One-dimensional discrete aggregation-fragmentation model

Abstract

We study here one-dimensional model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) on open chains. Isolated particles and the first particle of a cluster of particles hop one site forward with probability p;when the first particle of a cluster hops, the remaining particles of the same cluster may hop with a modified probability p m , modelling a special kinematic interaction between neighboring particles, or remain in place with probability 1 − p m . The model contains as special cases the TASEP with parallel update (p m = 0) and with sequential backward-ordered update (p m = p). These cases have been exactly solved for the stationary states and their properties thoroughly studied. The limiting case of p m = 1, which corresponds to irreversible aggregation, has been recently studied too. Its phase diagram in the plane of injection (α) and ejection (β) probabilities was found to have a different topology.Here we focus on the stationary properties of the gTASEP in the generic case of attraction p < p m < 1 when aggregation-fragmentation of clusters occurs. We find that the topology of the phase diagram at p m = 1 changes sharply to the one corresponding to p m = p as soon as p m becomes less than 1. Then a maximum current phase appears in the square domain α c (p, p m ) ≤ α ≤ 1 and β c (p, p m ) ≤ β ≤ 1, where α c (p, p m ) = β c (p, p m ) ≡ σ c (p, p m ) are parameter-dependent injection/ejection critical values. The properties of the phase transitions between the three stationary phases at p < p m < 1 are assessed by computer simulations and random walk theory.

Multivalent interactions facilitate motor-dependent protein accumulation at growing microtubule plus-ends

“…6c ). When we simulated cargo particles as synchronously moving oligomeric cargo trains 48 , the effective flux of cargo on the microtubule increased, but in the absence of any end-specific effects, this did not lead to accumulation of cargo at the microtubule end (Fig. 6c ).…”

“…Simulations were equilibrated for 10 5 s before 10 4 motor and cargo distributions were recorded in time intervals corresponding to the time it takes for one motor to traverse the system (~50 s). Equilibration times were particularly critical for cargo clustering conditions, since the motor distributions generically deviate from their classical equilibrium owing to the aggregation and fragmentation kinetics, as seen in similar systems 48 . Data analysis and plotting was performed using custom programs and scripts written in C++ and Python (Matplotlib).…”

Multivalent interactions facilitate motor-dependent protein accumulation at growing microtubule plus ends

“…6C ). To this end we implemented clustering of cargo particles into oligomeric cargo trains, which moved synchronously in the simulation (Bunzarova et al, 2019). Cargo trains increased the effective flux of cargo on the microtubule (due to synchronous stepping of clusters) but did not lead to accumulation of cargo at the microtubule end under the given conditions ( Fig.…”

“…Simulations were equilibrated for 10 5 sec before 10 4 motor and cargo distributions were recorded in time intervals corresponding to the time it takes for one motor to traverse the system (~50 sec). Equilibration times were particularly critical for cargo clustering conditions, since the motor distributions generically deviate from their classical equilibrium due to the aggregation and fragmentation kinetics, as seen in similar systems (Bunzarova et al, 2019). Data analysis and plotting was performed using custom programs and scripts written in C++ and Python (Matplotlib).…”