Cell Growth Calculators

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Cell growth refers to the increase in cell number (proliferation) or cell mass over time. In bacteria: cells divide by binary fission; growth follows lag → exponential → stationary → death phases. In mammalian cell culture: cells grow until contact inhibition (for non-transformed cells) or until nutrients are depleted. Growth is monitored by optical density (OD₆₀₀), viable cell count (CFU or hemocytometer), or total protein. The specific growth rate (μ) and doubling time (t_d = 0.693/μ) are the key kinetic parameters describing growth during the exponential phase.

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Bacterial Growth Phases

  • Lag phase: No growth; cells adapting to new medium; synthesizing enzymes; no change in OD or cell count
  • Exponential (log) phase: Constant doubling time; OD doubles each generation; μ is constant; best phase for experiments
  • Stationary phase: Growth rate = death rate; OD plateau; nutrient depletion or waste accumulation
  • Death (decline) phase: Death rate > growth rate; OD decreases; cells lyse

Key Growth Equations

N(t) = N₀ × 2^(t/t_d). Or: N(t) = N₀ × e^(μt). μ = ln(2)/t_d = 0.693/t_d. μ from OD₆₀₀: slope of ln(OD₆₀₀) vs. time during exponential phase.

Mammalian Cell Growth

Doubling time: 18–48 h for most mammalian cell lines. Contact inhibition: normal cells stop dividing at confluence; cancer cells continue. Passage number: cells may change phenotype with many passages; use low passage stocks. Growth curves: seed at low density; measure OD or count daily; fit sigmoid (logistic) curve.

Growth Measurement

OD₆₀₀: fast; not specific to live cells; non-linear at OD > 0.8. CFU plate count: counts viable culturable bacteria. Hemocytometer + trypan blue: counts live and dead separately.

Glossary

Specific Growth Rate (μ)
The exponential growth rate: N = N₀e^(μt); μ = slope of ln(OD₆₀₀) vs. time during exponential phase; units h⁻¹; doubling time = 0.693/μ.
Doubling Time
Time for a cell population to double: t_d = 0.693/μ; E. coli in LB ≈ 20 min; mammalian cells 18–48 h; constant during exponential phase; increases as nutrients deplete.
Contact Inhibition
Normal mammalian cells stop dividing when they contact neighboring cells at confluence; cancer cells lose this inhibition and continue to proliferate — a hallmark of malignancy.

Frequently Asked Questions

Bacterial growth in batch culture follows four phases: Lag phase: cells adapting to new medium — synthesizing new enzymes, repairing damage, adjusting metabolism. No net increase in OD or cell count. Duration depends on inoculum condition and medium difference. Exponential (log) phase: cells dividing at maximum rate; OD doubles every generation time; μ = constant; ln(OD) increases linearly with time. The most reproducible phase for experiments. Stationary phase: growth = death; net cell count stable; caused by nutrient depletion, accumulation of inhibitory metabolites, or limited O₂. Death (decline) phase: death rate exceeds growth rate; OD drops; cells lyse and release contents.

Plot OD₆₀₀ on a semi-log scale (ln(OD₆₀₀) on y-axis, time on x-axis). During exponential phase: the plot is linear. μ = slope of the linear portion = [ln(OD₂) − ln(OD₁)] / (t₂ − t₁). Example: OD₆₀₀ increases from 0.1 at t=0 to 0.8 at t=3 hours: μ = (ln 0.8 − ln 0.1) / 3 = (−0.223 − (−2.303)) / 3 = 2.080/3 = 0.693 h⁻¹. Doubling time = 0.693/μ = 0.693/0.693 = 1 hour.

Key differences: Doubling time: bacteria (E. coli in LB) ≈ 20 min; mammalian cells 18–48 hours depending on cell line. Contact inhibition: normal mammalian cells stop growing when they contact neighboring cells and form a monolayer (G₀ arrest). Cancer cells lose contact inhibition → continue growing in multilayers → form foci. CO₂ requirement: mammalian cells require 5% CO₂ to buffer bicarbonate medium; bacteria typically don't. Temperature: both 37°C for human pathogens and mammalian cells, but many bacteria grow at different optima. Growth medium complexity: mammalian cells require serum + amino acids + vitamins; bacteria can often grow on simple defined media. Passage effects: mammalian cell lines may undergo senescence after many passages (Hayflick limit for primary cells) or accumulate mutations.

Methods for measuring mammalian cell growth: Hemocytometer + trypan blue: count live (colorless) and dead (blue) cells; calculate viable cell count and viability%; most direct method; time-consuming. Automated cell counter (Bio-Rad TC20, Countess II): similar to hemocytometer but automated; faster with less operator variation. MTS/MTT/WST-1 assay (colorimetric): measures mitochondrial enzyme activity as proxy for cell number; high-throughput; cannot distinguish dead from dormant cells. Crystal violet staining (for adherent cells): stain fixed cells; measure absorbance → proportional to cell number; useful for drug sensitivity (IC₅₀) assays. CyQuant (DNA fluorescence): total DNA proportional to cell number; very sensitive; for low-density cultures.