Diffusion Dynamics of Motor-Driven Transport: Gradient Production and Self-Organization of Surfaces

Abstract

The interaction between cytoskeletal filaments (e.g., actin filaments) and molecular motors (e.g., myosin) is the basis for many aspects of cell motility and organization of the cell interior. In the in vitro motility assay (IVMA), cytoskeletal filaments are observed while being propelled by molecular motors adsorbed to artificial surfaces (e.g., in studies of motor function). Here we integrate ideas that cytoskeletal filaments may be used as nanoscale templates in nanopatterning with a novel approach for the production of surface gradients of biomolecules and nanoscale topographical features. The production of such gradients is challenging but of increasing interest (e.g., in cell biology). First, we show that myosin-induced actin filament sliding in the IVMA can be approximately described as persistent random motion with a diffusion coefficient (D) given by a relationship analogous to the Einstein equation (D = kT/gamma). In this relationship, the thermal energy (kT) and the drag coefficient (gamma) are substituted by a parameter related to the free-energy transduction by actomyosin and the actomyosin dissociation rate constant, respectively. We then demonstrate how the persistent random motion of actin filaments can be exploited in conceptually novel methods for the production of actin filament density gradients of predictable shapes. Because of regularly spaced binding sites (e.g., lysines and cysteines) the actin filaments act as suitable nanoscale scaffolds for other biomolecules (tested for fibronectin) or nanoparticles. This forms the basis for secondary chemical and topographical gradients with implications for cell biological studies and biosensing.

Self-Organization of Motor-Propelled Cytoskeletal Filaments at Topographically Defined Borders

“…In previous studies [19] of actomyosin-based self-organization on topographically and chemically nanopatterned surfaces we noted that the motor-propelled actin filaments tend to accumulate along edges of the motility supporting areas. We hypothesized [19] that this effect, that we here denote the “edge-tracing effect,” is attributed to: (1) higher local motor density at the corner between a wall and the floor of the motor supporting area or (2) reduced probability for filaments to leave their current path along the wall-floor junction because the thermal fluctuations of the free leading end of the filament are limited to one (rather than two, as on an open surface area) direction in the surface plane.…”

“…Thus, in the presence of cross-linking molecules, stable or meta-stable filament bundles of different shapes may form [18]. In the absence of cross-linkers, on the other hand, the filaments either move collectively in partly ordered, but dynamically changing swarms [19–21], or execute random diffusion like movement [19], depending on the conditions [22]. The diffusion-like behaviour can be partly controlled by chemical and topographical micro-, and/or nanopatterns and used as a versatile method to produce actin filament gradients [19] locked to the myosin-coated surface by removal of ATP.…”

“…In the absence of cross-linkers, on the other hand, the filaments either move collectively in partly ordered, but dynamically changing swarms [19–21], or execute random diffusion like movement [19], depending on the conditions [22]. The diffusion-like behaviour can be partly controlled by chemical and topographical micro-, and/or nanopatterns and used as a versatile method to produce actin filament gradients [19] locked to the myosin-coated surface by removal of ATP. Actin filaments are readily functionalized with various biomolecules for example, extracellular matrix proteins [19], and may serve as templates for formation of gradients of other biomolecules, useful, for example, for tissue engineering and studies of cell adhesion.…”

“…The diffusion-like behaviour can be partly controlled by chemical and topographical micro-, and/or nanopatterns and used as a versatile method to produce actin filament gradients [19] locked to the myosin-coated surface by removal of ATP. Actin filaments are readily functionalized with various biomolecules for example, extracellular matrix proteins [19], and may serve as templates for formation of gradients of other biomolecules, useful, for example, for tissue engineering and studies of cell adhesion. Alternatively, the filaments could be derivatized with gold [23] to produce complex electrical circuits.…”

Non-equilibrium assembly of microtubules: from molecules to autonomous chemical robots

“…178 This is the case e.g. for the directionality of smoothly gliding microtubules over distances exceeding the persistence length, 169, 173, 176, 179 but frequently the deviations from the intended direction or desired velocity of a gliding microtubule are not thermal in origin (originating e.g. from the encounter with a defective kinesin motor).…”