A stochastic first-order reaction gene translation and nuclear-to-cell ratio homeostasis model Cell size varies between different cell types, and between different growth and osmotic conditions. However, the nuclear-to-cell volume ratio (N/C ratio) is largely maintained. In this presentation, I will first introduce an osmotic pressure balance model of N/C ratio determination, which relates the N/C …
Understanding the effect of white matter delays on large scale brain dynamics The presence of myelin is a powerful structural factor that controls the conduction velocity of mammalian axons. It is the combination of local synaptic activity and non-local delayed axonal interactions within the cortex that is believed to be the major source of large-scale …
High-Order Accuracy Computation of Coupling Functions for Strongly Coupled Oscillators We develop a general framework for identifying phase reduced equations for finite populations of coupled oscillators that is valid far beyond the weak coupling approximation. This strategy represents a general extension of the theory from and yields coupling functions that are valid to higher-order accuracy …
Modelling intermediate filaments – from filament elongation to network organization Intermediate filaments (IFs) constitute a crucial component of the cytoskeleton, playing vital roles in maintaining cell shape, mechanical integrity, and providing support for cell migration and signalling. Unlike microtubules and actin filaments, intermediate filaments form a diverse family of proteins, including keratins, vimentin, desmin, and …
Mathematical Optimization of Drug Regimens Improvements in drug regimens can make a difference in both clinical trial success and patient outcomes. Optimal control can be used to mathematically optimize regimens, which can then be tested experimentally and clinically. I will show examples of optimization of regimens for math models of various diseases, and discuss some …
Simplifying Soil Organic Carbon Model Structures with First-Order Linear Decay: When, How, and Why? Soil organic matter is the largest terrestrial pool of carbon on Earth, containing more carbon than terrestrial vegetation and more carbon than even the atmosphere. Most Earth System Models (ESMs), designed to integrate and examine how the interdependent systems of the …
Turing Patterns as a Model for Brain Folding Development Neuroscientists are interested in correlating brain function with anatomy. However, the highly complex folding patterns of the brain and the high variability in folding patterns across individuals contribute to the difficulty in understanding healthy brain function and disease. Interestingly, there is no consensus in neurobiology as …
The Eye-Lens Growth Model Biological lens in the eye of a mammal focuses light on the retina. Its shape and size is crucial for that purpose. We provide the first ever mathematical growth model of the mouse eye-lens and succeed in capturing a variety of behavior about the size of the lens, number of cells …
Chaos and homeostasis in multiple timescales dynamics Complex nonlinear and network dynamics, as observed in many biological systems, are prone to generate complex chaotic activity. Fortunately, in nature, these systems are still able to maintain essential biological function, and may be robust to changes in the environment despite their chaotic nature, until they break down …
Cytoneme-mediated morphogenesis Morphogen protein gradients play an essential role in the spatial regulation of patterning during embryonic development. The most commonly accepted mechanism of protein gradient formation involves the diffusion and degradation of morphogens from a localized source. Recently, an alternative mechanism has been proposed, which is based on cell-to-cell transport via thin, actin-rich cellular …
