Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process

Abstract

Keratin intermediate filament networks are part of the cytoskeleton in epithelial cells.They were found to regulate viscoelastic properties and motility of cancer cells. Due to unique biochemical properties of keratin polymers, the knowledge of the mechanisms controlling keratin network formation is incomplete. A combination of deterministic and stochastic modeling techniques can be a valuable source of information since they can describe known mechanisms of network evolution while reflecting the uncertainty with respect to a variety of molecular events. We applied the concept of * These authors contributed equally. † corresponding author A c c e p t e d m a n u s c r i p tSimulating the formation of keratin filament networks by a PDMP piecewise-deterministic Markov processes to the modeling of keratin network formation in high spatiotemporal resolution. The deterministic component describes the diffusion-driven evolution of a pool of soluble keratin filament precursors fueling various network formation processes. Instants of network formation events are determined by a stochastic point process on the time axis. A probability distribution controlled by model parameters exercises control over the frequency of different mechanisms of network formation to be triggered. Locations of the network formation events are assigned dependent on the spatial distribution of the soluble pool of filament precursors.Based on this modeling approach, simulation studies revealed that the architecture of keratin networks mostly depends on the balance between filament elongation and branching processes. The spatial distribution of network mesh size, which strongly influences the mechanical characteristics of filament networks, mostly depends on lateral annealing processes. This mechanism which is a specific feature of intermediate filament networks appears to be a major and fast regulator of cell mechanics.

The homeostatic dynamics of feeding behaviour identify novel mechanisms of anorectic agents

“…In this paper we suggest such a technique: a class of models known as piecewise deterministic Markov processes [13]. These generalise Markov Chains to include exactly the kind of deterministically-varying transition rates required by models of homeostatic behaviour and have found a wide variety of uses in biology [14,15,16,17] and physics [18,19], although they have not previously been used to study food intake or energy balance. We use this model class to create a flexible and intuitive stochastic model of feeding behaviour governed by stomach fullness.…”

Keratin Dynamics: Modeling the Interplay between Turnover and Transport

“…Accounting for the three modes of transport and considering the turnover described by either linear and nonlinear models with 6 possible combinations of the profiles for the assembly and disassembly rates, a collection of 36 scenarios (models) is defined; each scenario follows the general form stated by system (1). Details of the 36 scenarios are given in Fig.…”

“…where J S is the flux of the soluble pool and J I is the flux of the insoluble pool as defined below system (1). The model parameters used in all the scenarios are listed in Table 1 Figure 5.…”

A Stochastic Method based on the Markov Model of Unit Jump for Analyzing Crack Jump in a Material

“…Bo-Siou et al (2009) have proposed a model of Markov chains for predicting the evolution of damage, with a method for constructing a stochastic curve for a number of Composite Material Systems. Beil et al (2009), Brandejsky et al (2013), Chiquet et al (2009), Davis (1984, Davis (1993), Dhondt (1995), Rowatt et al (1998), de Saporta et al (2010), de Saporta et al (2012, Zhang et al (2014) have presented a Markov Model based on the evolution of damage to characterize fatigue behavior. Based on these behavioral studies, we investigated modeling the crack using a Markov Model with a method of simple analysis.…”