CELL SURVIVAL CURVES

PRESENTER: DR.T.JOSEPH RAJIV

MODERATOR: DR.SHYAMA PREM

OUTLINE

• INTRODUCTION

• DEFINING CELL SURVIVAL CURVE

• POISSON’S DISTRIBUTION

• MODELS OF CELL SURVIVAL CURVE

• SUMMARY

OUTLINE

• INTRODUCTION

• DEFINING CELL SURVIVAL CURVE

• POISSON’S DISTRIBUTION

• MODELS OF CELL SURVIVAL CURVE

• SUMMARY

Introduction

• Survival Curve: A curve describing relationship between radiation

dose and proportion of cells that survive

• Cell survival models: Attempt to describe or explain the shape of

cell survival curves using a mathematical formula

Introduction : Definition of survival

Physiological

• Loss of principal function• Eg. Conduction for nerves,

Secretion for glandular cells, contraction for muscles

Reproductive

• Loss of reproductive integrity

• Eg. hematopoietic cells, intestinal epithelial cells

100Gy necessary to destroy cell function in nonproliferating cells2Gy sufficient for loss of proliferative capacity

Introduction : Creating cell line

• Divide tumour/ normal regenerative tissue, loosen intercellular connections and cell membrane enzymatically (trypsin, cellulose)

• Seed to culture dish, cover with growth medium ad incubate aseptically.• Few explants will proliferate but most of these eventually die. • Very few will pass this first crisis, they are separated from culture medium

enzymatically, & reseeded.• These now rapidly repopulate the culture = Established cell lines.

Introduction : Plating efficiencyEstablished cell line – 100 cells

plated

Allowed to grow for 7 days before

being stained

If 70 colonies are counted

Then, Plating efficiency is 70%

P.E = ( Number of colonies counted / Number of colonies seeded ) 100

Possible explanations

• Sub optimal growth conditions• Plating errors

Introduction : Survival fractionEstablished cell line – 100 cells

plated

Allowed to grow for 7 days before

being stained

If 70 colonies are counted

Then, Plating efficiency is 70%

Established cell line – 2000 cells plated

Exposed to a dose of 8 Gy (800 rad) of x-rays, and incubated for 1 to 2

weeks before being fixed and stained

1400 colonies expected as P.E = 70% However 32 colonies counted finally

Hence Survival fraction (S.F) = Colonies counted

Colonies seeded × (P.E/100)

= 0.023

Experimental Results from irradiation of cell lines:

A)Cells that have not divided but are alive

B)Cells that died an apoptotic death

C)Completed 1-2 divisions then stopped abortive colony

D)Grow into large colonies that are active

Only D is said to have survived because they retained their reproductive integrity

Clonegenic cell 50 cells or grown for 5 -6 generations

OUTLINE

• INTRODUCTION

• DEFINING CELL SURVIVAL CURVE

• POISSON’S DISTRIBUTION

• MODELS OF CELL SURVIVAL CURVE

• SUMMARY

WHAT IS A CELL SURVIVAL CURVE: LINEAR VS LOG

• N number of cells are irradiated with with different radiation doses

• N0 is the initial number of cells

• D is the radiation doses

• Graph is plotted with Number of cells on Y

• Dose on X axis

NUMBER OFCELLS

D O S E (D)

N0

ND

SF =ND/N0

WHAT IS A CELL SURVIVAL CURVE: LINEAR VS LOG

• Replacing the Y axis with survival fraction

• S at zero dose be 1

• As it is exponential cell kill

• S = e-ƛd

• Rate of decrease in cell number is given by ƛ (decay constant)

SURVIVING

FRACTION

D O S E (D)

1

0

SF = e-ƛD

Ln S

Dose• Cell killing is random then

survivalexponential function of dose, and this will be a straight line on a semi-log plot.

• Logarithmic scale more easily allows us to see and compare the very low cell survivals required to obtain a significant reduction in tumour size, or local tumour control

SEMI-LOG PLOT0

-1

Random nature of cell kill

• Delivery of an amount of radiation to a certain tumour volume will not always lead to the same results

• It is a random event, so is infliction of radiochemical injury.

• This means that every cell in a tumor has the same chance of being hit by a given dose of radiation.

• A given dose of radiation kills the same proportion of cells in a tumor, not the same number of cells

• If no hit cell survives and if it takes hit cell die

PROBABILITY OF CELL SURVIVAL: POISSON DISTRIBUTION

The number of times an event occurs in an interval of time or space.

The Poisson distribution is an appropriate model if the following assumptions are true.

• Events are independent.

• The rate of occurrence of events is constant.

• Two events cannot occur at exactly the same instant.

• The probability of an event in an interval is proportional to the length of the interval.

If these conditions are true, then the variable is a Poisson random variable, and the distribution is a Poisson distribution.

P(k) = ƛk (e-ƛ)

kỊWhere,ƛ = average number of events per intervale = Eulers number (base of natural logarithms (2.718)k =Specific number of eventskỊ = n ×(n-1) ×(n-2)×…..×2×1 is the factorial of k

• For example:• Average number of goals scored in world cup 2015 :2.5• To predict the number of goals in upcoming world cup

match• The probability of scoring zero goals:

P(k) = ƛk (e-ƛ)

kỊK = 0 , ƛ = 2.5 ,

P(0) = 2.50 (e-2.5 ) / 0Ị

0.082

Goals Probability

0 0.082

1 0.205

2 0.257

3 0.213

4 0.133

5 0.067

6 0.028

7 0.010

22 21

1 19 20

2 31 12 27

32 3 26 13 33

29 4 5 37

18 6 7 14

36 35 8 34

24 11 9

23 28 10 15

25 17 16 30

• Radiation is delivered such way each cell receives 1 hit

• But due to random nature of hits

• All cells do not receive equal hits

• Some may receive 4 or 3 or 2 or 1 or 0

• This given by POISSON distribution

• For 100 cells 37 cells will be left undisturbed

• P(0) = e-1 = 0.37 or 37%

P(k) = ƛk (e-ƛ)/ kỊ

TARGET THEORY

• Specific regions of the DNA that are important to maintain the reproductive ability of cells.

• Targets of radiation damage• Survival is related to the number of targets inactivated.• Radiation is considered to be a sequence of random projectiles;• The components of the cell are considered as the targets bombarded by these

projectiles

SINGLE HIT – SINGLE TARGET• Single impact in the sensitive part is enough to kill the cell.

• The survival curve is exponential

• Straight line in a semi-logarithmic plot of cell survival against dose

• Poisson statistics can be applied to derive the equation

• Survival can be given as k = 0 , ƛ = 1

P(k) = ƛk (e-ƛ)

kỊ

P(0) = e-ƛ

The average number of hits (ƛ) increases with increase in dose

S(D) = e-αD

=e-D/D0

• D0: Dose at mean lethal hit per cell is 1

• For a given straight survival line, D0 is a constant.

• D0: Dose required to reduce the fraction of cells to 1/e (0.37) of its previous value

Surviving fraction is an exponential function of dose; constant of proportionality is alpha

• The model was applicable to bacteria,viruses, some very sensitive mammalian cells.

• It describes the simple situation where if an individual cell receives an amount of radiation greater than D0 then it will die, otherwise it will survive

• For low linear energy transfer [LET] radiations (X rays), CSC starts out straight at low doses with known finite slope, explainable by the single target single hit model

• At higher doses, the curve bends. The bending occurs over the therapeutic dose range (few grays)

• The bent curve can be explained by multitarget models• Beyond therapeutic doses, the curve straightens again; surviving fraction again becomes

exponential function of dose.

MULTI TARGET – SINGLE HIT

• It proposes that a single hit to each of n sensitive targets within the cell is to cause cell death.

• The generated curve has a shoulder and decreases linearly with increasing dose.

• At low doses it predicts no cell death.

• DQ: Quasithreshold dose: intercept of 1/D0 at y=1, closest approximation to theoretical threshold dose for cell killing

• n (extrapolation number)= intercept of 1/D0 extrapolated to x=0 (interception of y axis)

V

PROBABILITY OF SURVIVAL FOR MULTI-TARGET MODEL

SINGLE HIT MULTI TARGET

• Proposes ‘n’ targets in a cell and single hits on each of the ‘n’ targets is required for cell death

• Introduces Quasi-threshold dose and n

Dq = D0 Logen• Dq is the dose before which there is no multi- hit killing

i.e. the dose beyond which cell killing becomes exponential• n- extrapolation number• The curve was found to be flat at low doses

PIT FALLS OF TARGET MODELS

• Specific radiation targets have not been identified for mammalian cells

• DNA strand breaks and their repair, with sites for such DNA damage being generally dispersed

throughout the cell nucleus

• MTSH predicts a response that is flat for very low radiation doses.

• Experimental data: evidence for significant cell killing at low doses and

for cell survival curves that have a finite initial slope

THE TWO-COMPONENT MODEL

• Formed after adding the single target component to the multitarget model

• The curve now correctly predicts finite cell killing in the low-dose region but the change in cell survival over the range 0 to Dq occurs almost linearly.

Two component ModelSurviving fractions plotted Survival curve drawnFound to have two straight components; initial slope 1/D1

Final slope 1/D0

DQ: Quasithreshold dose: intercept of 1/D0 at y=1, closest approximation to theoretical threshold dose for cell killingn (extrapolation number)= intercept of 1/D0 extrapolated to x=0

This implies that no sparing of damage should occur as dose per fraction is reduced below 2Gy which is not seen clinically/experimentally

LINEAR QAUDRATIC MODEL• A lethal event is supposed to be caused by

one hit due to one particle track (the linear component αD)

or • Two particle tracks (the quadratic component

βD2)• Dual radiation action• First component - cell killing is

proportional to dose• Second component - cell killing is

proportional to dose squared

Linear Quadratic Model• Surviving fraction data plottedCurve fitted to a linear quadratic function• Initially, log SF proportional to dose

(log SF=αD)• In next curved component, log SF is

proportional to square of the dose (log SF=βD2)

• By plotting αD (linear component) further, we observe a point where linear component contributes equally to cell kill as the quadratic component

• Dose at which linear component equals quadratic component (αD=βD2) is termed as the ratio α/β

• Curve is continuously bending but is a good fit for first few survival fractions

THE LINEAR-QUADRATIC MODEL• A better description of radiation response in the low dose

regions

• S = e-aD-bD2

• The shape of the curve is determined by the alpha/beta ratio – the dose at which the linear component of cell kill is equal to the quadratic component

• No D0, as the curve never straightens out

• Comparing 2 different models

• Effective D0 is not a constant but decreases with increasing dose

ALPHA-BETA RATIO

• αD component signifies repair shoulder; alpha kill is kill due to otherwise sublethal damage which becomes lethal due to apoptosis during DNA Damage Response (DDR)

• Higher α/β tissues: At lower doses, more cell kill owing to apoptosis during DNA Damage repair,

• Low α/β tissues: the repair shoulder is narrower, signifying earlier and more significant beta kill

• In other words, for early responding tissues, the α/β ratio is higher ( from 7 to 20) and for late responding tissues, it is lower (0.5 to 6)

• Carcinomas of the head and neck and lung, it is higher

• Melanomas, sarcomas ,prostate cancers etc it’s low

LINEAR QUADRATIC CUBIC MODEL

• To fulfil the deficit of LQ model at High doses

• Additional term proportional to the cube of the dose

• At dose DL the curve becomes straight

DL

NEWER MODELS – LPL MODEL

LETHAL–POTENTIALLY LETHAL (LPL) model as a ‘unified repair model’ of cell killing

• Ionizing radiation – 2 different type of lesion : • Repairable (i.e. potentially lethal) lesions

• Non-repairable (i.e. lethal) lesions

• The nonrepairable lesions produce single-hit lethal effects = Linear component of cell killing [exp(αD)]

• The eventual effect of the repairable lesions depends on competing processes of repair and binary misrepair.

• Binary misrepair = Quadratic component in cell killing.

Visible cells(No lesions)

Lethal lesions(Cell death)

Potentially lethal

(repairable lesions)

Lesions by irradiation

Binary misrepair

Correct repair• Two sensitivity parameters –

• ηL = number of non-repairable lesions produced per unit dose

• ηPL = number of repairable lesions. There are also two rate constants

• There are also two rate constants ξPL

determines the rate of repair of repairable

lesions

• ξ 2PL the rate at which they undergo interaction

and thus misrepair)

REPAIR SATURATION MODELS

• Propose that the shape of the survival curve depends only on a dose-dependent rate of repair

• Only one type of lesion and single-hit killing are postulated

• In the absence of any repair these lesions produce the steep dashed survival curve

• The final survival curve (solid)results from repair of some of these lesions

• However, if the repair enzymes become saturated (is not enough repair enzyme to bind to all damaged sites simultaneously and so the reaction velocity of repair no longer increases with increasing damage.

• Therefore at higher doses (more lesions), there is proportionally less repair during the time available before damage becomes fixed

• This will lead to more residual damage and to greater cell kill.

LPL Model Effect of repair becoming less effective Repair saturation at higher radiation doses

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

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