Protein Friction and Filament Bending Facilitate Contraction of Disordered Actomyosin Networks

Abstract

We use mathematical modelling and computation to investigate how protein friction facilitates contraction of disordered actomyosin networks. We simulate two-dimensional networks using an agent-based model, consisting of a system of force-balance equations for myosin motor proteins and semi-flexible actin filaments. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility. Exploiting this, we use repeated simulations of disordered networks to confirm that both protein friction and actin filament bending are required for contraction. We then use simulations of elementary two-filament assemblies to show that filament bending flexibility can generate contraction on the microscopic scale. Finally, we show that actin filament turnover is necessary to sustain contraction and prevent pattern formation. Simulations with and without turnover also exhibit contractile pulses. However, these pulses are aperiodic, suggesting that periodic pulsation can only be achieved by additional regulatory mechanisms.

F-Actin Bending Facilitates Net Actomyosin Contraction By Inhibiting Expansion With Plus-End-Located Myosin Motors

“…We represent bending and stretching forces as the variation of potential energy, where terms involving δ denote variations. We conceptualise drag as the combined effects of friction between the filaments and the cytoplasm, and protein friction (Tam, Mogilner, and Oelz 2021; McFadden et al 2017; Bormuth et al 2009; Tawada and Sekimoto 1991) acting at intersections between the two filaments and filaments in a background network. Figure 2.1b illustrates this scenario.…”

“…However, actomyosin networks in the cell cortex are disordered, with filaments distributed at random. Experiments (Murrell, Oakes, et al 2015; Pollard and O’Shaughnessy 2019) and simulations (Tam, Mogilner, and Oelz 2021; Ennomani et al 2016) have shown that disordered actomyosin networks also contract (Chalut and Paluch 2016). Sliding filament theory predicts that random networks would produce expansion or contraction with equal probability, and thus cannot explain this contraction.…”

“…Filament bending flexibility is commonly-hypothesised as a source of asymmetry that might explain contraction of disordered actomyosin networks (Murrell and Gardel 2012; De La Cruz and Gardel 2015; du Roure et al 2019; Head, Levine, and MacKintosh 2003; Tam, Mogilner, and Oelz 2021). Actin filaments are semi-flexible (Stachowiak et al 2014; Belmonte, Leptin, and Nédélec 2017), such that they undergo small but significant bending (Broedersz and Mackintosh 2014; Murrell and Gardel 2012).…”

“…This has been shown to generate network-scale bias to contraction over expansion (Belmonte, Leptin, and Nédélec 2017). Other studies have considered a related filament bending mechanism (Lenz 2014; Tam, Mogilner, and Oelz 2021; Head, Levine, and MacKintosh 2003; Popov, Komianos, and Papoian 2016; Kim 2015; Letort et al 2015) as a source of force asymmetry. This involves applying forces that pluck filaments transversely, as opposed to the longitudinal forces involved with buckling.…”

“…This involves applying forces that pluck filaments transversely, as opposed to the longitudinal forces involved with buckling. Lenz (2014) showed that filament bending produces forces that exceed those involved with longitudinal buckling, and Tam, Mogilner, and Oelz (2021) showed that this mechanism facilitates network-scale contraction.…”