Implementing vertex dynamics models of cell populations in biology within a consistent computational framework

Alexander G Fletcher1, James M Osborne, Philip K Maini

  • 1Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.

Summary

This study introduces a consistent computational framework for implementing vertex dynamics models of epithelial cell sheets. These models represent cells as polygons or polyhedrons whose vertices respond to forces. The framework, called Chaste, is open-source and fully tested. It allows researchers to modify assumptions about cell behavior and compare models more effectively. The authors demonstrate the framework's versatility using multiple biological examples. They provide detailed implementations and model extensions. This approach supports reproducibility and broader applications in studying cell dynamics.

Frequently Asked Questions

Related Concept Videos

Non-equilibrium in the Cell01:16

Non-equilibrium in the Cell

An important concept in studying metabolism and energy is that of chemical equilibrium. Most chemical reactions are reversible. They can proceed in both directions, releasing energy into their environment in one direction, and absorbing it from the environment in the other direction. The same is true for the chemical reactions involved in cell metabolism, such as the breaking down and building up of proteins into and from individual amino acids, respectively. Reactants within a closed system...
4.0K
Protein Dynamics in Living Cells01:19

Protein Dynamics in Living Cells

Different fluorescence-based techniques are used to study the protein dynamics in living cells. These techniques include FRAP, FRET, and PET.
Fluorescent recovery after photobleaching (FRAP) is a fluorescent-protein-based detection technique used to quantify protein movement rates within the cell. This method exposes a small portion of the cell to an intense laser beam. The laser beam causes permanent photobleaching of the fluorophore-tagged proteins in the exposed region. As the bleached...
1.9K
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
336
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
442
Growth Models with Integration: Problem Solving01:27

Growth Models with Integration: Problem Solving

In population modeling, integration provides a systematic way to determine accumulated quantities from known rates of change. One such application arises in ecology, where the total weight of a fish population in a body of water is referred to as its biomass. When the rate of growth of this biomass is known as a function of time, calculus can be used to determine the total biomass at a future date.Growth Rate and Biomass FunctionLet the growth rate of the fish population be represented by a...
167
Cytoskeletal Coordination in Cell Migration01:32

Cytoskeletal Coordination in Cell Migration

A migrating cell changes its shape during the cyclic events of attachment and detachment from the substratum and repositions the cell organelles correspondingly. These complex events are orchestrated by the dynamic cytoskeletal network comprising actin filaments, intermediate filaments, and microtubules. Cytoskeletal crosstalk — the direct and indirect communication between the different components — is crucial for this coordination. Direct communication involves various linker...
4.9K