scholarly journals Analysis of dynamic morphogen scale invariance

2009 ◽  
Vol 6 (41) ◽  
pp. 1179-1191 ◽  
Author(s):  
David M. Umulis
Keyword(s):  
Scale Invariance ◽  
Reaction Diffusion ◽  
Cell Types ◽  
Transport Processes ◽  
Reaction Diffusion Equations ◽  
Local Concentration ◽  
Flux Dynamic ◽  
Multipotent Cells ◽  
Total Input ◽  
Distinct Cell

During the development of some tissues, fields of multipotent cells differentiate into distinct cell types in response to the local concentration of a signalling factor called a morphogen. Typically, individual organisms within a population differ in size, but their body plans appear to be scaled versions of a common template. Similarly, closely related species may differ by three or more orders of magnitude in size, yet common structures between species scale to have similar proportions. In standard reaction–diffusion equations, the morphogen range has a length scale that depends on a balance between kinetic and transport processes and not on the length or size of the field of cells being patterned. However, as shown here for a class of morphogen-patterning systems, a number of conditions lead to scale invariance of the morphogen distribution at equilibrium and during the transient approach to equilibrium. Equilibrium scale invariance requires conservation of the total binding site number and total input flux. Dynamic scale invariance additionally requires sufficient binding to slow the diffusion of ligand. The equations derived herein can be extended to the study of other perturbations to gain further insight into the processes regulating the robustness and scaling of morphogen-mediated pattern formation.

scholarly journals Mix & Match: Phenotypic coexistence as a key facilitator of solid tumour invasion

2019 ◽  
Author(s):  
Maximilian A. R. Strobl ◽  
Andrew L. Krause ◽  
Mehdi Damaghi ◽  
Robert Gillies ◽  
Alexander R. A. Anderson ◽  
...  
Keyword(s):  
Alternative Hypothesis ◽  
Cell Movement ◽  
Reaction Diffusion ◽  
Cell Types ◽  
The Body ◽  
Reaction Diffusion Equations ◽  
Species Competition ◽  
Invasion Process ◽  
Malignant Tumours ◽  
Reaction Diffusion Model

AbstractInvasion of healthy tissue is a defining feature of malignant tumours. Traditionally, invasion is thought to be driven by cells that have acquired all the necessary traits to overcome the range of biological and physical defences employed by the body. However, in light of the ever-increasing evidence for geno- and phenotypic intra-tumour heterogeneity an alternative hypothesis presents itself: Could invasion be driven by a collection of cells with distinct traits that together facilitate the invasion process? In this paper, we use a mathematical model to assess the feasibility of this hypothesis in the context of acid-mediated invasion. We assume tumour expansion is obstructed by stroma which inhibits growth, and extra-cellular matrix (ECM) which blocks cancer cell movement. Further, we assume that there are two types of cancer cells: i) a glycolytic phenotype which produces acid that kills stromal cells, and ii) a matrix-degrading phenotype that locally remodels the ECM. We extend the Gatenby-Gawlinski reaction-diffusion model to derive a system of five coupled reaction-diffusion equations to describe the resulting invasion process. We characterise the spatially homogeneous steady states and carry out a simulation study in one spatial dimension to determine how the tumour develops as we vary the strength of competition between the two phenotypes. We find that overall tumour growth is most extensive when both cell types can stably coexist, since this allows the cells to locally mix and benefit most from the combination of traits. In contrast, when inter-species competition exceeds intra-species competition the populations spatially separate and invasion arrests either: i) rapidly (matrix-degraders dominate), or ii) slowly (acid-producers dominate). Overall, our work demonstrates that the spatial and ecological relationship between a heterogeneous population of tumour cells is a key factor in determining their ability to cooperate. Specifically, we predict that tumours in which different phenotypes coexist stably are more invasive than tumours in which phenotypes are spatially separated.

Fine Structure of the Malpighian Tubules of the Mosquito, Culex pipiens

1971 ◽  
Vol 29 ◽  
pp. 402-403
Author(s):  
Brendan Clifford
Keyword(s):  
Fine Structure ◽  
Culex Pipiens ◽  
Stellate Cell ◽  
Malpighian Tubule ◽  
Cell Types ◽  
Instar Larva ◽  
Malpighian Tubules ◽  
Calliphora Erythrocephala ◽  
Distinct Cell ◽  
Basal Plasma

An ultrastructural investigation of the Malpighian tubules of the fourth instar larva of Culex pipiens was undertaken as part of a continuing study of the fine structure of transport epithelia.Each of the five Malpighian tubules was found to be morphologically identical and regionally undifferentiated. Two distinct cell types, the primary and stellate, were found intermingled along the length of each tubule. The ultrastructure of the stellate cell was previously described in the Malpighian tubule of the blowfly, Calliphora erythrocephala by Berridge and Oschman.The basal plasma membrane of the primary cell is extremely irregular, giving rise to a complex interconnecting network of basal channels. The compartments of cytoplasm entrapped within this system of basal infoldings contain mitochondria, free ribosomes, and small amounts of rough endoplasmic reticulum. The mitochondria are distinctive in that the cristae run parallel to the long axis of the organelle.

On a Nonlinear System of Reaction-Diffusion Equations

2006 ◽  
Vol 11 (2) ◽  
pp. 115-121 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Weak Solution ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic System ◽  
Positive Parameter ◽  
Nonlinear Elliptic ◽  
Positive Weak Solution

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

scholarly journals NF-κB in Cancer Immunity: Friend or Foe?

Cells ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 355
Author(s):  
Guilhem Lalle ◽  
Julie Twardowski ◽  
Yenkel Grinberg-Bleyer
Keyword(s):  
Immune Responses ◽  
Therapeutic Potential ◽  
Cell Types ◽  
Transcriptional Activators ◽  
New Class ◽  
Complex Interactions ◽  
Cancer Immunity ◽  
Distinct Cell ◽  
Cancer Initiation ◽  
Cancer Outcome

The emergence of immunotherapies has definitely proven the tight relationship between malignant and immune cells, its impact on cancer outcome and its therapeutic potential. In this context, it is undoubtedly critical to decipher the transcriptional regulation of these complex interactions. Following early observations demonstrating the roles of NF-κB in cancer initiation and progression, a series of studies converge to establish NF-κB as a master regulator of immune responses to cancer. Importantly, NF-κB is a family of transcriptional activators and repressors that can act at different stages of cancer immunity. In this review, we provide an overview of the selective cell-intrinsic contributions of NF-κB to the distinct cell types that compose the tumor immune environment. We also propose a new view of NF-κB targeting drugs as a new class of immunotherapies for cancer.

scholarly journals Glucocorticoid Receptor β (GRβ): Beyond Its Dominant-Negative Function

2021 ◽  
Vol 22 (7) ◽  
pp. 3649
Author(s):  
Patricia Ramos-Ramírez ◽  
Omar Tliba
Keyword(s):  
Current Knowledge ◽  
Inflammatory Diseases ◽  
Cell Communication ◽  
Cell Types ◽  
The Body ◽  
Dominant Negative ◽  
Negative Effects ◽  
Independent Manner ◽  
Distinct Cell ◽  
Induced Apoptosis

Glucocorticoids (GCs) act via the GC receptor (GR), a receptor ubiquitously expressed in the body where it drives a broad spectrum of responses within distinct cell types and tissues, which vary in strength and specificity. The variability of GR-mediated cell responses is further extended by the existence of GR isoforms, such as GRα and GRβ, generated through alternative splicing mechanisms. While GRα is the classic receptor responsible for GC actions, GRβ has been implicated in the impairment of GRα-mediated activities. Interestingly, in contrast to the popular belief that GRβ actions are restricted to its dominant-negative effects on GRα-mediated responses, GRβ has been shown to have intrinsic activities and “directly” regulates a plethora of genes related to inflammatory process, cell communication, migration, and malignancy, each in a GRα-independent manner. Furthermore, GRβ has been associated with increased cell migration, growth, and reduced sensitivity to GC-induced apoptosis. We will summarize the current knowledge of GRβ-mediated responses, with a focus on the GRα-independent/intrinsic effects of GRβ and the associated non-canonical signaling pathways. Where appropriate, potential links to airway inflammatory diseases will be highlighted.

scholarly journals Integrodifference master equation describing actively growing blood vessels in angiogenesis

2020 ◽  
Vol 21 (7-8) ◽  
pp. 705-713 ◽  
Author(s):  
Luis L. Bonilla ◽  
Manuel Carretero ◽  
Filippo Terragni
Keyword(s):  
Master Equation ◽  
Blood Vessels ◽  
Transition Probabilities ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Birth Process ◽  
Sink Term ◽  
System Of Particles ◽  
Vessel Network ◽  
Tip Cells

AbstractWe study a system of particles in a two-dimensional geometry that move according to a reinforced random walk with transition probabilities dependent on the solutions of reaction-diffusion equations (RDEs) for the underlying fields. A birth process and a history-dependent killing process are also considered. This system models tumor-induced angiogenesis, the process of formation of blood vessels induced by a growth factor (GF) released by a tumor. Particles represent vessel tip cells, whose trajectories constitute the growing vessel network. New vessels appear and may fuse with existing ones during their evolution. Thus, the system is described by tracking the density of active tips, calculated as an ensemble average over many realizations of the stochastic process. Such density satisfies a novel discrete master equation with source and sink terms. The sink term is proportional to a space-dependent and suitably fitted killing coefficient. Results are illustrated studying two influential angiogenesis models.

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