NDLI: Direct vs. Synaptic Coupling in a Mathematical Model of Cytoneme-Based Morphogen Gradient Formation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bressloff, Paul C. Kim, Hyunjoong
Copyright Year	2018
Abstract	In developmental biology, an important problem is understanding the mechanisms underlying the formation of morphogen concentration gradients. The most commonly hypothesized mechanism involves the diffusion and degradation of morphogens from a localized source. Recently, however, an alternative mechanism has been proposed, which is based on cell-to-cell contacts mediated by thin, actin-rich cellular extensions known as cytonemes. In this paper, we develop a one-dimensional advection-diffusion transport model of cytoneme-based morphogenesis. In particular, we compare two distinct types of contact between a cytoneme tip and a target cell: direct contact and indirect contact mediated by a synapse. First, we calculate the steady-state concentration profiles and show that synaptic contacts generate broader concentration profiles, thus allowing for longer-range interactions. We then consider two alternative methods for determining how quickly the system approaches steady-state: either calculating the accumulation time using Laplace transforms, or analyzing the discrete spectrum of the associated evolution operator. The latter is a nontrivial eigenvalue problem due to the nature of the boundary conditions. Finally, we extend the direct contact model to the case of a stochastically switching boundary at the cytoneme tip, in order to take into account the fact that cytonemes dynamically grow and shrink, resulting in more temporary contacts with target cells.
Sponsorship	National Science Foundation
Starting Page	2323
Ending Page	2347
Page Count	25
File Format	PDF
ISSN	00361399
DOI	10.1137/18M1179699
e-ISSN	1095712X
Issue Number	5
Volume Number	78
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-09-04
Access Restriction	Subscribed
Subject Keyword	Initial-boundary value problems for second-order parabolic equations morphogenesis Developmental biology, pattern formation cytoneme advection-diffusion boundary value problem
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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