Epithelial-mesenchymal transition (EMT) and immunoevasion through upregulation of programmed death-ligand 1 (PD-L1) are important drivers of cancer progression. While EMT has been proposed to facilitate PD-L1-mediated immunosuppression, molecular mechanisms of their interaction remain obscure. Here, we provide insight into these mechanisms by proposing a mathematical model that describes the crosstalk between EMT and interferon gamma (IFN)-induced PD-L1 expression.
View Article and Find Full Text PDFBackground: Measuring polar auxin transport (PAT) in plants and drawing conclusions from the observed transport data is only meaningful if these data are being analysed with a mathematical model which describes PAT. In this report we studied the polar auxin transport in Panax ginseng stems of different age and grown on different substrates.
Methods: We measured polar IAA transport in stems using a radio labelled IAA and analysed the transport data with a mathematical model we developed for Arabidopsis.
We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly selected continuous transformation. It is assumed that the jumps appear at random moments, which coincide with the jump times of a Poisson process with intensity . The model of this type, although in a more general version, was examined in our previous papers, where we have shown, among others, that the Markov process under consideration possesses a unique invariant probability measure, say $\nu_{\lambda}^*$.
View Article and Find Full Text PDFThe special issue is available from: http://www.aimspress.com/newsinfo/1132.
View Article and Find Full Text PDFThe intercellular transport of auxin is driven by PIN-formed (PIN) auxin efflux carriers. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport either by direct translocation across the PM or by pumping auxin into secretory vesicles (SVs), leading to its secretory release upon fusion with the PM.
View Article and Find Full Text PDFBoth Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model.
View Article and Find Full Text PDFThe polar transport of the plant hormone auxin has been the subject of many studies, several involving mathematical modelling. Unfortunately, most of these models have not been experimentally verified. Here we present experimental measurements of long-distance polar auxin transport (PAT) in segments of inflorescence stems of Arabidopsis thaliana together with a descriptive mathematical model that was developed from these data.
View Article and Find Full Text PDFDifferent communities met in the research workshop ``Modeling with Measures" that took place at the Lorentz Center (Leiden, The Netherlands) during 26th--30th of August 2013. They were groups of researchers active in the following fields.
View Article and Find Full Text PDFWe consider a linear diffusion equation on Ω: = R(2) \ Ω[Symbol: see text], where Ω[Symbol: see text] is a bounded domain. The time-dependent flux on the boundary Γ: = ∂ Ω[Symbol: see text] is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of R(2) with a measure-valued point source in the origin and provide estimates for the quality of approximation.
View Article and Find Full Text PDFIn higher plants, cell-to-cell polar auxin transport (PAT) of the phytohormone auxin, indole-3-acetic acid (IAA), generates maxima and minima that direct growth and development. Although IAA is present in all plant phyla, PAT has only been detected in land plants, the earliest being the Bryophytes. Charophyta, a group of freshwater green algae, are among the first multicellular algae with a land plant-like phenotype and are ancestors to land plants.
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