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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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