[ Original research article ]

Journal of Apiculture - Vol. 40, No. 4, pp.337-345

ISSN: 1225-0252 (Print)

Print publication date 30 Nov 2025

Received 14 Oct 2025 Revised 23 Oct 2025 Accepted 24 Oct 2025

DOI: https://doi.org/10.17519/apiculture.2025.11.40.4.337

Screening the Candidate Postmortem Marker Genes for Estimating Postmortem Intervals in Nurse Bees (Apis mellifera)

HeeJin Kim¹ ; Young Ho Kim¹^{, 2}^{, 3}^{, *}

1Department of Vector Entomology, Kyungpook National University, Sangju 37224, Republic of Korea
2Department of Entomology, Kyungpook National University, Sangju 37224, Republic of Korea
3Research Institute of Invertebrate Vector, Kyungpook National University, Sangju 37224, Republic of Korea

Correspondence to: ^*E-mail: yhkim05@knu.ac.kr

Abstract

The honey bee (Apis mellifera) plays an essential role in global agriculture; however, colony losses have been frequently reported. Because several mRNAs remain active for a limited period after death, quantitative real-time PCR(qRT-PCR) analysis of mRNA degradation may be useful for estimating postmortem intervals(PMIs) in dead bees. In this study, the expression dynamics of thirteen candidate postmortem marker genes were analyzed in nurse bee carcasses from 1 to 7 days postmortem. Among them, RPS5 and RPS18 showed significant decreases in expression within the early postmortem phase (1-3 days). Based on cubic regression models, RPS5 (R²= 0.997) and RPS18 (R²= 0.982) demonstrated strong correlations with PMI. Furthermore, expression ratios using stably expressed genes as denominators revealed that RPS5/SDH and RPS18/SDH achieved the highest coefficients of determination (R²= 0.996), distinguishing carcasses between 1-2 and 3-7 days postmortem. These findings suggest that RPS5, RPS18, and their ratios with SDH can serve as molecular markers for PMI estimation in nurse bees. This molecular approach may support forensic analyses of honey bee mortality under both laboratory and field conditions.

Keywords:

Apis mellifera, Postmortem interval, mRNA degradation, RPS5, RPS18, SDH

INTRODUCTION

The western honey bee (Apis mellifera) is one of the most important pollinators contributing to agricultural productivity and global ecosystem stability. The Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) reported that approximately 35% of global crop production depends on pollination services, with an estimated economic value of 235-577 billion USD (Jung, 2008; IPBES, 2016). In Korea, honey bees are responsible for pollinating nearly 50% of fruit and vegetable crops, providing pollination services valued at approximately 4 billion USD (Jung, 2008). Similarly, Reilly et al.(2020) estimated that honey bee-mediated pollination contributes about 6.4 billion USD annually to U.S. crop yields, with almonds alone accounting for 4.2 billion USD.

However, these contributions have declined in parallel with the global reduction in honey bee populations (Sumner and Boriss, 2006; Meixner, 2010). Multiple factors-including exposure to pesticides and miticides, parasitic infestation, pathogens, and abnormal climatic conditions-have been identified as major stressors that threaten colony health and contribute to colony collapse (Meixner, 2010; Kim, 2022; Lee et al., 2022). Consequently, numerous studies have focused on the physiological effects of these stressors on surviving bees to identify potential lethal mechanisms (Zaobidna et al., 2017; Dolezal and Toth, 2018; Butolo et al., 2021; You et al., 2025).

Nevertheless, beekeepers often recognize colony losses only after large-scale mortality events occur, at which point most individuals are already dead. Thus, analyzing dead bees rather than survivors may provide more practical insight into the underlying causes of colony collapse. Following death, cellular metabolism ceases and autolytic degradation begins (Brooks and Sutton, 2017; Wenzlow et al., 2023). However, several studies have demonstrated that certain messenger RNAs (mRNAs) remain detectable for a limited period after death (Kimura et al., 2011; Pozhitkov et al., 2017; Shafeeq et al., 2020) reported that stress- and development-related genes continued to be expressed for 48-96 hours in postmortem mouse and zebrafish tissues, whereas Kimura et al. (2011) observed that circadian genes in mice maintained rhythmic expression patterns for up to 48 hours after death. In insects, Shafeeq et al. (2020) found that hsp70 expression increased for five days postmortem in Plodia interpunctella, while ultraspiracle transcripts remained stable.

Because the persistence of mRNA varies depending on the postmortem interval (PMI), these molecular changes have been proposed as biomarkers for estimating PMI (Scrivano et al., 2019; Cianci et al., 2024). Several analytical methods-such as the ΔC_q method, C_q ratio, and direct quantification of transcript abundance-have been employed to model the relationship between mRNA degradation and PMI (Kimura et al., 2011; Ali et al., 2017; Alshehhi and Haddrill, 2019; Wang et al., 2021). However, mRNA stability is affected by multiple variables, including tissue type, temperature, humidity, and time since death (Bauer, 2007; Sampaio-Silva et al., 2013). Moreover, the suitability of specific postmortem marker genes differs among species, underscoring the need to identify honey bee-specific markers for PMI estimation.

In this context, the present study aimed to identify reliable molecular markers that can be used to estimate PMI in nurse bee (A. mellifera) carcasses. To this end, the expression levels of ten housekeeping genes [RPS5 (40S ribosomal protein S5), RPS18 (40S ribosomal protein S18), GAPDH (Glyceraldehyde-3-phosphate dehydrogenase), ARF1 (ADP-ribosylation factor 1), PPI (Peptidyl-prolyl cis-trans isomerase), PGK (Phosphoglycerate kinase), SDH (Succinate dehydrogenase flavoprotein subunit), TBP (TATA-box-binding protein), EF1 (Elongation factor 1-alpha F2), and EcR (Ecdysone receptor)] and four putative postmortem genes-LOC410857 (protein lethal (2) essential for life), DAAM (disheveled-associated activator of morphogenesis-like protein), and Prx2 (Peroxiredoxin 1)-were examined using quantitative real-time PCR (qRT-PCR). Expression ratios between candidate genes and stable reference genes were further analyzed to enhance resolution across PMI time points. Mathematical regression models were then established to determine the most suitable markers and to propose an accurate method for estimating PMI in honey bee carcasses.

MATERIALS AND METHODS

1. Sample preparation

Colonies of the western honey bee (A. mellifera) were maintained at the experimental apiary in Sangju-si, Korea. Nurse bees were collected based on their labor-specific behaviors (Johnson, 2010) and stabilized in cages (Bugdorm-1, MegaView Science Co., Ltd., Taichung City, Taiwan) supplied with 50% sucrose solution. The bees were maintained for 24 h in a dark incubator at 32℃ (JS Research Inc.) prior to experiments. To obtain carcasses for different postmortem intervals (PMIs), the nurse bees were euthanized with CO₂ and maintained under controlled laboratory conditions. Carcasses were sampled at 1, 2, 3, 4, 5, 6, and 7 days postmortem, ensuring no fungal growth on the body surface. Samples were immediately stored at -80℃ until RNA extraction.

2. Candidate postmortem marker genes and primer design

Thirteen candidate postmortem marker genes were selected to evaluate their potential for PMI estimation: RPS5, RPS18, GAPDH, ARF1, PPI, PGK, SDH, TBP, EF1, LOC410857, DAAM, Prx2, and EcR gene was used as a reference gene based on its previously validated expression stability under postmortem conditions (Kim and Kim, 2025a). Primer sequences for ten genes (RPS5, RPS18, GAPDH, ARF1, RAB1a, PPI, PGK, SDH, TBP, and EF1) were obtained from previous reports (Moon et al., 2018; Jeon et al., 2020; Kim et al., 2022; Kim and Kim, 2025a, 2025b). Primers for LOC410857, DAAM, Prx2, and EcR were designed using the OligoCalc software (http://biotools.nubic.northwestern.edu/OligoCalc.html). PCR amplification efficiency was determined from standard curves derived from 10-fold serial dilutions of cDNA, and calculated using the formula E=10^-1/slope. All primer sets exhibited efficiencies between 92-107% with coefficients of determination (R²)>0.99, indicating acceptable performance for qRT-PCR analysis(Table 1).

Table 1.

Information of primer sets for candidate PMI marker gene and reference gene

3. RNA extraction, cDNA synthesis, qRT-PCR

For each sample, the antennae were removed to prevent contamination from damaged tissue. Total RNA was extracted from individual heads using the yesR Total Plus Kit (GenesGen, Busan, Korea) according to the manufacturer’s protocol. Genomic DNA was eliminated using gDNA Eliminator Buffer and DNase I(GenesGen). The concentration and purity of RNA were measured using a SpectraMax QuickDrop spectrophotometer(Molecular Devices, Sunnyvale, CA, USA). RNA samples were stored at -80℃ until use.

Complementary DNA (cDNA) was synthesized from 50 ng of total RNA using ReverTra Ace^TM qPCR RT Master Mix (Toyobo, Japan) following the manufacturer’s protocol. The thermal cycling conditions were 37℃ for 15 min, 50℃ for 5 min, and 98℃ for 5 min.

qRT-PCR was performed on a CFX Connect Real-Time PCR Detection System (Bio-Rad, Hercules, CA, USA) using Thunderbird SYBR qPCR Master Mix (Toyobo, Osaka, Japan). The reaction conditions were as follows: initial denaturation at 95℃ for 1 min, followed by 40 cycles of 95℃ for 15 s, 56℃ for 15 s, and 72℃ for 30 s. Each reaction was run in triplicate. Amplification specificity was confirmed by melting curve analysis. C_q values were obtained automatically using the CFX Manager software, and relative expression levels were normalized to RAB1a using the 2^-ΔΔCq method.

4. Statistical analysis and mathematical modeling

Normalized expression levels of each candidate gene across different PMIs were analyzed using one-way analysis of variance (ANOVA) followed by Tukey’s multiple comparison test (p<0.05). Expression ratios were calculated using the following formula:

$Ratio = expression level of target gene expression level of stable gene$

Stable genes used as denominators were selected based on their expression stability rankings, determined by the smallest average standard deviation of expression levels across all PMIs (Fig. 1) and supported by a previous study (Kim and Kim, 2025a).

Cubic polynomial regression models were constructed to evaluate the correlation between gene expression (or expression ratios) and PMIs. The model with the highest coefficient of determination (R²) was considered the most accurate for PMI estimation.

RESULTS

1. Expression patterns of candidate postmortem marker genes

The expression levels of thirteen candidate genes were quantified in nurse bee heads at seven postmortem intervals (1-7 days) using qRT-PCR (Fig. 1). Among them, five genes-RPS5, RPS18, GAPDH, PPI, and EF1-exhibited significant temporal changes after death (p<0.05), whereas the remaining eight genes (ARF1, PGK, SDH, TBP, LOC410857, DAAM, Prx2, and EcR) showed no significant differences across PMIs (p>0.05).

Fig. 1.

Expression patterns of postmortem marker genes under postmortem condition. The expression levels(average±standard deviation) of target genes were measured depending on PMI. The difference value (∆) represented the smallest gap between expression levels in PMI estimation ranges. The Different letters indicate significantly different values (p<0.05) that analyzing by One-way ANOVA with Turkey’s multiple comparison test.

Expression of RPS5 decreased markedly during the first 3 days postmortem, with statistically distinct levels at 1, 2, and 3 days (p<0.05). Thereafter, expression remained stable from 3 to 7 days, suggesting that RPS5 is a sensitive marker for distinguishing early (≤3 days) and late (≥3 days) postmortem phases (Fig. 1A). Similarly, RPS18 expression gradually declined from 1 to 4 days postmortem, with a clear separation between early (1-2 days) and mid-to-late (3-7 days) PMIs (p<0.05; Fig. 1B). In contrast, GAPDH, PPI, and EF1 showed significant downregulation only at 1 day postmortem (p<0.05), indicating limited utility for distinguishing longer PMIs (Fig. 1C-E).

Cubic regression analysis revealed strong correlations between PMI and the expression levels of RPS5 (R²=0.997) and RPS18 (R²=0.982), while other genes showed weaker associations (R²<0.90; Table 2). These results suggest that RPS5 and RPS18 can serve as quantitative indicators for estimating postmortem duration within 3 days after death.

Table 2.

The regression equations for candidate PMI markers (single gene or combinations of PMI-specific gene and stable gene) showing distinct PMI estimation ranges

2. Expression ratios of candidate genes

To improve PMI resolution, expression ratios were calculated between the five PMI-responsive genes (RPS5, RPS18, GAPDH, PPI, EF1) and the four stably expressed genes (ARF1, PPI, PGK, SDH). Among all combinations, ratios using SDH as the denominator exhibited the clearest differentiation among PMIs (Fig. 2). The RPS5/SDH and RPS18/SDH ratios significantly distinguished 1-, 2-, and 3-7-day postmortem groups (p<0.05), while GAPDH/SDH and EF1/SDH only separated 1-day samples from later time points. Ratios involving other denominators (e.g., RPS5/PPI, RPS18/PGK) showed partial separation between early (1-2 days) and late (3-7 days) intervals but exhibited lower model accuracy (R²<0.9).

Fig. 2.

The ratios of expression levels using PMI-specific marker genes and stable gene under postmortem condition. The expression ratios (average±standard deviation) showing distinct PMI estimated ranges were calculated using PMI-specific gene and stably expressed gene (ARF1, PPI, PGK, and SDH). The difference value (∆) represented the smallest gap between expression levels in PMI estimation ranges. The Different letters indicate significantly different values (p<0.05) that analyzing by One-way ANOVA with Turkey’s multiple comparison test.

In contrast, the cubic regression models for RPS5/SDH and RPS18/SDH achieved high coefficients of determination (R²=0.996 for both; Table 2), indicating strong predictive relationships between expression ratios and PMIs.

The mean difference values between PMI groups were also greatest for these two ratios: 27.3 between 1 and 2 days for RPS5/SDH and 53.5 between 1 and 3-7 days for RPS18/SDH. These results demonstrate that both ratios can reliably distinguish among multiple postmortem stages and are suitable molecular markers for PMI estimation in A. mellifera.

3. Summary of optimal regression models

Cubic polynomial models were generated to describe the relationship between gene expression (or ratio) and PMI (Table 2). The models for RPS5, RPS18, RPS5/SDH, and RPS18/SDH exhibited R²>0.98, demonstrating high accuracy for PMI prediction. The regression equations are summarized in Table 2. These models indicate that PMI estimation based on expression ratios provides slightly higher precision than estimation based on single-gene expression levels.

Overall, the results demonstrate that (1) RPS5 and RPS18 show predictable degradation patterns after death; (2) ARF1, PPI, PGK, and SDH are stable postmortem reference genes; and (3) the ratios RPS5/SDH and RPS18/SDH provide the highest accuracy for PMI estimation in nurse bee carcasses, effectively distinguishing carcasses within 1-2 days postmortem from those after 3 days.

DISCUSSION

The present study aimed to identify candidate postmortem marker genes that can be used to estimate postmortem intervals (PMIs) in nurse bee (A. mellifera) carcasses. Estimating PMI in dead bees is crucial for understanding the causes of colony losses, since beekeepers usually detect mortality events after colony collapse has already occurred. Previous studies have primarily focused on the physiological effects of stressors on living bees (Zaobidna et al., 2017; Dolezal and Toth, 2018; Butolo et al., 2021; You et al., 2025), but few have explored molecular indicators in carcasses.

In this study, the expression levels of thirteen candidate genes were analyzed across seven postmortem intervals. Among them, RPS5 and RPS18 showed clear, time-dependent degradation patterns, allowing the differentiation of carcasses within the first three days after death. The cubic regression models of these genes exhibited strong correlation with PMI (R²=0.997 and 0.982, respectively), confirming their reliability as postmortem molecular markers. In contrast, other genes (GAPDH, PPI, and EF1) showed significant decreases only at 1 day postmortem, indicating limited applicability for PMI estimation beyond the early phase.

Interestingly, both RPS5 and RPS18 have been used as reference genes under various experimental conditions, including postmortem tissues in other species (Sampaio-Silva et al., 2013; Lv et al., 2017; Wang et al., 2022). However, the present study revealed that their expression levels were not stable after death in honey bee tissues, as confirmed by BestKeeper and geNorm analyses in our previous study (Kim and Kim, 2025a). This instability suggests that RPS5 and RPS18 are unsuitable as reference genes but rather are potential postmortem markers whose degradation correlates strongly with time since death. Such discrepancies with previous studies likely reflect interspecific differences in tissue physiology and mRNA stability, as well as methodological variations in sample storage and qRT-PCR conditions.

To improve PMI estimation accuracy, this study also analyzed expression ratios between dynamic and stable genes. According to the previous study (Kim and Kim, 2025a), four genes (ARF1, PPI, PGK, and SDH) used as denominator were ranked among the top four in Ref Finder, confirming their high expression stability under postmortem conditions. In this study, these genes also showed low standard deviations of expression levels across all PMIs, supporting their suitability as denominators for calculating expression ratios in PMI estimation. Among all tested combinations, the RPS5/SDH and RPS18/SDH ratios showed the highest discrimination power among postmortem groups and exhibited strong polynomial relationships with PMI(R²=0.996 for both). These ratios reliably distinguished carcasses at 1, 2, and ≥3 days postmortem, extending the estimation range and improving accuracy compared with single-gene models. This finding supports previous research in which the use of gene expression ratios was shown to reduce variability and improve model robustness(Kimura et al., 2011; Cianci et al., 2024).

The superior performance of RPS5/SDH and RPS18/SDH may be attributed to two factors: (1) the high stability of SDH expression postmortem, and (2) the consistent degradation kinetics of RPS5 and RPS18. Since ribosomal protein genes are highly expressed in active cells and rapidly degrade after cell death, their relative decrease provides a sensitive molecular signature of tissue decay. This suggests that ribosomal gene degradation can serve as a universal postmortem indicator across species.

Although the regression models developed in this study showed high accuracy under controlled laboratory conditions, several factors may influence their performance in the field. Temperature, humidity, and microbial activity can alter mRNA degradation rates (Bauer, 2007; Sampaio-Silva et al., 2013), potentially affecting PMI estimates. Therefore, field validation studies incorporating environmental variables are required to establish practical thresholds for PMI estimation in natural conditions.

Overall, this study provides the first molecular approach to PMI estimation in honey bees using gene expression dynamics. The findings demonstrate that RPS5 and RPS18, along with their ratios to SDH, can serve as reliable molecular markers to differentiate early and late postmortem phases in A. mellifera carcasses. This molecular framework may contribute to future forensic analyses of colony mortality events and improve diagnostic accuracy in apicultural investigations.

Acknowledgments

This study was supported by a research fund (RS-2025-02303308) from the Rural Development Administration, Republic of Korea. This manuscript is based on the master’s thesis of HeeJin Kim.

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Table 1.

Information of primer sets for candidate PMI marker gene and reference gene

Gene		Primer					Reference
Symbol (Gene name)	Accession No.	Label	Sequence (5′–3′)	Size (bp)	GC (%)	Tm (°C)	Reference
^aRPS5 (40S ribosomal protein S5)	XM_006570237	F	GATGTTTCTCCGTTACGACGAGT	23	48	62.9	Jeon et al. (2020)
^aRPS5 (40S ribosomal protein S5)	XM_006570237	R	GAGTTCATCGGCTAAACATTCGG	23	48	62.9	Jeon et al. (2020)
^aRPS18 (40S ribosomal protein S18)	XM_625101	F	GATTCCCGATTGGTTTTTGAATAG	24	38	60.3	Moon et al. (2018)
^aRPS18 (40S ribosomal protein S18)	XM_625101	R	AACCCCCAATAATGCGCAAACC	22	45	60.1	Moon et al. (2018)
^aGAPDH (Glyceraldehyde-3-phosphate dehydrogenase)	XM_393605	F	CACCTTCTGCAAAATTATGGCG	22	45	60.1	Moon et al. (2018)
^aGAPDH (Glyceraldehyde-3-phosphate dehydrogenase)	XM_393605	R	ACCTTTGCCAAGTCTAACTGTTAA	24	38	60.3	Moon et al. (2018)
^aARF1 (ADP-ribosylation factor 1)	LOC409481	F	GGGCTTCATTCTCTCCGCAA	20	55	60.5	Kim et al. (2022)
^aARF1 (ADP-ribosylation factor 1)	LOC409481	R	AGAGCCAATCAAGACCCTCG	20	55	60.5	Kim et al. (2022)
^aRAB1a (Ras-related protein Rab-1A)	LOC102654987	F	CTTAGAGTGGGTCCTCCATC	20	55	60.5	Kim et al. (2022)
^aRAB1a (Ras-related protein Rab-1A)	LOC102654987	R	CAGCAGCATCCAGATTTAGAGG	22	50	62.1	Kim et al. (2022)
^aPPI (Peptidyl-prolyl cis-trans isomerase)	XM_393381	F	GCAGCTTCCATAGAGTGATCC	21	52	61.2	Kim and Kim (2025b)
^aPPI (Peptidyl-prolyl cis-trans isomerase)	XM_393381	R	TTGGACCAGCATTAGCCATGG	21	52	61.2	Kim and Kim (2025b)
^aPGK (Phosphoglycerate kinase)	XM_395047	F	GACGAGGAAGGAGCAAAAATCA	22	45	60.1	Kim and Kim (2025b)
^aPGK (Phosphoglycerate kinase)	XM_395047	R	CCCATCCAGCCATCAGGTAT	20	55	60.5	Kim and Kim (2025b)
^aSDH (Succinate dehydrogenase flavoprotein subunit)	XM_623062	F	ATGATCAGGATACAGTTGTGCC	22	45	60.1	Kim and Kim (2025b)
^aSDH (Succinate dehydrogenase flavoprotein subunit)	XM_623062	R	TTAGAGGGCCAATAGTTTCTCC	22	45	60.1	Kim and Kim (2025b)
^aTBP (TATA-box-binding protein)	XM_623085	F	CAAAATATGGTAGGCAGCTGTG	22	45	60.1	Kim and Kim (2025b)
^aTBP (TATA-box-binding protein)	XM_623085	R	CGATTCTAGGTTTAACCATACGAT	24	38	60.3	Kim and Kim (2025b)
^aEF1 (Elongation factor 1-alpha F2)	NM_001014993	F	GTCGTGGTTATGTTGCTGGTGAT	23	48	62.9	Jeon et al. (2020)
^aEF1 (Elongation factor 1-alpha F2)	NM_001014993	R	CGCATTTCTCTTTGATATCAGCGAA	25	40	62.5	Jeon et al. (2020)
LOC410857 (protein lethal(2)essential for life)	XM_006568175.3	F	CGGTGAAGACGGTCGGTAAT	20	55	60.5	This study
LOC410857 (protein lethal(2)essential for life)	XM_006568175.3	R	GTCGTGAGATGGAGGCAAGA	20	55	60.5	This study
DAAM (disheveled-associated activator of morphogenesis-like protein)	XM_006561849.3	F	GGCTCAGAAAGCTCCTCGAA	20	55	60.5	This study
	XM_006561849.3	R	GCATGTCCTCCTCGATATCC	20	55	60.5	This study
Prx2 (Peroxiredoxin 1)	XM_003249241.4	F	CCTTTTCTGATCGTGCTGATGA	22	45	60.1	This study
Prx2 (Peroxiredoxin 1)	XM_003249241.4	R	TCAAGTACGCCATAATCACGTG	22	45	60.1	This study
^aEcR (ecdysone receptor)	NM_001098215.2	F	CGGTATACGGAGCGATCAGA	20	55	60.5	Kim and Kim (2025a)
^aEcR (ecdysone receptor)	NM_001098215.2	R	GTTGCTCGTACTCGTTCTGG	20	55	60.5	Kim and Kim (2025a)

Candidate	The equation of regressive curve	R²
RPS5	y = −0.145x³ + 2.271x² − 11.566x + 20.366	0.997
RPS18	y = −0.026x³ + 0.862x² − 7.512x + 20.43	0.982
GAPDH	y = −0.103x³ + 1.439x² − 6.369x + 9.415	0.889
PPI	y = −0.028x³ + 0.37x² − 1.491x + 2.477	0.686
EF1	y = −0.148x³ + 2.112x² − 9.413x + 13.258	0.903
RPS5/ARF1	y = −0.224x³ + 3.601x² − 18.935x + 34.6	0.999
PPI/ARF1	y = −0.085x³ + 1.177x² − 4.968x + 7.549	0.862
EF1/ARF1	y = −0.281x³ + 4.001x² − 17.751x + 24.744	0.928
Prx2/ARF1	y = −0.199x³ + 2.837x² − 12.311x + 17.396	0.877
RPS5/PPI	y = 0.048x³ − 0.258x² − 1.721x + 10.729	0.765
EF1/PPI	y = −0.09x³ + 1.31x² − 5.983x + 8.935	0.952
RPS18/PGK	y = 0.699x³ − 6.752x² + 6.633x + 50.478	0.771
GAPDH/PGK	y = −0.367x³ + 5.072x² − 22.312x + 33.992	0.941
EF1/PGK	y = −0.311x³ + 4.373x² − 19.522x + 29.06	0.948
Prx2/PGK	y = −0.366x³ + 4.889x² − 20.16x + 28.343	0.875
RPS5/SDH	y = −0.64x³ + 10.251x² − 52.467x + 87.582	0.996
RPS18/SDH	y = −0.28x³ + 6.494x² − 44.946x + 98.156	0.996
GAPDH/SDH	y = −0.403x³ + 6.118x² − 28.932x + 43.167	0.944
EF1/SDH	y = −0.458x³ + 6.641x² − 30.094x + 42.525	0.944
Prx2/SDH	y = −0.461x³ + 6.553x² − 28.707x + 39.572	0.927