Micromechanical simulations of biopolymer networks with finite elements

Cyron, Christian J.; Müller, Kei W.; Bausch, Andreas R.; Wall, Wolfgang A.

doi:10.1016/j.jcp.2012.10.025

Cited by 41 publications

(49 citation statements)

References 47 publications

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“…Simulations are carried out using a Brownian dynamics finite element approach [24,25], which has already been applied to study the self-assembly of semi-flexible biopolymer networks [26] and the linear rheology of bundle networks [27]. In this approach, filaments and cross-linker molecules are discretized with non-linear, geometrically exact, three-dimensional Simo-Reissner beam elements.…”

Section: Methodsmentioning

confidence: 99%

A single charge in the actin binding domain of fascin can independently tune the linear and non-linear response of an actin bundle network

Maier

Müller

Heussinger³

et al. 2015

Eur. Phys. J. E

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Abstract. Actin binding proteins (ABPs) not only set the structure of actin filament assemblies but also mediate the frequency-dependent viscoelastic moduli of cross-linked and bundled actin networks. Point mutations in the actin binding domain of those ABPs can tune the association and dissociation dynamics of the actin/ABP bond and thus modulate the network mechanics both in the linear and non-linear response regime. We here demonstrate how the exchange of a single charged amino acid in the actin binding domain of the ABP fascin triggers such a modulation of the network rheology. Whereas the overall structure of the bundle networks is conserved, the transition point from strain-hardening to strain-weakening sensitively depends on the cross-linker off-rate and the applied shear rate. Our experimental results are consistent both with numerical simulations of a cross-linked bundle network and a theoretical description of the bundle network mechanics which is based on non-affine bending deformations and force-dependent crosslink dynamics.

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Section: Methodsmentioning

confidence: 99%

A single charge in the actin binding domain of fascin can independently tune the linear and non-linear response of an actin bundle network

Maier

Müller

Heussinger³

et al. 2015

Eur. Phys. J. E

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“…In [3,28], these binding sites coincide with the nodes of the beam finite elements. For motors, the nodal separation would have to equal the path distance h f = δ p .…”

Section: (C) Model Extensionsmentioning

confidence: 96%

“…In this section, we aim to give a compact summary of our Brownian dynamics finite-element approach employed in this paper, which we comprehensively described in [2,3] and which enables the simulation of large biopolymer networks [23] and their rheology [24]. It provides the basis for the new motor model discussed in §3.…”

Section: Brownian Dynamics Simulations Of Biopolymer Networkmentioning

confidence: 99%

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Beam finite-element model of a molecular motor for the simulation of active fibre networks

2016

Self Cite

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Molecular motors are proteins that excessively increase the efficiency of subcellular transport processes. They allow for cell division, nutrient transport and even macroscopic muscle movement. In order to understand the effect of motors in large biopolymer networks, e.g. the cytoskeleton, we require a suitable model of a molecular motor. In this contribution, we present such a model based on a geometrically exact beam finite-element formulation. We discuss the numerical model of a non-processive motor such as myosin II, which interacts with actin filaments. Based on experimental data and inspired by the theoretical understanding offered by the powerstroke model and the swinging-cross-bridge model, we parametrize our numerical model in order to achieve the effect that a physiological motor has on its cargo. To this end, we introduce the mechanical and mathematical foundations of the model, then discuss its calibration, prove its usefulness by conducting finite-element simulations of actin-myosin motility assays and assess the influence of motors on the rheology of semi-flexible biopolymer networks.

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“…Similarly, springs and dashpots are used to mathematically capture the viscoelastic response of disordered, nonsarcomeric actomyosin bundles, where spring elasticity in parallel with dashpot viscosity reflects, respectively, internal stiffness and friction (467). Spring and dashpot elements are useful also in simulations at the nanoscale level, although such fine-grain modeling requires inclusion of stochastic thermal fluctuations inherent in molecular interactions (86).…”

Section: Springs Dashpots and The Classical Approachmentioning

confidence: 99%

Mechanics of Vascular Smooth Muscle

Ratz

2015

Comprehensive Physiology

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Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress-development, sustained stress-maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip-catch bond, and a regulated two-step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress-strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure-function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM.

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Micromechanical simulations of biopolymer networks with finite elements

Cited by 41 publications

References 47 publications

A single charge in the actin binding domain of fascin can independently tune the linear and non-linear response of an actin bundle network

A single charge in the actin binding domain of fascin can independently tune the linear and non-linear response of an actin bundle network

Beam finite-element model of a molecular motor for the simulation of active fibre networks

Mechanics of Vascular Smooth Muscle

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