Pulling-force generation by ensembles of polymerizing actin filaments

The mechanisms of pulling-force generation by actin polymerization remain unclear compared to pushing-force mechanisms. While pushing forces are well-characterized in processes like cell motility, the specific roles of actin filaments in generating inward forces during endocytosis are less understood. Prior research has shown that actin filaments can exert forces on membranes through polymerization. However, the interplay between filament arrangement, membrane interactions, and force balance is not fully resolved. This gap motivated investigations into how filament positioning and membrane binding influence force generation. No prior work had resolved how filament bending and network elasticity contribute to these forces. The uncertainty around how gel rigidity affects force equilibration remains unresolved. The role of stress concentrations in filament detachment is also unclear. This paper contributes by analyzing the force dynamics of actin filaments in a controlled computational model.

The study aimed to clarify the basic mechanisms of pulling-force generation by actin polymerization in cellular processes. It focused on how filament arrangements and membrane interactions influence force balance. The specific problem addressed was the lack of understanding about how inner filaments generate pulling forces while outer filaments push. The motivation stemmed from the need to distinguish pulling from pushing mechanisms in endocytosis. The study sought to determine how filament positions and membrane binding affect force distribution. It also aimed to explore the role of gel rigidity in force equilibration. The researchers proposed to use a computational model with semiflexible actin filaments arranged in a square array. The model included interactions with a membrane and considered filament bending and network elasticity.

The study used stochastic polymerization simulations to model a square array of semiflexible actin filaments interacting with a membrane. The filaments had different binding potentials depending on their position in the array. Central filaments had a strong attractive component, while outer filaments had no potential well. The simulations explicitly included filament bending and actin-network elasticity. The researchers calculated forces exerted by filaments on the membrane and analyzed their spatial distribution. They varied the depth of the potential well and the rigidity of the gel to observe effects on force balance. The simulations tracked how force distributions changed over time. The model also considered how actin polymerization rates responded to changes in gel stiffness and filament binding.

The simulations revealed that outer filaments pushed on the membrane while inner filaments pulled, creating a net force balance. The total pulling force was maximized when central filaments had a deep potential well and outer filaments had no well. The steady-state force remained unchanged regardless of gel rigidity, but softer gels took longer to equilibrate. Force distributions were flat across pulling and pushing regions. Actin polymerization increased with softer gels or weaker filament-membrane binding. Filament detachment occurred in softer gels even with high binding energy (100 kBT or more). Detachment propagated via a stress-concentration mechanism similar to brittle crack propagation. The breaking stress followed a criterion analogous to Griffith theory of fracture.

The authors found that pulling forces arise from inner filaments with strong membrane binding, while outer filaments push. The total pulling force is maximized when central filaments bind strongly and outer filaments do not. Steady-state forces are independent of gel rigidity but equilibration time increases with softer gels. Force distributions are uniform across pulling and pushing regions. Actin polymerization is enhanced by softer gels or weaker binding. Detachment occurs via a stress concentration mechanism similar to brittle fracture. The breaking stress follows a criterion analogous to Griffith theory. These findings suggest that filament arrangement and membrane interactions are critical for force generation.