Taxonomy of rare genetic metabolic bone disorders.

UNLABELLED: This article reports a taxonomic classification of rare skeletal diseases based on metabolic phenotypes. It was prepared by The Skeletal Rare Diseases Working Group of the International Osteoporosis Foundation (IOF) and includes 116 OMIM phenotypes with 86 affected genes. INTRODUCTION: Rare skeletal metabolic diseases comprise a group of diseases commonly associated with severe clinical consequences. In recent years, the description of the clinical phenotypes and radiographic features of several genetic bone disorders was paralleled by the discovery of key molecular pathways involved in the regulation of bone and mineral metabolism. Including this information in the description and classification of rare skeletal diseases may improve the recognition and management of affected patients. METHODS: IOF recognized this need and formed a Skeletal Rare Diseases Working Group (SRD-WG) of basic and clinical scientists who developed a taxonomy of rare skeletal diseases based on their metabolic pathogenesis. RESULTS: This taxonomy of rare genetic metabolic bone disorders (RGMBDs) comprises 116 OMIM phenotypes, with 86 affected genes related to bone and mineral homeostasis. The diseases were divided into four major groups, namely, disorders due to altered osteoclast, osteoblast, or osteocyte activity; disorders due to altered bone matrix proteins; disorders due to altered bone microenvironmental regulators; and disorders due to deranged calciotropic hormonal activity. CONCLUSIONS: This article provides the first comprehensive taxonomy of rare metabolic skeletal diseases based on deranged metabolic activity. This classification will help in the development of common and shared diagnostic and therapeutic pathways for these patients and also in the creation of international registries of rare skeletal diseases, the first step for the development of genetic tests based on next generation sequencing and for performing large intervention trials to assess efficacy of orphan drugs.

Localization of a gene causing cystinuria to chromosome 2p.

Cystinuria is an autosomal recessive disorder of amino acid transport. It is a common hereditary cause of kidney stones worldwide, and is associated with significant morbidity. In 17 affected families, we found linkage between cystinuria and three chromosome 2p markers. Maximal two-point lod scores between cystinuria and D2S119, D2S391 and D2S288 were 8.23 (theta = 0.07), 3.73 (theta = 0.15) and 3.03 (theta = 0.12), respectively. Analysis of recombinants and multipoint linkage data indicated that the most likely order is cen-D2S391-D2S119-cystinuria-D2S177-tel. We also observed high rates of homozygosity for markers in this chromosomal region among 11 affected offspring of consanguineous marriages. Based on its map position and function, the recently cloned SLC3A1 amino acid transporter gene is a primary candidate gene for this disease.

Alendronate and atrial fibrillation: a meta-analysis of randomized placebo-controlled clinical trials.

UNLABELLED: In this meta-analysis of all Merck-conducted, placebo-controlled clinical trials of alendronate, the occurrence of AF was uncommon, with most studies reporting two or fewer events. Across all studies, no clear association between overall bisphosphonate exposure and the rate of serious or non-serious AF was observed. INTRODUCTION: To explore the incidence of atrial fibrillation (AF) and other cardiovascular endpoints in clinical trials of alendronate. METHODS: All double-blind, placebo-controlled studies of alendronate 5, 10, or 20 mg daily, 35 mg once-weekly, 35 mg twice-weekly, and 70 mg once-weekly of at least 3 months duration conducted by Merck were included in this meta-analysis. The primary method of analysis was exact Poisson regression. Estimated relative risk (RR) of alendronate versus placebo and the associated 95% confidence interval was derived from a model that included number of episodes with factors for treatment group and study and an offset parameter for number of person-years on study. RESULTS: Of 41 studies considered, 32 met all criteria for inclusion in the analysis (participants-9,518 alendronate, 7,773 placebo). Estimated RR for all AF events was 1.16 (95% CI = 0.87, 1.55; p = 0.33). Most trials had two or fewer AF events. The RR of AF classified as a serious adverse event was 1.25 (95% CI = 0.82, 1.93; p = 0.33), but became 0.97 (95% CI = 0.51, 1.85) when the clinical fracture cohort of the Fracture Intervention Trial was excluded, indicating that results were driven by events in that study. Estimated RRs for other cardiovascular endpoints were less than 1. CONCLUSIONS: The incidence of atrial fibrillation was low in Merck clinical trials of alendronate and was not significantly increased in any single trial nor in the meta-analysis. Based on this analysis, alendronate use does not appear to be associated with an increased risk of atrial fibrillation.

Treatment failure in osteoporosis.

UNLABELLED: Guidelines concerning the definition of failure of therapies used to reduce the risk of fracture are provided. INTRODUCTION: This study aims to provide guidelines concerning the definition of failure of therapies used to reduce the risk of fracture. METHODS: A working group of the Committee of Scientific Advisors of the International Osteoporosis Foundation was convened to define outcome variables that may assist clinicians in decision making. RESULTS: In the face of limited evidence, failure of treatment may be inferred when two or more incident fractures have occurred during treatment, when serial measurements of bone remodelling markers are not suppressed by anti-resorptive therapy and where bone mineral density continues to decrease. CONCLUSION: The provision of pragmatic criteria to define failure to respond to treatment provides an unmet clinical need and may stimulate research into an important issue.

Vitamin D3--resistant fibroblasts have immunoassayable 1,25-dihydroxyvitamin D3 receptors.

Cultured fibroblasts obtained from patients with tissue resistance to 1,25-dihydroxyvitamin D3 (vitamin D3--dependent rickets, type II) contain normal, low, or undetectable concentrations of this hormone's receptor protein as measured by a ligand-binding assay. Extracts from these cells were evaluated for receptors by immunoassay with a recently developed monoclonal antibody to the chick receptor. The results show that a protein sedimenting at 3.7S and recognizable by the antibody exists in comparable concentrations in cells from both normal and resistant patients, irrespective of the hormone-binding abnormalities of the cells. This implies that deficiencies in hormone binding associated with inherited tissue resistance to 1,25-dihydroxyvitamin D3 probably arise from structural variations in the receptor molecule and not from defective receptor synthesis.

MANAGEMENT OF ENDOCRINE DISEASE: Therapeutics of Vitamin D.

Objective: The central role of vitamin D in bone health is well recognized. However, controversies regarding its clinical application remain. We therefore aimed to review the definition of hypovitaminosis D, the skeletal and extra-skeletal effects of vitamin D and the available therapeutic modalities. Design: Narrative and systematic literature review. Methods: An international working group that reviewed the current evidence linking bone and extra-skeletal health and vitamin D therapy to identify knowledge gaps for future research. Results: Findings from observational studies and randomized controlled trials (RCTs) in vitamin D deficiency are discordant, with findings of RCTs being largely negative. This may be due to reverse causality with the illness itself contributing to low vitamin D levels. The results of many RCTs have also been inconsistent. However, overall evidence from RCTs shows vitamin D reduces fractures (when administered with calcium) in the institutionalized elderly. Although controversial, vitamin D reduces acute respiratory tract infections (if not given as bolus monthly or annual doses) and may reduce falls in those with the lowest serum 25-hydroxyvitamin D (25OHD) levels. However, despite large ongoing RCTs with 21 000­26 000 participants not recruiting based on baseline 25OHD levels, they will contain a large subset of participants with vitamin D deficiency and are adequately powered to meet their primary end-points. Conclusions: The effects of long-term vitamin D supplementation on non-skeletal outcomes, such as type 2 diabetes mellitus (T2DM), cancer and cardiovascular disease (CVD) and the optimal dose and serum 25OHD level that balances extra-skeletal benefits (T2DM) vs risks (e.g. CVD), may soon be determined by data from large RCTs.

Thyroid thermogenesis. Relationships between Na+-dependent respiration and Na+ + K+-adenosine triphosphatase activity in rat skeletal muscle.

The effect of thyroid status on QO2, QO2 (t) and NaK-ATPase activity was examined in rat skeletal muscle. QO2(t) (i.e. Na+-transport-dependent respiration) was estimated with ouabain or Na+-free media supplemented with K+. In contrast to the effects of ouabain on ion composition, intracellular K+ was maintained at about 125 meq/liter, and intracellular Na+ was almost nil in the Na+-free media. The estimates of QO2(t) were independent of the considerable differences in tissue ion concentrations. The increase in QO2(t) account for 47% of the increase in QO2 in the transition from the hypothyroid to the euthyroid state and 84% of the increase in the transition from the euthyroid to the hyperthyroid state. Surgical thyroidectomy lowered NaK-ATPase activity of the microsomal fraction (expressed per milligram protein) 32%; injections of triodothyronine (T3) increased this activity 75% in initially hypothyroid rats and 26% in initially euthyroid rats. Thyroidectomy was attended by significant falls in serum Ca and Pi concentrations. Administration of T3 resulted in further declines in serum Ca and marked increases in serum Ps concentrations. Similar effects were seen in 131I-treated rats, but the magnitude of the declines in serum Ca were less. The effects of T3 on QO2, QO2(t), and NaK-ATPase activity of skeletal muscle were indistinguishable in the 131I-ablated and surgically thyroidectomized rats. In thyroidectomized or euthyroid rats given repeated doses of T3, QO2(t) and NaA-ATPase activity increased proportionately. In thyroidectomized rats injected with single doses of T3, either 10, 50, or 250 mug/100 g body wt, QO2(t) increased linearly with NaK-ATPase activity. The kinetics of the NaK-ATPase activity was assessed with an ATP-generating system. T3 elicited a significant increase in Vmax with no change in Km for ATP.

Resistance to 1,25-dihydroxyvitamin D. Association with heterogeneous defects in cultured skin fibroblasts.

UNLABELLED: We evaluated the interaction of [3H]1,25(OH)2D3 with skin fibroblasts cultured from normal subjects or from affected members of six kindreds with rickets and resistance to 1-alpha, 25(OH)2D [1,25(OH)2D]. We analyzed two aspects of the radioligand interaction; nuclear uptake with dispersed, intact cells at 37 degrees C and binding at 0 degrees C with soluble extract ("cytosol") prepared from cells disrupted in buffer containing 300 mM KCl and 10 mM sodium molybdate. With normal fibroblasts the affinity and capacity of nuclear uptake of [3H]1,25(OH)2D3 were 0.5 nM and 10,300 sites per cell, respectively; for binding with cytosol these were 0.13 nM and 8,900 sites per cell, respectively. The following four patterns of interaction with [3H]1,25(OH)2D3 were observed with cells cultured from affected patients: (a) two kindreds; cytosol binding and whole-cell nuclear uptake both unmeasurable; (b) one kindred, decreased capacity and normal affinity both for binding in cytosol and for nuclear uptake in whole cells; (c) two kindreds, normal or nearly normal capacity and affinity of binding in cytosol but unmeasurable whole-cell nuclear uptake; and (d) one kindred, normal capacity and affinity of both cytosol binding and whole-cell nuclear uptake. In all cases where the radioligand bound with high affinity in nucleus or cytosol, the nucleus- or cytosol-associated radioligand exhibited normal sedimentation velocity on sucrose density gradients. When two kindreds exhibited similar patterns (i.e. pattern a or c) with the analyses of cultured fibroblasts, clinical features in affected members suggested that the underlying genetic defects were not identical. IN CONCLUSION: (a) Fibroblasts cultured from human skin manifest nuclear uptake and cytosol binding of [3H]1,25(OH)2D3 that is an expression of the genes determining these processes in target tissues. (b) Based upon data from clinical evaluations and from analyses of cultured fibroblasts, severe resistance to 1,25(OH)2D resulted from five or six distinct genetic mutations in six kindreds.

Selective expression of a normal action of the 1,25-dihydroxyvitamin D3 receptor in human skin fibroblasts with hereditary severe defects in multiple actions of that receptor.

We evaluated three actions of 1,25-dihydroxycholecalciferol [1,25-(OH)2D3] in human skin fibroblasts to test for heterogeneity in hormone-response coupling. In fibroblasts from normal subjects the 1,25-(OH)2D3 concentrations for half-maximal effect (EC50) were: for mitogenic effect 0.0001-0.0005 nM, for antimitogenic effect 1 nM, and for induction of 25-OHD3 24-hydroxylase (24-OHase) 5 nM. To evaluate the effects of mutations presumed to be in the gene for the 1,25-(OH)2D3 receptor we examined cell lines representing four kindreds with hereditary resistance to 1,25-(OH)2D3 ("mutant" cell lines). In one mutant cell line all three 1,25-(OH)2D3 actions were severely abnormal. In one mutant cell line 24-OHase induction and mitogenic action were undetectable, but EC50 and maximal effect were normal for antimitogenic action of 1,25-(OH)2D3. In two mutant cell lines 24-OHase induction and antimitogenic actions were undetectable or severely impaired but mitogenic action were undetectable or severely impaired but mitogenic action was normal in EC50 and normal or increased in maximal effect. The mitogenic and antimitogenic actions in normal cells showed a similar profile of potency ratios for 1,25-(OH)2D3 and six analogues. Whenever a mutant cell showed a normal or even an abnormal mitogenic or antimitogenic effect of 1,25-(OH)2D3, these effects showed potency ratios similar to wild type, suggesting mediation by a similar 1,25-(OH)2D3 receptor. We conclude that three 1,25-(OH)2D3 actions show important differences in hormone response coupling indicated by differences in EC50 for 1,25-(OH)2D3 and by different consequences of receptor mutations.

Defective binding and function of 1,25-dihydroxyvitamin D3 receptors in peripheral mononuclear cells of patients with end-organ resistance to 1,25-dihydroxyvitamin D.

Lectin-induced DNA synthesis by peripheral mononuclear cells from 17 normal donors was inhibited (40-60%) by 1,25-dihydroxyvitamin D3 (1,25[OH]2D3) at physiological concentrations (10(-10)-10(-9) M). The lymphocytes acquire specific receptors for 1,25(OH)2D3 upon activation by the lectins. This process precedes the inhibitory effect of 1,25(OH)2D3. We studied lymphocytes from six patients from four different kindreds with the syndrome of hereditary end-organ resistance to 1,25(OH)2D (the so-called vitamin D-dependent rickets type II). In five patients (three kindreds) peripheral blood mononuclear cells did not acquire receptors for 1,25(OH)2D3 upon phytohemagglutinin-induced activation. Moreover, in contrast to normal lymphocytes, the mitogenic stimulation of these patients' lymphocytes by phytohemagglutinin and concanavalin A was not inhibited by 1,25(OH)2D3. Activated lymphocytes of the sixth patient from a fourth kindred exhibited normal binding of [3H]1,25(OH)2D3 but the hormone failed to inhibit the mitogenic stimulation. A similar pattern of the vitamin D effector system was previously observed in fibroblasts cultured from skin biopsies of the same group of patients. The conclusions from these findings are: (a) the inhibition of mitogenic stimulation by 1,25(OH)2D3 is mediated by specific functional receptors to the hormone; and (b) the receptors for 1,25(OH)2D3 in mononuclear cells are probably controlled genetically by the same mechanisms as the effector system in well-characterized target organs of the hormone, such as intestine and kidney.

Vitamin D-dependent rickets type II. Defective induction of 25-hydroxyvitamin D3-24-hydroxylase by 1,25-dihydroxyvitamin D3 in cultured skin fibroblasts.

UNLABELLED: 1,25(OH)2D3 induces 25(OH)D3-24-hydroxylase (24-OHase) in cultured skin fibroblasts from normal subjects. We evaluated 24-OHase induction by 1,25(OH)2D3 in skin fibroblasts from 10 normal subjects and from four unrelated patients with hereditary resistance to 1,25(OH)2D or vitamin D-dependent rickets type II (DD II). Fibroblasts were preincubated with varying concentrations of 1,25(OH)2D3 for 15 h and were then incubated with 0.5 microM [3H]25(OH)D3 at 37 degrees C for 30 min; lipid extracts of the cells were analyzed for [3H]24,25(OH)2D3 by high performance liquid chromatography and periodate oxidation. Apparent maximal [3H]24,25(OH)2D3 production in normal cell lines was 9 pmol/10(6) cells per 30 min and occurred after induction with 10(-8) M 1,25(OH)2D3. 24-OHase induction was detectable in normal fibroblasts at approximately 3 X 10(-10) M 1,25(OH)2D3. [3H]24,25(OH)2D3 formation after exposure to 1,25(OH)2D3 was abnormal in fibroblasts from all four patients with DD II. In fibroblasts from two patients with DD II, [3H]24,25(OH)2D3 formation was unmeasurable (below 0.2 pmol/10(6) cells per 30 min) at 1,25(OH)2D3 concentrations up to 10(-6) M. Fibroblasts from the other two patients with DD II required far higher than normal concentrations of 1,25(OH)2D3 for detectable [3H]24,25(OH)2D3 induction. In one, [3H]24,25(OH)2D3 production reached 2.9 pmol/10(6) cells per 30 min at 10(-6) M 1,25(OH)2D3 (30% normal maximum at 10(-6) M 1,25(OH)2D3). In the other, [3H]24,25(OH)2D3 production achieved normal levels, 7.3 pmol/10(6) cells per 30 min after 10(-6) M 1,25(OH)2D3. The two patients whose cells had a detectable 24-OHase induction by 1,25(OH)2D3 showed a calcemic response to high doses of calciferols in vivo. Our current observations correlate with these two patients' responsiveness to calciferols in vivo and suggest that their target organ defects can be partially or completely overcome with extremely high concentrations of 1,25(OH)2D3. The two patients whose cells showed no detectable 24-OHase induction in vitro failed to show a calcemic response to high doses of calciferols in vivo. IN CONCLUSION: (a) the measurement of 24-OHase induction by 1,25(OH)2D3 in cultured skin fibroblasts is a sensitive in vitro test for defective genes in the 1,25(OH)2D effector pathway. (b) This assay provides a useful tool for characterizing the target tissue defects in DD II and predicting response to calciferol therapy.

Metabolic and calcium kinetic studies in idiopathic hypercalciuria.

Calcium balances and calcium kinetic studies using (47)Ca were performed in nine male patients with idiopathic hypercalciuria and in three normal male subjects. A sharp reduction in calcium intake in eight patients with idiopathic hypercalciuria caused a decrease in urinary calcium excretion, the latter remaining elevated above that reported for normal subjects on a low calcium diet. The hypercalciuric patients had an enlarged miscible calcium pool size, an increased calcium turnover rate, increased bone formation and bone resorption rates, and an elevated true intestinal calcium absorption rate, the increase of the latter three parameters being proportional to the increase of the turnover rate. The fraction of the calcium turnover rate excreted in the urine was elevated whereas that constituted by the endogenous fecal calcium excretion was decreased. Arguments are presented for the concept that the primary abnormality in idiopathic hypercalciuria is neither renal calcium hyperexcretion nor intestinal calcium hyperreabsorption, but a more fundamental disturbance in calcium metabolism of as yet unknown cause, leading to a high calcium turnover.

Vitamin D is a prooxidant in breast cancer cells.

The anticancer activity of the hormonal form of vitamin D, 1,25-dihydroxyvitamin D [1,25(OH)2D], is associated with inhibition of cell cycle progression, induction of differentiation, and apoptosis. In addition, 1,25(OH)2D3 augments the activity of anticancer agents that induce excessive reactive oxygen species generation in their target cells. This study aimed to find out whether 1,25(OH)2D3, acting as a single agent, is a prooxidant in cancer cells. The ratio between oxidized and reduced glulathione and the oxidation-dependent inactivation of glyceraldehyde-3phosphate dehydrogenase (GAPDH) are considered independent markers of cellular reactive oxygen species homeostasis and redox state. Treatment of MCF-7 breast cancer cells with 1,25(OH)2D3 (10-100 nM for 24-48 h) brought about a maximal increase of 41+/-13% (mean +/- SE) in the oxidized/reduced glutathione ratio without affecting total glutathione levels. The in situ activity of glutathione peroxidase and catalase were not affected by 1,25(OH)2D3, as assessed by the rate of H2O2 degradation by MCF-7 cell cultures. Neither did treatment with 1,25(OH)2D3 affect the levels of glutathione reductase or glutathione S-transferase as assayed in cell extracts. The hormone did not affect overall glutathione consumption and efflux as reflected in the rate of decline of total cellular glutathione after inhibition of its synthesis by buthionine sulfoximine. The extent of reversible oxidation-dependent inactivation of GAPDH in situ was determined by comparing the enzyme activity before and after reduction of cell extracts with DTT. The oxidized fraction was 0.13+/-0.02 of total GAPDH in control cultures and increased by 56+/-5.3% after treatment with 1,25(OH)2D3, which did not affect the total reduced enzyme activity. Treatment with 1,25(OH)2D3 resulted in a approximately 40% increase in glucose-6-phosphate dehydrogenase, the rate-limiting enzyme in the generation of NADPH. This enzyme is induced in response to various modes of oxidative challenge in mammalian cells. Taken together, these findings indicate that 1,25(OH)2D3 causes an increase in the overall cellular redox potential that could translate into modulation of redox-sensitive enzymes and transcription factors that regulate cell cycle progression, differentiation, and apoptosis.

1,25-Dihydroxyvitamin D3 enhances the susceptibility of breast cancer cells to doxorubicin-induced oxidative damage.

1,25-Dihydroxyvitamin D3 (1,25(OH)2D3), the hormonal form of vitamin D, has anticancer activity in vivo and in vitro. Doxorubicin exerts its cytotoxic effect on tumor cells mainly by two mechanisms: (a) generation of reactive oxygen species (ROS); and (b) inhibition of topoisomerase II. We studied the combined cytotoxic action of 1,25(OH)2D3 and doxorubicin on MCF-7 breast cancer cells. Pretreatement with 1,25(OH)2D3 resulted in enhanced cytotoxicity of doxorubicin. The average enhancing effect after a 72-h pretreatment with 1,25(OH)2D3 (10 nM) followed by a 24-h treatment with 1 microg/ml doxorubicin was 74+/-9% (mean +/- SE). Under these experimental conditions, 1,25(OH)2D3 on its own did not affect cell number or viability. 1,25(OH)2D3 also enhanced the cytotoxic activity of another ROS generating quinone, menadione, but did not affect cytotoxicity induced by the topoisomerase inhibitor etoposide. The antioxidant N-acetylcysteine slightly reduced the cytotoxic activity of doxorubicin but had a marked protective effect against the combined action of 1,25(OH)2D3 and doxorubicin. These results indicate that ROS are involved in the interaction between 1,25(OH)2D3 and doxorubicin. 1,25(OH)2D3 also increased doxorubicin cytotoxicity in primary cultures of rat cardiomyocytes. Treatment of MCF-7 cells with 1,25(OH)2D3 alone markedly reduced the activity, protein, and mRNA levels of the cytoplasmic antioxidant enzyme Cu/Zn superoxide dismutase, which indicated that the hormone inhibits its biosynthesis. This reduction in the antioxidant capacity of the cells could account for the synergistic interaction between 1,25(OH)2D3 and doxorubicin and may also suggest increased efficacy of 1,25(OH)2D3 or its analogues in combination with other ROS-generating anticancer therapeutic modalities.

Stimulatory and inhibitory effects of 1,25-dihydroxyvitamin D3 on thymocyte mitogenesis induced by phorbol ester and calcium ionophore.

UNLABELLED: Mouse medullary thymocytes have specific receptors for 1,25-dihydroxyvitamin D3 (1,25(OH)2D3). The mitogenic stimulation of these cells by phytohemagglutinin in the presence or absence of the phorbol ester TPA is inhibited by 1,25(OH)2D3. The calcium ionophore A23187 did not reverse the inhibition by 1,25(OH)2D3 of phytohemagglutinin. Stimulation of thymocytes with either TPA or A23187 alone did not result in proliferation. Co-stimulation of the thymocytes with TPA and A23187 induces cell proliferation. 1,25(OH)2D3 markedly enhanced the TPA and A23187-induced cell proliferation even when added 4 h after the initiation of the culture. In contrast, DNA synthesis by thymocytes incubated for 4 h in the presence of TPA and A23187 and then cultured in medium containing 1,25(OH)2D3 but in the absence of both TPA and A23187, was inhibited by 1,25(OH)2D3. The extent of inhibition was comparable to the inhibition of lectin-induced stimulation by the hormone. Using monoclonal antibodies to neutralize IL-2 and block IL-2 receptors we showed that 1,25(OH)2D3 enhanced the IL-2-independent component of the A23187- and TPA-induced mitogenesis. IN CONCLUSION: (1) The nature and presence of the mitogenic signal determines whether 1,25(OH)2D3 enhances or inhibits thymocyte stimulation. (2) Both stimulatory and inhibitory actions of 1,25(OH)2D3 seem to take place at points distal to the initial increase in intracellular calcium or activation of protein kinase C.

Central equilibria in multilocus systems. I. Generalized nonepistatic selection regimes.

The generalized nonepistatic selection regime encompasses combinations of multiplicative and neutral viability effects distributed across a set of loci. These subsume, in particular, mixtures of the classical modes of multiplicative and additive fitness evaluations for multilocus traits. Exact analytic conditions for existence and stability of a multilocus Hardy-Weinberg (H-W) polymorphic equilibrium configuration are ascertained. It is established that the central H-W polymorphism is stable only if the component loci are "over-dominant" and sufficient recombination is in force. The H-W central equilibrium is never stable for tight linkage whenever some multiplicative selection effects are contributed by at least two of the loci involved. In the case of additive selection expression and individual overdominant loci, the H-W polymorphism is stable independently of the level of recombination. In the context of "natural" recombination schemes, "more recombination" enhances the stability of the H-W polymorphic equilibrium.

Central Equilibria in Multilocus Systems. II. Bisexual Generalized Nonepistatic Selection Models.

This paper is a continuation of the paper "Central Equilibria in Multilocus Systems I," concentrating on existence and stability properties accruing to central H-W type equilibria in multilocus bisexual systems acted on by generalized nonepistatic selection forces coupled to recombination events. The stability conditions are discussed and interpreted in three perspectives, and the influence of sexual differences in linkage relationships together with sex-dependent selection is appraised. In this case we deduce that the stability conditions of the H-W polymorphism in the bisexual model coincide exactly with the conditions for the corresponding monoecious model, provided that the recombination distribution imposed is that of the arithmetic mean of the male and female recombination distributions. A second concern has the same recombination distribution for both sexes, but contrasting selection regimes between sexes. It is then established that, with respect to discerning the relevance of the H-W equilibrium, there is an equivalent monoecious selection regime which is an appropriate "weighted combination" of the male and female selection forms. Finally, in the case where the selection and recombination structures are both sex dependent, a hierarchy of comparisons is elaborated, seeking to unravel the nature of selection-recombination interaction for monoecious versus diocecious systems.

A symmetric two-locus fertility model.

A model in which selection is mediated by differential fertilities among the genotypes at two diallelic loci is proposed. Fertility depends only on the number of heterozygous loci participating in the mating. Classes analogous to symmetric equilibria in symmetric viability models are determined explicitly and shown to exhibit stability behavior very different from the viability results. Linkage equilibrium is shown to occur in a relatively asymmetric fashion and to overlap in stability with linkage disequilibrium. In many cases single-locus or two-locus polymorphism is shown to be stable simultaneously with chromosome fixation even under very tight linkage. It is suggested that historical effects may be of great significance in the evolution of systems in which fertility is the primary agent of natural selection.

On some models of fertility selection.

Additive, multiplicative and symmetric models of fertility controlled by one diallelic gene are studied. For the completely symmetric fertility system a complete equilibrium and local stability analysis is possible. Contrary to previous conjectures, asymmetric equilibria can be stable. Conditions are derived under which a multiplicative model can be regarded as equivalent to a symmetric fertility system.