In the nearly seven decades since the publication of Alan Turings work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his propose...

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2020.0268

Modern perspectives on near-equilibrium analysis of Turing systems

Periodic gene expression dynamics are key to cell and organism physiology. Studies of oscillatory expression have focused on networks with intuitive regulatory negative feedback loops, leaving unknown whether other common biochemical reactions can produce oscillations. Oscillation and noise have been proposed to support mammalian progenitor cells’ capacity to restore heterogenous, multimodal expression from extreme subpopulations, but underlying networks and specific roles of noise remained elusive. We use mass-action-based models to show that regulated RNA degradation involving as few as two RNA species—applicable to nearly half of human protein-coding genes—can generate sustained oscillations without imposed feedback. Diverging oscillation periods synergize with noise to robustly restore cell populations’ bimodal expression. The global bifurcation organizing this divergence relies on an oscillator and bistable switch which cannot be decomposed into two structural modules. Our work reveals surprisingly rich dynamics of post-transcriptional reactions and a potentially widespread mechanism useful for development and regeneration.

https://academic.oup.com/nar/article-pdf/50/7/3693/43402464/gkac217.pdf

Nonmodular oscillator and switch based on RNA decay drive regeneration of multimodal gene expression

Periodic gene expression dynamics are key to cell and organism physiology. Studies of oscillatory expression have focused on networks with intuitive regulatory negative feedback loops, leaving unknown whether other common biochemical reactions can produce oscillations. Oscillation and noise have been proposed to support mammalian progenitor cells' capacity to restore heterogenous, multimodal expression from extreme subpopulations, but underlying networks and specific roles of noise remained elusive. We use mass-action-based models to show that regulated RNA degradation involving as few as two RNA species-applicable to nearly half of human protein-coding genes-can generate sustained oscillations without explicit feedback. Diverging oscillation periods synergize with noise to robustly restore cell populations' bimodal expression on timescales of days. The global bifurcation organizing this divergence relies on an oscillator and bistable switch which cannot be decomposed into two structural modules. Our work reveals surprisingly rich dynamics of post-transcriptional reactions and a potentially widespread mechanism underlying development, tissue regeneration, and cancer cell heterogeneity. 

OUP accepted manuscript

Among oral tissues, the periodontium is permanently subjected to mechanical forces resulting from chewing, mastication, or orthodontic appliances. Molecularly, these movements induce a series of subsequent signaling processes, which are embedded in the biological concept of cellular mechanotransduction (MT). Cell and tissue structures, ranging from the extracellular matrix (ECM) to the plasma membrane, the cytosol and the nucleus, are involved in MT. Dysregulation of the diverse, fine-tuned interaction of molecular players responsible for transmitting biophysical environmental information into the cell’s inner milieu can lead to and promote serious diseases, such as periodontitis or oral squamous cell carcinoma (OSCC). Therefore, periodontal integrity and regeneration is highly dependent on the proper integration and regulation of mechanobiological signals in the context of cell behavior. Recent experimental findings have increased the understanding of classical cellular mechanosensing mechanisms by both integrating exogenic factors such as bacterial gingipain proteases and newly discovered cell-inherent functions of mechanoresponsive co-transcriptional regulators such as the Yes-associated protein 1 (YAP1) or the nuclear cytoskeleton. Regarding periodontal MT research, this review offers insights into the current trends and open aspects. Concerning oral regenerative medicine or weakening of periodontal tissue diseases, perspectives on future applications of mechanobiological principles are discussed.

From the Matrix to the Nucleus and Back: Mechanobiology in the Light of Health, Pathologies, and Regeneration of Oral Periodontal Tissues

The distribution of signaling molecules following mechanical or chemical stimulation of a cell defines cell polarization, with regions of high active Cdc42 at the front and low active Cdc42 at the rear. As reaction-diffusion phenomena between signaling molecules, such as Rho GTPases, define the gradient dynamics, we hypothesize that the cell shape influences the maintenance of the "front-to-back" cell polarization patterns. We investigated the influence of cell shape on the Cdc42 patterns using an established computational polarization model. Our simulation results showed that not only cell shape but also Cdc42 and Rho-related (in)activation parameter values affected the distribution of active Cdc42. Despite an initial Cdc42 gradient, the in silico results showed that the maximal Cdc42 concentration shifts in the opposite direction, a phenomenon we propose to call "reverse polarization". Additional in silico analyses indicated that "reverse polarization" only occurred in a particular parameter value space that resulted in a balance between inactivation and activation of Rho GTPases. Future work should focus on a mathematical description of the underpinnings of reverse polarization, in combination with experimental validation using, for example, dedicated FRET-probes to spatiotemporally track Rho GTPase patterns in migrating cells. In summary, the findings of this study enhance our understanding of the role of cell shape in intracellular signaling.

/pdf/on-the-influence-of-cell-shape-on-dynamic-reaction-diffusion-3zv0mj9ny8.pdf

On the influence of cell shape on dynamic reaction-diffusion polarization patterns.

The polarization and motility of eukaryotic cells depends on assembly and contraction of the actin cytoskeleton and its regulation by proteins called GTPases. The activity of GTPases causes assembly of filamentous actin (by GTPases Cdc42, Rac), resulting in protrusion of the cell edge. Mathematical models for GTPase dynamics address the spontaneous formation of patterns and nonuniform spatial distributions of such proteins in the cell. Here we revisit the wave-pinning model for GTPase-induced cell polarization, together with a number of extensions proposed in the literature. These include introduction of sources and sinks of active and inactive GTPase (by the group of A. Champneys), and negative feedback from F-actin to GTPase activity. We discuss these extensions singly and in combination, in 1D, and 2D static domains. We then show how the patterns that form (spots, waves, and spirals) interact with cell boundaries to create a variety of interesting and dynamic cell shapes and motion.

/pdf/spots-stripes-and-spiral-waves-in-models-for-static-and-4harmo4c7n.pdf

Yue Liu

Papers

Spots, stripes, and spiral waves in models for static and motile cells : GTPase patterns in cells.