‘Fat’s chances’: Loci for phenotypic dispersion in plasma leptin in mouse models of diabetes mellitus

Background Leptin, a critical mediator of feeding, metabolism and diabetes, is expressed on an incidental basis according to satiety. The genetic regulation of leptin should similarly be episodic. Methodology Data from three mouse cohorts hosted by the Jackson Laboratory– 402 (174F, 228M) F2 Dilute Brown non-Agouti (DBA/2)×DU6i intercrosses, 142 Non Obese Diabetic (NOD/ShiLtJ×(NOD/ShiLtJ×129S1/SvImJ.H2g7) N2 backcross females, and 204 male Nonobese Nondiabetic (NON)×New Zealand Obese (NZO/HlLtJ) reciprocal backcrosses–were used to test for loci associated with absolute residuals in plasma leptin and arcsin-transformed percent fat (‘phenotypic dispersion’; PDpLep and PDAFP). Individual data from 1,780 mice from 43 inbred strains was also used to estimate genetic variances and covariances for dispersion in each trait. Principal findings Several loci for PDpLep were detected, including possibly syntenic Chr 17 loci, but there was only a single position on Chr 6 for PDAFP. Coding SNP in genes linked to the consensus Chr 17 PDpLep locus occurred in immunological and cancer genes, genes linked to diabetes and energy regulation, post-transcriptional processors and vomeronasal variants. There was evidence of intersexual differences in the genetic architecture of PDpLep. PDpLep had moderate heritability (hs2=0.29) and PDAFP low heritability (hs2=0.12); dispersion in these traits was highly genetically correlated r = 0.8). Conclusions Greater genetic variance for dispersion in plasma leptin, a physiological trait, may reflect its more ephemeral nature compared to body fat, an accrued progressive character. Genetic effects on incidental phenotypes such as leptin might be effectively characterized with randomization-detection methodologies in addition to classical approaches, helping identify incipient or borderline cases or providing new therapeutic targets.

Leptin expression is affected by thyroid or coeliac disease, growth and mass, fatigue and biochemical mediators [5,12,13]. Sex affects leptin physiology in different ways; weight gain is initiated from the deactivation of leptin receptors in the proopiomelanocortin neurons of the arcuate nucleus in females and in males by deactivation of somatotropic leptin receptors [14]. Centrally, however, satiety and hunger are periodic (regulated feeding cycle) or episodic so that the expression of satiety and hunger signals like leptin have both natural entropy [12] and random ultradian pulses [15]. This core feature of hunger suggests that much of the genetic control of leptin production should also be ephemeral or semi-random over time, with some alleles conferring different periodic or episodic expression.
This in turn resembles an emergent phenomenon in which some alleles carry individual variance components in addition to means, distributed as ({N i {μ i ,σ 2 +b}) [16] and termed 'phenotypic dispersion' (PD) [17] or 'vQTL' [18]. Heritable dispersion loci occur in various systems [19] including medical traits. One locus for insulitis dispersion occurs on murine Chr 9 (120.8 MB) [20] linked to cholecystokinin (CCK) (121.4 MB) [21] and various chemokine receptors. Instability in diabetic phenotype may have epidemiological consequences: the frequency of random hypoglycaemic episodes prior to age five has been associated with reduced long-delay spatial memory [22], for example.
Using three curated mouse mapping datasets (F 2 Dilute Brown non-Agouti (DBA/2)×DU6i intercrosses [23], female Non Obese Diabetic (NOD)×(NOD×129S1/SvImJ.H2 g7 ) N 2 backcross [24], and male Nonobese Nondiabetic (NON)×New Zealand Obese (NZO/HlLtJ; T2DM model) backcrosses [11]) hosted by The Jackson Laboratories (ME) I detected several loci for randomized phenotypic dispersion in plasma leptin (PD pLep ), several of which were linked to insulitis loci. A possible consensus locus was detected in two cohorts on Chr 17. There was only one locus associated with dispersion in arc-transformed percent body fat (PD APF ); morphological traits may be less subject to genetic randomization. Coding polymorphisms at candidate genes linked to the Chr 17 consensus region included those involved with the response to cancer, inflammation, growth, post-transcriptional modification, metabolism and human diabetes incidence. These findings indicate that leptin expression may be partially controlled by randomizing mutations at genes for feeding behaviour and gastrointestinal function, operating on nearly-randomized schedules and undetectable by conventional approaches.
In Brockmann et al., 233 F 2 DBA/2×DU6i (an inbred subline of DU6 selected for high 6-wk weight (78 generations)) intercross males and 178 females were bred from F 1 parents from a DU6i sire and a DBA/2 dam ('Brockmann1', Cross 2 (https://phenome.jax.org/projects/ Brockmann1); MPD:213) [23]. Animals were provided al libitum access to a breeding diet (Altromin International #1314; 22.5% protein, 5.0% fat, 4.5% fibre, 6.5% ash, 13.5% water, 48.0% nitrogen-free extract and trace elements and minerals and housed in 350 cm 2 macrolon type II cages. Fat percentage was calculated from weight and fat mass, and arc-transformed as a proportional value for analysis [ These were used to breed 310 female NOD×(NOD×129.H2 g7 ) backcross (BC) mice. Mice were maintained on a 14:10 light:dark photoperiod, irradiated Lab Diet 5LG4 (PMI, Brentwood, MO) and acidified water in order to prevent pathogen exposure [24]. Total weight ('TW'; g), total lean mass ('TLM'; g) and total fat ('TF'; g) were measured by dual-energy X-ray absorptiometry (DXA) and percent fat was calculated from these (('PF' = TF/TW); g) [ [11]. BC mice were held on a 12:12 photoperiod cycle at a controlled temperature and humidity in double plexiglass boxes to the age of 24 weeks, fed NIH-31 grain meal (4% fat) with ad libitum access to food and water. Plasma leptin (pLep; ng/ml), body weight (g) and total fat (g) were measured at 24 weeks, with pLep being measured via a commercial radioimmunoassay kit (Linco, Inc.). DNA was isolated from 5mm tail clips or frozen kidney and liver and 83 microsatellite markers (average intermarker distance = 27.0 MB) genotyped using Perkin Elmer or MJ thermocyclers and agarose gels [11]. The Jackson Laboratories Animal Health Program (http://jaxmice.jax.org/genetichealth/ health_program.html) ensured the ethical treatment of all animals in the Leiter et al. and Reifsnyder et al. studies. Because of incomplete marker heterozygosity in the DU/6 line after selection, the markers D3Mit77, D5Mit10, D8Mit45 and D18Mit152 were not included in this analysis (see [11]).

Association analysis
Random genetic effects on pLep and APF were estimated at each locus in each cohort using a type III GLM (Leiter et al.), or mixed model (Brockmann et al., Reifsnyder et al.) [25] in a model of the form where y ik is trait value, μthe cohort mean, α i the effect of genotype i for each locus j, β MLH X MLH is the partial regression term for the effects of multilocus heterozygosity (MLH) on and ε ik the OLS residual. Studentized residualsε i�j ¼ε i =ðŝ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 1 À h ii p Þ were estimated from OLS residuals in SAS, where ε ik ¼ P m i¼1 x i À P are divided by the variance of the ith residual varðε i Þ ¼ s 2 ð1 À h ii Þ to control for distributional heterogeneity [26]. MLH was included to account for putative effects of Lerner's 'genetic homeostasis' [27] predicts that random phenotypic aberrancy is a function of internal genetic homogeneity, so that more inbred animals should have a greater rate or degree of phenoabberancy. In order to account for this possible effect, PD APF and PD pLep were regressed separately on multilocus heterozygosity (MLH = heterozygous loci / total loci) in a non-locus model otherwise as above to test effects of genetic homeostasis as a partial regression covariate. Locus effects were fit to account for the effects of undetected minor QTL. Sex, F 1 line and/or full sub family were included as appropriate, with full sib family fit as a random effect.
Studentized residuals for each locus were absolute-transformed ðĵε ik�j jÞ to express them as positive vectors of randomization within genotype ('phenotypic dispersion'; PD) [17]. Genotypic variance for PD was tested using Tobit quantitative limited models (QLIM) [25] fitting dispersion against MLH, full sib family, sex and pedigree where appropriate (as determined from a non-locus model) and for locus effects with a latent variable y � i related to an indicator vector x i by the quantitative vector β, so that and the defined censoring threshold τ where y � i does not exceed τ. In this system, the lower bound τ was set to zero so that

Linked SNP
SNP at nonsynonymous coding sites, mRNA-untranslated regions (UTR) and splice sites were identified over each range of markers significantly associated with dispersion traits with a minimum ±10 MB window for single markers. Gene identities for SNP were collected from Mouse Genome Informatics (MGI) (www.informatics.jax.org) and and gene functions were interpreted from GeneCards (www.genecards.org), UniProt (www.uniprot.org) and eEnsembl (useast.ensembl.org).

Heritability
The heritability of PD APF and PD pLep was calculated in a set of 43 Mouse Phenome Project strains (n = 1,780) hosted by the Mouse Phenome Database (MPD; http://www.jax.org/ phenome) with sample sizes ranging from 4-26 by strain and sex [31] ('Naggert1' (https:// phenome.jax.org/projects/Naggert1); MPD:143) ( Table 1). Studentized residuals and demographic effects on pLep and APF were estimated in the mixed model [25] where y ij was the original phenotype, μ the experiment-wide leptin mean, α i the (random) effect of strain, γ j the (fixed) effect of sex, α i γ j strain-sex interaction and ε ijk was error. Studentized residuals were absolute-transformed to PD pLep and PD APF as above. s Þ and genetic covariance between PD pLepp and PD APF in the model y = Xb + Ya + e, where y i is the n×r matrix for PD pLep (r 1 ) and PD APF (r 2 ), X is a fixed n×p incidence matrix (0, 1) for p nongenetic effects, b is the n×p coefficient vector for unknown fixed nongenetic effects, Y is the i×r incidence matrix for random genetic effects (strain (i)), a is the i×r coefficient matrix for random genetic effects (distributed as N~(0, σ 2 )) and e is the error matrix [35]. Coefficients for strain effects were solved using Gauss-Seidel (GS) iteration and sex by Jacobi iteration. Total strain genetic variance proportions for PD pLep and PD APF were calculated as h 2 s ¼ s 2 s =s 2 p (see [36]) and genetic correlation as r a ¼ s gðxyÞ = p ðs 2 gðxÞ s 2 gðyÞ Þ.

Protein variants
Coding non-synonymous (CNS) polymorphisms were identified within multiple-cohort consensus genomic locus areas for dispersion in the same trait (PD pLep or PD APF ), fitting the non-diabetic/non-obese line 129SV/SvImJ as a control ('reference') strain and the diabetic/obese NOD/ ShiLtJ line as the comparison ('affected') strain from Leiter et al. . Amino acid sequences for each source strain were extracted based on CNS codon differences for submission to the PredictProtein server meta-service [38], which produces predicted protein structure and activity on a by-amino acid basis for submitted strands. The PROFsec module [39,40] uses a neural network interface to predict squared solvent accessibility scores (predicted accessibility, 'PACC') as square Angstroms (Å 2 )) based on minimal atomic bonding distances [41]. Protein-protein, protein-DNA and protein-RNA binding sites were predicted on a by-residue basis using a machine-learning module, ISIS2, using a combination of empirical three-dimensional predictions and curated known activities [42,43]. Finally, binary predictions of polypeptide flexibility were made by residue using the META-Disorder module, which compiles sequence information from into a single two-state (binary 0/1) score along the length of a polypeptide, where flexibility was scored as B norm ¼ ðB À � B Ca Þ=s > +3 [44,45] (flexible state), where � B Ca is the average residue motility based on X-ray chromatography [46]. Only isoforms from well-represented transcribed RefSeq annotations (NM polypeptide accessions/NR RNA accessions) were used to predict polypeptide structure and function; unverified, probable and model sequences (XM/XR annotations) were discounted in constructing haploid protein constructs. For single genes with multiple interstrain CNS identified in MGI, all coding sequence polymorphisms were combined into single strain polypeptide strands for residue analysis.

Genetic mapping
APF was transformed as log(arcsin(APF))+1 prior to analysis. No standard or epistatic QTL or joint single-locus effects were detected for log(pLep) or log(APF) at the 5% significance threshold in Leiter et al.
PD pLep loci and their architecture were highly similar in F 2 DBA/2×DU6i males to those detected in the complete cohort, with D3Mit25 (overdominant), D5Mit66 (additive) and D19Mit30 (negative dominant; DU6i homozygotes having higher PD pLep than other genotypic classes) also being associated with PD pLep (P Benj < 0.05) (Figs 1 and 2; Table 2). D17Mit72 was significantly associated with PD pLep in female F 2 DBA/2×DU6i intercrosses but this locus was negative dominant in females (P < 0.001). D13Mit186 also had a negative dominant association with PD pLep in female F 2 s (Figs 1 and 2; Table 2). No significant marker-by-sex interaction was found using two-way mixed interactive models (P Benj > 0.1) so that differences in structure by sex were likely scalar rather than interactive [47]. Variance in plasma leptin was over twice as high in males (s 2 m = 25.0) as females (s 2 f = 9.8) in Brockmann et al., but variance in fat percentage by sex was roughly equivalent (s 2 m = 0.448, s 2 f = 0.460). Of all PD pLep loci in males and females, three were over-or underdominant (D1Mit236, D3Mit25 and D5Mit221), one was dominant (D12Mit46), two were additive (D4Mit54 and D5Mit66), two negative dominant (D13Mit186 and D19Mit30) and one which was additive in males but negative dominant in females (D17Mit49) (Fig 2; Table 2).
Positions on Chr 1, 6, 7, 11, 16 and 17 were associated with PD pLep in the Leiter et al. cohort (Fig 1; Table 2) while D15Mit42 and D17Mit247 were associated with PD pLep in Reifsnyder et al. (P Benj < 0.05). Genetic architecture could not be calculated in these cohorts since backcrosses differentiate only the homozygote and heterozygote state. Pedigree group was not asso-  Table 2).

. Genomic marker peaks for dispersion in plasma leptin (PD pLep ) and arcsin-transformed percent body fat (PD APF ), plasma in 402 (174F, 228M) F 2 Dilute Brown non-Agouti (DBA/2)×DU6i intercrosses (Brockman et al.), 142 female Non Obese Diabetic (T1DM model; NOD/ShiLtJ)×(NOD/ShiLtJ×129S1/SvImJ.H2 g7 ) N 2 backcross female mice (Leiter et al.), and 204 male Nonobese Nondiabetic (NON)×New Zealand Obese (NZO/HlLtJ; T2DM model) reciprocal backcrosses (Reifsnyder et al.) at Benjamini-Hochberg
Overall, there was little to no differentiation in predicted accessibility (PACC) or binary inferences of disorder across transcript types, except for some minor shifts in PACC between Synj2 b haplotypes near polymorphism sites (S1 Fig). However, most polypeptide sequences had from 1-5 differences in the presence or position of protein-protein binding sites (i.e. Synj2 c, e, Fndc1, Pde10a, Papbc6, Vmn2r96, Vmn2r111), usually within 50-100 residues of the CNS polymorphism (S1 Fig). Genotypes causing instability or lability in leptin production would fit with the profile of the inherent variability (periodic or episodic pulses) in plasma leptin [15,67]) according to satiety, so that heritable dispersion could well be an integral, mathematical-physiological facet of Genetic loci for dispersion in plasma leptin serum leptin. Significant random or apparently variation occurs in several other diabetic traits (i.e. glycaemia [68], CAPN10 [69], suggesting that periodic or episodic physiological variation might be a common feature of diabetes in general as a normal feature of hunger and gut emptying. Either form of dysregulation-excessive variability or physiological inflexibility-could be a precursor to irregular reactions to hunger, resulting in inappropriate or incorrectly controlled feeding behaviour. Such loci might thus reflect the various positions of individuals on the longer-term onset to full diabetes, or affect repeatability among analyses (i.e. [7,70]. This may be less true for accruing morphological characters like obesity, where adipose mass probably reflects complex, long-term leptin-diet relationships, leptin resistance and feedback [71,72]. Analytical solutions incorporating dispersive effects might help physiological uncertainties in diabetes. A database search (NCBI, RGD) found no identified QTL for amylin production but the Chr 6 PD pLep peak in Leiter et al. (141.5 MB) co-located with coding and UTR SNP at amylin (islet amyloid polypeptide (Iapp)) (142.3 MB), a leptin agonist and insulin/glucagon regulator which forms pancreatic amyloid processes with cytotoxic effects on pancreatic β cells in T2DM [73]. Agonistic amylin-leptin expression might operate reactively via randomization with incidental satiety or hunger touching off cycles of randomized counter-regulation.
The general basis of dispersive gene action-whether through genes with core physiological functions or those directly related to a given dispersed trait-is unclear [66]. Coding polymorphisms in the consensus Chr 17 area included those linked to cancer (Fndc1, Tiam2, Zdhhc14 Has1) [48,52,56,64], growth and development (Igf2r, Afdn, Tiam2, T2) [49,57,63], immunology [53] or diabetes itself via the energetic electron transfer chain (Tiam2, Pde10A) [50,51] or basal thermal metabolism [61]. Tiam2 modifies allele transmission and expression [48] in addition to its other roles, which could be a central modifier of the propensity to dispersive or stable physiological function. Pabpc6 was another possible core candidate linked to the consensus Chr 17 locus via its role in poly-A post-translational processing [62]. Alternatively, dispersion in leptin could be related to coding variants at the various vomeronasal Chr 17 genes; neurological pathway alleles affecting lability in food detection could similarly be involved with randomization in leptin production upstream or downstream of sensory components of feeding activity. Notably, SNP at Fndc1 were linked to loci associated with dispersion in urine albumin [66].

Fat
Only a single locus was detected for PD APF and heritability for dispersion in fat from Naggert et al. was low (h 2 s = 0.12). Morphological characters with physical benchmarks achieved on stable, progressive trajectories like weight or total fat proportion might be less susceptible to dispersion. An assay of 38 mouse mapping cohorts (� x = 133.2 markers, n = 238 mice/cohort, n T = 13,571) found relatively few loci for dispersion in body weight (Perry, unpub), suggesting that overall morphology is relatively immune to heritable randomization. As an anabolic process, morphological indicators of diabetes may be a result of numerous ontogenetic corrections to achieve an integrated final value for body proportion [74] commensurate with overall genetic and environmental proclivity to obesity.

Sex
Male/female differences in the expression of dispersion loci occurred in F 2 DBA/2×DU6i mice: only the Chr 17 45.4-79.4 MB locus was common to males and females, and both PD pLep loci in females were negative dominant. Architecture at that locus also varied between males (additive) and females (negative dominant). Sex-based differences in the quantitative genetic structure of disease traits is common [75], including insulin resistance in mouse models [76], leptin resistance [77] and the biochemical operation of leptin [14,78]. Heritable sex-related differences in leptin pulses might be as integral to diabetes onset as conventional means and biochemical action. Women experience greater signal amplitude in leptin expression [67], which could be partially determined by greater severity of dispersive gene action. Correspondingly, the percent variance (r 2 ) of residuals associated with locus effects was slightly higher in female F 2 s from Brockmann et al. (8.2%) than for males (5.1%). Leptin dispersion might even be a component of greater leptin resistance in males [77], with uncontrolled variance in leptin being ignored by a static, unresponsive physiognomy.

Genetic homeostasis
MLH was marginally positively correlated with PD APF in the Leiter et al. set, but was unassociated with other dispersed traits in these groups. In accordance with the predictions of genetic homeostasis [27], MLH is usually negatively associated with dispersion [66] (Perry, unpub) so that more inbred individuals tend to be more phenotypically divergent from the mean. The marginal association of MLH with PD APF may simply be likely random chance.

Conclusion
Loci for randomized variance in plasma leptin is in line with the notion of periodic or episodic variation in satiety, and the linkage of several leptin dispersion loci to diabetes susceptibility loci (see [24]) suggests a role for physiological randomization in diabetes physiology with insulitis itself. Dispersive effects on core diabetic traits like leptin production might help explain heterogenous presentation, progression and response to treatment (see [8,79]); of the nearly 400 million sufferers of diabetes mellitus, many incipient affecteds are unaware of their condition [80]. Quantification of heritable randomization in the structure of underlying diabetic phenotype might help elucidate both genetic labilities and liabilities, helping resolve unassigned statistical variance in the underlying elements of diabetic physiology.