Exploration of the R code-based mathematical model for PMI estimation using profiling of RNA degradation in rat brain tissue at different temperatures
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Precise estimation of postmortem interval (PMI) is crucial in some criminal cases. This study aims to find some optimal markers for PMI estimation and build a mathematical model that could be used in various temperature conditions. Different mRNA and microRNA markers in rat brain samples were detected using real-time fluorescent quantitative PCR at 12 time points within 144 h postmortem and at temperatures of 4, 15, 25, and 35 °C. Samples from 36 other rats were used to verify the animal mathematical model. Brain-specific mir-9 and mir-125b are effective endogenous control markers that are not affected by PMI up to 144 h postmortem under these temperatures, whereas the commonly used U6 is not a suitable endogenous control in this study. Among all the candidate markers, ΔCt (β-actin) has the best correlation coefficient with PMI and was used to build a new model using R software which can simultaneously manage both PMI and temperature parameters. This animal mathematical model is verified using samples from 36 other rats and shows increased accuracy for higher temperatures and longer PMI. In this study, β-actin was found to be an optimal marker to estimate PMI and some other markers were found to be suitable to act as endogenous controls. Additionally, we have used R code software to build a model of PMI estimation that could be used in various temperature conditions.
KeywordsPostmortem interval (PMI) RNA Reverse transcription quantitative real-time PCR R code
The precise estimation of postmortem interval (PMI) is a constant challenge in forensic science. Traditional methods used to estimate PMI in autopsy cases include livor mortis, rigor mortis, the digestive process of gastric contents and entomology, among others [1, 2]. However, none of these methods provides a complete solution to the question of PMI because the environment has many variables. In recent years different biomarkers such as proteins  and DNA  have been employed to build a mathematical model of PMI, demonstrating their great potential value in forensic cases. With crucial methodological advances in RNA extraction, reverse transcription, and the development of real-time quantitative polymerase chain reaction (RT-qPCR), many researchers have used RNA degradation to estimate PMI [5, 6, 7]. Various mRNA markers such as GAPDH, β-actin, and RPS-29 are considered to be appropriate endogenous control markers for biochemical research, while U6 snRNA is the most commonly used control marker in microRNA studies [5, 8]. However, despite their popularity, these molecules degrade over time, especially in harsh environments such as high temperatures, which reduces their efficacy as markers for PMI studies. Some studies have shown several RNA markers with good PMI correlation and that some microRNAs are sufficiently stable to be suitable as reference markers [6, 7].
In this study, the degradation rate of some RNA markers was explored under 4, 15, 25, and 35 °C to find the most suitable RNA markers for which ΔCt has the best correlation coefficient with prolonged PMI. This enables us to produce a robust mathematical model that can then be tested at various temperatures. R code software is a powerful tool for both model building and equation solving in such a complicated context.
Materials and methods
In total, 270 male and female Sprague–Dawley rats (body weight is 220 ± 20 g) were sacrificed by cervical dislocation and were randomly divided into a control group (PMI = 0 h) and four experimental groups, which were kept in a controlled environment chamber at 15 ± 1, 25 ± 1, and 35 ± 1°C respectively. Brain tissues were collected at 1, 3, 6, 12, 24, 36, 48, 72, 96, 120, and 144 h (n = 6) after death to develop mathematical models. To collect the tissue the brain was completely exposed by removing the scalp and skull. The anterior region of the brain was then carefully separated using ophthalmic scissors.
An additional 36 rats were sacrificed as described and randomly divided into three groups that were kept at 10 ± 1, 20 ± 1, and 30 ± 1 °C for validation of the models. Brain samples from these additional animals were collected at 10, 30, 50, and 100 h postmortem.
All samples were placed in RNA Latersolvent (Takara, Japan) immediately after collection. The animal experiments described in the present study were performed in accordance with the principles for the Care and Use of Laboratory Animals and were approved by the Science and Ethics Committee of Fudan University.
RNA isolation and integrity analysis
All equipment and bench surfaces that were used during this work were treated with RNase Away (Invitrogen, USA) prior to handling any of the samples to minimize the risk of RNA degradation by RNase during the experimental process. 80–500 mg of tissue from each sample was homogenized with 1 ml Trizol solvent (Invitrogen, USA) and 0.2 ml chloroform to cause protein denaturation. The supernatant was then decanted and mixed with 0.5 ml isopropanol before being stored at 20 °C for 1 h for precipitation. The mixture was then centrifuged at 10,000×g at 4 °C for 10 min. The resulting supernatant was discarded and the precipitate was washed with 75 % ethanol (3:1 DEPC-H2O). The washed samples were then centrifuged again and the supernatant was discarded. Finally the total RNA was dissolved in an appropriate volume of nuclease-free water to provide a solution with a concentration of 200–500 ng/μl. The concentration and purity of RNA were assessed by spectrophotometric analysis using NanoDrop 1000 (Erlangen, Germany). RNA integrity and the level of degradation were assessed by agarose gel electrophoresis.
Nine RNA markers were chosen in this study. β-actin and GAPDH are housekeeping genes which are commonly used as endogenous control markers. The ribosomal protein (RP) S29 mRNA (RPS29), was shown to be stable for normalizing in the first 12 h under 25 °C . 5SrRNA, 18SrRNA, and U6 are frequently used as control markers in microRNA studies [9, 10]. Tissue specific and abundant mature microRNAs (miRs) were chosen in this research because they were considered to be less susceptible to degradation owing to their small size of about 22 base pairs. miR-9 and miR-125b were chosen because their expression was specific to brain tissues according to the miR base database . Let-7a was also chosen because it was an abundant biomarker in all tissues .
Primers used to amplify RNA markers by RT-qPCR
Product size (bp)
Uni-miR qPCR primer
Uni-miR qPCR primer
Uni-miR qPCR primer
Uni-miR qPCR primer
Uni-miR qPCR primer
Real-time quantitative polymerase chain reaction (RT-qPCR)
Total RNA was reverse transcribed using a PrimeScript RT reagent Kit with gDNA Eraser (Perfect Real Time) (Takara, Japan) according to the manufacturer’s protocol. At the same time, 500 ng total RNA was reverse transcribed by adding a polyA tail using a One Step PrimeScript miRNA cDNA Synthesis Kit (Perfect Real Time) (Takara, Japan) according to the manufacturer’s protocol for microRNA analysis. The cDNA product was then diluted by a ratio of 1:10 for further use and stored at −20 °C for RT-qPCR.
Real-time PCR was performed in an ABI Prism 7500 fluorescence quantitative PCR instrument (Applied Biosystems, USA). An amplification mixture was prepared using the SYBR Premix Ex Taq kit (Takara, Japan) according to the manufacturer’s protocol. The reactions were performed in a total volume of 20 μl containing 2 μl cDNA, 10 μl SYBR premix, 0.4 μl dye, 0.4 μl forward primers, 0.4 μl reverse primers and 6.8 μl RNase-free dH2O. A standard curve was similarly produced in a 20 μl volume with 2 μl cDNA diluted 5–8 times. The cycling parameters were 30 s at 95 °C followed by 40 cycles of 5 s at 95 °C and 34 s at 64 °C. Reactions were prepared in duplicate for each sample and for each of the 3 assays. Copies of the specific endogenous markers were quantified and presented as the mean cycle threshold (Ct) values detected with sequence-detection system software v2.3 using a threshold value of 0.2 (Applied Biosystems, USA). All RT-qPCR experiments were performed according to the Quantitative Real-Time PCR Experiments (MIQE) guidelines .
Mathematical model and statistical method
ΔCt represents the differences in Ct values between target biomarkers and control biomarkers. The bivariate cubic curve fit was explored to show the trends over time for the Ct and ΔCt values. Curve estimation analysis of ΔCt values, temperature, and PMIs of rat samples was performed to derive an optimal mathematical model using R software (v3.0.1), a tool for statistical computing and graphics. With R software, a quadratic equation was built with three unknowns (temperature, PMI, and ΔCt). First, the equation was composed by including the terms t, PMI, PMI × t, and PMI2. The animal data was used to fit this type of equation in the R software, and statistical significance (P < 0.05) was applied to compose the final equation. This was then transformed into a three-dimensional visual statistical model with Matlab7.0 software.
The R code for the calculating procedure and the Matlab7.0 code for the visual transformation are presented in Supplemental Material 1.
The statistical significance of the resulting data was analyzed with GraphPad v5.0 (GraphPad software Inc., USA), Excel 2010 (Microsoft, USA), with α = 0.05.
RNA extraction and integrity
Correlation between ΔCt value and PMI in the rat model
Amplifications were successfully performed for all candidate biomarkers though RT-qPCR. The tests used to validate the specificity of the RT-qPCR (Supplemental Material 2) included amplification plots, dissociation curves, standard curves, and PCR efficiency of candidate biomarkers [13, 15].
Standard deviation of Ct values at different temperatures
Correlation between ∆Ct and PMI at different temperatures
Building a visual three-dimensional statistically animal model
Verification of animal samples
Verification of the mathematical model
Average ± SD
Error rate (%)
11.2 ± 5.87
23.53 ± 3.72
58.43 ± 4.8
97.27 ± 21.29
12.47 ± 8.29
20.97 ± 6.71
53.63 ± 24.27
94.87 ± 18.3
14.3 ± 6.77
30.37 ± 11.64
51.37 ± 12.16
110.47 ± 6.86
PMI is defined as the time interval between physiological death and the examination of the deceased. Traditional methods of PMI estimation using postmortem phenomena are often imprecise or experimental. However, innovative research is underway to estimate PMI based on algor mortis using new technology and physical sciences software for enhanced accuracy [16, 17]. Retrospective study of postmortem phenomena, such as re-establishment of rigor mortis and mechanically stimulated idiomuscular contraction, also present further evidence that can be commonly used in forensic practice.
In recent years, the development of technology to detect biological markers after death has enhanced accuracy in PMI estimation. RNA is an extremely labile molecule that is prone to damage from either intrinsic factors such as enzymatic degradation by RNases, or external factors such as light, humidity, or high temperatures . RNA is thought to degrade very quickly after death and was considered unsuitable for estimating PMI unless the degradation rate could be quantitatively measured. This is now possible with RT-qPCR. From semi quantification by RT-PCR to absolute quantification by qRT-PCR, recent research has explored postmortem RNA degradation to assess its potential value in indicating PMI [5, 19, 20, 21]. Some studies have explored the differences of intragroup RIN  and others use ΔCt values to help estimate PMI . However, most of the experimental work uses rats or pigs for long-term research projects  and such studies are often conducted without consideration of parameters like temperature. Although autopsy samples can be analyzed reliably using qRT-PCR according to Inoue , using human postmortem tissues for mRNA expression studies is challenging because of the high biological variability between cases . The lack of human data to verify the animal model also makes it controversial for practical forensic applications.
For absolute quantification of RNA transcript levels in molecular research, the mRNA transcript level is always normalized by using housekeeping genes as an internal control . However, even housekeeping genes degrade with prolonged PMI, complicating their use as internal control markers. More stable RNA markers are still needed for this purpose.
MicroRNA (miR) refers to a class of small non-coding single-stranded RNA, only 21–25 nucleotides long, thought to be highly conserved in the evolution of genomes and relatively stable in comparison to mRNA. Studies using human adipose tissues and cells indicate that microRNAs could be considered suitable candidates for endogenous controls .
Animal-based PMI research shows that heart-abundant miR-1 is stable within 7 days after death . In this study, we selected brain-specific miR-9 and miR-125b to explore their potential as internal standards. Results show that they maintain high stability over 6 days even under high temperature. Both miR-9 and miR-125b were chosen as endogenous control markers to normalize the target markers for which the relationship between PMI and ΔCt values was analyzed.
The small nuclear RNA, U6 snRNA, only exists in the eukaryotic nucleus and is highly stable because of its short hairpin structure and lack of nuclease . However, it begins to degrade after 96 h, even at temperatures under 15 °C, and more rapidly under higher temperatures (Fig. 3). This may be because U6 becomes directly exposed to nucleases without the protection of ribonucleoproteins, which degrade quickly . Similarly, some studies also demonstrate that U6 is not suitable as an endogenous control in some research [28, 29].
β-actin, known as a housekeeping gene, is commonly used as reference in biomedical research because of its multiple sources and homology. Many researchers have used its degradation rate to estimate PMI [5, 7]. Similarly, our results for the ΔCt values of β-actin show significant and consistent degradation with increased PMI, especially at higher temperatures, making it the most reliable and valuable marker for PMI estimation. Through testing of four temperature groups, a multi-parametric mathematical model was established and was found to be effective in the verification of data from rat samples. However, research using human data is scarce but still necessary to extend this field of research further in the future.
The statistical method of linear regression is often used in the study of PMI estimation in legal medicine. However, its use in estimating PMI is questionable because the linear assumptions lack a means for verification. Very little research has explored alternative ways to improve the estimation, such as using R code-based PMICALC software . Similarly, the degradation of RNA doesn’t always follow a linear path, especially with longer PMI, and the profile of RNA degradation varies with temperature. To take temperature into consideration, R software was chosen because it provides a method to build the model with three unknowns and makes it easy to solve the equation using the iterative method.
In summary, we have created a standardized animal model for PMI estimation, showing the influence of temperature and allowing verification. However, the postmortem RNA degradation in human tissues is not only dependent on PMI but also other factors, and particularly environmental conditions, cause of death and the individual’s circumstances. It is necessary to next apply this model to human samples, and assess the other compounding factors. Further studies will also need to find more effective biomarkers to be able to accurately determine PMI with this methodology.
Brain-specific mir-9 and mir-125b are effective endogenous control markers that are not affected by PMI up to 144 h at temperatures between 10 ± 1 and 35 ± 1 °C.
U6 degrades with PMI, particularly at higher temperatures, demonstrating that it was not a suitable endogenous control for this study.
ΔCt (β-actin) has the best correlation coefficient with PMI among the markers we chose, demonstrating that β-actin is an optimal RNA marker to estimate PMI.
Our animal model of PMI estimation using R software could be used in various temperature conditions. It is a powerful tool for both model building and equation solving in such a complicated context.
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