Flow Induced Symmetry Breaking in a Conceptual Polarity Model

Abstract

Important cellular processes, such as cell motility and cell division, are coordinated by cell polarity, which is determined by the non-uniform distribution of certain proteins. Such protein patterns form via an interplay of protein reactions and protein transport. Since Turing’s seminal work, the formation of protein patterns resulting from the interplay between reactions and diffusive transport has been widely studied. Over the last few years, increasing evidence shows that also advective transport, resulting from cytosolic and cortical flows, is present in many cells. However, it remains unclear how and whether these flows contribute to protein-pattern formation. To address this question, we use a minimal model that conserves the total protein mass to characterize the effects of cytosolic flow on pattern formation. Combining a linear stability analysis with numerical simulations, we find that membrane-bound protein patterns propagate against the direction of cytoplasmic flow with a speed that is maximal for intermediate flow speed. We show that the mechanism underlying this pattern propagation relies on a higher protein influx on the upstream side of the pattern compared to the downstream side. Furthermore, we find that cytosolic flow can change the membrane pattern qualitatively from a peak pattern to a mesa pattern. Finally, our study shows that a non-uniform flow profile can induce pattern formation by triggering a regional lateral instability.

Cell patterning by secretion-induced plasma membrane flows

“…Biochemical reactions are also modulated by physical processes such as fluid flows, which may happen in the cytosol and at the membrane. In large metazoan cells, cytoskeletal-driven cortical and cytosolic fluid flows, causing advective protein movements, play important roles in cell polarization ( 5 ) and can, in principle, promote polarity establishment ( 6 ). Membrane flows are predicted to occur and equilibrate membrane tension between spatially segregated zones of exo- and endocytosis, such as in tip growth of walled pollen tubes ( 7 , 8 ) or in cell migration, as initially proposed in ( 9 ).…”

Directing Min protein patterns with advective bulk flow

“…This differential flow-induced propagation has been theoretically studied for two-component mass-conserving reaction diffusion models. 44 There, it was shown that flow drives the upstream propagation of patterns that are stationary in the absence of flow.…”

“…The same holds true for the influence of advective flow on biological pattern formation, which has rarely been studied, both experimentally and theoretically. 16,27,40,42,50–52 Insight into the detailed biochemical mechanisms of the MinD-MinE interactions (such as cooperative MinD self-recruitment, dimerization of MinD and MinE, MinE membrane binding, etc.) is likely needed to make progress.…”

Biophysical Models of PAR Cluster Transport by Cortical Flow in C. elegans Early Embryogenesis

“…A number of models have been developed to understand properties of the PAR signaling network. These models are typically partial differential equation models that capture the diffusion, biochemical reactions, and transport due to flow in the system (Aras et al, 2018; Dawes and Iron, 2013; Geßele et al, 2020; Goehring et al, 2011; Gross et al, 2018; Kravtsova and Dawes, 2014; Seirin-Lee et al, 2020; Wigbers et al, 2020). Goehring et al (2011) for example found that a wave-pinning like mechanism (Holmes and Edelstein-Keshet, 2016; Holmes et al, 2012a,b, 2017; Jilkine and Edelstein-Keshet, 2011; Jilkine et al, 2007; Lin et al, 2012; Marée et al, 2006; Mata et al, 2013; Mori et al, 2008; Zmurchok and Holmes, 2020) may be responsible for stabilization of the anterior-posterior border.…”