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

Abstract

The clustering of membranebound proteins facilitates their transport by cortical actin flow in early Caenorhabditis elegans embryo cell polarity. PAR3 clustering is critical for this process, yet the bio physical processes that couple protein clusters to cortical flow remain unknown. We develop a discrete, stochastic agentbased model of protein clustering and test four hypothetical models for how clusters may interact with the flow. Results show that the canonical way to assess transport characteristics from single particle tracking data used thus far in this area, the Péclet number, is insufficient to distinguish these hypotheses and that all models can account for transport characteristics quantified by this measure. However, using this model, we demonstrate that these different clustercortex interactions may be dis tinguished using a different metric, namely, the scalar projection of cluster displacement on to the flow displacement vector. Our results thus provide a testable way to use existing single particle tracking data to test how endogenous protein clusters may interact with the cortical flow to localize during polarity es tablishment. To facilitate this investigation, we also develop both improved simulation and semianalytic methodologies to quantify motion summary statistics (e.g., Péclet number and scalar projection) for these stochastic models as a function of biophysical parameters.

Design principles for selective polarization of PAR proteins by cortical flows

“…Specifically, the mobility of PAR-3 clusters appears to be restricted by the actin cortex in embryos ( Sailer et al, 2015 ). Thus, an attractive model for explaining cluster-dependent transport is that clustering results in an increase in effective friction with the cortex arising from size-dependent binding or corralling ( Zmurchok and Holmes, 2022 ), similar to what has been proposed at the immunological synapse ( Hartman et al, 2009 ). In such a model, clustering would effectively tune the physical coupling of molecules to the actomyosin cortex, allowing molecules to selectively “sense flows.” Consistent with such a model, recent work has postulated a strict size threshold for directional transport by cortical flows ( Chang and Dickinson, 2022 ).…”

Design principles for selective polarization of PAR proteins by cortical flows

“…A key requirement for transport of molecules by cortical flow is that their motion be entrained by that of the underlying actomyosin cortex, a process referred to as advection. An attractive model for explaining cluster-dependent transport is that clustering results in an increase in effective friction arising from size-dependent binding to or corralling of clusters by the flowing actin cortex (Chang and Dickinson, 2022;Zmurchok and Holmes, 2022), similar to what has been proposed at the immunological synapse (Hartman et al, 2009). In such a model clustering would effectively tune the physical coupling of molecules to the actomyosin cortex, allowing molecules to selectively 'sense flows.'…”