Mathematical approach to nonlocal interactions using a reaction-diffusion system.
Dev Growth Differ
; 59(5): 388-395, 2017 Jun.
Article
em En
| MEDLINE
| ID: mdl-28573780
ABSTRACT
In recent years, spatial long range interactions during developmental processes have been introduced as a result of the integration of microscopic information, such as molecular events and signaling networks. They are often called nonlocal interactions. If the profile of a nonlocal interaction is determined by experiments, we can easily investigate how patterns generate by numerical simulations without detailed microscopic events. Thus, nonlocal interactions are useful tools to understand complex biosystems. However, nonlocal interactions are often inconvenient for observing specific mechanisms because of the integration of information. Accordingly, we proposed a new method that could convert nonlocal interactions into a reaction-diffusion system with auxiliary unknown variables. In this review, by introducing biological and mathematical studies related to nonlocal interactions, we will present the heuristic understanding of nonlocal interactions using a reaction-diffusion system.
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MEDLINE
Assunto principal:
Modelos Teóricos
Tipo de estudo:
Prognostic_studies
Idioma:
En
Ano de publicação:
2017
Tipo de documento:
Article