Related papers: Robust Approximate Characterization of Single-Cell…
Time-lapse fluorescent microscopy (TLFM) combined with predictive mathematical modelling is a powerful tool to study the inherently dynamic processes of life on the single-cell level. Such experiments are costly, complex and labour…
Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are…
3D microscopy is key in the investigation of diverse biological systems, and the ever increasing availability of large datasets demands automatic cell identification methods that not only are accurate, but also can imply the uncertainty in…
We study a continuous time stochastic process on strings made of two types of particles, whose dynamics mimics the behaviour of microtubules in a living cell; namely, the strings evolve via a competition between (local) growth/shrinking as…
Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of…
A simulation approach to the stochastic growth of bacterial towers is presented, in which a non-uniform and finite nutrient supply essentially determines the emerging structure through elementary chemotaxis. The method is based on cellular…
In literature, a stochastic model for spreading nodes in a cellular cell is available. Despite its existence, the current method does not offer any versatility in dealing with sectored layers. Of course, this needed adaptability could be…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
The stochastic simulation algorithm commonly known as Gillespie's algorithm is now used ubiquitously in the modelling of biological processes in which stochastic effects play an important role. In well-mixed scenarios at the sub-cellular…
For microscale heterogeneous PDEs, this article further develops novel theory and methodology for their macroscale mathematical/asymptotic homogenization. This article specifically encompasses the case of quasi-periodic heterogeneity with…
Cells achieve size homeostasis by regulating their division timing based on their size, added size, and cell cycle time. Previous research under steady-state conditions demonstrated the robustness of these mechanisms. However, their dynamic…
A panel dataset satisfies marginal homogeneity if the time-specific marginal distributions are homogeneous or time-invariant. Marginal homogeneity is relevant in many economic settings, including dynamic discrete games,…
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
Inspired by the need for effective stochastic models to describe the complex behavior of biological motor proteins that move on linear tracks exact results are derived for the velocity and dispersion of simple linear sequential models (or…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
Single-Cell RNA sequencing (scRNA-seq) measurements have facilitated genome-scale transcriptomic profiling of individual cells, with the hope of deconvolving cellular dynamic changes in corresponding cell sub-populations to better…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…
We consider a multiscale stochastic compartmental model with three types of cells (stem cells, immature cells and mature cells) which combines cell proliferation and cell differentiation. We derive a hydrodynamic limit when the number of…
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the…
Tracking cells and detecting mitotic events in time-lapse microscopy image sequences is a crucial task in biomedical research. However, it remains highly challenging due to dividing objects, low signal-tonoise ratios, indistinct boundaries,…