Bidirectional crosstalk between epithelial-mesenchymal plasticity and IFNγ-induced PD-L1 expression promotes tumour progression.

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 (IFNγ)-induced PD-L1 expression. Our model shows that via interaction with microRNA-200 (miR-200), the multi-stability of the EMT regulatory circuit is mirrored in PD-L1 levels, which are further amplified by IFNγ stimulation. This IFNγ-mediated effect is most prominent for cells in a fully mesenchymal state and less strong for those in an epithelial or partially mesenchymal state. In addition, bidirectional crosstalk between miR-200 and PD-L1 implies that IFNγ stimulation allows cells to undergo EMT for lower amounts of inducing signal, and the presence of IFNγ accelerates EMT and decelerates mesenchymal-epithelial transition (MET). Overall, our model agrees with published findings and provides insight into possible mechanisms behind EMT-mediated immune evasion, and primary, adaptive, or acquired resistance to immunotherapy. Our model can be used as a starting point to explore additional crosstalk mechanisms, as an improved understanding of these mechanisms is indispensable for developing better diagnostic and therapeutic options for cancer patients.

Extracting relevant physiological information from polar auxin transport data in Panax ginseng.

BACKGROUND: 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. RESULTS: We found that PAT in ginseng stems, as compared to Arabidopsis inflorescence stems, has a 2-fold lower transport velocity and a 3-fold lower steady state auxin flux. CONCLUSION: We were able to pinpoint two physiological parameters that influenced the observed transport characteristics in ginseng which differ from Arabidopsis, namely an increase in immobilization together with a reduced reflux of IAA from the surrounding tissue back to the transporting cells.

Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process.

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 λ. 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 $\nu_{\lambda}^*$. The aim of this paper is to prove that the map $\lambda\mapsto\nu_{\lambda}^*$ is continuous (in the topology of weak convergence of probability measures). The studied dynamical system is inspired by certain stochastic models for cell division and gene expression.

Modeling biological gradient formation: combining partial differential equations and Petri nets.

Both 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. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

Modelling the dynamics of polar auxin transport in inflorescence stems of Arabidopsis thaliana.

The 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. It is based on a general advection-diffusion equation for auxin density, as suggested by the chemiosmotic theory, but is extended to incorporate both immobilization of auxin and exchange with the surrounding tissue of cells involved in PAT, in order to account for crucial observations. We found that development of the present model assisted effectively in the analysis of experimental observations. As an example, we discuss the analysis of a quadruple mutant for all four AUX1/LAX1-LAX3 influx carriers genes. We found a drastic change in the parameters governing the exchange of PAT channels with the surrounding tissue, whereas the velocity was still of the order of magnitude of the wild type. In addition, the steady-state flux of auxin through the PAT system of the mutant did not exhibit a saturable component, as we found for the wild type, suggesting that the import carriers are responsible for the saturable component in the wild type. In the accompanying Supplementary data available at JXB online, we describe in more detail the data-driven development of the model, review and derive predictions from a mathematical model of the chemiosmotic theory, and explore relationships between parameters in our model and processes and parameters at the cellular level.

Modelling with measures: approximation of a mass-emitting object by a point source.

We 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. For all time t, we derive an L(2)([0,t];L2(Γ))-bound on the difference in flux on the boundary. Moreover, we derive for all t > 0 an L(2)(Ω)-bound and an L2([0,t];H(1)(Ω))-bound for the difference of the solutions to the two models.

Preface to '' Modeling with measures ''.

Different 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.

Polar auxin transport: an early invention.

In 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. IAA has been detected in members of Charophyta, but its developmental role and the occurrence of PAT are unknown. We show that naphthylphthalamic acid (NPA)-sensitive PAT occurs in internodal cells of Chara corallina. The relatively high velocity (at least 4-5 cm/h) of auxin transport through the giant (3-5 cm) Chara cells does not occur by simple diffusion and is not sensitive to a specific cytoplasmic streaming inhibitor. The results demonstrate that PAT evolved early in multicellular plant life. The giant Chara cells provide a unique new model system to study PAT, as Chara allows the combining of real-time measurements and mathematical modelling with molecular, developmental, cellular, and electrophysiological studies.