Surviving Fraction Calculators

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Surviving fraction (SF) is the proportion of irradiated (or treated) cells that retain the ability to divide indefinitely and form colonies, compared to untreated controls. It is determined by clonogenic (colony formation) assay: cells are irradiated or treated, plated at low density, incubated for 10–14 days, and colonies (≥50 cells) are counted. SF = (colonies counted) / (cells plated × plating efficiency). The dose-response relationship in radiobiology follows the linear-quadratic (LQ) model: SF = e^(−αD − βD²). Surviving fraction quantifies cytotoxicity for radiation therapy, chemotherapy, and other treatments.

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Surviving Fraction Formula

SF = colonies counted / (cells plated × plating efficiency)

Plating efficiency (PE) = colonies in untreated control / cells plated in untreated control. SF normalizes to the control plating efficiency to account for baseline colony-forming ability.

Example: Untreated: 50 colonies from 100 cells plated → PE = 50/100 = 0.50 (50%). Treated (5 Gy): 8 colonies from 100 cells plated → SF = 8/(100 × 0.50) = 8/50 = 0.16. Interpretation: 5 Gy reduced clonogenic survival to 16% of control.

Linear-Quadratic (LQ) Model

SF = e^(−αD − βD²)

α = linear component (single-hit cell killing); β = quadratic component (two-hit cell killing); D = dose (Gy). α/β ratio: tissues with high α/β (>10 Gy, e.g., tumor cells, rapidly dividing tissue) = less sensitive to fractionation; low α/β (<3 Gy, e.g., late-responding normal tissue, prostate cancer) = more sensitive to large dose fractions.

D10 Value

D10 = dose reducing SF to 10% (= 0.10). D10 = 2.303/D₀ (for exponential portion of cell survival curve). Radioresistant cells have high D10; radiosensitive cells have low D10.

Clonogenic Assay Protocol

Irradiate cells; trypsinize; count; plate known numbers in complete medium; incubate 10–14 days (depends on doubling time); fix with methanol; stain with crystal violet; count colonies ≥ 50 cells with microscope or automated counter.

Glossary

Surviving Fraction (SF)
The proportion of treated cells retaining unlimited proliferative potential: SF = colonies counted / (cells plated × PE); measured by clonogenic assay; SF = 1 = no kill; SF = 0.01 = 99% kill.
Linear-Quadratic (LQ) Model
SF = e^(−αD − βD²); models cell survival vs. radiation dose; α/β ratio characterizes repair capacity; high α/β = acute-responding tissue; low α/β = late-responding tissue.
Plating Efficiency (PE)
PE = colonies formed / cells plated in untreated control; normalizes for baseline colony-forming ability; used in denominator of SF calculation; typical value 20–80% for cell lines.

Frequently Asked Questions

Surviving fraction (SF) measures the proportion of cells retaining unlimited proliferative potential after a treatment. Measured by clonogenic assay: (1) Treat cells (radiation, drug, etc.). (2) Trypsinize and count surviving cells. (3) Plate a known number at low density (to avoid colony merging). (4) Incubate 10–14 days until visible colonies form. (5) Fix, stain, count colonies (minimum 50 cells per colony). (6) SF = (colonies counted) / (cells plated × plating efficiency), where PE = colonies in untreated wells / cells plated in untreated wells. SF = 1.0 = no cell kill; SF = 0.01 = 99% of cells killed (1% clonogenic survivors).

The linear-quadratic model describes cell survival after radiation: SF = e^(−αD − βD²), where D = dose (Gy), α = sensitivity to single-hit (double-strand break) killing (Gy⁻¹), β = sensitivity to two-hit killing (Gy⁻²). The α/β ratio (in Gy) is a key parameter: High α/β (8–15 Gy): acute-responding tissues and most tumors; shoulder on the survival curve is less pronounced; less repair between fractions. Low α/β (1–4 Gy): late-responding normal tissues (spinal cord, kidney, lung) and some tumors (prostate, breast); greater repair capacity; highly sensitive to dose per fraction. Hypofractionation (large doses per fraction) exploits the difference in α/β between tumor and late-responding tissue.

D10 is the radiation dose required to reduce clonogenic survival to 10% (SF = 0.10). From the exponential portion of the survival curve: D10 = ln(10)/k = 2.303/k, where k is the slope of log survival vs. dose. For the LQ model, D10 is the dose D satisfying e^(−αD − βD²) = 0.1. Higher D10 = more radiation needed to achieve a 1-log cell kill = more radioresistant. Typical D10 values: sensitive cell lines 2–3 Gy; moderately resistant 4–6 Gy; very resistant 8–12 Gy. D10 helps compare radiosensitivity between cell lines and predict radiotherapy outcomes.

Clonogenic assay directly measures what matters most in cancer therapy: the ability of a cell to reproduce indefinitely. Other cell viability assays (MTT, trypan blue, flow cytometry) measure immediate viability — whether a cell is metabolically active or has an intact membrane at one time point. A cell can be temporarily metabolically active or exclude trypan blue but still have irreparable DNA damage preventing it from ever dividing again (mitotic death). Only the clonogenic assay distinguishes these 'living dead' cells from true survivors. Limitation: labor-intensive; takes 10–14 days; works best for cell lines; difficult for primary cells with poor plating efficiency; some cells clump and don't form discrete colonies.