Self-organization of actin filament orientation in the dendritic-nucleation/array-treadmilling model

Abstract

The dendritic-nucleation/array-treadmilling model provides a conceptual framework for the generation of the actin network driving motile cells. We have incorporated it into a 2D, stochastic computer model to study lamellipodia via the self-organization of filament orientation patterns. Essential dendritic-nucleation submodels were incorporated, including discretized actin monomer diffusion, Monte-Carlo filament kinetics, and flexible filament and plasma membrane mechanics. Model parameters were estimated from the literature and simulation, providing values for the extent of the leading edge-branching/capping-protective zone (5.4 nm) and the autocatalytic branch rate (0.43/sec). For a given set of parameters, the system evolved to a steady-state filament count and velocity, at which total branching and capping rates were equal only for specific orientations; net capping eliminated others. The standard parameter set evoked a sharp preference for the ؎35 degree filaments seen in lamellipodial electron micrographs, requiring Ϸ12 generations of successive branching to adapt to a 15 degree change in protrusion direction. This pattern was robust with respect to membrane surface and bending energies and to actin concentrations but required protection from capping at the leading edge and branching angles >60 degrees. A ؉70/0/؊70 degree pattern was formed with flexible filaments Ϸ100 nm or longer and with velocities <Ϸ20% of free polymerization rates.lamellipodium ͉ cytoskeleton ͉ plasma membrane T he polymerization of soluble actin monomers between filament ''barbed ends'' and the plasma membrane (PM) generates the force of protrusion in cell motility (1, 2). Other proteins required for lamellipodial motility (3) are arp2/3, which nucleates (branches) free barbed ends at Ϸ70 degrees from existing ones (4); a PMbound activator of arp2/3 (5); ADF/cofilin, which promotes the depolymerization of pointed ends (6) and perhaps debranching reactions (7); and capping protein, a terminator of barbed end growth (8). The generation and persistence of lamellipodia from these elements is described in the ''dendritic-nucleation/arraytreadmilling'' conceptual model (2,4,9). This model can be subdivided into three main processes: the kinetics of filament (de)polymerization, branching, and capping; filament-PM interactions, which limit polymerization rates; and the diffusion of actin monomers and other soluble components. Such a system is ''complex'' in the sense that many copies of each component type interact to exhibit ''emergent'' system properties not expected from the individual rules of interaction (10). In contrast to ''complicated'' systems of many dissimilar components with precisely defined interactions, complex systems can self-organize and adapt to environmental change.An important emergent property is the self-organization of lamellipodial actin filaments into orientations at Ϯ35 degrees with respect to the direction of protrusion (11,12). Maly and Borisy (11) predicted Ϯ35 or ϩ70/0/Ϫ70 degree patterns with a 2D mathematical...

Actin branching in the initiation and maintenance of lamellipodia

“…S1). The modeling compares with other approaches, where filaments are treated as stiff or flexible rods with stochastic processes describing nucleation, branching, polymerization and capping (Alberts and Odell, 2004;Schaus et al, 2007;Carlsson, 2001;Schreiber et al, 2010). We limited ourselves to a minimal number of factors sufficient to reproduce the essential average properties extracted from tomograms.…”

Mathematics of cell motility: have we got its number?

“…Such Monte Carlo-like methods are usually simulations of agent-based models, in which each molecule is represented explicitly and interactions between them obey simple rules. Excellent recent example of such approach, pioneered in [16], is the recent studies [99,100] that simulated the lamellipodial dendritic network growing against resistive elastic membrane. This model confirmed many predictions of models described above without simplifications necessary to use continuous math tools.…”

“…Recent evidence points out that the lamellipodial filaments can bend together and 'zipper' into such parallel bundles [114]. Some preliminary modeling of both emergence and maintenance of filopodia is done [6,43,72,99], but comprehensive model of this phenomenon (?) is lacking.…”

How actin network dynamics control the onset of actin-based motility

“…These macroscopic continuous approaches offer valuable insights into actindriven force generation, stress buildup prior to symmetry breaking and network reorganization at a mesoscopic scale (7, 8, 10). The other class of models rely on the chemical mechanisms responsible for filament nucleation, filament branching and filament entanglement (1,11,12). However, despite experimental and modeling efforts, the link between microscopic properties of actin networks and the production of force at a macroscopic scale remains poorly understood.…”