Mathematical modelling in developmental biology

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

doi:10.1530/rep-12-0081

Cited by 8 publications

(7 citation statements)

References 60 publications

(62 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We focus on the features to which biologists may wish to pay attention to appreciate the main modelling assumptions and the type of information that can be gained from a specific computational study. More mathematically oriented reviews in relation with the modelling techniques described here below can be found in (Newman, 2005;Soneji et al, 2007;Zhou and Huang, 20011;Swat et al, 2012;Vasieva et al, 2013;D'Alessandro et al, 2014), among others. In this section, when listing various modelling approaches, we mainly refer to models that will be discussed later in this review.…”

Section: Key Modelling Choicesmentioning

confidence: 99%

Computational models for the dynamics of early mouse embryogenesis

Tosenberger¹,

Gonze²,

Chazaud³

et al. 2019

Int. J. Dev. Biol.

View full text Add to dashboard Cite

Early embryonic development, from the zygote to the blastocyst, is a paradigm of a dynamic, self-organised process. It involves gene expression, mechanical interactions between cells, cell division and inter- and intracellular signalling. Imaging and transcriptomic data have significantly improved our understanding of early embryogenesis in mammals. However, they also reveal a great level of complexity. How the genetic, mechanical, and regulatory processes interact to ensure reproducible development is thus much investigated by computational modelling, which allows a dissection of the mechanisms controlling cell fate decisions. In this review, we discuss the main types of modelling approaches that have been used to investigate the dynamics of preimplantation mammalian development. We also discuss the insights provided by modelling into our understanding of the specification processes leading to the three types of cells in the embryo 4.5 days after fertilization: the trophectoderm, the epiblast and the primitive endoderm.

show abstract

Section: Key Modelling Choicesmentioning

confidence: 99%

Computational models for the dynamics of early mouse embryogenesis

Tosenberger¹,

Gonze²,

Chazaud³

et al. 2019

Int. J. Dev. Biol.

View full text Add to dashboard Cite

show abstract

“…Mathematical modeling is an excellent method that has been used successfully to study many developmental processes (Fletcher et al, 2017;George et al, 2015;George and Lubkin, 2018;Vasieva et al, 2013). It has significantly improved our understanding of zebrafish development (Sharpe, 2017;Wertheim and Roose, 2017;Yamaguchi et al, 2007;Zhu et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of the interaction between yolk utilization and fish growth in zebrafish,Danio rerio

et al. 2021

View full text Add to dashboard Cite

Optimal embryonic development plays a major role in the health of an individual beyond the developmental stage. Nutritional perturbation during development is associated with cardiovascular and metabolic disease later in life. With both nutritional uptake and overall growth being risk factors for eventual health, it is necessary to understand not only the behavior of the processes during development but also their interactions. In this study, we used differential equations, image analyses, curve fittings, parameter estimation and laboratory experiments to quantify the rate of yolk absorption and its effect on early development of a vertebrate model (Danio rerio). Findings from this study establish a nonlinear functional relationship between nutrient absorption and early fish growth. We found that the rate of change in fish length and yolk utilization is logistic, that is the yolk decays rapidly for a period of time before leveling out. An interesting finding from this study is that yolk utilization reaches its maximum at 84 h post-fertilization. We validated our mathematical models against experimental observations, making them powerful tools for replication and future simulations.

show abstract

“…Biological pattern formation is a complex phenomenon which is studied experimentally in a number of model organisms [1] and theoretically by means of various mathematical techniques [2,3]. One of the model organisms commonly used in biological studies of pattern formation is the fly (Drosophila) embryo [4].…”

Section: Introductionmentioning

confidence: 99%

Formation of Morphogenetic Patterns in Cellular Automata

Rasolonjanahary

Vasiev

2020

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

One of the most important problems in contemporary science, and especially in biology, is to reveal mechanisms of pattern formation. On the level of biological tissues, patterns form due to interactions between cells. These interactions can be long-range if mediated by diffusive molecules or short-range when associated with cell-to-cell contact sites. Mathematical studies of longrange interactions involve models based on differential equations while shortrange interactions are modelled using discrete type models. In this paper, we use cellular automata (CA) technique to study formation of patterns due to shortrange interactions. Namely, we use von Neumann cellular automata represented by a finite set of lattices whose states evolve according to transition rules. Lattices can be considered as representing biological cells (which, in the simplest case, can only be in one of the two different states) while the transition rules define changes in their states due to the cell-to-cell contact interactions. In this model, we identify rules resulting in the formation of stationary periodic patterns. In our analysis, we distinguish rules which do not destroy preset patterns and those which cause pattern formation from random initial conditions. Also, we check whether the forming patterns are resistant to noise and analyse the time frame for their formation. Transition rules which allow formation of stationary periodic patterns are then discussed in terms of pattern formation in biology.

show abstract

Mathematical modelling in developmental biology

Cited by 8 publications

References 60 publications

Computational models for the dynamics of early mouse embryogenesis

Computational models for the dynamics of early mouse embryogenesis

Mathematical modeling of the interaction between yolk utilization and fish growth in zebrafish,Danio rerio

Formation of Morphogenetic Patterns in Cellular Automata

Contact Info

Product

Resources

About