Morphogen protein gradients play an essential role in the spatial regulation of patterning during embryonic development. The most commonly accepted mechanism of protein gradient formation involves the diffusion from a localized source. Recently, there is growing experimental evidence for an alternative mechanism, which is based on direct cell contact via thin actin-rich cellular extensions known as cytonemes. We have developed several mathematical models of cytoneme-based morphogenesis at different levels of detail.
Arinemes relayed by macrophages
Another example of protrusion-based pattern formation has been observed in zebrafish. Similar to cytonemes in vertebrates, airinemes are dynamic cell extensions. One unique feature of airinemes is that their tips are relayed by macrophages. As yet, no one knows how this mechanism is evolutional benefit quantitatively. In an ongoing collaboration with Jun Allard, Dae-Seok Eom and Sohyeon Park, we are investigating this mechanism based on a stochastic model.
- S. Park, H. Kim, D.S. Eom, and J. Allard, “Zebrafish airinemes and optimally curvature for search,” In preparation, 2019+.
Signaling “bursts” via cytonemes
In vertebrates, cytonemes have a dynamic mechanism for transporting morphogens to targets. Morphogens are localized at the cytoneme tip, and are released immediately once the tip makes a contact with a target. This process generates morphogen “bursting” in a target cell. A crucial issue for this form of transport is how cytoneme tips find their targets. Two pathfinding hypotheses have been proposed: (i) random searching by rapid extension and retraction, or (ii) attraction by a chemoattractant. Here we analyze a doubly stochastic process for cytoneme-based search-and-capture in vertebrates. To deal with the complex nature of the stochastic process, we made use of some results in probability theory: the strong Markov property and queuing theory.
- P.C. Bressloff and H. Kim, “Search-and-capture model of cytoneme-mediated morphogen gradient formation,” Physical Review E, 99 052401, 2019.
- H. Kim and P.C. Bressloff, “Impulsive signaling model of cytoneme-based morphogen gradient formation,” Physical Biology, 16 056005, 2019.
Cytoneme transport mechanisms for gradient formation
In invertebrates, there are several hypotheses regarding the nature of interactions between cytonemes and target cells. Cytonemes from a single source can link to multiple target cells such that the number of cytonemes per target is non-uniform. Moreover, contact between a cytoneme tip and a target cell could involve a direct contact or an indirect contact mediated by a synapse. Here we compare the several different hypotheses concerning the contact mechanism between cytoneme tips and target cells in invertebrates based on PDE models.
- P.C. Bressloff and H. Kim, “Bidirectional transport model of morphogen gradient formation via cytonemes,” Physical Biology, 15 026101, 2018.
- H. Kim and P.C. Bressloff, “Direct vs. synaptic coupling in a mathematical model of cytoneme-based morphogen gradient formation,” SIAM Journal on Applied Mathematics, 78 2323-2347, 2018.