Delay-driven oscillations via Axin2 feedback in the Wnt/β-catenin signalling pathway

Turing Pattern Formation in Reaction-Cross-Diffusion Systems with a Bilayer Geometry

Conditions for self-organisation via Turing's mechanism in biological systems represented by reaction-diffusion or reaction-cross-diffusion models have been extensively studied. Nonetheless, the impact of tissue stratification in such systems is under-explored, despite its ubiquity in the context of a thin epithelium overlying connective tissue, for instance the epidermis and underlying dermal mesenchyme of embryonic skin. In particular, each layer can be subject to extensively different biochemical reactions and transport processes, with chemotaxis - a special case of cross-diffusion - often present in the mesenchyme, contrasting the solely molecular transport typically found in the epidermal layer. We study Turing patterning conditions for a class of reaction-cross-diffusion systems in bilayered regions, with a thin upper layer and coupled by a linear transport law. In particular, the role of differential transport through the interface is explored together with the presence of asymmetry between the homogeneous equilibria of the two layers. A linear stability analysis is carried out around a spatially homogeneous equilibrium state in the asymptotic limit of weak and strong coupling strengths, where quantitative approximations of the bifurcation curve can be computed. Our theoretical findings, for an arbitrary number of reacting species, reveal quantitative Turing conditions, highlighting when the coupling mechanism between the layered regions can either trigger patterning or stabilize a spatially homogeneous equilibrium regardless of the independent patterning state of each layer. We support our theoretical results through direct numerical simulations, and provide an open source code to explore such systems further.

Exosomal-long non-coding RNAs journey in colorectal cancer: Evil and goodness faces of key players

Exosomes are nano-vesicles (NVs) secreted by cells and take part in cell-cell communications. Lately, these exosomes were proved to have dual faces in cancer. Actually, they can contribute to carcinogenesis through epithelial-mesenchymal transition (EMT), angiogenesis, metastasis and tumor microenvironment (TME) of various cancers, including colorectal cancer (CRC). On the other hand, they can be potential targets for cancer treatment. CRC is one of the most frequent tumors worldwide, with incidence rates rising in the recent decades. In its early stage, CRC is asymptomatic with poor treatment outcomes. Therefore, finding a non-invasive, early diagnostic biomarker tool and/or suitable defender to combat CRC is mandatory. Exosomes provide enrichment and safe setting for their cargos non-coding RNAs (ncRNAs) and proteins, whose expression levels can be upregulated ordown-regulated in cancer. Hence, exosomes can be used as diagnostic and/or prognostic tools for cancer. Moreover, exosomes can provide a novel potential therapeutic modality for tumors via loading with specific chemotherapeutic agents, with the advantage of possible tumor targeting. In this review, we will try to collect and address recent studies concerned with exosomes and their cargos' implications for CRC diagnosis and/or hopefully, treatment.

Fixed and Distributed Gene Expression Time Delays in Reaction-Diffusion Systems

Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can shrink the Turing space, thereby inhibiting patterns from forming across large ranges of parameters. Such delays can also increase the time taken for pattern formation even when Turing instabilities occur. Here, we consider reaction-diffusion models incorporating fixed or distributed time delays, modelling the underlying stochastic nature of gene expression dynamics, and analyse these through a systematic linear instability analysis and numerical simulations for several sets of different reaction kinetics. We find that even complicated distribution kernels (skewed Gaussian probability density functions) have little impact on the reaction-diffusion dynamics compared to fixed delays with the same mean delay. We show that the location of the delay terms in the model can lead to changes in the size of the Turing space (increasing or decreasing) as the mean time delay, [Formula: see text], is increased. We show that the time to pattern formation from a perturbation of the homogeneous steady state scales linearly with [Formula: see text], and conjecture that this is a general impact of time delay on reaction-diffusion dynamics, independent of the form of the kinetics or location of the delayed terms. Finally, we show that while initial and boundary conditions can influence these dynamics, particularly the time-to-pattern, the effects of delay appear robust under variations of initial and boundary data. Overall, our results help clarify the role of gene expression time delays in reaction-diffusion patterning, and suggest clear directions for further work in studying more realistic models of pattern formation.

Signalling dynamics in embryonic development

In multicellular organisms, cellular behaviour is tightly regulated to allow proper embryonic development and maintenance of adult tissue. A critical component in this control is the communication between cells via signalling pathways, as errors in intercellular communication can induce developmental defects or diseases such as cancer. It has become clear over the last years that signalling is not static but varies in activity over time. Feedback mechanisms present in every signalling pathway lead to diverse dynamic phenotypes, such as transient activation, signal ramping or oscillations, occurring in a cell type- and stage-dependent manner. In cells, such dynamics can exert various functions that allow organisms to develop in a robust and reproducible way. Here, we focus on Erk, Wnt and Notch signalling pathways, which are dynamic in several tissue types and organisms, including the periodic segmentation of vertebrate embryos, and are often dysregulated in cancer. We will discuss how biochemical processes influence their dynamics and how these impact on cellular behaviour within multicellular systems.

Relating simulation studies by provenance-Developing a family of Wnt signaling models

For many biological systems, a variety of simulation models exist. A new simulation model is rarely developed from scratch, but rather revises and extends an existing one. A key challenge, however, is to decide which model might be an appropriate starting point for a particular problem and why. To answer this question, we need to identify entities and activities that contributed to the development of a simulation model. Therefore, we exploit the provenance data model, PROV-DM, of the World Wide Web Consortium and, building on previous work, continue developing a PROV ontology for simulation studies. Based on a case study of 19 Wnt/β-catenin signaling models, we identify crucial entities and activities as well as useful metadata to both capture the provenance information from individual simulation studies and relate these forming a family of models. The approach is implemented in WebProv, a web application for inserting and querying provenance information. Our specialization of PROV-DM contains the entities Research Question, Assumption, Requirement, Qualitative Model, Simulation Model, Simulation Experiment, Simulation Data, and Wet-lab Data as well as activities referring to building, calibrating, validating, and analyzing a simulation model. We show that most Wnt simulation models are connected to other Wnt models by using (parts of) these models. However, the overlap, especially regarding the Wet-lab Data used for calibration or validation of the models is small. Making these aspects of developing a model explicit and queryable is an important step for assessing and reusing simulation models more effectively. Exposing this information helps to integrate a new simulation model within a family of existing ones and may lead to the development of more robust and valid simulation models. We hope that our approach becomes part of a standardization effort and that modelers adopt the benefits of provenance when considering or creating simulation models.

We revise a provenance ontology for simulation studies of cellular biochemical models. Provenance information is useful for understanding the creation of a simulation model because it not only contains information about the entities and activities that have led to a simulation model but also their relations, all of which can be visualized. It provides additional structure by explicitly recording research questions, assumptions, and requirements and relating them along with data, qualitative models, simulation models, and simulation experiments through a small set of predefined but extensible activities.

We have applied our concept to a family of 19 Wnt signaling models and implemented a web-based tool (WebProv) to store the provenance information from these studies. The resulting provenance graph visualizes the story line of simulation studies and demonstrates the creation and calibration of simulation models, the successive attempts of validation and extension, and shows, beyond an individual simulation study, how the Wnt models are related. Thereby, the steps and sources that contributed to a simulation model are made explicit.

Our approach complements other approaches aimed at facilitating the reuse and assessment of simulation products in systems biology such as model repositories as well as annotation and documentation guidelines.