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BME1450H Bioengineering Science Term Paper
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Cytotoxic Cell Assay-Statistical Model for
Concentration-Dependent Efficacy
Irena Barbulovic-Nad, PhD Candidate
Abstract—Cytotoxic cell assays are performed to asses the
toxicity of various compounds or unicellular organisms on target
cells. While there is a vast of study conducted to develop new
assays, incorporating new labeling and detection techniques, this
paper rather focuses on a typical cytotoxic assay for testing
concentration–based efficacy of a toxic compound. Four different
concentrations of the same cytotoxic agent are tested on
mammalian target cells in a 96-well plate using viability dyes to
detect the levels of toxicity-percentage of dead cells. Statistical
analysis of the obtained results shows that more than a two-fold
increase in a concentration of the tested cytotoxic agent does not
significantly affect the viability of cells.
Index Terms—cytotoxicity, F-test, live/dead assay, variance
analysis
I. INTRODUCTION
P
henotyic screening is a technique for evaluating chemical
compounds, small molecules and potential drug candidates
on the basis of their effects on living organisms. Mammalian
cells, bacteria, yeast, fruit flies, zebrafish and mice are often
used for this process. Phenotypic testing is especially
important in drug screening as it probes efficacy of the
potential drugs, while simultaneously evaluating specificity,
absorption, drug-drug interactions and toxicity. It is also used
for cytotoxicity testing of chemical compounds, drugs, or even
cytotoxic cells (cell-mediated cytotoxicity) [1].
The standard method for evaluating cytotoxicity is the 51Crrelease assay [2]. Although reliable, this radioisotopic method
requires special licensing and numerous storage, handling and
disposal hazards. As a result many other non-radioisotopic
methods have been developed, many of which require
expensive flow cytometers [3], [4] or measure the release of
endogenous enzymes [5], [6]. Methods using fluorescent
viability dyes have been extensively investigated in
mammalian in vitro assays to avoid complications present in
enzymatic analysis.
Viability assays are mainly based on one of two
characteristic parameters: metabolic activity or cell membrane
integrity of healthy cells. Metabolic activity is generally
measured via incubation with a tetrazolium salt that is cleaved
Manuscript received November 7th, 2005. Irena Barbulovic-Nad is with the
Institute for Biomaterials and Biomedical Engineering, University of Toronto,
Toronto, ON M5S 3E5 Canada.(e-mail: [email protected])
into a colored formazan product in metabolically active cells.
Alternatively, metabolic activity assay can also measure ATP
status of cells and give an indication for cellular energy
capacity and therefore viability. Assays based on cytoplasmic
membrane integrity take advantage of uncompromised
membrane in healthy cells, which excludes dyes such as
trypan blue. This dye is typically used to stain dead cells so
that live cells can be distinguished and simply counted.
This paper presents a sample of a typical cytotoxic assay for
measuring concentration-dependent potency of a toxic
compound - an agent A. Agent A is tested on suspended
mammalian cells in a 96-well plate. Prior to this assay, this
compound was found as a cytotoxic hit in a high throughput
screening (HTS) of potential toxics and selected for further
testing since it showed to be toxic at the concentration as
small as 0.5 % (v/v). The definition of the toxicity adopted in
this work is the lethal effect of a substance on at least 50 % of
the tested cells (lethal concentration 50, LC50). In order to
determine the effect of the concentration of the agent on the
cell viability and to possibly determine the minimum
concentration that will be lethal to at least 50 % of cells, an
assay with four different concentrations of Agent A, 0.5, 0.3,
0.2 and 0.1 % (v/v), is created. Each agent concentration is
tested in 8 wells. The percentage of dead cells in each well is
determined by measuring the fluorescence signal from the
labeled cells and the statistically analyzed data is used to asses
the efficacy of the agent A.
II. EXPERIMENTAL DESIGN
A. Cytotoxicity Assay
The cytotoxicity assay considered here utilizes
LIVE/DEAD® Viability/Cytotoxicity Kit (Molecular Probes,
Invitrogen) based on membrane integrity and intracellular
esterase activity in healthy cells. The kit consists of two dyes
calcein acetoxymethyl (calcein AM) and ethidium homodimer
(EthD-I). Nonfluorescent calcein AM can pass through the
cell membrane of viable cells due to its enhanced
hydrophobicity as compared to calcein, for example. After it
permeates into the cytoplasm, it is hydrolyzed by esterases to
fluorescent calcein, which remains inside the cell. The
excitation and emission wavelengths of calcein are 490 nm
and 515 nm, respectively. EthD-I can permeate only damaged
membranes and after binding to nucleic acid it produces a red
fluorescence (495 nm excitatation/635 nm emission) [7]. Both
dyes can be detected simultaneously with a fluorescent plate
BME1450H Bioengineering Science Term Paper
reader. This assay should have low background noise levels
since the dyes are nonfluorescent before interacting with cells.
Prior to assay, cells are gently washed in Dulbecco’s
phosphate-buffered saline (D-PBS) to remove esterase activity
generally present in serum supplemented grow media.
Extracellular esterase could hydrolyze calcein AM before it
enters cells. Cells are suspended in a D-PBS and 100 μL of
104 cell/mL suspension is added to each well an incubated
with agent A for 5h. Calcein AM and EthD-1 diluted in DPBS are added to the wells resulting in final concentrations of
1 μM and 2 μM, respectively, as these concentrations have
shown to be optimal (lowest concentrations that give
sufficient signal) in a similar assay [7]. After addition of dies
to 96-well microplate wells, cells are incubated for 45 min at
room temperature and fluorescent signals are detected with a
microplate reader.
B. Fluorescence Measurements Using a Microplate Reader
The fluorescence is measured using appropriate excitation
and emission filters in a microplate reader. Microplate readers
are optical systems used for HTS in different assays (protein
and DNA quantification, molecular binding assays, enzyme
activity and kinetics assays, cell based assays) with detection
technologies such as fluorescence intensity, fluorescence
polarization, time-resolved fluorescence and luminescence.
The specific wavelengths are achieved by either employing
optical filters or monochromators. Calcein is excited with
fluorescein optical filter (485±10 nm), while EthD-1 is excited
with rhodamine optical filter (530±12.5 nm). The fluorescence
emissions are detected separately at 530±12.5 nm for calcein
and 645±20 nm for EthD-1. Optical spectra of these two dyes
are presented in Figure 1.
2
3) Sample where all cells are alive and labeled with
EthD-1 only - fluorescence F(530)min,
4) Sample where all cells are alive and labeled with
calcein AM only - fluorescence F(530)max.
The control samples are of the same volume and cell
concentration as the experimental samples. Reagent
concentrations, incubation times and temperatures are kept
constant. Samples with all dead cells are obtained by killing
cells with 70 % methanol.
The percentage of live and dead cells can be calculated
from the fluorescence readings as follows [7]:
F (645) e − F (645) min
(dead cells)
F (645) max − F (645) min
F (530) e − F (530) min (live cells)
Y (%) =
F (530) max − F (530) min
(1)
X (%) =
(2)
where index e refers to the fluorescence measured in
experimental sample wells. Although only number of dead
cells is used in the following analysis, number of live cells is
also determined as a control percentage.
III. RESULTS AND DISCUSSION
A. Data
The percentage of dead cells was calculated in each
experimental well using (1) and measured fluorescence. Each
of four concentration of the tested agent A, 0.5, 0.3, 0.2 and
0.1 %, statistically termed levels of the factor or treatments,
yields a sample of 8 observations (percentage of dead cells) or
replicates listed in Table 1.
In other words, the response for each of the four treatments
is a random variable Yi,j (i=1, 2,..., a; j=1, 2,…, n, a=4, n=8)
which can be expressed with the following equation [9]:
Yij = μi + ε ij = μ + τ i + ε ij
(3)
μi is the mean of the i-th treatment, εij is the random error
component, μ is the overall mean of all treatments and τi is
treatment effect such that μ i = μ + τ i . The treatment effects
4
are actually deviations from the overall mean so that ∑ τ i = 0 .
Figure 1: Normalized fluorescence emission spectra of
calcein and EthD-1 bounded to DNA. Spectral separation
is used to simultaneously detect live and dead cells [8].
To account for the background noise, control cell samples
without any dye are placed on the well plate as well.
Background fluorescence readings F(530)0 and F(645)0 are
subtracted from all corresponding values of detected
fluorescence. Also, few additional control cell samples are
prepared and measured:
1) Sample where all cells are dead and labeled with
EthD-1 only - fluorescence F(645)max,
2) Sample where all cells are dead and labeled with
calcein AM only - fluorescence F(645)min,
i =1
It is assumed that the errors εij are normally and independently
distributed with mean zero and variance σ2. Hence, a treatment
can be considered as a normal population with mean μi and
variance σ2. Sample means are graphically presented in Figure
2 where error bars corresponding to the standard error.
There are various sources of error in this experiment.
Whenever a fluorescent measuring is done, intrinsic
fluorescence of the cell buffer, cytotoxic agent and the well
plate appear as a background noise. The noise of a detection
device also contributes significantly to the measurement error.
BME1450H Bioengineering Science Term Paper
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Precentage of Dead Cells (%)
Table 1: Percentage of dead cells at four concentrations of agent A
Agent A Concentration
Dead Cells (%)
(% v/v)
1
2
3
4
5
6
7
0.5
58
55 53 54
53 57 59
0.3
55
55 52 51
54 53 57
0.2
54
50 51 55
52 55 54
0.1
50
53 48 49
53 54 48
60
μ=50.63
s=±2.39
55
μ=55.50
s=±2.27
μ=54.13
s=±2.03
45
0
0.1
0.2
Total
Average
444
433
424
405
1706
55.50
54.13
53.00
50.63
53.31
H 0 :τ1 = τ 2 = τ 3 = τ 4 = 0
H a : τ i ≠ 0 for at least one i
μ=53.00
s=±1.85
50
8
55
56
53
50
0.3
0.4
0.5
0.6
Agent A Concentration (% v/v)
Figure 2: Dead cells percentage means and standard
errors for varying concentration of agent A.
Most of these errors are canceled when the signal measured in
control wells with no fluorescent dye is subtracted from the
experimental sample signals. When measuring fluorescent
signal of two dyes with different emission spectra, as in the
considered assay, the overlap of their spectra, i.e. interference
of their fluorescence, is additional source of error that can be
factored out with calculations shown in (1) and (2). Another
source of error in the fluorescent measurements is target cell
attributes. It is important that all cells are from the same
harvest so the error induced by their individual differences is
minimized. Also, number of cells has to be consistent from
well to well as it directly reflects on the fluorescence intensity,
which means cell density and the suspension volume in each
well has to be constant.
For the following statistical analysis randomization of
experimental runs is another important factor in overall
experimental strategy. By achieving the complete
randomization, any undesirable variable that may influence
fluorescence readings is balanced out. For example, the order
of the well readings should be as random as possible so that
certain temporal device conditions, e. g. warm-up period,
affect not only one treatment, but rather all four treatments
equally. Plate readers generally provide randomized well plate
readings in combination with random spatial distribution of
samples on the well plate.
B. Statistical Model
To determine if changing the concentration of the agent A
has an effect on cell viability, a test of the equality of four
population means is done. As the equality of the means is
equivalent to equality of the treatment factors, the following
hypothesis is tested:
(4)
If the null hypothesis is true, than each observation is a sum of
the overall mean μ and the random error εij. That is, all 32
observations are taken from the same normal distribution with
mean μ and variance σ2.
The hypothesis (4) will be tested through variance analysis.
The total variability in the data (described with the total sum
of squares SST), consists of two parts: differences between
observed treatment means and the grand mean (described with
the treatment sum of squares SSTreat) and differences of
observations within a treatment (described with error sum of
squares SSE) [9]:
a
n
SST = ∑ ∑ ( yij − y.. ) 2 = SSTreat + SS E
i =1 j =1
a
SSTreat = n∑ ( yi. − yi.. ) 2
(5)
i =1
a
n
SS E = ∑ ∑ ( yij − y. ) 2 ,
i =1 j =1
n
a
n
where y = ∑ y , yi. = yi. , y = ∑ ∑ y and yi.. = yi.. .
i.
ij
i ..
ij
n
an
j =1
i =1 j =1
For analysis of variance expected values of SSTreat and SSE
need to be examined. Mean square of treatments MSTreat and
error mean square MSE and their expected values are defined
as follows [8]:
a
n∑ τ i2
SSTreat and
SS
E ( Treat ) = σ 2 + i =1
a −1
a −1
a −1
SS E and E ( SS ) = a(n − 1)σ 2
MS E =
E
a(n − 1)
MSTreat =
(6)
If each of four populations is assumed to have normal
distribution, then the ratio
F0 =
SSTreat /(a − 1) MSTreat ,
=
SS E /[a (n − 1)]
MS E
(7)
to be used as a test statistics, has an F distribution with a-1
and a(n-1) degrees of freedom. Equation 5 shows that MSTreat
BME1450H Bioengineering Science Term Paper
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is an unbiased estimator of variance σ2 when H0 is true - if H1
is true, then MSTreat is greater than σ2. On the other hand MSE
is an unbiased estimator of variance σ2 regardless of whether
H0 is true or not. Therefore, under alternative hypothesis, the
expected value of the numerator is greater than the expected
value of the denominator in (7). Hence we should reject H0 if
FO is large, i.e. if f 0 > fα ,a −1,a ( n−1) (upper-tail, one-tail critical
region).
The analysis of variance for the measurements is
summarized in Table 2. For a 99 % confidence level (α=0.01)
and 3 and 28 degrees of freedom, f0.1, 3, 28 = 4.57, calculated
test statistics is f0 = 7.40 and P-value for this statistics is 0.001.
Since P-value is smaller than α = 0.01, H0 is rejected at level
0.01. This means that changing the levels of factor affects the
mean response, i.e. reducing the concentration of the cytotoxic
agent from 0.5 to 0.1 % (v/v) affect the cell viability. The four
means of the measured percentage values area greater or equal
to 50%, meaning they are all toxic according to LC50
definition of toxicity.
Table 2: The analysis of variance for measured
percentage of dead cells.
Source of
Sum of
Degrees of
Mean
F0
Variation
Squares
Freedom
Square
Treatments
102.13
3
34.04
7.40
Error
128.75
28
4.60
Total
230.88
31
When the same statistical analysis is applied to each two
and each three tested concentrations, some means showed not
to be significantly different, as Figure 3 illustrates. Such are
means of 0.5, 0.3 and 0.2 % (v/v) treatments, where calculated
P-value for f0 = 2.96 is 0.074 which is greater than level 0.01,
so that H0 is not rejected and these three treatments are
considered to belong to the same population. Similarly, for a
case with two treatments: 0.1 and 0.2 % (v/v), P-value = 0.043
for f0 = 4.95, and therefore two means are not significantly
different at confidence level 0.01.
It is observed that concentrations of agent A in the range
from 0.2 to 0.5 % (v/v) cause identical mean percentage
number of dead cells (54.21 %), i.e. there is not enough
evidence that the effects of the tested concentrations on cell
viability are significantly different. Concentration of 0.1 %
(v/v) of agent A has shown to have significantly lower effect
on the cell viability than other three concentrations. This
concentration is on the border of LC50.
IV. CONCLUSION
A cytotoxic cell assay for testing toxicity levels of four
different concentrations of a toxic compound, agent A, is
performed. Toxicity was probed with viability dyes Calcein
AM and EthD-1 and number of dead cells, a marker for
toxicity, was calculated from the measured fluorescence
signal. A statistical model for cytoxicity assays, based on the
variance analysis and F-test for more than two means, was
used to asses the toxicity of different concentrations. No
significant difference in toxicity of the concentrations raging
from 0.2 to 0.5 % (v/v) was observed, while 0.1 % (v/v)
seemed to be borderline LC50.
The result of the previous analysis is significant if the
amount of the toxic agent is to be optimized, i.e. minimized
for the desirable level of toxicity. Amounts of used cytotoxic
agents are preferably kept as low as possible since their source
is often limited (natural cytotoxic substances) or they may be
very expensive. In the presented assay, 0.2 % of the agent A
will have the same effect on cells as 0.5 % of the same agent both concentrations cause death of around 54 % of cells.
However, general conclusion on toxicity dependence on agent
concentration can be drawn only after a similar analysis is
performed on a wide range of concentrations.
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Precentage of Dead Cells (%)
[2]
60
A
[3]
A
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55
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[5]
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45
0
0.1
0.2
0.3
0.4
0.5
0.6
[7]
Agent A Concentration (% v/v)
Figure 3: Impact of agent A varying concentration on cell
viability. Bars marked with the same letter indicate means
that are not significantly different.
[8]
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