Genetic basis of voluntary water consumption in two divergently selected strains of inbred mice

Abstract Background Inbred mouse strains with normal renal function show a substantial difference in daily water consumption across strains. This study uses two strains of inbred mice C57BR/CDJ (BR), which are high consumers, and C57BL/10J (BL), which are low consumers, their reciprocal F 1 crosses, inter se bred F 2s and backcrosses produced by breeding high consuming F 2 animals to the low consumer parent strain and low consuming F 2 animals to the high consuming parent strain. Consumption was corrected for body weight prior to analysis. Methods The effective number of genes controlling water consumption was estimated using the Castle–Wright estimator. Additive and dominance genotypic values as well as the degree of dominance were calculated using estimated strain means. Results According to Castle–Wright, a minimum of 10 factors were estimated to affect the difference in consumption across the two strains. Between seven and eight are expected to be high effect factors. Using the Zeng adjustment, it was determined that 30–40 factors potentially affect the difference in consumption. Conclusions These numbers were surprising but may be related to several sources of variation present in the BR strain. A negative degree of dominance indicated the BL strain has more dominant factors.

Under the premise of genetic control being conserved across species, a long-term backcross study to isolate genes that control water consumption in two divergently selected strains of mice was designed.
In standard laboratory conditions, inbred mouse strains with unaltered kidney function show about a fourfold range of daily water consumption . Using this information, a high consuming strain and a low consuming strain were selected. The objective of the present study is to estimate the effective gene number controlling the difference in consumption between these two strains and estimate additive and genotypic values for the trait.

| Experimental animals
Foundation C57BL/10J (Black) and C57BR/CDJ (Brown) were purchased from Jackson Laboratories (Bar Harbor, ME). These strains were chosen based on previously quantified difference (Blacks: 0.35 mL/g 0.667 /d; Browns: 0.80 mL/g 0.667 /d) in water consumption . The strains show no difference in renal function (Thaisz et al., 2012). These animals were bred to establish two single-strain colonies at the University of Missouri, Columbia. In accordance with the suggested design for diallel crosses (Griffing, 1956), females from each strain were bred to males from the opposite to produce F 1 reciprocal crosses. F 1 animals were then bred inter se to produce the F 2 generation. To produce backcross animals, the two highest consuming and two lowest consuming male, F 2 animals were selected for breeding. Animals were then bred to the opposite parental strain; high consumers to Blacks and low consumers to Browns. Backcrosses produced from the high consumer were referred to as High Backcross 1s (HB1s). Those from the low consumer were referred to as Low Backcross 1s (LB1s).
Consumption and weight data were collected on 848 animals: 68 Black, 81 Brown, 117 F 1 , 338 F 2 , 129 HB1 and 115 LB1. Animals were housed in plastic tub containers with corn cob bedding per ACUC approved protocol 8565. All males were individually housed, breeder females were group housed and experimental animals were individually housed during water consumption measurements. The temperature was maintained at 24 ± 1°C.

| Weight and consumption measurement
Animals were weaned at 4 weeks, weighed, and separated into individual cages with custom-built 25-ml serological pipette water bottles based upon a previous design (Bachmanov, Tordoff, & Beauchamp, 1996). To see a more specific description of data collection methods, refer to Haag, Wells, and Lamberson (2018).

| Statistical analysis and selection
Regression analysis of measured water intake on body weight, strain and sex was conducted prior to other analyses.
To estimate means, variances and standard errors mixed model analysis of adjusted consumption were conducted using PROC MIXED in SAS software. Adjusted consumption was designated as the dependent variables and fitted to a linear mixed model in the analysis: In this model, N ijkl is the dependent variable, adjusted consumption, μ is the mean, strain i , sex j and strain i *sex j are the designated fixed effects for strain, sex and the strain*sex interaction, respectively, sire k (strain) i is the sire within strain random effect and, finally, e ijkl is the error term.
Effective gene number was estimated using the Castle-Wright estimator (Castle, 1921;Cockerham, 1986;Lande, 1981;Wright, 1968): To yield a less biased estimation, Zeng's adjustment equation (Zeng, 1992) was used to calculate n e : To evaluate assumptions associated with the Castle-Wright estimator, adjusted consumption data were evaluated for epistasis and additivity. Epistasis testing was completed using the equation (Lynch & Walsh, 1998): where Δ represents the epistatic estimate, z(F 2 ), z(P 1 ), z(P 2 ) and z(F 1 ) represent the observed line means for the F 2 , Black, Brown and F 1 animals, respectively. As the observed Δ was not zero for the dataset, a sampling variance of Δ was estimated using the following equation: where Var(Δ) is the sample variance for estimated Δ value, Var[z(F 2 )], Var[z(F 1 )], Var[z(P 1 )] and Var[z(P 2 )] are the observed sampling variances for F 2 , F 1 , Black and Brown animals, respectively. The ratio of |Δ|/ √ Var(Δ) then provides a t test for evaluation of significance.
The joint scaling test (Cavalli, 1952;Gale, Mather, & Jinks, 1977;Mather & Jinks, 1971)  There are several methods to estimate segregation variance; however, these methods can produce highly variable results (Lande, 1981;Lynch & Walsh, 1998). To avoid high variability, the least squares analysis method (Lynch & Walsh, 1998) was selected: The matrix M contains the coefficients of the variance components for Black, Brown, F 1 , F 2 , HB1 and HB2, respectively. Iterative analysis eventually results in the final least squares parameter estimates for σ 2 (P 1 ), σ 2 (P 2 ) and 2 S . Additive and dominance genotypic values were calculated in the population with means from Black, Brown and F 1 animals (Falconer & Mackay, 1996). Additive genotypic value (a), was determined using the equation: In this equation, the parental line with the highest phenotypic value should be first in the numerator, or Black from Brown.
Dominance genotypic value (d) was determined using the equation: In this equation, the mean of the parental strains is subtracted from the mean of the F 1 strain. To estimate the degree of dominance, the dominance value was divided by the additive value.

| RE SULTS
A significant sex*strain interaction was observed in the dataset.
This previously observed interaction (Haag et al., 2018;McGivern, Henschel, Hutcheson, & Pangburn, 1996;, was accounted for by analysing each sex separately for all analyses in the study. Brown animals consumed more water (P < .0001) than Black animals (Table 1). F 1 animals had higher water consumption but were much closer to that of the Black animals (Table 1). F 2 animals showed a range of phenotypes encompassing both parental phenotypes as well as higher variance than the F 1 animals. However, variance in the F 2 was not as high as that observed in the Brown animals. Backcross animals showed means and variances moving towards parental strain values each generation.
Prior to factor number estimation, the epistatic, additive and dominance effects were analysed to determine how well the data fit the assumptions for Castle-Wright. Both sexes showed a significant indication (P < .0001) of epistatic effects ( Segregation variances ( 2 S ) determined using least squares were used to estimate factor number (n e ). The estimated factor number was higher in females than males, indicating some factors may be Xlinked causing an overestimation in females and an underestimation in males (Otto & Jones, 2000). The square roots of the variances were used to estimate the number of effective factors for each sex.
TA B L E 1 Number of animals per sex and strain, least squares means + SE (ml/g/wt 0.67 ) of water consumption for each sex and strain and the estimated variance for each sex and strain Finally, n e was used to estimate a more unbiased number of factors (n) (Table 3). Again, differences in effective factor number and n are likely related to estimation biases based on sex.
A similar analysis of weight data, however, yielded a negative value for the Castle-Wright estimator. This was likely due to the strains not being differentiated enough for weight. This lack of divergence was expected since lines were partially selected based on similar size. This was done to reduce the number of potential factors affecting water consumption differences.

| D ISCUSS I ON
These results indicate many genes control the difference in water consumption between these two strains. In fact, this estimation is likely minimized due to violations of Castle-Wright estimator assumptions.
To produce an unbiased prediction with the Castle-Wright estimator several assumptions must be met (Castle, 1921;Wright, 1968): 1. All alleles increasing the value of the phenotype are fixed in one line and all those that lower it are fixed in the other line.
2. Allelic effect differences are equal at all loci.
Expectedly, the data showed significant epistatic effects due to the quantitative nature of the trait (Cordell, 2002). Dominance effects were also observed which moved the F 1 and F 2 phenotypes nearer to the Black parent than the mid-parent value. However, joint scale testing indicated the data were adequately fit by the additive model. This signalled the data could be analysed using the Castle-Wright estimator.
It should be noted though, research (Huang & Mackay, 2016)  results. This indicates the robustness of the estimator and reduces concerns about the additivity of the data (Wu, Bradshaw, & Stettler, 1997).
The number of genes controlling the difference in consumption may be surprisingly high from two closely related strains (Beck et al., 2000). However, previous work has indicated higher than expected genetic variance and divergence in the strains, particularly in regard to copy number variation (Cutler, Marshall, Chin, Baribault & Kassner, 2007). Further, the Brown strain has been noted for its high degree of genetic distinctiveness potentially related to mutation rate (Taylor, 1972) as well as a higher level of haplotypic introgression than typically observed in inbred strains (Yang et al., 2011). Regarding water consumption specifically, previous research has indicated differential androgen regulation in males (Melanitou, Cohn, Bardin, & Janne, 1987); however, no differences in androgen receptor or affinity (Kemp & Drinkwater, 1989). Brown females have also been noted for lowered ovarian hormone production (Maronpot, 2009) which can increase water intake (McGivern et al., 1996;Tarttelin & Gorski, 1971). This level of phenotypic diversity in the strain could explain the high levels of variance observed in the Brown strain.

| CON CLUS ION
In conclusion, the difference in water consumption between these two strains is controlled by many genes. This indicates a requirement for a very large number of animals to conduct a QTL analysis. It may be advisable to instead evaluate this trait using less genetically diverse strains such as C57BL/6J and C57BL/10J which still have a sufficient difference in water consumption .

ACK N OWLED G EM ENTS
We would like to acknowledge Anna Goldkamp, Danielle Magee, Catherine Roques and Katharine Sharp for assistance with data collection in this project.

S O U RCE O F FU N D I N G
Funding for this project provided by the University of Missouri Ag Experiment Station.

CO N FLI C T O F I NTE R E S T
The authors declare that they have no competing interests.