Yinghao Chena,
Shan Chena,
Tianhong Pan*a and
Xiaobo Zoub
aSchool of Electrical and Information Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China. E-mail: thpan@live.com; Tel: +86-15805298357b
bSchool of Food and Biological Engineering, Jiangsu University, Zhenjiang, Jiangsu 212013, China
First published on 11th April 2017
Real time cellular analyzers (RTCA) are widely used to test the cytotoxicity of chemicals. However, there are some uncontrollable factors, which are detrimental to the experimental quality. One of the fundamental issues is the edge effect. Abnormal time-dependent cellular response curves (TCRCs) are observed when the wells are located at the edge of the E-plate. In this paper, the Smirnov test was used to detect the edge effect. The average normalized cell index (NCI) of the negative control located in the inner wells was taken as the standard. Thereafter, all TCRCs were divided into several intervals, and their corresponding empirical distribution functions (EDFs) of the mean NCI and NCI located at the edge wells were calculated, and hypothesis testing was used to determine the differences of the EDFs. The experimental results evaluated the performance of the proposed algorithm. This framework provided a systematic method for edge-effect detection.
In the RTCA experiment, the cellular response in the edge well of the E-plate is usually different from that of the inner well, especially in the E-plate ×96 and ×384 formats, which is described as the edge effect. There are two main reasons why the edge effect appears in RTCA experiments: one reason is that the evaporation of long-term incubation causes the edge effect (evaporation effect), because the evaporation efficiency of water in the edge well is higher than that in the inner well; and the other reason is that the temperature of the edge well reaches the desired incubation temperature faster than that of the inner well owing to plate stacking (temperature effect).13 To weaken the edge effect, Lundholt and Scudder14 pre-incubated newly seeded plates in ambient conditions (air at room temperature), which resulted in an even distribution of the cells in each well. However, the result of this method is not stable and would be invalid for long-term cultivation (>24 h). Furthermore, a special anti-volatile lid has been developed to restrain the edge effect,15 but the performance is limited. Malo and Hanley16 proposed a statistical method to optimize the configuration of the reference wells for reducing the positional effects of wells within plates. In a nutshell, those methods are designed to reduce the edge effect on the experimental process or device, nevertheless, they cannot completely eliminate the edge effect. Furthermore, there is no effective method to identify the edge effect.
To avoid the edge effect, researchers tend to abandon the data located at edge wells, which decreases the testing efficiency of the RTCA and will make a lot of waste, especially in E-plate ×96 formats (37.5%). Furthermore, researchers manually screen the edge effect, which is time consuming and can result in inaccuracies. In this work, the Smirnov test was used to determine the edge effect. Compared with manual selection, the proposed method is efficient and reliable.
This paper has been organized as follows: in Section 2, the problem of edge effect has been described. In Section 3, the Smirnov test was applied to identify the edge effect with related variables. In Section 4, several RTCA experiments were used to validate the proposed method. Finally, Section 5 included concluding remarks.
Fig. 1 Experiment and its edge effect. (a) The schematic diagram of RTCA. (b) TCRCs of negative control. |
The procedure of the cytotoxicity assay is as follows: first, a certain cell line was added to each well of the ×384 E-plate and incubated in the culture medium about 24 h; second, different chemicals with different concentrations were added to the E-plate, which followed a particular protocol: the same chemical was added to every two columns of wells, and the same concentration of chemical decreasing from top to bottom was added to every two rows of wells. According to this protocol, each concentration of each chemical was repeated four times (for example, as shown in Fig. 1(a), A3, A4, B3, and B4 wells have the same culture environment; C3, C4, D3, and D4 have the same culture environment) to enhance the robustness of the experiment. An experiment lasted about 96 h. The time-dependent cellular response profiles were dynamically recorded in RTCA, which was termed the Normalized Cell Index (NCI) (shown in Fig. 1(b)). In the cell based in vitro assay, the data after the cellular exposure was important (from 24 to 96 h), so the total sampling time was 72 h.
As shown in Fig. 1(b), the time-dependent cellular response curves (TCRCs) of A21/A22/P21/P22 (edge wells) were significantly different from the TCRCs of inner wells. NCIs of the inner wells were lesser than those of edge wells, this was named the edge effect. To describe the differences, the standard deviations of NCIs in the sampling interval located at edge/inner well were calculated and shown in Fig. 2. The mean NCIs of the inner wells were set as standard. The boxplots of edge wells were obviously different from those of the inner wells. As mentioned previously, the abnormal TCRCs located at the edge wells were screened manually. The automatic detection of the edge effect was the key issue in the RTCA experiment. To develop a validated method, the data of negative control were selected as examples, since cells without chemicals grow naturally in the culture medium. This eliminates the error cause by different cell growth environment.
(1) |
As shown in Fig. 1(b), the TCRCs located at inner wells were similar to each other, and different from the TCRCs located at edge wells (denoted asNCIm, m = 1, 2, 3, 4). Here, NCIs of inner wells were averaged as a standard:
(2) |
It is difficult to distinguish the difference between and NCIm directly, because TCRC is one type of time series. To develop a validated method, the empirical distribution of NCI was used and the range interval was set as:
{[δj, δj + 1)}j=0J | (3) |
(4) |
For each TCRC, the cumulative frequency of each interval was calculated as follows:
(5) |
Through the interval segmentation and frequency accumulation, the time series NCI was transformed into independent random variables. Then the corresponding empirical distribution function (EDF) of each TCRC was computed:
(6) |
As a result, the EDFs of NCI of each edge-well (Fm) and mean NCI of inner wells () were obtained. The Smirnov test was used to determine whether the TCRC's EDFs of the edge wells were equal to the mean TCRC's EDFs, i.e.:
(7) |
To compare the EDFs of two different samples without assuming any underlying parametric model for the sample, i.e. it is a nonparametric test,19 the Smirnov test is taken for consideration in this work.
The statistical magnitude of Smirnov test Dm was given by:
Dm = max|k − Fkm| | (8) |
(9) |
Range interval | Cumulative frequency | Empirical distribution function | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
νj1 | νj2 | νj3 | νj4 | j | Fk1 | Fk2 | Fk3 | Fk4 | k | |
[0,1) | 1 | 1 | 1 | 1 | 1 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
[1,2) | 14 | 13 | 15 | 15 | 20 | 0.014 | 0.014 | 0.014 | 0.014 | 0.014 |
[2,3) | 10 | 11 | 10 | 10 | 37 | 0.208 | 0.194 | 0.222 | 0.222 | 0.292 |
[3,4) | 10 | 11 | 10 | 10 | 14 | 0.347 | 0.347 | 0.361 | 0.361 | 0.806 |
[4,5) | 37 | 19 | 11 | 36 | 0 | 0.486 | 0.500 | 0.500 | 0.500 | 1 |
[5,6) | 0 | 17 | 25 | 0 | 0 | 1 | 0.764 | 0.653 | 1 | 1 |
Edge-well | A21 | A22 | P21 | P22 |
---|---|---|---|---|
Dm = max|k − Fkm| | 0.514 | 0.500 | 0.500 | 0.500 |
Dm > D36,1−0.05 | Yes | Yes | Yes | Yes |
Edge effect | Yes | Yes | Yes | Yes |
As shown in Table 2, the values of the statistical magnitude Dm of the four edge-well TCRCs were calculated, which were greater than the critical region D36,1−0.05 = 0.22119 (Table 3). According to the Smirnov test, hypothesis H0 was rejected. Therefore, the edge effects occurred in four edge-well TCRCs of experiment 1 and those TCRCs should be removed before the cytotoxicity assay.
The results of three other experiments are shown in Table 4. It can be seen there are many edge-effect TCRCs, which are consistent with the actual situation (Fig. 3 and 4). Therefore, the proposed method could effectively detect the edge effect.
Experiment | Edge-well | Dm | Edge-effect |
---|---|---|---|
2016-02-03 | A21 | 0.514 | Yes |
A22 | 0.500 | Yes | |
P21 | 0.500 | Yes | |
P22 | 0.500 | Yes | |
2016-02-09 | A21 | 0.306 | Yes |
A22 | 0.542 | Yes | |
P21 | 0.292 | Yes | |
P22 | 0.202 | No | |
2016-02-17 | A21 | 0.486 | Yes |
A22 | 0.516 | Yes | |
P21 | 0.186 | No | |
P22 | 0.186 | No | |
2016-02-23 | A21 | 0.284 | Yes |
A22 | 0.486 | Yes | |
P21 | 0.284 | Yes | |
P22 | 0.284 | Yes |
To compare the effects of different levels of significance of the experiment, another significant level was applied where α = 0.1. The corresponding critical region was D36,1−0.1 = 0.19910. The results are shown in Table 5.
Experiment | Edge-well | Dm | Edge-effect |
---|---|---|---|
2016-02-03 | A21 | 0.514 | Yes |
A22 | 0.500 | Yes | |
P21 | 0.500 | Yes | |
P22 | 0.500 | Yes | |
2016-02-09 | A21 | 0.306 | Yes |
A22 | 0.542 | Yes | |
P21 | 0.292 | Yes | |
P22 | 0.202 | Yes | |
2016-02-17 | A21 | 0.486 | Yes |
A22 | 0.516 | Yes | |
P21 | 0.186 | No | |
P22 | 0.186 | No | |
2016-02-23 | A21 | 0.284 | Yes |
A22 | 0.486 | Yes | |
P21 | 0.284 | Yes | |
P22 | 0.284 | Yes |
The P22 of experiment 2 (2016-02-09) was distinguished as an edge effect with α = 0.1. However, from Fig. 3, the TCRC of P22 fluctuated up and down with a mean curve in a small range, which is common when taking real cell growth into account. Therefore, in this work, it was too harsh to set α = 0.1, accordingly, in this work α = 0.05 was recommended.
Furthermore, the wells with chemicals were also tested by using the presented Simonov test. As mentioned before, each concentration of each chemical was repeated four times, and only two inner wells were set as references. The results were shown in Table 6. Based on the proposed algorithm, the wells with edge-effect were screened out (“×” in Fig. 5) automatically, which can reduce the technician's workload and remove the careless operation.
Edge-well | Dm | Edge-effect | Edge-well | Dm | Edge-effect |
---|---|---|---|---|---|
A1 | 0.514 | Yes | P1 | 0.514 | Yes |
A2 | 0.202 | No | P2 | 0.202 | No |
A3 | 0.186 | No | P3 | 0.306 | Yes |
A4 | 0.186 | No | P4 | 0.486 | Yes |
A5 | 0.306 | Yes | P5 | 0.368 | Yes |
A6 | 0.542 | Yes | P6 | 0.368 | Yes |
A7 | 0.202 | No | P7 | 0.486 | Yes |
A8 | 0.202 | No | P8 | 0.202 | No |
A9 | 0.186 | No | P9 | 0.386 | Yes |
A10 | 0.186 | No | P10 | 0.128 | No |
A11 | 0.070 | No | P11 | 0.128 | No |
A12 | 0.070 | No | P12 | 0.292 | Yes |
A13 | 0.284 | Yes | P13 | 0.292 | Yes |
A14 | 0.486 | Yes | P14 | 0.306 | Yes |
A15 | 0.128 | No | P15 | 0.128 | No |
A16 | 0.284 | Yes | P16 | 0.128 | No |
A17 | 0.306 | Yes | P17 | 0.070 | No |
A18 | 0.306 | Yes | P18 | 0.070 | No |
A19 | 0.128 | No | P19 | 0.070 | No |
A20 | 0.146 | No | P20 | 0.070 | No |
A21 | 0.514 | Yes | P21 | 0.284 | Yes |
A22 | 0.070 | No | P22 | 0.284 | Yes |
A23 | 0.070 | No | P23 | 0.202 | No |
A24 | 0.486 | Yes | P24 | 0.306 | Yes |
Although the results demonstrated the effectiveness of the proposed method, future research should include the following:
● The choice of significant levels should be discussed based on the specific data, since the performance of this method is affected by the range interval;
● Other edge wells should be tested in addition to the negative control;
● Except for the TCRC of edge wells, the abnormal TCRC of inner wells with certain screening strategies should be discussed.
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