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Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…
The spatial localization or sequestering of motile cargo and their dispersal within cells is an important process in a number of physiological contexts. The morphology of the cytoskeletal network, along which active, motor-driven…
How the very first nervous systems evolved remains a fundamental open question. Molecular and genomic techniques have revolutionized our knowledge of the molecular ingredients behind this transition but not yet provided a clear picture of…
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population…
A central problem of neuroscience involves uncovering the principles governing the organization of nervous systems which ensure robustness in brain development. The nematode Caenorhabditis elegans provides us with a model organism for…
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the…
We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…
The applicability of computational and dynamical systems models to organisms is scrutinized, using examples from developmental biology and cognition. Developmental morphogenesis is dependent on the inherent material properties of developing…
A single axon can generate branches connecting with plenty synaptic targets. Process of branching is very important for making connections in central nervous system. The interstitial branching along primary axon shaft occurs during nervous…
Recent advancements in the ability to construct three-dimensional (3D) tissues and organoids from stem cells and biomaterials have not only opened abundant new research avenues in disease modeling and regenerative medicine but also have…
Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically…
It is becoming increasingly appreciated that the signal transduction systems used by eukaryotic cells to achieve a variety of essential responses represent highly complex networks rather than simple linear pathways. While significant effort…
Score-based diffusion models generate new samples by learning the score function associated with a diffusion process. While the effectiveness of these models can be theoretically explained using differential equations related to the…
Extending deterministic compartments pharmacokinetic models as diffusions seems not realistic on biological side because paths of these stochastic processes are not smooth enough. In order to extend one compartment intra-veinous bolus…
Spatially annotated single-cell datasets provide unprecedented opportunities to dissect cell-cell communication in development and disease. Heterotypic signaling includes interactions between different cell types and is well established in…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
We propose a novel discrete model of central pattern generators (CPG), neuronal ensembles generating rhythmic activity. The model emphasizes the role of nonsynaptic interactions and the diversity of electrical properties in nervous systems.…
This work concerns a many-body deterministic model that displays life-like properties as emergence, complexity, self-organization, spontaneous compartmentalization, and self-regulation. The model portraits the dynamics of an ensemble of…
Diabetic neuropathy is a disorder characterized by impaired nerve function and reduction of the number of epidermal nerve fibers per epidermal surface. Additionally, as neuropathy related nerve fiber loss and regrowth progresses over time,…
We formulate the search for phenomenological models of synaptic plasticity as an optimization problem. We employ Cartesian genetic programming to evolve biologically plausible human-interpretable plasticity rules that allow a given network…