Diffusive wave dynamics beyond the continuum limit

Modeling the Reactive Oxygen Species (ROS) wave in Chlamydomonas reinhardtii colonies

Reactive oxygen species (ROS) play a crucial role as signaling molecules in both plant and animal cells, enabling rapid responses to various stimuli. Among the many cellular mechanisms used to generate and transduce ROS signals, ROS-induced-ROS release (RIRR) is emerging as an important pathway involved in the responses of various multicellular and unicellular organisms to environmental stresses. In RIRR, one cellular compartment, organelle, or cell generates or releases ROS, triggering an increased ROS production and release by another compartment, organelle, or cell, thereby giving rise to a fast propagating ROS wave. This RIRR-based signal relay has been demonstrated to facilitate mitochondria-to-mitochondria communication in animal cells and long-distance systemic signaling in plants in response to biotic and abiotic stresses. More recently, it has been discovered that different unicellular microorganism communities also exhibit a RIRR cell-to-cell signaling process triggered by a localized stress treatment. However, the precise mechanism underlying the propagation of the ROS signal among cells within these unicellular communities remained elusive. In this study, we employed a reaction-diffusion model incorporating the RIRR mechanism to analyze the propagation of ROS-mediated signals. By effectively balancing production and scavenging processes, our model successfully reproduces the experimental ROS signal velocities observed in unicellular green algae (Chlamydomonas reinhardtii) colonies grown on agar plates, furthering our understanding of intercellular ROS communication.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

From localized to well mixed: How commuter interactions shape disease spread

Interactions between commuting individuals can lead to large-scale spreading of rumors, ideas, or disease, even though the commuters have no net displacement. The emergent dynamics depend crucially on the commuting distribution of a population, that is how the probability to travel to a destination decays with distance from home. Applying this idea to epidemics, we will demonstrate the qualitatively different infection dynamics emerging from populations with different commuting distributions. If the commuting distribution is exponentially localized, then we recover a reaction-diffusion system and observe Fisher waves traveling at a speed proportional to the characteristic commuting distance. If the commuting distribution has a long tail, then no finite-velocity waves can form, but we show that, in some regimes, there is nontrivial spatial dependence that the well-mixed approximation neglects. We discuss how, in all cases, an initial dispersal-dominated regime can allow the disease to go undetected for a finite amount of time before exponential growth takes over. This "offset time" is a quantity of huge importance for epidemic surveillance and yet largely ignored in the literature.