Early postmortem interval (EPMI) estimation using differentially expressed gene transcripts

Legal Medicine 38 (2019) 83–91

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Legal Medicine journal homepage: www.elsevier.com/locate/legalmed

Early postmortem interval (EPMI) estimation using differentially expressed gene transcripts

T

Hui Wanga,1, Jianlong Mab,1, Hongmei Xua, Yehui Lyuc, Li Taoa, Wencan Lid, Yan Zenge, ⁎ ⁎ Kaijun Maf, Bi Xiaof, , Long Chena, a

Department of Forensic Medicine, School of Basic Medical Sciences, Fudan University, 131 Dongan Road, Shanghai 200032, PR China Shenzhen Institute of Criminal Science and Technology, Investigation Department of Shenzhen Public Security Bureau, Key Laboratory of Forensic Pathology, Ministry of Public Security, Shenzhen 518000, PR China c Shanghai University of Medicine & Health Sciences, 279 ZhouzhuHwy, Shanghai 201318, PR China d Forensic Lab, Criminal Science and Technology Institute, Pudong Branch, Shanghai Public Security Bureau, 255 Yanzhong Road, Shanghai 200125, PR China e Children’s Hospital, Fudan University, 399 Wanyuan Road, Shanghai 201102, PR China f Forensic Lab, Criminal Science and Technology Institute, Shanghai Public Security Bureau, 803 North Zhongshan Road, Shanghai 200082, PR China b

ARTICLE INFO

ABSTRACT

Keywords: Forensic pathology Gene transcripts Early postmortem interval R software Three-dimensional models

Genes differentially expressed after death were selected to construct a mathematical model for early postmortem interval estimation. Sprague Dawley rats were sacrificed and placed at temperatures of 4 °C, 15 °C, 25 °C, and 35 °C. Brain tissues were collected at 0, 6, 12, 18, and 24 h after death and total RNA was extracted. Changes in gene transcript levels after death were detected using microarray expression profiling and differentially expressed genes was screened. Expanded experiments were performed to validate gene transcript levels at different temperatures using the reverse transcription real-time quantitative polymerase chain reaction. Six genes with high coefficients of determination were chosen for construction of mathematical models. Optimal ternary cubic equations were built using R software with temperature, postmortem interval and ΔCq defined as the independent variable x, y and z, respectively. Equations were converted into a three-dimensional visual statistical model using MATLAB. Animal samples were used to validate the mathematical models. Results showed that the 5srRNA showed best stability at four temperatures. The genes Ninj2, Grifin, Arpp19, and Hopx showed high coefficients of determination (> 80%) and low error (< 3h) in verification experiments which indicate that they are potential markers for early postmortem interval estimation.

1. Introduction Postmortem interval (PMI) is the period between the time of death and the discovery of a cadaver [1]. Precise estimation of PMI is an important topic and constant challenge in forensic practice. The distinction between early PMI (EPMI) and late PMI (LPMI) depends on the length of the PMI and on postmortem processes. EPMI generally refers to the period within 24 h after death, when there is no obvious putrefaction of the cadaver. During the EPMI, when putrefaction is not severe and witness memories are clearer, criminal investigators can collect more complete evidence, which improves the efficiency of case detection. Therefore, compared with LPMI, EPMI is more significant in forensic practice. Total RNA content is reduced by 21% within 24 h after death [2], suggesting that the predictable rate of RNA degradation may be used to

estimate PMI. Pozhitkov [3] proposed the existence of the “twilight of death,” a period when some cells still operate after organ death. It has been shown that genes related to survival, stress, epigenetic inheritance, developmental regulation, and tumors are differentially expressed after death and that their expression is correlated with PMI. This indicates that, in addition to RNA degradation, gene expression is an important tool for PMI estimation, especially EPMI estimation. A series of studies have been conducted to estimate PMI on the basis of RNA quantification [4–8], however these studies had several deficiencies. (1) Most studies focused on LPMI estimation using micromolecular RNAs as markers, but the accuracy of these markers for EPMI estimation needs to be improved. (2) The majority of these studies were limited to one temperature, and there was a lack of evidence at different temperatures. (3) Markers used in most studies were limited to housekeeping genes, and many coincident genes were omitted.

Corresponding authors. E-mail addresses: [email protected] (B. Xiao), [email protected] (L. Chen). 1 These authors contributed equally to this work. ⁎

https://doi.org/10.1016/j.legalmed.2019.04.008 Received 7 January 2019; Received in revised form 7 April 2019; Accepted 30 April 2019 Available online 02 May 2019 1344-6223/ © 2019 Elsevier B.V. All rights reserved.

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Therefore, this research explored gene expression in the rat brain after death using microarray profiling with an emphasis on genes that were substantially differentially expressed. Real-time quantitative polymerase chain reaction (qPCR) was used to validate the veracity of candidate genes using an expanded sample size. We identified four genes that were highly associated with PMI and constructed a ternary cubic equation relating temperature and PMI using R software. Validation using animal samples showed that several genes were suitable for PMI estimation and had the potential to be used for examination of human samples.

2.3. Microarray expression profiling and data analysis

2. Materials and methods

A microarray composed of 31,099 probe sets (http://www. capitalbiotech.com) was used in this study. Total RNA extracted from brain tissue was diluted to 100 ng/μL and was sequenced by whole transcript sense target labeling (Affymetrix, High Wycombe, UK). The resulting data were pretreated by robust multi-array average [9]. Differentially expressed genes were screened using the significance analysis of microarray procedure with a q-value < 5% and a fold change ≥2 or ≤ 0.5. Differentially expressed genes were analyzed using Cluster (Euclidean distance, hierarchical cluster). Cluster analysis results were visualized using TreeView [10].

2.1. Animal samples

2.4. Reverse transcription real-time quantitative polymerase chain reaction

All animals were purchased from the Department of Laboratory Animals of Fudan University in Shanghai Province, China (Permit Number: SCXK (Shanghai) 2014-004). The animal experiments described in the present study were performed in accordance with the National Institutes of Health guide for the Care and Use of Laboratory Animals and were approved by the Science and Ethics Committee of Fudan University (2016-006). Animals used in the present study were male Sprague Dawley rats weighing 200 ± 20 g. All rats were sacrificed by cervical dislocation for subsequent procedures. For tissue collection, the scalp and skull were removed to completely expose the brain. The anterior region of the brain was then separated and collected using sterile ophthalmic scissors and tweezers. Five sacrificed rats were placed at an ambient temperature of 10 °C. Brain tissue was collected 0, 6, 12, 18, and 24 h after death and sent to CapitalBio Technology Co., Ltd. (Beijing, China) for preliminary microarray screening. A total of 60 sacrificed rats were randomly divided into four groups and placed at ambient temperatures of 4 ± 1 °C, 15 ± 1 °C, 25 ± 1 °C, and 35 ± 1 °C. Brain tissue was collected 0, 6, 12, 18, and 24 h after death to construct mathematical models. An additional 24 sacrificed rats were randomly divided into three groups placed at ambient temperatures of 10 ± 1 °C, 20 ± 1 °C, and 30 ± 1 °C. Brain tissue was collected 3, 9, 15, and 21 h after death to validate the constructed mathematical models. All brain tissue was immediately submerged in RNA Later solvent (Takara, Kusatsu, Japan) after collection. Samples were stored at −80 °C until further use.

The qPCR was performed using an ABI Prism 7500 fluorescence quantitative PCR instrument (Applied Biosystems, Foster City, CA, USA). An amplification mixture was prepared using a SYBR® Premix Ex Taq™ Kit (Takara) following the manufacturer’s protocol. The 10 μL reaction solution contained 1 μL cDNA, 5 μL SYBR + ROX reference dye premix (100:1), 0.7 μL each forward and reverse primer solution, and 2.6 μL RNase-free ddH2O. A standard curve was produced using a 10 μL solution containing 1 μL cDNA 10× serially diluted 5–6 times. The cycling parameters were 30 s at 95 °C, followed by 40 cycles of 5 s at 95 °C, and 34 s at 60 °C. Reactions were prepared in duplicate for each sample and for each of the three assays. Copies of endogenous markers were quantified and are presented as mean cycle threshold (Ct) values detected with sequence-detection system software v2.3 (Applied Biosystems) using a threshold value of 0.2. 2.5. Selection of reference and target biomarkers Thirteen genes that are commonly used as reference markers or have been referred to in the literature [11–14] were chosen as candidates for reference markers in this study. The Cq-value of each candidate gene were statistically analyzed using the online software refFinder (http://www.leonxie.com/reference.php), a comprehensive tool for reference marker selection [15]. Twenty-four differentially expressed genes were chosen as target markers based on data analysis (Fig. 1). ΔCq values of target genes were calculated by normalizing Cq-values according to the formula ΔCq = CqTarget − CqReference using Excel 2010 (Microsoft, Redmond, WA, USA). Cubic equations relating ΔCq and PMI at four different temperatures as well as fitted curves were constructed using GraphPad Prism (GraphPad Software Inc., San Diego, CA, USA) based on singlesample qPCR experiments. Genes with high coefficients of determination (R2 > 90% in each temperature group) were chosen for mathematical model construction. Primers were designed to span at least one exon/exon boundary to ensure cDNA-specific amplification and detection. All primers were designed using Primer Premier 6 and were verified using Primer-BLAST online (https://www.ncbi.nlm.nih.gov/tools/primer-blast). Primer details are given in Table 1.

2.2. Total RNA extraction and reverse transcription Each 40–60 mg sample of brain tissue was homogenized with 1 mL TRIzol solvent (Invitrogen, Waltham, MA, USA) and 0.2 mL chloroform. The mixture was then centrifuged at 12,000×g for 15 min. The supernatant was decanted and mixed with 0.5 mL isopropanol before being stored at −20 °C for 45 min. The mixture was then centrifuged at 10,000×g for 10 min and the supernatant was discarded. The remaining precipitate was washed twice with 1 mL 75% ethanol (3:1 Diethy pyrocarbonate-ddH2O) to remove impurities on the surface of the RNA. The total RNA was then dissolved in an appropriate volume of nuclease-free water to produce a solution with a concentration of 400–600 ng/μL. The concentration of total RNA was measured using a NanoDrop ND-1000 spectrophotometer (Thermo, Sunnyvale, CA, USA) and the RNA integrity and level of degradation were evaluated by agarose gel electrophoresis at 110 V for 20 min. A 1 μg sample of total RNA was reverse transcribed in a total volume of 20 μL using a PrimeScript™ RT Reagent Kit (Takara) following the manufacturer’s protocol. Finally, the cDNA solution was diluted 1:10 and was stored at −20 °C until further use.

2.6. Mathematical model construction and verification An optimal mathematical model with three variates was constructed for each gene using R software v3.2.3. Temperature was defined as independent variate x, PMI as independent variate y, and ΔCq as dependent variate z to construct the ternary cubic equation as below, with α = 0.01. z = k1 × x 3 + k2 × x 2 + k3 × x + k 4 × x × y + k5 × y + k6 × y 2 + k7 × y 3 + k 0

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for the final ranking of computational programs (BestKeeper, geNorm, Normfinder and the comparative ΔCq method) and gives the optimum candidate reference genes [17]. Using refFinder, scores were generated for all candidate reference markers (Fig. 3). A lower score represents a more stable reference marker, whereas a score higher than 6 indicates that the candidate gene is unstable [18]. Based on integrated scores of all candidate reference genes at four different temperatures, 5srRNA had the lowest score among all of the candidate markers. In contrast, Actb was the least stable, and Gapdh was not stable, although it had a low score at 15 °C, suggesting that these genes could be used as target genes for PMI estimation [5]. RPL13A and RPS29 were relatively stable at low temperatures. However, at higher temperatures degradation of these genes increased as PMI increased. 4.1. Selection of target markers R2 values based on single-sample qPCR tests of 24 target genes at different temperatures are shown in Table 2. The expression of six of these 24 genes was highly correlated with PMI (R2 > 90% at each temperature). These included genes encoding Ninjurin 2 (Ninj2), cAMPregulated phosphoprotein 19 (Arpp19), homeodomain only protein X (Hopx), synaptoporin (Synpr), synaptopodin 2 (Synpo2), and galectinrelated inter-fiber protein (Grifin). The fitted curves between ΔCq and PMI at different temperatures are shown in Fig. 4. These six genes were chosen for mathematical model construction based on expandedsample qPCR experiments. 4.2. Mathematical model construction Ternary cubic equations constructed using R software showed that the x3, x2, x, xy, y, y2, y3, and k0 terms were statistically significant (P < 0.01). Equations and R2 values are shown in Table 3. The order of correlation of these six genes based on R2 values was Hopx > Grifin > Ninj2 > Arpp19 > Synpr > Synpo2. When temperature was considered as a variable in the equation, the R2 values of Synpr and Synpo2 declined significantly. However, the R2 values of Ninj2, Arpp19, Hopx, and Grifin were consistently high, indicating that these four genes were suitable for temperature-associated model and PMI estimation. Three-dimensional visual models of Ninj2, Arpp19, Hopx, and Grifin were constructed using MATLAB (Fig. 5). Visual models relating gene expression with PMI did not reveal a single downward trend in the early stages of death. The expression of Ninj2 increased briefly during the early stages of death and then decreased, indicating that this gene was still transcribed for a short time after death. In the later stages of death, the ΔCq of Ninj2 increased significantly, indicating that either the rate of mRNA degradation was greater than gene expression or that transcription stopped after death. Expression of Grifin rose continually as PMI increased. In contrast, the decrease rates of Hopx and Arpp19 increased gradually as PMI increased. The different temperatures had a significant influence on Δ Cq-values. Immediately following death (0 h), gene expression varied between tissues collected at different ambient temperatures. In general, the ΔCq-values of Ninj2 were higher at higher temperatures in tissues collected at the same time point. The expression of Hopx remained nearly unchanged as PMI increased at low temperatures; however, its expression was strongly correlated with PMI at higher temperatures. The ΔCq-values of Arpp19 rose stably with PMI at 4–20 °C, but levels plateaued at 20–35 °C. In contrast to the other three genes, there was no obvious effect of temperature on Grifin expression.

Fig. 1. Differential expression of 24 genes in rat brain 0, 6, 12, 18, and 24 h after death Red pixels represent increased expression and green pixels represent decreased expression.

The parameter k of each variable was calculated from R software. The equations were then converted into a three-dimensional visual statistical model using MATLAB v7.0 (MathWorks, Natick, MA, USA). For mathematical model verification, known temperature and ΔCqvalues were inserted into the existing equations. R software was used to estimate PMI at intervals of 0.1 until the smallest deviation between corresponding output ΔCq and experimental Δ Cq-values was found, indicating that optimal EPMI was equal to predicted EPMI. Error was calculated to assess the quality of the model according to the formula Error = ∣PMIPredicted − PMIActual∣. The R code for mathematical model construction and verification are presented in Supplemental Material 1. The MATLAB 7.0 code for the visual transformation are presented in Supplemental Material 2. 3. Results 3.1. Total RNA isolation and integrity analysis Total RNA was successfully extracted from all rat brains and the extracted RNA was stably amplified. The average A260/280 absorbance ratio was 2.05 ± 0.05 (range: 1.98–2.15) after purification. The average A260/230 absorbance ratio was 2.08 ± 0.09 (range: 1.91–2.25) after purification. Electrophoresis revealed that RNA integrity was good (Fig. 2). Degradation was present only 24 h after death at 35 °C. Research has shown that RNA extracted from brain tissue is relatively stable compared to other tissues since the skull protects it from exogenous RNases [6,16].

4.3. Verification

4. Reference marker assessment

An additional 24 rats were sacrificed to verify the accuracy of the equations. The estimated EPMIs of the mathematical models and their relative errors are shown in Table 4. According to our calculations, we

RefFinder measures the geometric mean of the attributed weights 85

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Table 1 Primers of reference markers and target markers. Gene Symbol

Sequence (5′–3′)

Sequence (5′–3′)

Accession Number

GAPDH ACTB 5SrRNA 18SrRNA RPS29 RPL13 UBC B2M PGK1 HPRT PPIA Ywhaz RPLP1 Grifin Ninj2 Arpp19 Hopx Apod Klk6 S1pr5 Camk2a Camkk2 Fam126b Fhl2 Gas7 Gria3 Itpka Jam2 Klhl23 Matr3 Nrxn3 Rbm26 Satb2 Sorbs2 Synpr Tnnc2 Synpo2

CAACGACCCCTTCATTGACC GTCTTCCCCTCCATCGTG CATACCACCCTGAACGCG GCCATGCATGTCTAAGTACGC CTAACCGCCACGGTCTGAT AAGGTGGTGGTTGTACGCTGTG CCTGACAGGCAAGACCATCACC ACTCCCCAAATTCAAGTGTACT CCCTAAGTCGACCTAGTGTTTT CCAGCGTCGTGATTAGTGATGATG GTGGTGACTTCACACGCCATAATG GAAAATGAAGGGTGACTACTAC CTGCACGACGACGAGGTGAC AGGTGGAGGTGAGTGCAGAC GGCTGAAATCAGTCCTGGAG CCCGGATAAGACAGAGGTCA GAGGACCAGGTGGAGATCCT ACCACAACCGAAGGACAAAG CCATCCAGTGTGCTGATGTC GGCTAACTCGCTGCTGAATC TATCGTCCGACTCCATGACA TGGACAAGAACCCAGAGTCC GAAACAGCATCAGCCATCAA ACGAGACCTGCTTCACCTGT CCTCAAGTTCTCTGCCAAGC GCAATGACAGCTCATCCTCA TGCAAGGAGATGCTGAAGTG TGTTGTGGAGCTACGGTGTC CTGTGCTCAGTTCCGTTTGA GGTAGGGATTCACAGGGTCA GGGCAAAGTGAAATCTTGGA CTTTCATCTGGCCGAGGTAG CAGGCCCAAGGAATAATCAA GCAAAGCCTCGGTAGTTGAG GGCTGGAAACATTTGGTTTG GGGAAGAGCGAAGAGGAACT GTGTATTCAGTCCCGGCCTA

GACCAGCTTCCCATTCTCAG AGGGTCAGGATGCCTCTCTT CTACAGCACCCGGTATTCCC CCGTCGGCATGTATTAGCTC AGCCTATGTCCTTCGCGTACT CGAGACGGGTTGGTGTTCATCC GCGAAGGACCAGGTGCAAGG TCCTTCAGAGTGACGTGTTTAA TGAACGTAGTAGATGAATCCCG GAGCAAGTCTTTCAGTCCTGTCC ACAAGATGCCAGGACCTGTATGC CTGATTTCAAATGCTTCTTGG GCAGATGAGGCTTCCAATGTTGAC CTCGCACTCTGGTGATGGTA GCGATGACCACAAGAAGGAT GCTAGCAACAAGGGATGGTT AAACCATTTCTGCGTCTGCT ACCGGGATCTTCTCGATTTC CGTTCCCTTCTCTCTTGTCG GTTGGAGGAGTCTTGGTTGC CTGGCATCAGCCTCACTGTA TCGACCAGTGTGCAGTTCTC CTTCATCGGTGTCAGCTCAA ACACACTGCAGGGCATACTG CTTACGGAGGTCAGCGATGT GCCTTCATAGCGCTCATTTC GGTCATGCACGAAGAGGAGT TACGAGCTGTTCCTGTGTGC CTCCATCCTCCTCTCCATCA CCTGGTTCATCCTTCCAAGA GCAGCCCACATAACCGTAGT GGGTCGGTGATCCACTACAG CTTCAGCGTCACAACGTGAT AATAAGCCTGTGCAGGATGC GTTGTAGCCGCCTTGATTGT TCCTCGTCTGTCACATGCTC GGAGGTCGTTTCTTGCTTTG

NM_031144 NM_017008 NR_033176 NR_046237 NM_012876 NM_173340 NM_017314 NM_012512 NM_053291 NM_012583 NM_017101 NM_013011 NM_001007604 NM_057187 NM_021595 NM_031660 NM_133621 NM_012777 NM_019175 NM_021775 NM_012920 NM_031338 NM_001025710 NM_031677 NM_053484 NM_001112742 NM_031045 NM_001034004 NM_001134504 NM_019149 NM_053817 NM_001277160 NM_001109306 NM_053770 NM_023974 NM_001037351 NM_001191963

Fig. 2. Results of electrophoresis to assess RNA integrity at four temperatures (A)–(D) are the results of electrophoresis to assess RNA integrity from 0–24 h at 4 °C, 15 °C, 25 °C, and 35 °C, respectively.

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Fig. 3. Geometric means of refFinder ranked genes at four temperatures. Lower scores represent more stable reference genes. Table 2 Coefficients of determination of target markers at four temperatures. Gene

Apod Arpp19 Camk2a Camkk2 Fam126b Fhl2 Gas7 Gria3 Grifin Hopx Itpka Jam2

R2

Gene

4 °C

15 °C

25 °C

35 °C

0.9648 0.9997 0.9601 0.9097 0.9135 0.9991 0.9749 0.9984 0.9264 0.9368 0.7518 0.8956

0.9592 0.9989 0.9550 0.9378 0.8698 0.9952 0.5696 0.8244 0.9613 0.9233 0.8427 0.8062

0.8256 0.9972 0.9867 0.9984 0.9944 0.9522 0.9993 0.9996 0.9860 0.9800 0.9997 0.9973

0.9913 0.9218 0.8851 0.5263 0.8707 0.5966 0.8750 0.9529 0.9473 0.9795 0.0779 0.8849

Klhl23 Klk6 Matr3 Ninj2 Nrxn3 Rbm26 S1pr5 Satb2 Sorbs2 Synpr Tnnc2 Synpo2

found that there were no significant correlations between the length of PMI and the accuracy of the models. However, the error was smaller during the first 3 h. We speculated that mRNA degradation was not significant during the early stages of death; therefore, gene expression contributed significantly to RNA content. However, during the later stages of death, RNA degradation increased gradually, increasing the associated error. Errors in our models were lower at high temperatures than at low temperatures, suggesting that models for PMI estimation using variations in gene expression are more suitable at high temperatures, such as during the summer and early autumn. Among the four models, the order of accuracy based on the average error was Ninj2 > Grifin > Hopx > Arpp19. Taking the R2 values into account, there was no correlation between the errors and the R2 values. At the end of the experiment, the error calculated by averaging the

R2 4 °C

15 °C

25 °C

35 °C

0.9175 0.6789 0.9490 0.9846 0.9862 0.9905 1.0000 0.9420 0.9929 0.9857 0.6430 0.9798

0.7128 1.0000 0.9971 1.0000 0.9190 0.8805 0.9990 0.9077 0.8019 0.9706 0.9384 1.0000

0.9962 0.6579 0.9894 0.9785 0.7200 0.8600 0.5785 0.6056 0.7535 0.9159 0.9966 0.9581

0.7650 0.9834 0.8317 0.9991 0.9426 0.9086 0.9953 0.9969 0.9999 0.9838 0.9991 0.9518

PMI derived from the four models could be reduced to 1.2 h, indicating that a model constructed using multiple genes may be more accurate than a model constructed using a single gene due to a reduction in interference caused by individual differences. 5. Discussion Due to the importance of PMI estimation in forensic pathology, scholars have devoted to seeking PMI-related markers in recent years. However, different methods have their advantages and limitations. As for traditional methods including algor mortis, livor mortis and rigor mortis [19], although they are still classical in caseworks, they are subjective and empirical, and thus specific standards are difficult to confirm. Meanwhile, algor mortis will be greatly influenced by the 87

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Fig. 4. Equations calculated independently of temperature using GraphPad Prism (A)–(F) are the fitted curves of Ninj2, Hopx, Grifin, Arpp19, Synpr, and Synpo2, respectively. The abscissa is EPMI, and the ordinate is ΔCq. Blue, red, green, and purple lines represent the results at 4 °C, 15 °C, 25 °C, and 35 °C, respectively.

internal and external environment including temperature, humidity, ventilation, clothing, age and bodily form; livor mortis and rigor mortis are often used to estimate a period of time but an accurate time point. As for forensic entomology and microorganisms, although they play an important role in LPMI estimation [20,21], especially for those highly decomposed cadavers, they are of little significance for EPMI estimation. Meanwhile, cadaver nutrients, photoperiod and difference

between regions may alter the results [22,23]. Since EPMI represents the critical time for crime detection, its precise estimation demands prompt solution, and RNA quantification is one of the feasible method. With the maturity of qPCR, RNA quantification has been widely used in the field of forensic pathology to estimate cause of death (COD), time of injury, the pathophysiology of death processes, and, in particular, PMI estimation [7,24,25]. The qPCR is a combination of DNA

Table 3 Coefficients of determination and temperature-dependent equations of six genes. Gene Arpp19

Grifin Hopx

Synpr

Synpo2 Ninj2

R2 0.8557

0.9397 0.9698 0.8308 0.7403 0.8936

Equation

Cq = 0.2266 × T + 0.0006 × T × PMI

0.1414 × PMI

0.0108 × T2 + 0.0001 × T3 + 0.0109 × PMI2

0.0002 × PMI3 + 0.8644

Cq = 0.2974 × T + 0.0007 × T × PMI

0.2289 × PMI

0.0211 × T2 + 0.0004 × T3 + 0.0077 × PMI2

0.0002 × PMI3 + 9.4974

Cq = 0.4620 × T + 0.0067 × T × PMI

0.1361 × PMI

0.0358 × T2 + 0.0007 × T3 + 0.0051 × PMI2 + 5.493

Cq = 0.7528 × T + 0.0047 × T × PMI

0.1211 × PMI

0.0454 × T2 + 0.0008 × T3 + 0.0023 × PMI2 + 0.8274

Cq = 0.4198 × T

0.2612 × PMI

0.0322 × T2 + 0.0006 × T3 + 0.0019 × PMI2 + 0.0003 × PMI3 + 12.1040

Cq =

0.0003 × T × PMI

0.0091 × T + 0.0029 × T × PMI

0.3778 × PMI

0.0045 × T2 + 0.0001 × T3 + 0.0100 × PMI2 + 0.0001 × PMI3 + 10.0162

Annotation: The variables ΔCq, T and PMI in equations represent measured ΔCq value, ambient temperature and postmortem interval, respectively. 88

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Fig. 5. Three-dimensional visual mathematical models for four genes. (A)–(D) are the models for Ninj2, Grifin, Hopx, and Arpp19, respectively. The x axis represents temperature (°C), the y axis represents EPMI, and the z axis represents ΔCq.

amplification and post-PCR analysis that monitors the amount of DNA amplified in each PCR cycle [26]. Its speed, sensitivity, simplicity, and small sample size requirements solve the technical problems of PMI estimation. According to MIQE guidelines, stable reference genes must be selected before subsequent qPCR to reduce the error associated with the procedure [27]. Some tissue-specific microRNAs have been proposed to be suitable reference genes [28]. However, because a large number of microRNAs are lost in the process of total RNA extraction, microRNA

extraction generally requires a special kit, and the use of microRNAs as reference genes results in increased error in mRNA experiments. Therefore, selection of non-microRNA markers that remain stable for a long duration after death is necessary. In this study, 5srRNA can be amplified well from total RNA extraction, and was found to be the most stable in the first 24 h after death. Due to its short fragment and locating mainly in ribosomal protein complexes, 5srRNA is a suitable reference gene for PMI-related research. In previous studies of PMI estimation using RNA quantification,

Table 4 Predicted postmortem interval and errors from the established equations of four suitable genes. T °C

real PMI

10 3 10 9 10 15 10 21 20 3 20 9 20 15 20 21 30 3 30 9 30 15 30 21 Average errors

Ninj2

Arpp19

Grifin

Hopx

estPMI

error

estPMI

error

estPMI

error

estPMI

error

6.3/3.8 7.5/8.1 17.8/13.9 25.5/19.2 2.6/3.5 9.6/9.9 16.4/12.9 22.1/18.9 2.4/3.2 8.5/7.8 16.9/19.3 22.8/21.0

3.3/0.8 1.5/0.9 2.8/1.1 4.5/1.8 0.4/0.5 0.6/0.9 1.4/2.1 1.1/2.1 0.6/0.2 0.5/1.2 1.9/4.3 1.8/0.0 1.5

3.7/7.8 14.1/1.5 11.6/15.1 23/15.9 2.4/7.3 7.3/7.3 13.1/14.4 20.8/14.2 3.7/6.9 6.9/6.9 19.3/17.7 21.0/19.7

0.7/4.8 5.1/7.5 3.4/0.1 2/5.1 0.6/4.3 1.7/1.7 1.9/0.6 0.2/6.8 0.7/3.9 2.1/2.1 4.3/2.7 0.0/1.3 2.7

4.9/5 7.9/7.5 12.8/10.3 17.4/16.8 4.5/4.2 11/7.4 12.7/14.6 18.6/19.4 3.2/3 8.2/10.5 16.0/16.1 18.5/22.1

1.9/2 1.1/1.5 2.2/4.7 3.6/4.2 1.5/1.2 2/1.6 2.3/0.4 2.4/1.6 0.2/0 0.8/1.5 1.0/1.1 2.5/1.1 1.8

0.7/7.4 10.8/11.1 18.4/16.1 29.4/27 1.3/8.6 9.4/11.4 12/16 20.3/18.6 4.6/2.7 8.7/8.5 18.1/13.7 22.1/24.9

2.3/4.4 1.8/2.1 3.4/1.1 8.4/6 1.7/5.6 0.4/2.4 3/1 0.7/2.4 1.6/0.3 0.3/0.5 3.1/1.3 1.1/3.9 2.5

89

Integrated estPMI

Integrated errors

4.95 11.1 14.5 21.775 4.3 9.1625 14.0125 19.1125 3.7125 8.25 17.1375 21.5125

1.95 1.05 0.65 2.05 1.6 0.1625 0.9875 1.8875 0.7125 0.75 2.1375 0.5125 1.2

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accuracy was higher at high temperatures than at low temperatures, and errors increased when models were applied to EPMI estimation [4–8]. A possible explanation for this may be that the genes assessed in previous studies were mainly housekeeping genes, and the main target of these studies was the relationship between mRNA degradation and PMI. The time at which the lysosomal membrane ruptures after death, the amount of RNase released from the lysosome, and the amount of RNA degradation are random, which cause large differences between individuals and may be a cause of significant error. Therefore, on the basis of the gene transcripts with various abundance maxima and durations at different PMIs and diverse functions [29], this experiment improved the previous model and focused on genes differentially expressed after death, and thus, established a more sensitive and accurate equation for EPMI estimation. Actually, after organismal death, the blood perfusion ceases and leads to the lack of oxygen and nutrient supply in cells. Hence, all tissues and cells have been through hypoxia condition after death. Compared with other tissues, brain tissue is particularly sensitive to oxygen deprivation and possesses a high metabolic demand [30]. We expected that gene expression in brain tissue would change significantly when hemoperfusion was terminated. Meanwhile, the RNA degradation in brain tissue is not obvious in the early stage of PMI due to the protection from the cranial cavity and blood-brain barrier, which will reduce the influence of RNA degradation on gene transcript level [31]. As brain tissue is a necessary material in routine anatomy and reasons stated above, we suggested that brain is a fitting material for EPMI estimation. In this study, Ninj2, Arpp19, Grifin, and Hopx had higher R2 values than other genes. The verification of the equations confirmed the potential of these genes for analysis of human samples. However, equations based on transcription level of each gene existed advantages and limitations. Compared with other genes, expression of Ninj2 showed two different trends that it rose as PMI increased, peaked approximately 12 h after death, and then gradually decreased. This may cause calculation errors or decrease the range of application. One weakness of Arpp19 is its small range of ΔCq-values due to its wide distribution in the mammalian brain [32], which increases errors. Transcript levels of Hopx did not change significantly at low temperatures, indicating that Hopx may be a more suitable marker for PMI estimation at higher temperatures. In contrast, temperature had a smaller effect on Grifin than other genes, indicating that it can be used to estimate PMI at a large range of temperatures. Therefore, we suggested an average value of results calculated from different genes to estimate PMI, which helped to reduce the errors between each gene. When applied to human samples, more influence factors need consideration. There is no doubt that temperature has a large effect on all methods of PMI estimation, including our method. In this experiment, in order to improve the applicability of the equation, four temperature groups were constructed to simulate the temperature of four seasons. We also suggested a wide range of temperature applications for other PMI-related experiments. Factors affecting the level of gene transcription may influence the results. It is reported that some diseases before death, such as Alzheimer disease [33], Parkinson disease [34] and hyperthermia [35] may show abnormal expression in brain. In forensic fields, COD is a necessary factor which must be considered. For example, compared with other COD, death from mechanical asphyxia underwent an up-regulation of some specific genes [24]. Some of the genes may also reflect behaviors in the certain period before death, such as constraint and torment [36]. Therefore, it is suggested that biomarkers in PMI-related research should not be related with COD, diseases and other factors before death. In forensic practice, COD, disease before death and details of cases should be carefully studied. And when the genes were selected as biomarkers for PMI estimation, more validation experiment should be conducted to eliminate ambiguous genes. Since that no abnormal expression was found between these four

genes and other conditions, they have great potential of application to humans. However, the equation calculated from animal samples could not apply directly to human samples. Due to the difference between species, the equation of the human needs, of course, reconstruction. In view of the scarcity of human samples, animal experiments have their own value. Because of the strict control of experimental conditions, animal experiments can better screen out the differentially expressed genes, whereas human samples are needed for the construction of accurate equations in further study if the model was to apply to caseworks. Finally, the three-dimensional mathematical models of these genes provide a basis for the selection of target genes for further studies. We proposed that the selection of target genes should conform to the following characteristics according to qPCR results: (1) the change in gene transcript levels as PMI increases should display a single trend or no more than two trends; (2) gene transcripts should change significantly in a short period of time to ensure a large range of ΔCq-values, which reduces errors associated with the procedure; and (3) the difference between ΔCq-values of samples from different temperatures should be minimal at the time of death (0 h). 6. Conclusion 5srRNA is an effective reference gene for EPMI-related researches. Animal validation has proved that Ninj2, Grifin, Hopx and Arpp19 showed good numeral relation with EPMI. In order to make the equation of animal experiment better applicable to human samples, we suggested that animal experiments were performed to screen out biomarkers, whereas sufficient human samples with known PMI were performed for equation construction. Compliance with ethical standards Ethical approval All animal experiments complied with the ARRIVE guidelines. The National Institutes of Health guide for the care and use of Laboratory animals (NIH Publications No. 8023, revised 1978) were followed. All procedures performed in studies involving animals were in accordance with the ethical standards of the institution at which the studies were conducted. Informed consent This article does not contain any studies with human participants performed by any of the authors. Funding This work was supported by the National Natural Science Foundation of China (NSFC fund: 81671863, 81373242 and 81172896) and Key Laboratory of Forensic Pathology, Ministry of Public Security (GAFYBL201702). Declaration of Competing Interest None. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.legalmed.2019.04.008. References [1] M. van den Berge, D. Wiskerke, R.R. Gerretsen, J. Tabak, T. Sijen, DNA and RNA

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