Bistability theorem in a cancer model

2018 ◽  
Vol 11 (01) ◽  
pp. 1850004 ◽  
Author(s):  
Jens Christian Larsen
Keyword(s):  
Vector Space ◽  
Cancer Metastasis ◽  
Metastatic Cancer ◽  
Three Dimensional ◽  
Rate Of Change ◽  
Mass Action ◽  
Cancer Growth ◽  
Ode Model ◽  
Euclidean Vector Space ◽  
Appl Math

In this paper, I continue the study of the mathematical models presented in [J. C. Larsen, Models of cancer growth, J. Appl. Math. Comput. 53(1–2) (2015) 613–645] and [J. C. Larsen, The bistability theorem in a model of metastatic cancer, to appear in Appl. Math.]. I shall prove the bistability theorem for the ODE model from [Larsen, 2015]. It is a mass action kinetic system in the variables [Formula: see text] cancer, GF growth factor and GI growth inhibitor. This theorem says that for some values of the parameters, there exist two positive singular points [Formula: see text], [Formula: see text] of the vector field. Here [Formula: see text] and [Formula: see text] is stable and [Formula: see text] is unstable, see Sec. 2. There is also a discrete model in [Larsen, 2015], it is a linear map ([Formula: see text]) on three-dimensional Euclidean vector space with variables [Formula: see text] where these variables have the same meaning as in the ODE model above. In [Larsen, 2015], I showed that one can sometimes find affine vector fields on three-dimensional Euclidean vector space whose time one map is [Formula: see text]. I shall also show this in the present paper in a more general setting than in [Larsen, 2015]. This enables me to find an expression for the rate of change of cancer growth on the coordinate hyperplane [Formula: see text] in Euclidean vector space. I also present an ODE model of cancer metastasis with variables [Formula: see text] where [Formula: see text] is primary cancer and [Formula: see text] is metastatic cancer and GF, GI are growth factors and growth inhibitors, respectively.

scholarly journals Tissue-specific tregs in cancer metastasis: opportunities for precision immunotherapy

2021 ◽  
Author(s):  
Laura A. Huppert ◽  
Michael D. Green ◽  
Luke Kim ◽  
Christine Chow ◽  
Yan Leyfman ◽  
...  
Keyword(s):  
Cancer Immunotherapy ◽  
Cancer Metastasis ◽  
Metastatic Cancer ◽  
High Volume ◽  
Therapy Resistance ◽  
Term Treatment ◽  
The Body ◽  
Tissue Specific ◽  
Tissue Repair And Regeneration ◽  
Long Term Treatment

AbstractDecades of advancements in immuno-oncology have enabled the development of current immunotherapies, which provide long-term treatment responses in certain metastatic cancer patients. However, cures remain infrequent, and most patients ultimately succumb to treatment-refractory metastatic disease. Recent insights suggest that tumors at certain organ sites exhibit distinctive response patterns to immunotherapy and can even reduce antitumor immunity within anatomically distant tumors, suggesting the activation of tissue-specific immune tolerogenic mechanisms in some cases of therapy resistance. Specialized immune cells known as regulatory T cells (Tregs) are present within all tissues in the body and coordinate the suppression of excessive immune activation to curb autoimmunity and maintain immune homeostasis. Despite the high volume of research on Tregs, the findings have failed to reconcile tissue-specific Treg functions in organs, such as tolerance, tissue repair, and regeneration, with their suppression of local and systemic tumor immunity in the context of immunotherapy resistance. To improve the understanding of how the tissue-specific functions of Tregs impact cancer immunotherapy, we review the specialized role of Tregs in clinically common and challenging organ sites of cancer metastasis, highlight research that describes Treg impacts on tissue-specific and systemic immune regulation in the context of immunotherapy, and summarize ongoing work reporting clinically feasible strategies that combine the specific targeting of Tregs with systemic cancer immunotherapy. Improved knowledge of Tregs in the framework of their tissue-specific biology and clinical sites of organ metastasis will enable more precise targeting of immunotherapy and have profound implications for treating patients with metastatic cancer.

scholarly journals The In Vivo Selection Method in Breast Cancer Metastasis

2021 ◽  
Vol 22 (4) ◽  
pp. 1886
Author(s):  
Jun Nakayama ◽  
Yuxuan Han ◽  
Yuka Kuroiwa ◽  
Kazushi Azuma ◽  
Yusuke Yamamoto ◽  
...  
Keyword(s):  
Cancer Cells ◽  
Cell Lines ◽  
Cancer Metastasis ◽  
Metastatic Cancer ◽  
Expression Patterns ◽  
Selection Method ◽  
Gene Signatures ◽  
In Vivo Selection ◽  
Metastatic Cancer Cells

Metastasis is a complex event in cancer progression and causes most deaths from cancer. Repeated transplantation of metastatic cancer cells derived from transplanted murine organs can be used to select the population of highly metastatic cancer cells; this method is called as in vivo selection. The in vivo selection method and highly metastatic cancer cell lines have contributed to reveal the molecular mechanisms of cancer metastasis. Here, we present an overview of the methodology for the in vivo selection method. Recent comparative analysis of the transplantation methods for metastasis have revealed the divergence of metastasis gene signatures. Even cancer cells that metastasize to the same organ show various metastatic cascades and gene expression patterns by changing the transplantation method for the in vivo selection. These findings suggest that the selection of metastasis models for the study of metastasis gene signatures has the potential to influence research results. The study of novel gene signatures that are identified from novel highly metastatic cell lines and patient-derived xenografts (PDXs) will be helpful for understanding the novel mechanisms of metastasis.

scholarly journals Targeting the Metabolic Adaptation of Metastatic Cancer

Cancers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1641
Author(s):  
Josep Tarragó-Celada ◽  
Marta Cascante
Keyword(s):  
Colorectal Cancer ◽  
Cancer Metastasis ◽  
Metastatic Cancer ◽  
Breast Cancer Metastasis ◽  
Metabolic Inhibitors ◽  
Current Status ◽  
Metabolic Adaptation ◽  
Metastatic Cells ◽  
Colorectal Cancer Metastasis ◽  
Metastatic Process

Metabolic adaptation is emerging as an important hallmark of cancer and metastasis. In the last decade, increasing evidence has shown the importance of metabolic alterations underlying the metastatic process, especially in breast cancer metastasis but also in colorectal cancer metastasis. Being the main cause of cancer-related deaths, it is of great importance to developing new therapeutic strategies that specifically target metastatic cells. In this regard, targeting metabolic pathways of metastatic cells is one of the more promising windows for new therapies of metastatic colorectal cancer, where still there are no approved inhibitors against metabolic targets. In this study, we review the recent advances in the field of metabolic adaptation of cancer metastasis, focusing our attention on colorectal cancer. In addition, we also review the current status of metabolic inhibitors for cancer treatment.

scholarly journals Identities Generalizing the Theorems of Pappus and Desargues

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1382
Author(s):  
Roger D. Maddux
Keyword(s):  
Projective Plane ◽  
Vector Space ◽  
Invariant Theory ◽  
Lattice Theory ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Dimensional Vector Space

The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants and cross products. These identities are proved to hold in the three-dimensional vector space over a field. They are closely related to the Arguesian identity in lattice theory and to Cayley-Grassmann identities in invariant theory.

scholarly journals MiR-146a Regulates Migration and Invasion by Targeting NRP2 in Circulating-Tumor Cell Mimicking Suspension Cells

Genes ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 45
Author(s):  
Yeojin Do ◽  
Jin Gu Cho ◽  
Ji Young Park ◽  
Sumin Oh ◽  
Doyeon Park ◽  
...  
Keyword(s):  
Cancer Metastasis ◽  
Metastatic Cancer ◽  
Molecular Networks ◽  
Migration And Invasion ◽  
Integrated Analysis ◽  
Molecular Characteristics ◽  
Breast Cancer Patients ◽  
Sequencing Data ◽  
Suspension Cells

Cancer metastasis is the primary cause of cancer-related death and metastatic cancer has circulating-tumor cells (CTCs), which circulate in the bloodstream before invading other organs. Thus, understanding the precise role of CTCs may provide new insights into the metastasis process and reduce cancer mortality. However, the molecular characteristics of CTCs are not well understood due to a lack of number of CTCs. Therefore, suspension cells were generated from MDA-MB-468 cells to mimic CTCs, and we investigate the microRNA (miRNA)-dependent molecular networks and their role in suspension cells. Here, we present an integrated analysis of mRNA and miRNA sequencing data for suspension cell lines, through comparison with adherent cells. Among the differentially regulated miRNA–mRNAs axes, we focus on the miR-146a-Neuropilin2 (NRP2) axis, which is known to influence tumor aggressiveness. We show that miR-146a directly regulates NRP2 expression and inhibits Semaphorin3C (SEMA3C) signaling. Functional studies reveal that miR-146a represses SEMA3C-induced invasion and proliferation by targeting NRP2. Finally, high-NRP2 is shown to be associated with poor outcomes in breast cancer patients. This study identifies the key role of the miR-146a–NRP2 signaling axis that is critical for the regulation of migration and invasion in CTC-mimicking cells.

Is Medicaid expansion associated with increases in palliative treatments for metastatic cancer?

2021 ◽  
Author(s):  
Alexander P Cole ◽  
Stuart R Lipsitz ◽  
Adam S Kibel ◽  
Brandon A Mahal ◽  
Nelya Melnitchouk ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Affordable Care Act ◽  
Odds Ratio ◽  
Metastatic Cancer ◽  
Mixed Effects ◽  
Rate Of Change ◽  
Medicaid Expansion ◽  
Demographic Differences ◽  
Men And Women ◽  
Lower Baseline

Background: Medicaid expansion following the 2010 Affordable Care Act has an unknown impact on palliative treatments. Materials & methods: This registry-based study of individuals with metastatic cancer from 2010 to 2016 identified men and women with metastatic cancer in expansion and non-expansion states who received palliative treatments. A mixed effects logistic regression compared trends in expansion and non-expansion states and generated risk-adjusted probabilities or receiving palliative treatments each year. Results: Despite lower baseline use of palliative treatments, the rate of change was more rapid in expansion states (odds ratio [OR]: 1.02; 95% CI: 1.01–1.03; p < 0.001). The adjusted probability of receiving palliative treatments rose from 21.3 to 26.0% in non-expansion states, and from 19.7 to 26.9% in expansion states. Conclusion: Use of palliative treatments among metastatic cancer patients increased from 2010 to 2016 with a significantly greater increase in Medicaid expansion states, even when adjusting for demographic differences between states.

Biomechanical Models for Radial Distance Determination by the Rat Vibrissal System

2007 ◽  
Vol 98 (4) ◽  
pp. 2439-2455 ◽  
Author(s):  
J. Alexander Birdwell ◽  
Joseph H. Solomon ◽  
Montakan Thajchayapong ◽  
Michael A. Taylor ◽  
Matthew Cheely ◽  
...  
Keyword(s):  
Angular Position ◽  
Three Dimensional ◽  
Radial Distance ◽  
Rate Of Change ◽  
Dynamic State ◽  
Rhythmic Movements ◽  
Tactile Information ◽  
Biomechanical Models ◽  
Object Distance ◽  
Dimensional Object

Rats use active, rhythmic movements of their whiskers to acquire tactile information about three-dimensional object features. There are no receptors along the length of the whisker; therefore all tactile information must be mechanically transduced back to receptors at the whisker base. This raises the question: how might the rat determine the radial contact position of an object along the whisker? We developed two complementary biomechanical models that show that the rat could determine radial object distance by monitoring the rate of change of moment (or equivalently, the rate of change of curvature) at the whisker base. The first model is used to explore the effects of taper and inherent whisker curvature on whisker deformation and used to predict the shapes of real rat whiskers during deflections at different radial distances. Predicted shapes closely matched experimental measurements. The second model describes the relationship between radial object distance and the rate of change of moment at the base of a tapered, inherently curved whisker. Together, these models can account for recent recordings showing that some trigeminal ganglion (Vg) neurons encode closer radial distances with increased firing rates. The models also suggest that four and only four physical variables at the whisker base—angular position, angular velocity, moment, and rate of change of moment—are needed to describe the dynamic state of a whisker. We interpret these results in the context of our evolving hypothesis that neural responses in Vg can be represented using a state-encoding scheme that includes combinations of these four variables.

scholarly journals Rare case of invasive lobular breast cancer metastasis to the endometrium

2020 ◽  
Vol 48 (2-3) ◽  
pp. 116-118
Author(s):  
Damir Danolić ◽  
◽  
Luka Marcelić ◽  
Ilija Alvir ◽  
Ivica Mamić ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Cancer Metastasis ◽  
Metastatic Cancer ◽  
Female Genital Tract ◽  
Breast Cancer Metastasis ◽  
Breast Cancers ◽  
Endometrial Sampling ◽  
Invasive Lobular Breast Cancer ◽  
Postmenopausal Vaginal Bleeding ◽  
Female Genital

Metastases to the female genital tract from extra-genital primary cancers are uncommon and usually occur during widespread metastatic disease. Breast cancers are the most frequent primaries, predominantly the lobular type. Here, we report a case of a 55-year-old woman with breast cancer endometrial metastasis who presented with postmenopausal vaginal bleeding. We highlight the importance of endometrial sampling to confirm the diagnosis and distinguish primary from metastatic cancer of the endometrium since the treatment and prognosis of these conditions are entirely different.

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