Related papers: Simulation of morphogen and tissue dynamics
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
An adult human body is made up of some 30 to 40 trillion cells, all of which stem from a single fertilized egg cell. The process by which the right cells appear to arrive in their right numbers at the right time at the right place --…
Tissue growth underpins a wide array of biological and developmental processes, and numerical modeling of growing systems has been shown to be a useful tool for understanding these processes. However, the phenomena that can be captured are…
The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that…
During organogenesis tissue grows and deforms. The growth processes are controlled by diffusible proteins, so-called morphogens. Many different patterning mechanisms have been proposed. The stereotypic branching program during lung…
We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models…
Simulations of biophysical systems inevitably include steps that correspond to time integrations of ordinary differential equations. These equations are often related to enzyme action in the synthesis and destruction of molecular species,…
Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics…
Biological cells utilize membranes and liquid-like droplets, known as biomolecular condensates, to structure their interior. The interaction of droplets and membranes, despite being involved in several key biological processes, is so far…
A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a…
Mollusk shells are an ideal model system for understanding the morpho-elastic basis of morphological evolution of invertebrates' exoskeletons. During the formation of the shell, the mantle tissue secretes proteins and minerals that calcify…
We propose a unified mechanism that reproduces the sequence of dynamical transitions observed during somitogenesis, the process of body segmentation during embryonic development, that is invariant across all vertebrate species. This is…
Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling…
Morphogens are secreted signaling molecules that mediate tissue patterning and growth of embryonic tissues. They are secreted in a localized region and spread through the tissue to form a graded concentration profile. We present a…
This paper presents a generic framework for the numerical simulation of transformation-diffusion processes in complex volume geometric shapes. This work follows a previous one devoted to the simulation of microbial degradation of organic…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
The gradual accumulation of damage and dysregulation during the aging of living organisms can be quantified. Even so, the aging process is complex and has multiple interacting physiological scales -- from the molecular to cellular to whole…
Our knowledge of how individual cells self-organize to form complex multicellular systems is being revolutionized by a data outburst, coming from high-throughput experimental breakthroughs such as single-cell RNA sequencing and spatially…
Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but…