Cdc42 localized in the CatSper signaling complex regulates cAMP-dependent pathways in mouse sperm.

Sperm acquire the ability to fertilize in a process called capacitation and undergo hyperactivation, a change in the motility pattern, which depends on Ca2+ transport by CatSper channels. CatSper is essential for fertilization and it is subjected to a complex regulation that is not fully understood. Here, we report that similar to CatSper, Cdc42 distribution in the principal piece is confined to four linear domains and this localization is disrupted in CatSper1-null sperm. Cdc42 inhibition impaired CatSper activity and other Ca2+ -dependent downstream events resulting in a severe compromise of the sperm fertilizing potential. We also demonstrate that Cdc42 is essential for CatSper function by modulating cAMP production by soluble adenylate cyclase (sAC), providing a new regulatory mechanism for the stimulation of CatSper by the cAMP-dependent pathway. These results reveal a broad mechanistic insight into the regulation of Ca2+ in mammalian sperm, a matter of critical importance in male infertility as well as in contraception.

Everything you ever wanted to know about PKA regulation and its involvement in mammalian sperm capacitation.

The 3', 5'-cyclic adenosine monophosphate (cAMP) dependent protein kinase (PKA) is a tetrameric holoenzyme comprising a set of two regulatory subunits (PKA-R) and two catalytic (PKA-C) subunits. The PKA-R subunits act as sensors of cAMP and allow PKA-C activity. One of the first signaling events observed during mammalian sperm capacitation is PKA activation. Thus, understanding how PKA activity is restricted in space and time is crucial to decipher the critical steps of sperm capacitation. It is widely accepted that PKA specificity depends on several levels of regulation. Anchoring proteins play a pivotal role in achieving proper localization signaling, subcellular targeting and cAMP microdomains. These multi-factorial regulation steps are necessary for a precise spatio-temporal activation of PKA. Here we discuss recent understanding of regulatory mechanisms of PKA in mammalian sperm, such as post-translational modifications, in the context of its role as the master orchestrator of molecular events conducive to capacitation.

Corrigendum to "Angiogenesis in Pituitary Adenomas: Human Studies and New Mutant Mouse Models".

[This corrects the article DOI: 10.1155/2014/608497.].

Chronic high prolactin levels impact on gene expression at discrete hypothalamic nuclei involved in food intake.

To study the pathological effects of continuous hyperprolactinemia on food intake mechanisms we used female mice that lack dopamine D2 receptors in lactotropes (lacDrd2KO). These mice had lifelong hyperprolactinemia, increased food intake, and gradual development of obesity from 5 to 10 months of age. Ongoing endogenous prolactin signaling in lacDrd2KO mice was evidenced by increased basal phosphorylation of STAT5b in hypothalamic areas related to food intake, such as the arcuate (ARN), dorsomedial (DMN), and ventromedial nuclei. In the ARN of young lacDrd2KO mice there were higher Prlr mRNA levels and in obese 10-month-old lacDrd2KO mice increased expression of the orexigenic genes Neuropeptide Y (Npy) and Agouti-related peptide, compared to controls. Furthermore, Npy expression was increased in the DMN, probably contributing to increased food intake and decreased expression of Uncoupling protein-1 in brown adipose tissue, both events favoring weight gain. Leptin resistance in obese lacD2RKO mice was evidenced by its failure to lower food intake and a dampened response of STAT3 phosphorylation, specifically in the mediobasal hypothalamus. Our results suggest that pathological chronically high prolactin levels, as found in psychiatric treatments or patients with prolactinomas, may impact on specific hypothalamic nuclei altering gene expression, leptin response, and food intake.

CFTR/ENaC-dependent regulation of membrane potential during human sperm capacitation is initiated by bicarbonate uptake through NBC.

To fertilize an egg, sperm must reside in the female reproductive tract to undergo several maturational changes that are collectively referred to as capacitation. From a molecular point of view, the HCO3--dependent activation of the atypical soluble adenylyl cyclase (ADCY10) is one of the first events that occurs during capacitation and leads to the subsequent cAMP-dependent activation of protein kinase A (PKA). Capacitation is also accompanied by hyperpolarization of the sperm plasma membrane. We previously reported that PKA activation is necessary for CFTR (cystic fibrosis transmembrane conductance regulator channel) activity and for the modulation of membrane potential (Em). However, the main HCO3- transporters involved in the initial transport and the PKA-dependent Em changes are not well known nor characterized. Here, we analyzed how the activity of CFTR regulates Em during capacitation and examined its relationship with an electrogenic Na+/HCO3- cotransporter (NBC) and epithelial Na+ channels (ENaCs). We observed that inhibition of both CFTR and NBC decreased HCO3- influx, resulting in lower PKA activity, and that events downstream of the cAMP activation of PKA are essential for the regulation of Em. Addition of a permeable cAMP analog partially rescued the inhibitory effects caused by these inhibitors. HCO3- also produced a rapid membrane hyperpolarization mediated by ENaC channels, which contribute to the regulation of Em during capacitation. Altogether, we demonstrate for the first time, that NBC cotransporters and ENaC channels are essential in the CFTR-dependent activation of the cAMP/PKA signaling pathway and Em regulation during human sperm capacitation.

Disruption of protein kinase A localization induces acrosomal exocytosis in capacitated mouse sperm.

Protein kinase A (PKA) is a broad-spectrum Ser/Thr kinase involved in the regulation of several cellular activities. Thus, its precise activation relies on being localized at specific subcellular places known as discrete PKA signalosomes. A-Kinase anchoring proteins (AKAPs) form scaffolding assemblies that play a pivotal role in PKA regulation by restricting its activity to specific microdomains. Because one of the first signaling events observed during mammalian sperm capacitation is PKA activation, understanding how PKA activity is restricted in space and time is crucial to decipher the critical steps of sperm capacitation. Here, we demonstrate that the anchoring of PKA to AKAP is not only necessary but also actively regulated during sperm capacitation. However, we find that once capacitated, the release of PKA from AKAP promotes a sudden Ca2+ influx through the sperm-specific Ca2+ channel CatSper, starting a tail-to-head Ca2+ propagation that triggers the acrosome reaction. Three-dimensional super-resolution imaging confirmed a redistribution of PKA within the flagellar structure throughout the capacitation process, which depends on anchoring to AKAP. These results represent a new signaling event that involves CatSper Ca2+ channels in the acrosome reaction, sensitive to PKA stimulation upon release from AKAP.

Notch system is differentially expressed and activated in pituitary adenomas of distinct histotype, tumor cell lines and normal pituitaries.

Pituitary adenomas are among the most frequent intracranial neoplasms and treatment depends on tumor subtype and clinical features. Unfortunately, non responder cases occur, then new molecular targets are needed. Notch system component expression and activation data are scarce in pituitary tumorigenesis, we therefore aimed to characterize Notch system in pituitary tumors of different histotype. In human pituitary adenomas we showed NOTCH1-4 receptors, JAGGED1 ligand and HES1 target gene expression with positive correlations between NOTCH1,2,4 and HES1, and NOTCH3 and JAGGED1 denoting Notch system activation in a subset of tumors. Importantly, NOTCH3 positive cells were higher in corticotropinomas and somatotropinomas compared to non functioning adenomas. In accordance, Notch activation was evidenced in AtT20 tumor corticotropes, with higher levels of NOTCH1-3 active domains, Jagged1 and Hes1 compared to normal pituitary. In the prolactinoma cell lines GH3 and MMQ, in vivo GH3 tumors and normal glands, Notch system activation was lower than in corticotropes. In MMQ cells only the NOTCH2 active domain was increased, whereas NOTCH1 active domain was higher in GH3 tumors. High levels of Jagged1 and Dll1 were found solely in GH3 cells, and Hes1, Hey1 and Hey2 were expressed in a model dependent pattern. Prolactinomas harbored by lacDrd2KO mice expressed high levels of NOTCH1 active domain and reduced Hes1. We show a differential expression of Notch system components in tumoral and normal pituitaries and specific Notch system involvement depending on adenoma histotype, with higher activation in corticotropinomas. These data suggest that targeting Notch pathway may benefit non responder pituitary adenomas.

Chronic hyperprolactinemia evoked by disruption of lactotrope dopamine D2 receptors impacts on liver and adipocyte genes related to glucose and insulin balance.

We studied the impact of high prolactin titers on liver and adipocyte gene expression related to glucose and insulin homeostasis in correlation with obesity onset. To that end we used mutant female mice that selectively lack dopamine type 2 receptors (D2Rs) from pituitary lactotropes (lacDrd2KO), which have chronic high prolactin levels associated with increased body weight, marked increments in fat depots, adipocyte size, and serum lipids, and a metabolic phenotype that intensifies with age. LacDrd2KO mice of two developmental ages, 5 and 10 mo, were used. In the first time point, obesity and increased body weight are marginal, although mice are hyperprolactinemic, whereas at 10 mo there is marked adiposity with a 136% increase in gonadal fat and a 36% increase in liver weight due to lipid accumulation. LacDrd2KO mice had glucose intolerance, hyperinsulinemia, and impaired insulin response to glucose already in the early stages of obesity, but changes in liver and adipose tissue transcription factors were time and tissue dependent. In chronic hyperprolactinemic mice liver Prlr were upregulated, there was liver steatosis, altered expression of the lipogenic transcription factor Chrebp, and blunted response of Srebp-1c to refeeding at 5 mo of age, whereas no effect was observed in the glycogenesis pathway. On the other hand, in adipose tissue a marked decrease in lipogenic transcription factor expression was observed when morbid obesity was already settled. These adaptive changes underscore the role of prolactin signaling in different tissues to promote energy storage.

Role of Actin Cytoskeleton During Mammalian Sperm Acrosomal Exocytosis.

Mammalian sperm require to undergo an exocytotic process called acrosomal exocytosis in order to be able to fuse with the oocyte. This ability is acquired during the course of sperm capacitation. This review is focused on one aspect related to this acquisition: the role of the actin cytoskeleton. Evidence from different laboratories indicates that actin polymerization occurs during capacitation, and the detection of several actin-related proteins suggests that the cytoskeleton is involved in important sperm functions. In other mammalian cells, the cortical actin network acts as a dominant negative clamp which blocks constitutive exocytosis but, at the same time, is necessary to prepare the cell to undergo regulated exocytosis. Thus, F-actin stabilizes structures generated by exocytosis and supports the physiological progression of this process. Is this also the case in mammalian sperm? This review summarizes what is currently known about actin and its related proteins in the male gamete, with particular emphasis on their role in acrosomal exocytosis.

Dopaminergic drugs in type 2 diabetes and glucose homeostasis.

The importance of dopamine in central nervous system function is well known, but its effects on glucose homeostasis and pancreatic ß cell function are beginning to be unraveled. Mutant mice lacking dopamine type 2 receptors (D2R) are glucose intolerant and have abnormal insulin secretion. In humans, administration of neuroleptic drugs, which block dopamine receptors, may cause hyperinsulinemia, increased weight gain and glucose intolerance. Conversely, treatment with the dopamine precursor l-DOPA in patients with Parkinson's disease reduces insulin secretion upon oral glucose tolerance test, and bromocriptine improves glycemic control and glucose tolerance in obese type 2 diabetic patients as well as in non diabetic obese animals and humans. The actions of dopamine on glucose homeostasis and food intake impact both the autonomic nervous system and the endocrine system. Different central actions of the dopamine system may mediate its metabolic effects such as: (i) regulation of hypothalamic noradrenaline output, (ii) participation in appetite control, and (iii) maintenance of the biological clock in the suprachiasmatic nucleus. On the other hand, dopamine inhibits prolactin, which has metabolic functions; and, at the pancreatic beta cell dopamine D2 receptors inhibit insulin secretion. We review the evidence obtained in animal models and clinical studies that posited dopamine receptors as key elements in glucose homeostasis and ultimately led to the FDA approval of bromocriptine in adults with type 2 diabetes to improve glycemic control. Furthermore, we discuss the metabolic consequences of treatment with neuroleptics which target the D2R, that should be monitored in psychiatric patients to prevent the development in diabetes, weight gain, and hypertriglyceridemia.

PKA-dependent phosphorylation of LIMK1 and Cofilin is essential for mouse sperm acrosomal exocytosis.

Mammalian sperm must acquire their fertilizing ability after a series of biochemical modifications in the female reproductive tract collectively called capacitation to undergo acrosomal exocytosis, a process that is essential for fertilization. Actin dynamics play a central role in controlling the process of exocytosis in somatic cells as well as in sperm from several mammalian species. In somatic cells, small GTPases of the Rho family are widely known as master regulators of actin dynamics. However, the role of these proteins in sperm has not been studied in detail. In the present work we characterized the participation of small GTPases of the Rho family in the signaling pathway that leads to actin polymerization during mouse sperm capacitation. We observed that most of the proteins of this signaling cascade and their effector proteins are expressed in mouse sperm. The activation of the signaling pathways of cAMP/PKA, RhoA/C and Rac1 is essential for LIMK1 activation by phosphorylation on Threonine 508. Serine 3 of Cofilin is phosphorylated by LIMK1 during capacitation in a transiently manner. Inhibition of LIMK1 by specific inhibitors (BMS-3) resulted in lower levels of actin polymerization during capacitation and a dramatic decrease in the percentage of sperm that undergo acrosomal exocytosis. Thus, we demonstrated for the first time that the master regulators of actin dynamics in somatic cells are present and active in mouse sperm. Combining the results of our present study with other results from the literature, we have proposed a working model regarding how LIMK1 and Cofilin control acrosomal exocytosis in mouse sperm.

Pituitary and brain dopamine D2 receptors regulate liver gene sexual dimorphism.

Liver sexual gene dimorphism, which depends mainly on specific patterns of GH secretion, may underlie differential susceptibility to some liver diseases. Because GH and prolactin secretion are regulated by dopaminergic pathways, we studied the participation of brain and lactotrope dopamine 2 receptors (D2Rs) on liver gene sexual dimorphism, to explore a link between the brain and liver gene expression. We used global D2R knockout mice (Drd2(-/-)) and conducted a functional dissection strategy based on cell-specific Drd2 inactivation in neurons (neuroDrd2KO) or pituitary lactotropes. Disruption of neuronal D2Rs (which impaired the GH axis) decreased most of male or female-predominant class I liver genes and increased female-predominant class II genes in males, consistent with the positive (class I) or negative (class II) regulation of these genes by GH. Notably, sexual dimorphism was lost for class I and II genes in neuroDrd2KO mice. Disruption of lactotrope D2Rs did not modify class I or II genes in either sex, because GH axis was preserved. But surprisingly, 1 class II gene (Prlr) and female-predominant class I genes were markedly up-regulated in lacDrd2KO females, pointing to direct or indirect effects of prolactin in the regulation of selected female-predominant liver genes. This suggestion was strengthened in the hyperprolactinemic Drd2(-/-) female mouse, in which increased expression of the same 4 liver genes was observed, despite a decreased GH axis. We hereby demonstrate endocrine-mediated D2R actions on sexual dimorphic liver gene expression, which may be relevant during chronic dopaminergic medications in psychiatric disease.

Angiogenesis in pituitary adenomas: human studies and new mutant mouse models.

The role of angiogenesis in pituitary tumor development has been questioned, as pituitary tumors have been usually found to be less vascularized than the normal pituitary tissue. Nevertheless, a significantly higher degree of vasculature has been shown in invasive or macropituitary prolactinomas when compared to noninvasive and microprolactinomas. Many growth factors and their receptors are involved in pituitary tumor development. For example, VEGF, FGF-2, FGFR1, and PTTG, which give a particular vascular phenotype, are modified in human and experimental pituitary adenomas of different histotypes. In particular, vascular endothelial growth factor, VEGF, the central mediator of angiogenesis in endocrine glands, was encountered in experimental and human pituitary tumors at different levels of expression and, in particular, was higher in dopamine agonist resistant prolactinomas. Furthermore, several anti-VEGF techniques lowered tumor burden in human and experimental pituitary adenomas. Therefore, even though the role of angiogenesis in pituitary adenomas is contentious, VEGF, making permeable pituitary endothelia, might contribute to adequate temporal vascular supply and mechanisms other than endothelial cell proliferation. The study of angiogenic factor expression in aggressive prolactinomas with resistance to dopamine agonists will yield important data in the search of therapeutical alternatives.

Novel, low cost, highly effective, handmade steroid pellets for experimental studies.

The basic component of Silastic® glue (Dow Corning) used to prepare Silastic® pellets is polydimethylsiloxane. This compound is also present in other commercial adhesives such as FASTIX® (Akapol SA) that are available in any store for that category. In the present study we developed low cost, easy to prepare handmade steroid pellets (HMSP) by mixing 17ß-estradiol, progesterone or other synthetic steroids with FASTIX® adhesive. We assessed serum levels of 17ß-estradiol, progesterone, prolactin and luteinizing hormone in ovariectomized mice treated for 24 and 48 h or 7, 14 and 28 days with 20 µg or 5 mg of 17ß-estradiol or 5 mg progesterone HMSP. We found a time dependent and significant increase in the levels of both natural hormones, and a downregulation of serum luteinizing hormone levels, while both 17ß-estradiol doses increased serum prolactin. Uterine weights at sacrifice and histological examination of the uteri and the mammary glands correlated with estrogen or progestin action. Finally, we evaluated the biological effects of HMSP compared to commercial pellets or daily injections in the stimulation or inhibition of hormone dependent mammary tumor growth, and found that HMSP were as effective as the other methods of hormone administration. These data show that HMSP represent a useful, low cost, easily accessible method for administering steroids to mice.

Central dopamine D2 receptors regulate growth-hormone-dependent body growth and pheromone signaling to conspecific males.

Competition between adult males for limited resources such as food and receptive females is shaped by the male pattern of pituitary growth hormone (GH) secretion that determines body size and the production of urinary pheromones involved in male-to-male aggression. In the brain, dopamine (DA) provides incentive salience to stimuli that predict the availability of food and sexual partners. Although the importance of the GH axis and central DA neurotransmission in social dominance and fitness is clearly appreciated, the two systems have always been studied unconnectedly. Here we conducted a cell-specific genetic dissection study in conditional mutant mice that selectively lack DA D2 receptors (D2R) from pituitary lactotropes (lacDrd2KO) or neurons (neuroDrd2KO). Whereas lacDrd2KO mice developed a normal GH axis, neuroDrd2KO mice displayed fewer somatotropes; reduced hypothalamic Ghrh expression, pituitary GH content, and serum IGF-I levels; and exhibited reduced body size and weight. As a consequence of a GH axis deficit, neuroDrd2KO adult males excreted low levels of major urinary proteins and their urine failed to promote aggression and territorial behavior in control male challengers, in contrast to the urine taken from control adult males. These findings reveal that central D2Rs mediate a neuroendocrine-exocrine cascade that controls the maturation of the GH axis and downstream signals that are critical for fitness, social dominance, and competition between adult males.

Enhanced nestin expression and small blood vessels in human pituitary adenomas.

The role of angiogenesis in human pituitary tumor progression is questioned. Our aim was to characterize the morphologic changes that occur in the vasculature of pituitary adenomas, in correlation with the expression of nestin, a protein found in endothelial cells of newly formed vessels of developing organs. We also evaluated the relation of angiogenic markers and nestin with Ki-67 index. Immunohistochemical studies were performed on paraffin embedded samples of 47 pituitary adenomas and six normal pituitaries. We determined microvessel density (number of CD31+ or CD34+ vessels per square millimetre), vascular area (cumulative area occupied by vessels), average vessel size, and further classified vessels as small (< 100 µm2) or large (> 100 µm2). We correlated the above parameters with nestin expression and Ki-67 index. Lower vascular area compared to normal tissue was found in adenomas (p < 0.05). Interestingly, pituitary adenomas had significantly more small vessels than control pituitaries (p < 0.04 for CD31 and CD34). In tumors many capillaries were positive for nestin, while scarce staining was detected in controls, so that nestin positive area was significantly higher in tumors. Furthermore, nestin area correlated positively with the % of small vessels. Ki-67 correlated neither with vascular area nor with nestin expression. In human pituitary tumors there was a predominance of small capillaries in correlation with increased expression of the progenitor marker nestin. We suggest that angiogenesis is an active process in these tumors, in spite of their low total vascular area when compared to normal pituitaries.

Inhibitory effects of antivascular endothelial growth factor strategies in experimental dopamine-resistant prolactinomas.

Prolactin-secreting adenomas are the most frequent type among pituitary tumors, and pharmacological therapy with dopamine agonists remains the mainstay of treatment. But some adenomas are resistant, and a decrease in the number or function of dopamine D2 receptors (D2Rs) has been described in these cases. D2R knockout [Drd2(-/-)] mice have chronic hyperprolactinemia and pituitary hyperplasia and provide an experimental model for dopamine agonist-resistant prolactinomas. We described previously that disruption of D2Rs increases vascular endothelial growth factor (VEGF) expression. We therefore designed two strategies of antiangiogenesis using prolactinomas generated in Drd2(-/-) female mice: direct intra-adenoma mVEGF R1 (Flt-1)/Fc chimera (VEGF-TRAP) injection for 3 weeks [into subcutaneously transplanted pituitaries from Drd2(-/-) mice] and systemic VEGF neutralization with the specific monoclonal antibody G6-31. Both strategies resulted in substantial decrease of prolactin content and lactotrope area, and a reduction in tumor size was observed in in situ prolactinomas. There were significant decreases in vascularity, evaluated by cluster of differentiation molecule 31 vessel staining, and proliferation (proliferating cell nuclear antigen staining) in response to both anti-VEGF treatments. These data demonstrate that the antiangiogenic approach was effective in inhibiting the growth of in situ dopamine-resistant prolactinomas as well as in the transplanted adenomas. No differences in VEGF protein expression were observed after either anti-VEGF treatment, and, although serum VEGF was increased in G6-31-treated mice, pituitary activation of the VEGF receptor 2 signaling pathway was reduced. Our results indicate that, even though the role of angiogenesis in pituitary adenomas is contentious, VEGF might contribute to adequate vascular supply and represent a supplementary therapeutic target in dopamine agonist-resistant prolactinomas.

New insights into the endocrine and metabolic roles of dopamine D2 receptors gained from the Drd2 mouse.

Dopamine D2 receptor (D2R) participation in prolactin regulation is well documented, but the role of D2Rs in the control of other hormones involved in growth, food intake and glucose metabolism has not been extensively studied. The study of D2R knockout mice (Drd2(-/-)) puts forward new insights into the role of the D2R in growth hormone (GH)-releasing hormone-GH regulation, peptides involved in food intake, glucose homeostasis, as well as in prolactinoma development. The expected phenotype of chronic hyperprolactinemia and prolactinoma development was found in the Drd2(-/-) mouse, and this model constitutes a valuable tool in the study of dopamine-resistant prolactinomas. Unexpectedly, these mice were growth retarded, and the importance of functional hypothalamic D2Rs in the neonatal period was revealed. In the Drd2(-/-) mouse there was a failure of high neonatal GH levels and therefore the expansion of pituitary somatotropes was permanently altered. These mice also had increased food intake, and a sexually dimorphic participation of the D2R in food intake regulation is suggested. The effect described is probably secondary to D2R regulation of prolactin secretion. Furthermore, the negative modulation of D2Rs on α-melanocyte-stimulating hormone release and positive action on the hypothalamic expression of orexins reveals the complex D2R regulation of food intake. Finally, pancreatic D2Rs inhibit glucose-stimulated insulin release. Lack of dopaminergic inhibition throughout development in the Drd2(-/-) mouse may exert a gradual deteriorating effect on insulin homeostasis, so that eventually glucose intolerance develops. These results highlight the complex endocrine actions of the D2Rs at different levels, hypothalamus, pituitary or pancreas, which function to improve fitness, reproductive success and survival.

VEGF and CD31 association in pituitary adenomas.

Pituitary tumors are usually less vascularized than the normal pituitary, and the role of angiogenesis in these adenomas is contentious. Appraisal of microvascular density and expression of the potent angiogenic vascular endothelial growth factor (VEGF) by immunohistochemistry has yielded controversial results, as a broad spectrum of immunostaining can be found. We determined the protein expression of VEGF and CD31, an endothelial marker, in a series of 56 surgically removed pituitary adenomas using Western blot assay. Prolactinomas had higher VEGF protein expression compared to nonfunctioning or ACTH- and GH-secreting adenomas, while CD31 was similar in the different adenoma histotypes. VEGF and CD31 were not affected by sex, age, years of adenoma evolution, or proliferation rate (Ki67 and PCNA) for all adenoma types. Only in nonfunctioning adenomas CD31 concentration increased significantly with age. There was a positive correlation between CD31 and VEGF expression when all adenoma histotypes were considered, or when prolactinomas and nonfunctioning adenomas were evaluated separately. The positive association of VEGF and CD31 expression suggests the participation of angiogenesis in adenoma development, while epithelial cell proliferation in pituitary tumors is not directly related to VEGF or CD31 expression, and other factors, such as primary genetic alterations may be involved.