucose in 1 liter = Glucose concentration (in mol/L) × Volume (in L)

       Moles of glucose in 1 liter = 0.1 mM × 1 L × 10⁻³ mol/mM = 0.0001 mol

 

39. Q: Calculate the enzymatic reaction rate if an enzyme converts 1,000 substrate molecules into products per minute.

    A: Enzymatic reaction rate = Number of substrate molecules converted / Time

       Enzymatic reaction rate = 1,000 molecules / 1 minute = 1,000 molecules per minute

 

40. Q: A cell has a doubling time of 8 hours. How many generations will pass in 32 hours?

    A: Number of generations = Time elapsed / Doubling time

       Number of generations = 32 hours / 8 hours = 4 generations

 

41. Q: Calculate the half-life of a radioactive substance if 25% of it remains after 10 days.

    A: Half-life = Time elapsed / Number of half-lives

       Number of half-lives = log(Remaining percentage) / log(0.5)

       Number of half-lives = log(25%) / log(0.5) ≈ 2.32

       Half-life = 10 days / 2.32 ≈ 4.31 days

 

42. Q: If a cell has 200 μg of protein and 5% of its mass is composed of nitrogen, how many grams of nitrogen are present?

    A: Mass of nitrogen = (Percentage of nitrogen / 100) × Mass of protein

       Mass of nitrogen = (5% / 100) × 200 μg = 0.05 × 200 μg = 10 μg

 

43. Q: Calculate the fluorescence intensity of a cell if it emits 1,000 photons per second and each photon has an energy of 2.5 eV.

    A: Fluorescence intensity = Number of photons emitted per second × Energy per photon

       Fluorescence intensity = 1,000 photons/s × 2.5 eV = 2,500 eV/s

 

44. Q: If a cell has a haploid chromosome number of 6 and undergoes meiosis, how many chromosomes will each daughter cell have after telophase II?

    A: Each daughter cell after telophase II will have the haploid chromosome number.

       Each daughter cell will have 6 chromosomes.

 

45. Q: A cell's membrane potential is -90 mV, and the Nernst potential for sodium (Na+) is +60 mV. What is the equilibrium potential for sodium?

    A: Equilibrium potential for sodium (ENa) = Nernst potential for sodium (ENa⁺) = +60 mV

 

46. Q: Calculate the mitotic rate of a tissue with 500 cells, where 50 cells are in the process of mitosis.

    A: Mitotic rate = (Number of cells in mitosis / Total number of cells) × 100

       Mitotic rate = (50 / 500) × 100 = 10%

 

47. Q: If a cell consumes 20 molecules of glucose during glycolysis to produce 40 molecules of pyruvate, what is the glucose-to-pyruvate ratio?

    A: Glucose-to-pyruvate ratio = Number of glucose molecules / Number of pyruvate molecules = 20 / 40 = 1:2

 

48. Q: A cell has a diameter of 20 μm and takes 3 minutes to complete one full rotation during ciliary movement. What is the speed of ciliary movement in μm/s?

    A: Speed = Distance traveled / Time taken

       Distance traveled = Circumference of the circle = π × Diameter = 3.14 × 20 μm ≈ 62.8 μm

       Speed = 62.8 μm / 180 s ≈ 0.349 μm/s

 

49. Q: A cell has an osmolarity of 1.2 osmol/L. If the cell contains 3 moles of solute, what is its volume in liters?

    A: Osmolarity (osmol/L) = Moles of solute / Volume (in L)

       1.2 osmol/L = 3 moles / Volume

       Volume = 3 moles / 1.2 osmol/L ≈ 2.5 L

 

50. Q: Calculate the rate of diffusion of carbon dioxide (molecular weight: 44 g/mol) through a cell membrane with a thickness of 5 nm, a surface area of 2 μm², and a concentration gradient of 0.05 mol/L.

    A: Rate of diffusion = (Diffusion constant × Surface area × Concentration gradient) / Membrane thickness

       Rate of diffusion = ((1.0 × 10⁻⁵ cm²/s) × 2 × 10⁻⁸ cm² × 0.05 mol/L) / 5 × 10⁻⁷ cm ≈ 2 × 10⁻⁶ mol/s

 

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