Cell Survival Curve

Dr. Vandana, King George’s Medical University, Lucknow

Cell Survival Curve It describes relationship between radiation

dose and the fraction of cells that “survive” that dose.

This is mainly used to assess biological effectiveness of radiation.

To understand it better, we need to know about a few basic things e.g. Cell Death Estimation of Survival / Plating Efficiency Nature of Cell killing etc.

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Cell Death

Cell death can have different meanings: loss of a specific function - differentiated cells

(nerve, muscle, secretory cells)

loss of the ability to divide - proliferating cells such as stem cells in hematopoietic system or intestinal epithelium loss of reproductive integrity - “reproductive death”

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Relevant Dose 100 Gy

destroys cell function in non-proliferating systems (for example: nerve, muscle cells)

2 Gy mean lethal dose for loss of proliferative capacity

for proliferating cells

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Survival

Conversely - “Survival” means retention of reproductive integrity the capacity for sustained proliferation in cells

that proliferate

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Proof of reproductive integrity - the capability of a single cell to grow into a large colony, visible to the naked eye

A surviving cell that has retained its reproductive integrity and is able to proliferate indefinitely is said to be clonogenic

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Estimating Survival

In order to determine the surviving fraction, we must know the plating efficiency

PE is the percentage of cells (in control batch) that grow into colonies in other words, those cells that survive the

plating process

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Derivation of Survival Curves

Cells have been taken from stock culture and placed in seed dishes

Then irradiated (0 Gy to 6 Gy)and allowed to grow into colonies for 1-2 weeks

Colonies have been counted for survival data

Always will have a controlbatch to determine PE.

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Surviving Fraction

Equal to the fraction of cells that plate successfully and survive irradiation (without losing their reproductive integrity) to grow into colonies

PE/100seededcellscountedColonies

fractionSurviving

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Dose (Gy)

SurvivingFraction

2 64

0.01

0.1

1

0.001

SF(2) = = 0.272 colonies

400 seeded x 0.9 plated

As Ionizations produced within cells by irradiation are distributed randomly.

So consequently, cell death follows random probability statistics, the probability of survival decreasing geometrically with dose.

Quantization of cell killing A dose of radiation that

introduces an average of one lethal event per cell leaves 37% still viable is called D0 dose.

Cell killing follows exponential relationship. A dose which reduces cell survival to 50% will, if repeated, reduce survival to 25%, and similarly to 12.5% from a third exposure.

This means Surviving fraction never becomes zero.

A straight line results when cell survival (from a series of equal dose fractions) is plotted on a logarithmic scale as a function of dose on linear scale.

The slope of such a semi-logarithmic dose curve could be described by the D0, the dose to reduce survival to 37%, D50, the dose to reduce survival to 50%, the D10, the dose to reduce survival to 10%.

D0 usually lies between 1 and 2 Gy

D10= 2.3 x D0

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Survival Curve Features Simple to describe qualitatively

Difficulty lies in explaining underlying biophysical events

Many models have been proposed

Steepness of curve represent the radio-sensitiveness.

Survival Curve Shape general shapes of survival

curves for mammalian cells exposed to radiation

Initial portion has a shoulder and terminal portion become straight line.

In low dose region ,some dose of radiation goes waste.

Terminal portion follow exponential relationship means same dose increment result into equal reduction in surviving fraction.

Mammalian Cell Survival Curve Shoulder Region

Shows accumulation of SUB-LETHAL DAMAGE.

The larger the shoulder region, the more dose will initally be needed to kill the same proportion of cells.

Beyond the shoulder region The D0 dose, or the inverse

of the slop of the curve, indicates the relative radiosensitivity. The smaller the D0 dose, the greater the radiosensitivity.

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Two General Survival Models

Linear-quadratic model “dual radiation action” first component - cell killing is proportional to

dose second component - cell killing is

proportional to dose squared Multi-target model

based on probability of hitting the “target” widely used for many years; still has merit

L-Q Model

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Linear Quadratic Model

S = e-(aD + bD2)

where: S represents the fraction of cells surviving D represents dose a and b are constants that characterize the slopes

of the two l portions of the semi-log survival curve biological endpoint is cell death

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Linear Quadratic Model

Linear and quadratic contributions to cell killing are equal when the dose is equal to the ratio of a to b D = a/ b or aD = b D2

a component is representative of damage caused by a single event (hit, double-strand break, “initiation / promotion” etc.)

b component is representative of damage caused by multiple events (hit/hit, 2 strand breaks, initiation then promotion, etc.)

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a and b Determination

100

10-1

10-2

0 123 6 9

/a b

bD2

aD

Dose, Gy

Su

rviv

al

Multi-target Model

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Multi-target Model

Quantified in terms of:

measure of initial slope due to single-event killing, D1

measure of final slope due to multiple-event killing, D0

width of the shoulder, Dq or n

D1 and D0 are

1. reciprocals of the initial and final slopes

2. the doses required to reduce the fraction of surviving cells by 37%

3. the dose required to deliver, on average, one inactivating event per cell

4. D1,reduces survivivig fraction to 0.37

5. D0, from 0.1 to 0.037, or from 0.01 to 0.0037 ,and so on.

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Multi-target Model

Shoulder-width measures: the quasi-threshold dose (Dq)

the dose at which the extrapolated line from the straight portion of the survival curve (final slope) crosses the axis at 100% survival

the extrapolation number (n) This value is obtained by extrapolating

the exponential portion of the curve to the vertical line.

“broad shoulder” results in larger value of n

“narrow shoulder” results in small value of n

n = exp[Dq / D0]

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Multi-Target Model

Dose, Gy

100

10-1

10-4

0 123 6 9

Su

rviv

al

10-3

10-2

Initial slope measure, D1,due to single-event killing

Final slope measure, D0,due to multiple-event killing

Dq

nn or Dq represents the sizeor width of the shoulder

Linear –quadratic model Multi-target model

Neither the L-Q not the M-T model has any established biological basis.

At high doses the LQ model predicts a survival curve that bends continuosly, whereas the M-T model become linear.

At low doses the LQ model describes a curve that bends more than a M-T curve.

Factors affecting cell survival curve

1. LET

2. Fractionation

3. Dose rate effect

4. Intrinsic radiosesitivity

5. Cell age

6. Oxygen presence

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LET

Low-LET radiations: low dose region

shoulder region appears high dose region

survival curve becomes linear and surviving fraction to an exponential function of dose

surviving fraction is a dual exponential

S = e-(aD+bD2)

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High-LET radiations: survival curve is linear surviving fraction is a pure exponential function of

dose

S = e-(aD)

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Survival Curves and LET

Increasing LET: increases the

steepness of the survival curve

results in a more linear curve

shoulder disappears due to increase of killing by single-events

Fractionation

If the dose is delivered as equal fractions with sufficient time ,repair of sub-lethal damage ocurs

Elkind’ s Recovery takes place between radiation exposure , cell act as fresh target.

Elkind & Sutton showed that when two exposure were given few hours apart ,the shoulder reappeared.

Dq

Two D

oses

Single Dose

Dq

Dose (Gy)5 10 15 20 25

104

103

102

101

100

10-1

10-2

D0

n = exp[Dq / D0]

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The Effective Survival Curve: Fractionation

If the dose is delivered as equal fractions with sufficient time between for repair of the sub-lethal (non-killing) damage, the shoulder of the survival curve is repeated many times.

The effective survival curve becomes a composite of all the shoulder repetitions.

Dose required to produce the same reduction in surviving fraction increases.

D0 is 3 Gy

Showing ~28 Gyin 14 fractions.

Dose-rate effect

Dose rate determines biological impact

reduction in dose rate causes reduced cell killing, due to repair of SLD

reduction in dose rate generally reduces survival-curve slope (D0 increases)

inverse dose-rate effect occurs in some cell lines at ‘optimal’ dose rate due to accumulation of cells in G2

Dose-Rate Effect in CHO Cells

Dose rate effect is more dramatic in CHO than in HeLa Cells

Broad shoulder to survivalcurve

Composite survival curves for 40 Human Cell Lines

Low Dose Rate: SurvivalCurves show greater variation,Greater range in repair times

Less variation

Evidence for Dose Rate Effect in vivo: Crypt Cells

27436

4.5

0.92

0.54 rad/min

Crypt cells: rapid dividingDramatic dose rate effectExposure time is longer thanCell cycle (repopulation)

Intrinsic radiosensitivity

Due to the differences in DNA content

represents bigger target for radiation damage

Sterilizing radiation dose for bacteria is 20,000 Gy

Mammalian cells are significantly more radio-sensitive than microorganisms:

Age response:Cell Cycle

Late S—least sens.

M>G2>G1>early S>late S for sensitivityDifference caused by cell cycle are similar to difference caused by Oxygen effect

Cells are most sensitive to radiation at or close to M

Cells are most resistant to radiation in late S

For prolonged G1 a resistant period is evident early G1 followed be a sensitive period in late G1

Cells are usually sensitive to radiation in G2 (almost as sensitive as in M)

Oxygen modifies the biological effects of ionizing radiation

02 effect does not require that 02 be present during radiation – just added within 5 msec after generation of free radical

OER – oxygen enhancement ratio: ratio of hypoxic: aerated doses needed to achieve the same biological effect

X-Rays/γ-Rays at high doses is 2.5-3.5 OER is ~2.5 at lower doses

OER is absent for high LET radiations like alpha-particles and is intermediate for fast neutron.

OER is lower for types of radiation predisposed to killing cells by single-hit mechanisms

The Oxygen Effect

Cells are more sensitive toRadiation in the presence ofOxygen than in its absence High dose region of survival

curve

Low dose region of survivalcurve

Summary A cell survival curve is the relationship between the

fraction of cells retaining their reproductive integrity and absorbed dose.

Conventionally, surviving fraction on a logarithmic scale is plotted on the Y-axis, the dose is on the X-axis . The shape of the survival curve is important.

The cell-survival curve for densely ionizing radiations (α-particles and low-energy neutrons) is a straight line on a log-linear plot, that is survival is an exponential function of dose.

The cell-survival curve for sparsely ionizing radiations (X-rays, gamma-rays has an initial slope, followed by a shoulder after which it tends to straighten again at higher doses.

At low doses most cell killing results from “α-type” (single-hit, non-repairable) injury, but that as the dose increases, the“β –type” (multi-hit, repairable) injury becomes predominant, increasing as the square of the dose.

Survival data are fitted by many models. Some of them are: multitarget hypothesis, linear-quadratic hypothesis.

The survival curve for a multifraction regimen is also an exponential function of dose.

The D10, the dose resulting in one decade of cell killing, is related to the Do by the expression D10 = 2.3 x Do

Cell survival also depends on the dose, dose rate and the cell type

Summary

Thank You