Traffic jams and shocks of molecular motors inside cellular protrusions

Abstract

Molecular motors are involved in key transport processes inside actin-based cellular protrusions. The motors carry cargo proteins to the protrusion tip which participate in regulating the actin polymerization, and play a key role in facilitating the growth and formation of such protrusions. It is observed that the motors accumulate at the tips of cellular protrusions, and in addition form aggregates that are found to drift towards the protrusion base at the rate of actin treadmilling. We present a one-dimensional driven lattice model, where motors become inactive after delivering their cargo at the tip, or by loosing their cargo to a cargo-less neighbor. The results suggest that the experimental observations may be explained by the formation of traffic jams that form at the tip. The model is solved using a novel application of mean-field and shock analysis. We find a new class of shocks that undergo intermittent collapses, and on average do not obey the Rankine-Hugoniot relation.

Self-organization of waves and pulse trains by molecular motors in cellular protrusions

“…Moreover, we will show that focusing on the selection origin at tip allows to effectively distinguish between two distinct transport mechanisms, i.e., transport by TWs or by pulses. Our work is the first to treat this phenomenon using a continuum model, which can be compared to a discrete model proposed recently 22 . In order to correspond to the experiments we use in the calculations the actin treadmilling velocity observed in the filopodia: nm/sec.…”

“…With respect to the local transition rates, the continuum description always admits coexistence between stalled and processive motors at the same location z along the protrusion. While this is impossible microscopically for a strictly one dimensional track 22 , our one dimensional space effectively represents all the actin filaments at the surface of the bundle inside the protrusion, whereby hopping between multiple tracks allows the “tunneling” of processive motors through a region that is rich in stalled motors. Furthermore, at present it is unknown if the observed aggregates span the entire bundle surface, or form on just several (or even one) actin filaments.…”

“…The dynamics within the filopodia are probably affected by several additional sources, such as noise (thermal and active), temporal dependence of the chemical reactions at the tip (here β was treated as a fixed control parameter) and a relation between the actin polymerization rate at the tip and the density of motors (and their cargo) there. The relation between a continuum model and microscopic (discrete) models for these aggregates 22 is another interesting issue for further investigation.…”

Self-organized system-size oscillation of a stochastic lattice-gas model

“…There are many possible extensions of these models, which are both interesting in their own right and can help us to understand important biological processes. Examples include large networks of biofilaments [36][37][38], limited protein resources [6,[39][40][41][42][43][44][45], the fact that proteins in the cytosol do not form a spatially uniform reservoir because their dynamics is limited by diffusion [6,[46][47][48][49][50][51], and that proteins may be spatially confined, as they are in fungal hyphae or filopodia [6,9,46,51,52].…”

Spontaneous pulsing states in an active particle system

“…Systems in the half-open tube geometry have been of particular interest in the modelling of protrusions such as filopodia, lamellapodia, or microvilli [28,29,25], tubulation [30] and fungal hyphae growth [31]. The boundary condition at the closed end of the tube controls the length and may be either growing, treadmilling or no flux.…”