Related Experiment Video
Updated: Oct 7, 2025

High-Throughput Live Imaging of Microcolonies to Measure Heterogeneity in Growth and Gene Expression
Published on: April 18, 2021
Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a
Jan-Erik Busse1, Sílvia Cuadrado2, Anna Marciniak-Czochra3
1Institute of Applied Mathematics, Interdisciplinary Center for Scientific Computing (IWR) and BIOQUANT Center, Heidelberg, Germany.
Abstract:
In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (leukemic cells) undergoing mutation and clonal selection. We prove existence and uniqueness of non-trivial steady states and study their asymptotic stability. The results are compared to those of the system without mutation. Existence of equilibria is proved by formulating the steady state problem as an eigenvalue problem and applying a version of the Krein-Rutmann theorem for Banach lattices. The stability at equilibrium is analysed using linearisation and the Weinstein-Aronszajn determinant which allows to conclude local asymptotic stability.
Related Concept Videos
Cells Coordinate Growth and Proliferation
Transmission-Line Differential Equations
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
Non-equilibrium in the Cell
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Mutation, Gene Flow, and Genetic Drift
Cancers Originate from Somatic Mutations in a Single Cell

