A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud

We have previously demonstrated that overexpression of parathyroid hormone-related protein (PTHrP) in the mammary glands of transgenic mice results in defects in ductal elongation and branching during puberty and in lobuloalveolar development during pregnancy. In addition, we have shown that PTHrP is necessary for the formation of the initial ductal tree during embryonic mammary development. In order to examine the effect of varying the timing of PTHrP overexpression on mammary development, we created tetracycline-regulated, K14-tTA/Tet(O)-PTHrP double transgenic mice. In this report, we document that this 'tet-off' system directs transgene expression to the mammary gland and that it is fully repressed in the presence of tetracycline. Using these mice, we demonstrate that transient overexpression of PTHrP before birth causes defects in ductal branching during puberty and that overexpression of PTHrP during puberty decreases the rate of ductal elongation. Furthermore, we demonstrate that if PTHrP overexpression is initiated after ductal morphogenesis is completed, lobuloalveolar development is unaffected. Finally, we demonstrate that the impairment in ductal elongation caused by PTHrP is associated with an increase in the basal rate of epithelial cell apoptosis in terminal end buds and a failure to increase end bud cell proliferation and decrease apoptosis in response to estrogen and progesterone.

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Repressor of Estrogen Receptor Activity (REA) Is Essential for Mammary Gland Morphogenesis and Functional Activities: Studies in Conditional Knockout Mice

Endocrinology ◽

10.1210/en.2011-1100 ◽

2011 ◽

Vol 152 (11) ◽

pp. 4336-4349 ◽

Cited By ~ 15

Author(s):

Sunghee Park ◽

Yuechao Zhao ◽

Sangyeon Yoon ◽

Jianming Xu ◽

Lan Liao ◽

...

Keyword(s):

Estrogen Receptor ◽

Mammary Gland ◽

Mammary Gland Development ◽

Gene Dosage ◽

Conditional Knockout ◽

Loss Of Function ◽

Breast Tumorigenesis ◽

Pregnancy And Lactation ◽

Ductal Elongation ◽

Gland Development

Estrogen receptor (ER) is a key regulator of mammary gland development and is also implicated in breast tumorigenesis. Because ER-mediated activities depend critically on coregulator partner proteins, we have investigated the consequences of reduction or loss of function of the coregulator repressor of ER activity (REA) by conditionally deleting one allele or both alleles of the REA gene at different stages of mammary gland development. Notably, we find that heterozygosity and nullizygosity for REA result in very different mammary phenotypes and that REA has essential roles in the distinct morphogenesis and functions of the mammary gland at different stages of development, pregnancy, and lactation. During puberty, mice homozygous null for REA in the mammary gland (REAf/f PRcre/+) showed severely impaired mammary ductal elongation and morphogenesis, whereas mice heterozygous for REA (REAf/+ PRcre/+) displayed accelerated mammary ductal elongation, increased numbers of terminal end buds, and up-regulation of amphiregulin, the major paracrine mediator of estrogen-induced ductal morphogenesis. During pregnancy and lactation, mice with homozygous REA gene deletion in mammary epithelium (REAf/f whey acidic protein-Cre) showed a loss of lobuloalveolar structures and increased apoptosis of mammary alveolar epithelium, leading to impaired milk production and significant reduction in growth of their offspring, whereas body weights of the offspring nursed by females heterozygous for REA were slightly greater than those of control mice. Our findings reveal that REA is essential for mammary gland development and has a gene dosage-dependent role in the regulation of stage-specific physiological functions of the mammary gland.

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STAT5 deletion in macrophages alters ductal elongation and branching during mammary gland development

Developmental Biology ◽

10.1016/j.ydbio.2017.06.007 ◽

2017 ◽

Vol 428 (1) ◽

pp. 232-244 ◽

Cited By ~ 9

Author(s):

Nicholas J. Brady ◽

Michael A. Farrar ◽

Kathryn L. Schwertfeger

Keyword(s):

Mammary Gland ◽

Mammary Gland Development ◽

Ductal Elongation ◽

Gland Development

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The lactation curve in cattle: a mathematical model of the mammary gland

The Journal of Agricultural Science ◽

10.1017/s0021859600037710 ◽

1983 ◽

Vol 101 (2) ◽

pp. 389-400 ◽

Cited By ~ 60

Author(s):

Heather D. St. C. Neal ◽

J. H. M. Thornley

Keyword(s):

Mathematical Model ◽

Mammary Gland ◽

Good Description ◽

Total Activity ◽

Variable Number ◽

Secretory Cells ◽

Machine Milking ◽

Lactation Curve ◽

Undifferentiated Cells ◽

Number Of Cells

SUMMARYA simple model of the mammary gland is described. In this model secretory cells are produced by cell division from undifferentiated cells, and the rate of division is determined by the level of a postulated hormone. The total activity of the milk secreting cells depends on the number of cells, substrate supply (assumed constant), and the amount of milk currently present in the animal. The secretory cells have a finite life, although their death may be expedited by milk remaining in the animal over a longer period of time. The model gives a good description of an experimental lactation curve; it is able to simulate the removal of milk by a suckling calf and machine milking with a variable number of milking periods a day.

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BMP-binding protein twisted gastrulation is required in mammary gland epithelium for normal ductal elongation and myoepithelial compartmentalization

Developmental Biology ◽

10.1016/j.ydbio.2012.10.007 ◽

2013 ◽

Vol 373 (1) ◽

pp. 95-106 ◽

Cited By ~ 17

Author(s):

Cynthia L. Forsman ◽

Brandon C. Ng ◽

Rachel K. Heinze ◽

Claire Kuo ◽

Consolato Sergi ◽

...

Keyword(s):

Mammary Gland ◽

Binding Protein ◽

Twisted Gastrulation ◽

Ductal Elongation

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Chemokine receptors ACKR2 and CCR1 coordinate macrophage dynamics and mammary gland development

10.1101/747360 ◽

2019 ◽

Author(s):

Gillian J Wilson ◽

Ayumi Fukuoka ◽

Samantha R Love ◽

Jiwon Kim ◽

Marieke Pingen ◽

...

Keyword(s):

Breast Cancer ◽

Mammary Gland ◽

Chemokine Receptor ◽

Chemokine Receptors ◽

Mammary Gland Development ◽

Branching Morphogenesis ◽

Unknown Mechanism ◽

Key Population ◽

Ductal Elongation ◽

Gland Development

AbstractMacrophages are key regulators of developmental processes, including those involved in mammary gland development. We previously demonstrated that the atypical chemokine receptor, ACKR2, contributes to control of ductal epithelial branching in the developing mammary gland by regulating macrophage dynamics. ACKR2 is a chemokine-scavenging receptor, which mediates its effects through collaboration with inflammatory chemokine receptors (iCCRs). Here we reveal that ACKR2, and the iCCR CCR1, reciprocally regulate branching morphogenesis in the mammary gland, whereby stromal ACKR2 modulates levels of the shared ligand CCL7 to control the movement of a key population of CCR1-expressing macrophages to the ductal epithelium. In addition estrogen, which is essential for ductal elongation during puberty, upregulates CCR1 expression on macrophages. The age at which girls develop breasts is decreasing, which raises the risk of diseases including breast cancer. This study presents a previously unknown mechanism controlling the rate of mammary gland development during puberty and highlights potential therapeutic targets.SummaryIn the mammary gland during puberty, availability of the chemokine CCL7 is controlled by a scavenging receptor ACKR2 and provides a key signal to macrophages which have the receptor CCR1. Together, this controls the timing of development.

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Development of a dynamic mathematical model for investigating mammary gland metabolism in lactating cows

The Journal of Agricultural Science ◽

10.1017/s0021859609990244 ◽

2009 ◽

Vol 148 (1) ◽

pp. 31-54 ◽

Cited By ~ 4

Author(s):

V. VOLPE ◽

J. P. CANT ◽

R. C. BOSTON ◽

P. SUSMEL ◽

P. MOATE

Keyword(s):

Mathematical Model ◽

Sensitivity Analysis ◽

Mammary Gland ◽

Milk Protein ◽

Energy Charge ◽

Atp Synthesis ◽

Protein Yield ◽

Future Research ◽

Lactating Cows ◽

Dynamic Mathematical Model

SUMMARYA dynamic mathematical model of a closed mammary system in lactating cows was developed to incorporate the setpoint concept of tissue activity, using equations where nutrient supply and absorption are locally regulated so as to maintain a given rate of milk protein yield. The model consists of 12 differential equations, 11 of which are concerned with intracellular biochemical compartments and one describes the volume of tissue actively perfused by blood (AP). The intracellular compartments are: amino acids (AAs), acetate, fatty acids (FAs), β-hydroxybutyrate, glucose-6-phosphate, fructose-6-phosphate, phospho-glyceraldehyde, pyruvate, mitochondrial acetyl-CoA, adenosine triphosphate (ATP) and adenosine diphosphate (ADP). The model simulates mechanisms which are aimed at reproducing and, thereby, explain variations in mammary plasma flow (MPF) observed experimentally. The AP changes according to variations in the metabolic status or in the metabolic requirements of the gland. Should the tissue energy charge (i.e. ATP/ADP ratio) exceed a baseline ratio, then AP decreases and consequently MPF declines. Conversely, when milk protein yield increases, AP increases and MPF rises. In the present model, AA uptake by the mammary gland is inhibited by intracellular AAs. It is also assumed that, when milk protein yield diminishes, the respiratory chain and ATP synthesis become uncoupled and consequently ATP yield is reduced. Model evaluation included behavioural analysis and sensitivity analysis. Behaviour analysis was conducted to test whether the model mechanisms reproduced the scenarios from which the model hypotheses were developed, and took into consideration: an increase in arterial glucose concentration (HIGLC), increases in arterial concentrations of non-esterified FAs, triacylglycerol and β-hydroxybutyrate (HIFAT), a 50% reduction of arterial histidine concentration (LOHIS), and a hyperinsulinaemic euglycaemic clamp (HIINS). Both HIGLC and HIFAT resulted in a decrease in MPF and in milk protein yield; moreover, the scenario HIGLC also produced a notable decrease in the extraction of glucose. The scenario LOHIS resulted in increased MPF and extraction of His from plasma. However these responses were not sufficiently large to prevent a severe reduction of milk protein yield which was accompanied by a reduction in the extraction of other essential AAs. The scenario HIINS resulted in an increase of MPF and of milk protein yield, in the extraction of His and of other essential AAs. Model sensitivity analysis focused on variation of both affinity and inhibition constants of some of the Michaelis–Menten equations. Improvements in model structure and directions for future research suggested by the modelling analysis are discussed.

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Modelling Diffusion in a Physically Constrained System: A Numerical Approach

STEM Fellowship Journal ◽

10.17975/sfj-2016-008 ◽

2016 ◽

Vol 2 (1) ◽

pp. 38-48

Author(s):

Adam Jozefiak ◽

Jim Zhang Hao Li

Keyword(s):

Mathematical Model ◽

Numerical Approach ◽

Dimensional System ◽

Two Dimensional ◽

Hydraulic Systems ◽

Experimental Conditions ◽

Constrained System ◽

Exponential Factor ◽

System A ◽

Geometrically Constrained

Diffusion has been described on a microscopic scale by Einstein as a probabilistic collision of particles. On a macroscale, diffusion has been thoroughly described by Fick’s laws. However, the solutions to Fick’s laws are limited to idealized physical systems. The aim of this experimental study is to provide a mathematical model for diffusion which incorporates both macroscopic and microscopic properties to effectively model diffusion in a geometrically constrained two-dimensional system. Based on macroscopic and microscopic properties, two-dimensional diffusion was modelled as a summation of equally probable paths of diffusion. The point source diffusion of hydrochloric acid in an arena with variable barrier dimensions was monitored continuously using a pH probe. The numerical solution of the mathematical model for each experimental condition was determined and the pre-exponential factor was fit to the measurements. The average pre-exponential value was determined for each experimental condition, and t-scores were calculated to compare the average pre-exponential values which were found to be statistically similar. This indicates that the proposed model is an accurate model as it predicts identical pre-exponential values between experimental conditions, accounting for all variants that it attempts to model. This model provides a bridge between the microscopic and macrcoscopic theoretical descriptions of diffusion that were independently postulated by Einstein and Fick. Applications of the model include the approximation of locations of leakage in hydraulic systems.

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