Involutions In Groups Research Articles

Sixfolds of generalized Kummer type and K3 surfaces

We prove that any hyper-Kähler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm {K}3^{[3]}$ type. It is obtained as crepant resolution of the quotient of $K$ by a group of symplectic involutions acting trivially on its second cohomology. When $K$ is projective, the variety $Y_K$ is birational to a moduli space of stable sheaves on a uniquely determined projective $\mathrm {K}3$ surface $S_K$. As an application of this construction we show that the Kuga–Satake correspondence is algebraic for the K3 surfaces $S_K$, producing infinitely many new families of $\mathrm {K}3$ surfaces of general Picard rank $16$ satisfying the Kuga–Satake Hodge conjecture.

On Yang-Baxter groups

A group is said to be an involutive Yang-Baxter group, or simply an IYB-group, if it is isomorphic to the permutation group of an involutive, non-degenerate set-theoretic solution of the Yang-Baxter equation. In this paper, Yang-Baxter groups (YB-groups for short) associated with not necessarily involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation are introduced and studied. Sufficient conditions for a group that can be factorised as a product of two YB-groups to be a YB-group are provided. Some earlier results for finite IYB-groups are also generalised for arbitrary (non-necessarily finite) YB-groups as a consequence of our main theorem.

Identification and validation of key miRNAs and miRNA-mRNA regulatory network associated with uterine involution in postpartum Kazakh sheep.

MicroRNAs (miRNAs) are widely expressed in different mammalian tissues and exert their biological effects through corresponding target genes. miRNA target genes can be rapidly and efficiently identified and screened by combining bioinformatics prediction and experimental validation. To investigate the possible molecular regulatory mechanisms involving miRNAs during uterine involution in postpartum ewes, we used Illumina HiSeq sequencing technology to screen for the number and characteristics of miRNAs in faster uterine involution and normal uterine involution group. A total of 118 differentially expressed miRNAs, including 33 known miRNAs and 85 new miRNAs, were identified in the hypothalamic library, whereas 54 miRNAs, including 5 known miRNAs and 49 new miRNAs, were identified in the uterine library. Screening with four types of gene prediction software revealed 73 target genes associated with uterine involution, and subsequently, GO annotation and KEGG pathway analysis were performed. The results showed that, in the hypothalamic–uterine axis, uterine involution in postpartum ewes might primarily involve two miRNA-target gene pairs, namely, miRNA-200a–PTEN and miRNA-133–FGFR1, which can participate in GnRH signal transduction in the upstream hypothalamus and in the remodeling process at the downstream uterus, through the PI3K–AKT signaling pathway to influence the recovery of the morphology and functions of the uterus during the postpartum period in sheep. Therefore, identification of differentially expressed miRNAs in this study fills a gap in the research related to miRNAs in uterine involution in postpartum ewes and provides an important reference point for a comprehensive understanding of the molecular mechanisms underlying the regulation of postpartum uterine involution in female livestock.

Abstract LT004: Immune suppression established by postpartum liver involution promotes liver metastasis

Abstract A postpartum diagnosis of breast cancer in women ≤45 yoa is an independent predictor of liver metastasis, suggesting a liver metastatic advantage (PMID: 27974414). In rodents, we identified a postpartum liver biology that supports liver metastasis in mouse models. This biology is weaning-induced liver involution and is characterized by a transient period of hepatocyte cell death, catabolic metabolism, immune influx, and stromal remodeling (PMID: 27974414). Here, we sought to investigate the mechanism by which post-wean liver involution supports breast cancer metastasis. Liver metastases were induced by portal vein injection of mouse mammary tumor cells into nulliparous or post-wean, involution hosts (PMID: 28060292). Compared to nulliparous mice, involution mice had increased incidence of liver metastasis, as well as more liver lesions per mouse. However, there was no group differences in tumor size or proliferation index. These data are consistent with the involution liver providing an environment that promotes tumor cell establishment, not proliferation. To further investigate, we intraportally injected GFP-tagged tumor cells into GFP-tolerant mice, and assessed tumor cell abundance in the liver at 90 minutes, and 1, 3, and 14 days post injection. Contrary to our expectations, the nulliparous group had more tumor cells present at 90 minutes, 1 day, and 3 days post tumor cell injection. We saw the metastatic advantage in the involution group emerge by 14 days after tumor cell injection. We also observed increased abundance of PD1+ CD4 T cells in addition to heightened IL-10 signaling in the involution group at baseline (i.e. no tumor). Based on these observations, we hypothesized that the involution metastatic niche may be characterized by immune suppression, permitting tumor cell escape from immune surveillance. To address if the involution host liver is immune suppressed, we used an in vivo T cell activation assay where we adoptively transferred antigen-specific T cells systemically, and subsequently injected the cognate antigen into the liver of tumor free mice. Five days later, we assessed antigen-specific T cell number as a measure of T cell priming and activation. We found significantly impaired naïve T cell priming in the normal involution host liver compared to the nulliparous host. These data raise the possibility that impaired adaptive immunity could be responsible for increased liver metastasis in the involution group. In support, when we depleted CD8 T cells in our liver metastasis model, we found that metastasis in the anti-CD8 treated nulliparous group was similar to the untreated involution group, showing that depletion of cytotoxic immune cells in nulliparous hosts can recapitulate the involution host metastatic advantage. Taken together, our findings suggest the normal postpartum liver is in an immune suppressed state, which can provide a pro-metastatic advantage to circulating breast cancer cells. Future work will investigate therapeutic targeting of the postpartum liver niche. Citation Format: Alexandra Quackenbush, Nathan Penncok, Pepper Schedin. Immune suppression established by postpartum liver involution promotes liver metastasis [abstract]. In: Proceedings of the AACR Virtual Special Conference on the Evolving Tumor Microenvironment in Cancer Progression: Mechanisms and Emerging Therapeutic Opportunities; in association with the Tumor Microenvironment (TME) Working Group; 2021 Jan 11-12. Philadelphia (PA): AACR; Cancer Res 2021;81(5 Suppl):Abstract nr LT004.

Conway topograph, -dynamics and two-valued groups

Conway’s topographic approach to binary quadratic forms and Markov triples is reviewed from the point of view of the theory of two-valued groups. This leads naturally to a new class of commutative two-valued groups, which we call involutive. It is shown that the two-valued group of Conway’s lax vectors plays a special role in this class. The group describing the symmetries of the Conway topograph acts by automorphisms of this two-valued group. Binary quadratic forms are interpreted as primitive elements of the Hopf 2-algebra of functions on the Conway group. This fact is used to construct an explicit embedding of the Conway two-valued group into and thus to introduce a total group ordering on it. The two-valued algebraic involutive groups with symmetric multiplication law are classified, and it is shown that they are all obtained by the coset construction from the addition law on elliptic curves. In particular, this explains the special role of Mordell’s modification of the Markov equation and reveals its connection with two-valued groups in -theory. The survey concludes with a discussion of the role of two-valued groups and the group in the context of integrability in multivalued dynamics. Bibliography: 104 titles.

Immunohistochemical and ultrastructural evidence for telocytes in the different physiological stages of the female rat mammary gland

IntroductionTelocytes (TCs) are recently described to integrate a variety of different cells.Aim of the work.The aim was to investigate the presence of TCs in the rat mammary gland at its different physiological stages. Material and methodsTwenty four adult female albino rats were classified into 4 groups: resting, mid-pregnancy, lactating, and involution groups. Inguinal mammary glands were processed for immunohistochemical and transmission electron microscopic (TEM) examination. ResultsTCs were immune-positive for c-kit and CD34 and showed significant differences in the different studied groups indicating variable roles at the different stages. TEM results characterized TCs by its shape and the long slender and moniliform telopodes linking the cells into stromal networks. The extracellular exosomes, homo-cellular synapsis and hetero-cellular synapsis were observed. ConclusionOur study provides evidence for the presence of TCs in all stages of the gland; not only in the resting stage as proved by other studies, but with immune-labeling differences suggesting different structural and physiological roles of TCs according to the stage requirements. These functions might via controlling the proliferation during pregnancy and lactation and the involution of the gland after weaning. Thus, more future functional studies of TCs will be important to help understanding the mechanism by which TCs contribute to tissue homeostasis concerning the role of the stromal/epithelial interactions in mammary gland biology and pathology including breast cancer which would be revolutionary for future therapeutic applications.

Ibuprofen supports macrophage differentiation, T cell recruitment, and tumor suppression in a model of postpartum breast cancer

BackgroundWomen diagnosed with breast cancer within 5 years postpartum (PPBC) have poorer prognosis than age matched nulliparous women, even after controlling for clinical variables known to impact disease outcomes. Through rodent modeling, the poor prognosis of PPBC has been attributed to physiologic mammary gland involution, which shapes a tumor promotional microenvironment through induction of wound-healing-like programs including myeloid cell recruitment. Previous studies utilizing immune compromised mice have shown that blocking prostaglandin synthesis reduces PPBC tumor progression in a tumor cell extrinsic manner. Given the reported roles of prostaglandins in myeloid and T cell biology, and the established importance of these immune cell populations in dictating tumor growth, we investigate the impact of involution on shaping the tumor immune milieu and its mitigation by ibuprofen in immune competent hosts.MethodsIn a syngeneic (D2A1) orthotopic Balb/c mouse model of PPBC, we characterized the impact of mammary gland involution and ibuprofen treatment on the immune milieu in tumors and draining lymph nodes utilizing flow cytometry, multiplex IHC, lipid mass spectroscopy and cytokine arrays. To further investigate the impact of ibuprofen on programming myeloid cell populations, we performed RNA-Seq on in vivo derived mammary myeloid cells from ibuprofen treated and untreated involution group mice. Further, we examined direct effects of ibuprofen through in vitro bone marrow derived myeloid cell cultures.ResultsTumors implanted into the mammary involution microenvironment grow more rapidly and display a distinct immune milieu compared to tumors implanted into glands of nulliparous mice. This milieu is characterized by increased presence of immature monocytes and reduced numbers of T cells and is reversed upon ibuprofen treatment. Further, ibuprofen treatment enhances Th1 associated cytokines as well as promotes tumor border accumulation of T cells. Safety studies demonstrate ibuprofen does not impede gland involution, impact subsequent reproductive success, nor promote auto-reactivity as detected through auto-antibody and naïve T cell priming assays.ConclusionsIbuprofen administration during the tumor promotional microenvironment of the involuting mammary gland reduces overall tumor growth and enhances anti-tumor immune characteristics while avoiding adverse autoimmune reactions. In sum, these studies implicate beneficial prophylactic use of ibuprofen during the pro-tumorigenic window of mammary gland involution.

Set-theoretic solutions of the Yang–Baxter equation, braces and symmetric groups

We involve simultaneously the theory of braided groups and the theory of braces to study set-theoretic solutions of the Yang–Baxter equation (YBE). We show the intimate relation between the notions of “a symmetric group”, in the sense of Takeuchi, i.e. “a braided involutive group”, and “a left brace”. We find new results on symmetric groups of finite multipermutation level and the corresponding braces. We introduce a new invariant of a symmetric group (G,r), the derived chain of ideals ofG, which gives a precise information about the recursive process of retraction of G. We prove that every symmetric group (G,r) of finite multipermutation level m is a solvable group of solvable length ≤m. To each set-theoretic solution (X,r) of YBE we associate two invariant sequences of involutive braided groups: (i) the sequence of its derived symmetric groups; (ii) the sequence of its derived permutation groups; and explore these for explicit descriptions of the recursive process of retraction of (X,r). We find new criteria necessary and sufficient to claim that (X,r) is a multipermutation solution.

Relationship of vaginal discharge characteristics evaluated by Metricheck device to metabolic status in postpartum dairy cows.

The relationship between vaginal discharge characteristics and metabolic status has been studied in postpartum dairy cows. Vaginal discharges at 2-6weeks postpartum were scored weekly on a 1 (clear) to 5 (purulent material with stench) scale using the Metricheck device and classified into three groups as follows: Endometritis group (n=19), greater than or equal to score 4 until 3weeks postpartum; Delayed involution group (n=9), score 2 or 3 after having score 1; Healthy group (n=23), cows except those belonging to the Delayed involution and Endometritis groups. The uterus and cervix were assessed using ultrasonography. Blood samples were collected twice weekly from 1 to 6weeks postpartum from all cows and were additionally obtained for 13,14-dihydro-15-keto-prostaglandin F2α (PGFM) measurements from multiparous cows. Cows with delayed involution had delayed onset of luteal activity (p<0.05) and higher serum urea nitrogen (BUN) concentrations (p<0.01) than healthy animals. Cows with endometritis had more peripartum diseases (p<0.05), lower milk yield (p<0.05), longer cervix diameter (p<0.05), and lower serum albumin (p<0.01), total cholesterol (p<0.01), and magnesium (p<0.01) concentrations, and higher aspartate aminotransferase levels (p<0.05) than healthy cows. Plasma PGFM concentrations tended to be higher in the Delayed involution group (p=0.083) and lower in the Endometritis group (p=0.085) than in the Healthy group. In summary, delayed involution was shown to be associated with higher BUN concentration, and endometritis may have been caused by peripartum diseases and hepatic dysfunction.

Involutive groups, unique 2-divisibility, and related gyrogroup structures

In this paper, we establish a strong connection between groups and gyrogroups, which provides the machinery for studying gyrogroups via group theory. Specifically, we prove that there is a correspondence between the class of gyrogroups and a class of triples with components being groups and twisted subgroups. This in particular provides a construction of a gyrogroup from a group with an automorphism of order two that satisfies the uniquely 2-divisible property. We then present various examples of such groups, including the general linear groups over [Formula: see text] and [Formula: see text], the Clifford group of a Clifford algebra, the Heisenberg group on a module, and the group of units in a unital C[Formula: see text]-algebra. As a consequence, we derive polar decompositions for the groups mentioned previously.

Wound healing‐like immune program facilitates postpartum mammary gland involution and tumor progression

Women diagnosed with breast cancer within 5 years postpartum have poor survival rates. The process of postpartum mammary gland involution, whereby the lactating gland remodels to its prepregnant state, promotes breast cancer progression in xenograft models. Macrophage influx occurs during mammary gland involution, implicating immune modulation in the promotion of postpartum breast cancer. Herein, we characterize the postpartum murine mammary gland and find an orchestrated influx of immune cells similar to that which occurs during wound healing. Further, the normal involuting gland may be in an immunosuppressed state as discerned by the transient presence of Foxp3(+) regulatory T cells and IL-10(+) macrophages with T cell suppressive function. To determine the influence of the postpartum immune microenvironment on mammary tumor promotion, we developed an immune-competent model. In this model, mammary tumors in the involution group are sixfold larger than nulliparous group tumors, have decreased CD4(+) and CD8(+) T cell infiltrates and contain a greater number of macrophages with the ability to inhibit T cell activation. Targeting involution with a neutralizing antibody against the immunosuppressive cytokine IL-10 reduces tumor growth in involution group mice but not in nulliparous mice, implicating the involution microenvironment as the primary target of αIL-10 treatment. Relevance to women is implicated, as we find postlactational human breast tissue has transient high IL-10(+) and Foxp3(+) immune cell infiltrate. These data show an immune modulated microenvironment within the normal involuting mammary gland suggestive of immunosuppression, that when targeted reduces tumor promotion, revealing possible immune-based strategies for postpartum breast cancer.

Dynamic changes in high and low mammographic density human breast tissues maintained in murine tissue engineering chambers during various murine peripartum states and over time

Mammographic density (MD) is a strong heritable risk factor for breast cancer, and may decrease with increasing parity. However, the biomolecular basis for MD-associated breast cancer remains unclear, and systemic hormonal effects on MD-associated risk is poorly understood. This study assessed the effect of murine peripartum states on high and low MD tissue maintained in a xenograft model of human MD. Method High and low MD human breast tissues were precisely sampled under radiographic guidance from prophylactic mastectomy specimens of women. The high and low MD tissues were maintained in separate vascularised biochambers in nulliparous or pregnant SCID mice for 4weeks, or mice undergoing postpartum involution or lactation for three additional weeks. High and low MD biochamber material was harvested for histologic and radiographic comparisons during various murine peripartum states. High and low MD biochamber tissues in nulliparous mice were harvested at different timepoints for histologic and radiographic comparisons. Results High MD biochamber tissues had decreased stromal (p=0.0027), increased adipose (p=0.0003) and a trend to increased glandular tissue areas (p=0.076) after murine postpartum involution. Stromal areas decreased (p=0.042), while glandular (p=0.001) and adipose areas (p=0.009) increased in high MD biochamber tissues during lactation. A difference in radiographic density was observed in high (p=0.0021) or low MD biochamber tissues (p=0.004) between nulliparous, pregnant and involution groups. No differences in tissue composition were observed in high or low MD biochamber tissues maintained for different durations, although radiographic density increased over time. Conclusion High MD biochamber tissues had measurable histologic changes after postpartum involution or lactation. Alterations in radiographic density occurred in biochamber tissues between different peripartum states and over time. These findings demonstrate the dynamic nature of the human MD xenograft model, providing a platform for studying the biomolecular basis of MD-associated cancer risk.

Abstract B29: A novel mammary intraductal delivery model that permits study of human ductal carcinoma in situ progression.

Abstract Young African American women have an increased risk of developing aggressive forms of breast cancer (i.e. triple negative/basal-like) than young non-Hispanic white women. Recent epidemiological data show increased risk of basal-like breast cancer with increased childbearing in African American women (Millikan et al 2008; Palmer et al 2011). Breast cancers associated with a recent pregnancy (pregnancy-associated breast cancer) are more likely to be metastatic (Lyons et al 2011). We predict that the triple negative/basal-like breast cancer subtype is promoted by a recent pregnancy, accounting in part, for the poor prognosis of young African American breast cancer patients. We have developed a murine intraductal mammary model to examine the effect of host reproductive status on the progression of early stage human breast cancer. Our model delivers human mammary tumor cells directly through the intact mouse teat into the correct anatomical location for ductal carcinoma in situ (DCIS) without surgical manipulations. MCF10ADCIS.com (triple negative/basal cell line) or HCC70 (triple negative cell line derived from a young African American woman) cells were delivered into the mammary gland via intraductal injection to assess influence of host reproductive state (nulliparity, pregnancy, active post-partum involution) on tumor progression. Lesions from both cell lines displayed the full representation of human DCIS histologic subtypes, which progressed to DCIS through an atypical ductal hyperplasia stage. Although the MCF10ADCIS.com cell line is typically triple negative in vitro and other in vivo models, established tumors in the intraductal model were observed to re-express estrogen receptor. HCC70 tumors maintained the triple negative phenotype in our model. Using the MCF10ADCIS.com model to assess the effects of host reproductive status on DCIS progression, we found tumor burden in the pregnancy group was not significantly different than nulliparous controls. Within the pregnant group, tumors appear to be less proliferative and have slightly lower ER expression than nulliparous control tumors. Tumor burden in the postpartum involution group is significantly greater than the respective nulliparous control group; however, the Ki67 proliferative index is lower 4 weeks post injection in comparison to nulliparous controls. DCIS progression to locally invasive disease occurred with progressive loss of myoepithelial cell differentiation markers. In both cell line models, the loss of p63 was identified as an early indicator of compromised myoepithelium. Further, our data suggest that the protective myoepithelial cell layer may be preferentially compromised by tumors formed in postpartum involuting mammary glands. Our murine mammary intraductal model of human breast cancer provides a rigorous approach to study early stage-tumor progression, and is well suited to study the effect of the host reproductive state on DCIS progression. Since occult tumors in women develop within ducts, we propose that this teat injection model will aid research of early disease progression, a requisite for research focused on breast cancer prevention and inhibition of local invasion. Further, this model may provide a unique opportunity to address and study tumor growth disparities among African American and non-Hispanic white women. Citation Format: Tanya D. Russell, Samiat Agunbiade, Sonali Jindal, Jaime Fornetti, Virginia Borges, Pepper Schedin. A novel mammary intraductal delivery model that permits study of human ductal carcinoma in situ progression. [abstract]. In: Proceedings of the Fifth AACR Conference on the Science of Cancer Health Disparities in Racial/Ethnic Minorities and the Medically Underserved; 2012 Oct 27-30; San Diego, CA. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2012;21(10 Suppl):Abstract nr B29.

A Quantum Representation for Involution Groups

We answer a question posed by Martin et al. at MFPS XXVI in the affirmative: the free affine monoid over a finite involution group has a quantum representation, in addition to the classical representation already shown to exist in [Martin, K., J. Feng, and S. Krishnan. A Free Object in Quantum Information Theory. Electronic Notes in Theoretical Computer Science 267 (2010), 35–47]. In particular, this implies that in every dimension there are non-trivial classes of quantum channels that have classical representations which were not present in the lower dimensions. En route to establishing this result, we give two characterizations of the diagonal n-qubit channels (one of which is stated in [Bourdon, P.S, and H.T. Williams, Unital quantum operations on the Bloch ball and Bloch region, Phys. Rev. A. 69 (2004), 022314]) and necessary conditions for a Bloch matrix to satisfy.

Commutative semigroups with cancellation law: a representation theorem

Any commutative, cancellative semigroup S with 0 equipped with a uniformity can be embedded in a topological group \(\widetilde{S}\). We introduce the notion of semigroup symmetry T which enables us to turn \(\widetilde{S}\) into an involutive group. In Theorem 2.8 we prove that if S is 2-torsion-free and T is 2-divisible then the decomposition of elements of \(\widetilde{S}\) into a sum of elements of the symmetric subgroup \(\widetilde{S}_{s}\) and the asymmetric subgroup \(\widetilde{S}_{a}\) is polar. In Theorem 3.7 we give conditions under which a topological group \(\widetilde{S}\) is a topological direct sum of its symmetric subgroup \(\widetilde{S}_{s}\) and its asymmetric subgroup \(\widetilde{S}_{a}\). Theorem 2.8 and Theorem 3.7 are designed to be useful tools in studying Minkowski–Radstrom–Hormander spaces (and related topological groups \(\widetilde{S}\)), which are natural extensions of semigroups of bounded closed convex subsets of real Hausdorff topological vector spaces.

Abstract 1590: A preclinical mammary intraductal model to study early stage human breast cancer

Abstract Our goal is to develop a murine intraductal mammary model to examine the progression of early stage human breast cancer. Current models include injection of human mammary epithelial cell lines into the mammary fat pad (MFP) of immunocompromised mice or intraductal injection via cleaved nipple. With the MFP model, these cells are injected into the correct anatomical location for primary invasive tumors but do not form in the location of initiation, i.e., the mammary ducts. Intraductal models allow direct study of tumor cell formation and dissemination from mammary ducts; however, surgical manipulations performed to expose the teat canal are confounded by wound healing and inflammatory programs that are reported to be tumor promotional in other contexts. Our intraductal model of human breast cancer delivers human mammary tumor cells directly through the mouse teat into the correct anatomical location for ductal in situ carcinoma (DCIS) without surgical manipulations. Further, our model provides co-evolution of tumor progression with stromal changes versus the MFP model where the stroma responds to tumor cells at time of injection. Using the bi-potential progenitor MCF10ADCIS.com cell line and harvesting tissue 4 weeks post-injection, we corroborate reported studies showing DCIS lesions with distinct characteristics of the main human subtypes and progression to invasive disease. Immunohistochemical (IHC) analysis shows that these cells incorporate into the mouse mammary ducts and form E-cadherin-based junctional complexes with neighboring cells, including other human tumor cells or normal mouse epithelial cells. Although these cells have been characterized as estrogen receptor (ER) negative both in vitro and in vivo, IHC revealed that some tumors developed within our model were ER positive according to the Allred scoring method. Our model permits a rigorous evaluation of the effects that physiologic-induced changes in mammary tissue remodeling (i.e. postpartum involution) has on tumor progression. We investigated tumor incidence and burden in the postpartum involution setting and found much greater increases in the involution group compared to the respective nulliparous control group. Interestingly, the Ki67 proliferative index is lower in the involution compared to the respective nulliparous control, suggesting a mechanism other than proliferation is driving tumor promotion in the postpartum setting. In summary, our murine intraductal model of human breast cancer provides a rigorous approach to studying early stage tumor progression. This model is particularly suited to studying host effects on tumor progression and future studies will determine the effects of physiological endocrine status on tumor cell dissemination from mammary ducts. Since mammary ducts are the primary sites of occult tumors in women, we propose that this teat injection model will be a more relevant model for all stages of human disease. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 102nd Annual Meeting of the American Association for Cancer Research; 2011 Apr 2-6; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2011;71(8 Suppl):Abstract nr 1590. doi:10.1158/1538-7445.AM2011-1590

Involution Is an Inflammatory Tumor Promoting Event That Increases Metastasis in Pregnancy Associated Breast Cancer.

Abstract Breast cancer diagnosed up to 6 years after a completed child-birth has an increased risk of metastatic recurrence and death, which is independent of current prognostic factors. These pregnancy-associated breast cancers (PABC) account for 45% of all young women's breast cancers and have a 10 year survival rate of 44% compared with 69% for non-PABC. After parturition or lactation, a physiologically normal tissue remodeling program is activated that mimics wound healing and inflammation, including high matrix metalloproteinase -2, -3, and -9 activities, release of bioactive fragments of FN and LN, deposition of fibrillar collagen, and increased cytokine levels. We hypothesize that the normal physiologic, but pro-inflammatory remodeling of breast during involution accounts for increased breast cancer metastasis of PABC.To demonstrate that the human breast is characterized by a pro-inflammatory microenvironment with wound-healing characteristics, formalin fixed breast biopsy tissues were obtained for women who were age-matched nulliparous, pregnant, lactating, whose breast tissue was actively involuting at the time of biopsy or who were &amp;gt; 5 years from a completed pregnancy. Using a novel imaging program, over 1500 images of human breast tissue have been quantitated for CD45 (common leukocyte antigen) and CD68 (macrophage lysosomal marker). CD45 and CD68 staining in the human breast demonstrates 4 times more staining in involuting compared to pregnant tissue. Further, CD45 and CD68 staining returns to baseline level in the fully regressed breast. Further characterization of the macrophages in involution demonstrates an M2 phenotype, similar to immune suppressive tumor associated macrophages. Likewise, increased collagen deposition is present with involution in comparison to the other tissue subgroups, which may help promote immune cell recruitment.To test for the impact of involution on invasion and metastasis of PABC, we have developed the MCF-10DCIS human cell line into a murine model for PABC. In this model, the cancer cells will form in situ ductal carcinoma like lesions that progress over time with loss of their myoepithelial barrier and subsequent invasion present. Orthotopic injection of the MCF-10DCIS cells into SCID mice that whose mammary glands were nulliparous versus actively involuting following timed weaning demonstrated an increased incidence of tumor of 78% involution group versus 50% in the nulliparous group. Tumor size was increased 4 fold and presence of invasive lesions increased 2 fold for the involution group. Moreover, increased lung metastasis that was independent of the primary tumor size was seen in the involuting mice compared with nulliparous controls, isolating the event of involution (independent of the potential potentiating effect of the pregnancy state on the tumor) as the driving feature for the metastatic increase.These data demonstrate for the first time that human mammary gland involution is characterized by a pro-inflammatory microenvironment, implicating physiologic tissue inflammation in the poor prognosis of PABC. Likewise, in a murine model for PABC, involution is associated with increased tumor invasion and metastasis. Citation Information: Cancer Res 2009;69(24 Suppl):Abstract nr 50.

The radical RN and the weakly solvable radical of linear groups over associative rings

This paper is devoted to the computation of the radicals RN and RN* and the weakly solvable radical for a number of basic classical linear groups over rings, including the unitary group over a ring with involution and matrix groups normalized by elementary Chevalley groups.

Trigonal quotients of modular curves $X_{0}(N)$

Let $W(N)$ be the group of Atkin-Lehner involutions on the modular curve $X_0(N)$. The purpose of this article is to give complementary result to [7, 8, 9]; namely, we determine trigonal curves of the form $X_0(N)/W'$, where $W'$ is a subgroup of $W(N)$ such that $2< |W'| < |W(N)|$.

Symmetric Sets With Midpoints and Algebraically Equivalent Theories

In this paper we consider an algebraic generalization of symmetric spaces of noncompact type to a more general class of symmetric structures equipped with midpoints. These symmetric structures are shown to have close relationships to and even categorical equivalences with a variety of other algebraic structures: axiomatic midpoint spaces, uniquely 2-divisible twisted subgroups, transversal twisted subgroups of involutive groups, a special class of loops called B-loops, and gyrocommutative gyrogroups.