Evolution of genomic imprinting with biparental care: implications for Prader-Willi and Angelman syndromes

Abstract

The term "imprinted gene" refers to genes whose expression is conditioned by their parental origin. Among theories to unravel the evolution of genomic imprinting, the kinship theory prevails as the most widely accepted, because it sheds light on many aspects of the biology of imprinted genes. While most assumptions underlying this theory have not escaped scrutiny, one remains overlooked: mothers are the only source of parental investment in mammals. But, is it reasonable to assume that fathers' contribution of resources is negligible? It is not in some key mammalian orders including humans. In this research, I generalize the kinship theory of genomic imprinting beyond maternal contribution only. In addition to deriving new conditions for the evolution of imprinting, I have found that the same gene may show the opposite pattern of expression when the investment of one parent relative to the investment of the other changes; the reversion, interestingly, does not require that fathers contribute more resources than mothers. This exciting outcome underscores the intimate connection between the kinship theory and the social structure of the organism considered. Finally, the insight gained from my model enabled me to explain the clinical phenotype of Prader-Willi syndrome. This syndrome is caused by the paternal inheritance of a deletion of the PWS/AS cluster of imprinted genes in human Chromosome 15. As such, children suffering from this syndrome exhibit a striking biphasic phenotype characterized by poor sucking and reduced weight before weaning but by voracious appetite and obesity after weaning. Interest in providing an evolutionary explanation to such phenotype is 2-fold. On the one hand, the kinship theory has been doubted as being able to explain the symptoms of patients with Prader-Willi. On the other hand, the post-weaning symptoms remain as one of the primary concern of pediatricians treating children with Prader-Willi. In this research, I reconcile the clinical phenotype of Prader-Willi syndrome with the kinship theory, contending that paternal investment relative to maternal investment increases after weaning. I also propose a genetic composition of the PWS/AS cluster, discuss the effects of new types of mutations, and contemplate the potential side effects of reactivating silent genes for medical purposes.

Figure 1. Biparental Care in Mammals

The phylogeny of mammalian orders [53] is followed by the percentage of genera showing biparental care [11]. The gray and red colors in the pie charts represent the percentage of genera within the order that exhibit maternal and biparental care respectively. The green color in the order Rodentia corresponds to the percentage of genera expected to exhibit biparental care. While the percentage of genera exhibiting biparental care in mammals as a whole does not exceed 10%, the percentage of genera exhibiting biparental care in Perissodactyla and Carnivora exceeds 30% is close to 40% in primates and is expected to exceed 40% in Rodentia.

Figure 2. Mating System and Cost Distribution

Each rectangle represents an offspring; the two rectangles contained in each offspring represent the parents—mother in red and father in blue—that produced the offspring and the fraction of resources contributed by each parent. The fraction of resources contributed by the mother is σ. The first rectangle corresponds to the current offspring and the following rectangles correspond to future offspring. If the future offspring is aligned with the current one—and carries the same color combination—then it has the same parents as the current offspring. If the future offspring is not aligned with the current one—and carries a different color combination—then it either has a different mother if it is above the current one or has a different father if it is below the current one. Any investment in the current offspring translates into a cost to the father and the mother in terms of residual reproductive value. In this example, the cost experienced by the father is also suffered by the mother with probability κ_P and the cost experienced by the mother is also suffered by the father with probability κ_M. The cost of providing an additional unit of investment is different for the father C_Pi and the mother C_Mi. In case A, mothers contribute more than fathers, σ = ¾, the maternal costs shared by the father affects to κ_M = ½ of the father's residual reproductive value, the paternal cost shared by the mother affects κ_P = ¾ of the mother's residual reproductive value. The paternal cost for each unit of investment is almost two times the maternal cost. In this scenario, the paternal cost not shared with the mother is equal to the maternal cost not shared with the father. In case B, there is lifetime monogamy and when the mother dies, the father does not produce any more offspring even if he had resources to do so. In case C, there is sequential monogamy and when the mother dies, the father finds a new mate. In case D, father and mother change partners to produce every single offspring.

Figure 3. ESS Pattern of Expression

The horizontal axis represents the fraction of resources contributed by the mother σ. The vertical axis represents the total level of expression of an RE (top row) and an RI (bottom row). The continuous line corresponds to the optimal level of expression from the perspective of the maternally inherited allele as a function of the fraction of resources contributed by mothers σ. The discontinuous line corresponds to the optimal level of expression from the perspective of the paternally inherited allele as a function of the fraction of resources contributed by mothers σ. The intersection of both these lines corresponds to the value σ in which the conflict becomes extinct, σ̂. In the top part of each figure, the evolutionary stable pattern of expression is represented. If (1−κ_M)C_Pi < (1−κ_P)C_Mi (first column) the conflict becomes extinct when mothers contribute less resources than fathers, σ < ½. If (1−κ_M)C_Pi = (1−κ_P)C_Mi (second column) the conflict becomes extinct when mothers contribute as many resources as fathers, σ = ½. If (1−κ_M)C_Pi > (1−κ_P)C_Mi (third column) the conflict becomes extinct when mothers contribute more resources than fathers, σ > ½. The figure inserted at the bottom right corner represents the offspring fitness function v_O (in green) and the parental fitness functions (maternal v_M and paternal v_P) (in gray) used to elaborate the figure, where v_o = log(1 + i_M + i_P), v_M = z_Mi_M + κ_Mz_Pi_P, and v_P = κ_P z_M i_M + z_Pi_P) where z_M and z_P are constants.

Figure 4. Contribution of Resources as Function of Time

I present two pairs of figures. The horizontal axis corresponding to the first figure in each pair represents time, t, in the life of an individual. The window of expression of gene g occurs from 0 to T. The vertical axis represents the fraction of resources contributed by the mother σ. The dotted line corresponds to the more realistic case when the fraction of maternal resources changes continuously from little paternal contribution before weaning to greater paternal contribution afterwards. The continuous line corresponds to a two-period scenario when mothers contribute σ^b > σ̂ before weaning and σ^a < σ̂ afterwards. The second figure corresponds to the top right graphic from Figure 3 where the fraction of resources contributed by the mother has been specified. Case A corresponds to genes expressed before g ₁ and after g ₂ weaning. The ESS expression is if g ₁ expressed before weaning and if g expressed after weaning. Case B corresponds to a gene expressed before and after weaning that can adjust its level of expression. The ESS expression is .

Figure 5. Human PWS/AS Cluster of Imprinted Genes

The colors red and blue represent the maternally and paternally inherited alleles. Continuous and dashed lines represent expressed and silent genes respectively.

Figure 6. Portrait of Eugenia Martinez Vallejo at Museo del Prado (Madrid)

Eugenia Martinez Vallejo was portrayed by Spanish painter Juan Carreño Miranda in 1680. It has been suggested that she had PWS [19]. At the time of the painting, she was 6 years old and in the hyperphagic (over eating) phase of the disease, which occurs after weaning. She weighed 120 pounds (∼54 kg) and was portrayed with two pieces of food in her hands, which correspond to these patients' voracious appetite. Other symptoms pointing toward this disease include her short stature, almond-shaped eyes, small triangular mouth, and small hands.

Figure 7. Composition of PWS/AS Cluster

Each figure represents the composition in terms of type of gene (resource enhancer or resource inhibitor) and window of expression of each gene (either before weaning, or after weaning, or before and after weaning). Within each figure, I represent the genotype of a patient with PWS and AS. I use a zigzag line to represent a deleted strand. Underneath each scheme, I note the predicted phenotype. I assume that before weaning, the maternal contribution of resources (relative to the paternal one) is greater than σ̂#x0963; σ̂#x0302; but after weaning, the relative maternal contribution of resources is less than σ̂. I present two alternative compositions: (A) corresponds to the possibility that genes are expressed in each period (before or after weaning) but not across periods (before and after weaning). (B) corresponds to the possibility that genes are expressed across periods.