A pilot design to propose an apoptosis definition based on gene expression data

Introduction: Apoptosis is a programmed cell death commonly investigated in researches. Objectives: According to the lack of a gold standard for definition of apoptosis, we conducted a pilot analysis to propose a new definition for apoptosis based on a previous gene expression data. Materials and Methods: As a secondary analysis, a gene expression data of a vitrification thawing induced model of apoptosis conducted on ten mice ovaries was used. Half of the samples had been treated with selenium. P53 , Fas , Bax and Bcl2 were considered as apoptosis related genes. Their +∆CTs were reported. An apoptosis scoring system was designed based on regression analysis. Results: In multiple regression of the genes, the only significant association was for Bcl2 expression for prediction of apoptosis. Then a model was designed consisting of Bcl2 and some interactions that the calculated amount of its formula was considered as the scoring system (R 2 = 0.989, P (>F) <0.001, Root mean square deviation = 0.082). Bax/Bcl2 ratio showed an acceptable goodness of fit for prediction of this score (R 2 = 0.845, P (>F) <0.001, root mean square deviation = 0.219). No conclusive result was found for factor analysis. Conclusion: The present study used a simple approach to propose statistical models for apoptosis. A comprehensive criterion should be designed apoptosis and other biological systems to be considered as a gold standard.


Introduction
Apoptosis is a programed cell death that can be physiologic or pathologic. Any problem in regulation of apoptosis (either inhibition or activation) may result in different diseases or complications such as cancers, autoimmunity, inflammation, neurodegenerative disorders and developmental defects (1). Apoptosis is a complex process consisting of intrinsic and extrinsic pathways. In extrinsic pathway, cell surface death receptors such as Fas are activated by their ligands. In intrinsic pathway, Bcl2 family or pro-apoptotic proteins lead to mitochondrial changes (2). Both pathways terminates to caspase proteins, and the pathways become common from the level of caspase3 (3). Among the apoptosis proteins, Bcl2 (as a member of Bcl2 family) is an inhibitory protein while Fas, Bax and P53 are activating proteins (4).
Due to the key roles of apoptosis in pathogenesis of many diseases, animal models of this process are used to investigate its mechanisms and effects of treatments (5,6). Knowing the mechanisms of apoptosis helps the researchers to find better ways for diagnosis, management and treatment of diseases like cancers (1,7). It is obvious that we need diagnostic methods for detection of apoptosis. Currently, there are some technics including electron microscopy (ultra-structural study), TUNEL assay and flow cytometry. Despite many of these methods, there are still some challenges (8). The limitations may also results in some pitfalls and mistakes (9). In addition, some serum and tissue biomarkers are used (10). Some of these biomarkers are apoptosis related molecules including Fas, Bax, Bcl2, P53, etc. Bax/Bcl2 (Bcl2/Bax) ratio is also used as a biomarker for its prognostic roles in some cancers (11).

Objectives
According to the lack of a gold standard for definition of apoptosis as well as little information about the diagnostic role of biomarkers at gene expression level, the present study was designed to perform a pilot analysis to propose a new definition for apoptosis based on a previous gene expression data.

Model design
As a secondary analysis study, the gene expression data of our previous study (5) on a vitrification thawing DOI:10.34172/jpd.2022.9135

Implication for health policy/practice/research/ medical education
There is no gold standard for definition of apoptosis. We conducted this pilot analysis based on gene expression data to propose a new definition for apoptosis. Statistical modeling should be used further in future for biological systems.
induced model of apoptosis conducted on 10 NMRI mice ovaries was used. Among the samples, half of them had been treated with selenium in their cryomedia to inhibit apoptosis.

Definitions and variables
Apoptosis modeling samples: All the samples of the study as they underwent vitrification thawing process were considered as apoptosis modeling samples. Lack of a gold standard to approve the success of the modeling was a limitation.
Apoptosis positive samples: the half of the apoptosis modeling samples that were not treated with selenium in their cryomedia were considered as apoptosis positive samples.
Apoptosis negative samples: The half of the apoptosis modeling samples that were treated with selenium in their cryomedia were considered as apoptosis negative samples. Lack of a gold standard to rule apoptosis out was limitation.
Apoptosis related genes: P53, Fas, Bax and Bcl2 were considered as apoptosis related genes. Their efficiency adjusted +∆CTs (in comparison to GAPDH internal control) were reported as their expression unit.
Bax/Bcl2 ratio: the expression of Bax per Bcl2 was also calculated as a common biomarker.
Score: a scoring system was designed based on the best model of regression formula.
Latent variable: apoptosis was considered as an abstract concept analyzed as a latent variable. Apoptosis related genes were the observed variables.

Statistical analysis
Multiple linear regression was used for prediction of apoptosis negative samples (using logistic regression was not possible as the outcome was fully fitted). Then a regression model was designed consisting of significant covariates and interactions with a stepwise approach. Thereafter, a scoring system was reported based on the regression formula. Confirmatory factor analysis (CFA) was used to show the apoptosis related genes as predictors of a common abstract concept (i.e. apoptosis). In addition, exploratory factor analysis was performed to find the components predicted by the apoptosis related genes. All the analysis were done in Stata 14 (StataCrop. LLC, USA) with significance level of 0.05.

Results
In the source study, P53 and Bcl2 expression were associated with the groups (up-regulation and down regulation respectively in favor of the apoptosis control group). In its multiple regression modeling, only Bcl2 expression was significantly associated with the groups.
Multiple linear regression was performed to predict apoptosis negative samples. As it had been shown in the source study, the only significant association was for Bcl2 expression. Then all the possible interactions were added to model and after that the non-significant interactions were removed ( Since the scoring formula was complex, a multiple linear regression was performed to predict the score based on single genes expression. However, the only significant effect was for Bcl2 expression (Table 2). Therefore, two simple linear regressions were used to predict the score based on Bcl2 and Bax/Bcl2 ratio. Among these two models, Bax/Bcl2 ratio showed a better goodness of fit (Table 3, equation 2). According to this model, +∆CT (Bax/Bcl2) <3 was in favor of apoptosis ( Figure 1). It meant that the fold change (Bax/Bcl2) >8 was in favor of apoptosis (fold change =2 -∆∆CT ).  CFA was conducted to show the predictive role of apoptosis related genes for apoptosis as an abstract concept. However, no significant path was found with the latent variable (Table 4). In addition, EFA showed only one factor with Eigenvalue >1 which had positive correlation with Bcl2 and negative correlation with P53 expression (considering +∆CT) ( Table 5).

Discussion
Nowadays apoptosis has a very important role in many diseases. This importance needs a gold standard definition and also verified assay methods. Nevertheless, a practical definition was challenging and its assay was difficult (8,9). The present study was not aimed to design a gold standard, but wanted to conduct statistical modeling at gene expression level. Accordingly, a multiple linear regression model was designed and the score resulted from the model was considered as a variable to be used as the concept of apoptosis. Then Bax/Bcl2 ratio -as a common practical biomarker -was compared with the resulted score. This biomarker had an acceptable goodness of fit with the score.
In general, mathematical approach in systems biology had a good background. Apoptosis was not an exception among the biological systems. So far, few researchers tried to design statistical models for apoptosis. According to the study of Schleich and Lavrik, the first mathematical  (12,13). This model was more mechanistic than statistical in contrast to our study. However, there were some studies with statistical modeling. Yang et al designed a Bayesian neural network for caspase cleavage (14). Afantitis et al designed a multiple linear regression model based on chemical compounds (15). Passante et al conducted principal component factor analysis. They proposed tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) and dacarbazine to induce apoptosis in researches (16).

Conclusion
The present study used a simple approach to propose statistical models for apoptosis. Among the investigated apoptosis related genes, Bcl2 expression and some genegene interactions could predict the samples that underwent vitrification thawing induced model of apoptosis without anti-apoptotic treatments.

Limitations of the study
The limitations of this study were lack of a gold standard test in the source study and hence, the positivity and negativity of apoptosis was just contractual. It seems that in fact the concept of apoptosis is also abstract and  contractual. Although we did not find conclusive results for factor analysis, larger studies were necessary to find its pathophysiologic criteria. Over-fitting of the models was another limitation. A comprehensive criterion should be designed to be considered as a gold standard.