**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:

- 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).

- 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).

- 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%

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.)

- 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

- 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

- 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%

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.)

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.

- 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

- 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%

- 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

- 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

- 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

- 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