相关论文: Mathematical models in biology

Mathematical models that describe the tumor growth process have been formulated by several authors in order to understand how cancer develops and to develop new treatment approaches. In this study, it is aimed to investigate the long-time…

We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating).…

Microorganisms often perform chemotaxis, (i.e., sensing and moving toward a region with a higher concentration of an attractive chemical) by changing the rate of tumbling for random walk. We studied several models with internal adaptive…

While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we…

Multicellular chemotaxis can occur via individually chemotaxing cells that are mechanically coupled. Alternatively, it can emerge collectively, from cells chemotaxing differently in a group than they would individually. Here we consider…

This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two…

The phenomenon where cells with elongated protrusions, such as neurons, communicate by contacting other cells and arrange themselves appropriately is termed cell sorting through haptotaxis. This phenomenon is described by partial…

Mathematical models have been widely used to describe the collective movement of bacteria by chemotaxis. In particular, bacterial concentration waves traveling in a narrow channel have been experimentally observed and can be precisely…

Cells are constantly exposed to diverse stimuli-chemical, mechanical, or electrical-that guide their movement. In physiological conditions, these signals often overlap, as seen during infections, where neutrophils and dendritic cells…

Based on recent experiments with time-lapse fluorescent imaging, we propose a cellular automaton model for the dynamics of vascular endothelial cells (ECs) in angiogenic morphogenesis. The model successfully reproduces cell mixing behavior,…

Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a…

Auto-chemotaxis, the directed movement of cells along gradients in chemicals they secrete, is central to the formation of complex spatiotemporal patterns in biological systems. Since the introduction of the Keller--Segel model, numerous…

This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on…

Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…

Cells and microorganisms adopt various strategies to migrate in response to different environmental stimuli. To date, many modeling research has focused on the crawling-based Dictyostelium discoideum (Dd) cells migration induced by…

The collective chemotaxis of multicellular clusters is an important phenomenon in various physiological contexts, ranging from embryonic development to cancer metastasis. Such clusters often display interesting shape dynamics and…

Models for chemotaxis are based on gradient sensing of individual organisms. The key contribution of Keller and Segel is showing that erratic movements of individuals may result in an accurate chemotaxis phenomenon as a group. In this paper…

Aberrantly regulated cell motility is a hallmark of cancer cells. A hybrid agent-based model has been developed to investigate the synergistic and antagonistic cell motility-impacting effects of three microenvironment variables…

Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and…

The ability of many living systems to actively self-propel underlies critical biomedical, environmental, and industrial processes. While such active transport is well-studied in uniform settings, environmental complexities such as geometric…