Bidirectional transport model of morphogen gradient formation via cytonemes

Abstract

Morphogen protein gradients play an important role in the spatial regulation of patterning during embryonic development. The most commonly accepted mechanism for gradient formation is diffusion from a source combined with degradation. Recently, there has been growing interest in an alternative mechanism, which is based on the direct delivery of morphogens along thin, actin-rich cellular extensions known as cytonemes. In this paper, we develop a bidirectional motor transport model for the flux of morphogens along cytonemes, linking a source cell to a one-dimensional array of target cells. By solving the steady-state transport equations, we show how a morphogen gradient can be established, and explore how the mean velocity of the motors affects properties of the morphogen gradient such as accumulation time and robustness. In particular, our analysis suggests that in order to achieve robustness with respect to changes in the rate of synthesis of morphogen, the mean velocity has to be negative, that is, retrograde flow or treadmilling dominates. Thus the potential targeting precision of cytonemes comes at an energy cost. We then study the effects of non-uniformly allocating morphogens to the various cytonemes projecting from a source cell. This competition for resources provides a potential regulatory control mechanism not available in diffusion-based models.

Diffusion vs. direct transport in the precision of morphogen readout

“…Several past studies have focused on the formation dynamics of morphogen profiles ( Berezhkovskii et al, 2011 ; Bressloff and Kim, 2018 ; Shvartsman and Baker, 2012 ; Teimouri and Kolomeisky, 2016a ). Here, we model profiles in the steady state regime, as most of the experimental measurements to which we will later compare our results were taken during stages when the steady state approximation is valid ( Grimm et al, 2010 ; Gregor et al, 2007b ; Kicheva et al, 2007 ; Yu et al, 2009 ; Kanodia et al, 2009 ).…”

“…Therefore, as in past studies ( Gregor et al, 2007a ; Tostevin et al, 2007 ), we define the precision as , where is the standard deviation of the number of morphogen molecules arriving at cell j , and is the difference between the molecule number in that cell and the adjacent cell. As is typical in studies of both the DT ( Teimouri and Kolomeisky, 2016a ; Bressloff and Kim, 2018 ) and SDC ( Berezhkovskii et al, 2011 ; Shvartsman and Baker, 2012 ; Teimouri and Kolomeisky, 2016b ) mechanisms, we focus on a one-dimensional line of target cells. However, we derive analogous results for 2D and 3D systems, and we generally find that the dimensionality does not qualitatively change our results, as we discuss later.…”

“…They are supported by actin filaments, and it is thought that morphogen molecules are actively transported along the filaments via molecular motors ( Kornberg and Roy, 2014 ; Kornberg, 2014 ; Sanders et al, 2013 ; Huang and Kornberg, 2015 ). It was recently shown that a DT model that includes forward and backward transport of molecules within cytonemes reproduces experimentally measured accumulation times ( Teimouri and Kolomeisky, 2016a ; Bressloff and Kim, 2018 ), although the noise properties of this model were not considered. Here, we review the steady state properties of this model and derive its noise properties.…”

“…One well-known mechanism is the synthesis-diffusion-clearance (SDC) model in which morphogen molecules are produced by localized source cells and diffuse through extracellular space before degrading or being internalized by target cells ( Akiyama and Gibson, 2015 ; Gierer and Meinhardt, 1972 ; Lander et al, 2002 ; Müller et al, 2013 ; Rogers and Schier, 2011 ; Wilcockson et al, 2017 ). Alternatively, a direct transport (DT) model has been proposed where morphogen molecules travel through protrusions called cytonemes directly from the source cells to the target cells ( Akiyama and Gibson, 2015 ; Bressloff and Kim, 2018 ; Kornberg and Roy, 2014 ; Müller et al, 2013 ; Wilcockson et al, 2017 ). The presence of these two alternative theories raises the question of whether there exists a difference in the performance capabilities between cells utilizing one or the other.…”

“…The establishment of the Hedgehog morphogen gradient in Drosophila is highly correlated in both space and time with the formation of cytonemes ( Bischoff et al, 2013 ), while Wnt morphogens have been found to be highly localized around cell protrusions such as cytonemes ( Huang and Kornberg, 2015 ; Stanganello and Scholpp, 2016 ). Theoretical studies of both the SDC and DT models have examined these measurable effects ( Berezhkovskii et al, 2011 ; Bressloff and Kim, 2018 ; Shvartsman and Baker, 2012 ; Teimouri and Kolomeisky, 2016a ), but direct comparisons between the two models have thus far been poorly explored. In particular, it remains unknown whether one model allows for a cell to sense its local morphogen concentration more precisely than the other given biological parameters such as the number of cells or the characteristic lengthscale of the profile.…”