Modelling of cross-linked actin networks – Influence of geometrical parameters and cross-link compliance

A coarse-grained approach to model the dynamics of the actomyosin cortex

Background

The dynamics of the actomyosin machinery is at the core of many important biological processes. Several relevant cellular responses such as the rhythmic compression of the cell cortex are governed, at a mesoscopic level, by the nonlinear interaction between actin monomers, actin crosslinkers, and myosin motors. Coarse-grained models are an optimal tool to study actomyosin systems, since they can include processes that occur at long time and space scales, while maintaining the most relevant features of the molecular interactions.

Results

Here, we present a coarse-grained model of a two-dimensional actomyosin cortex, adjacent to a three-dimensional cytoplasm. Our simplified model incorporates only well-characterized interactions between actin monomers, actin crosslinkers and myosin, and it is able to reproduce many of the most important aspects of actin filament and actomyosin network formation, such as dynamics of polymerization and depolymerization, treadmilling, network formation, and the autonomous oscillatory dynamics of actomyosin.

Conclusions

We believe that the present model can be used to study the in vivo response of actomyosin networks to changes in key parameters of the system, such as alterations in the attachment of actin filaments to the cell cortex.

Supplementary Information

The online version contains supplementary material available at (10.1186/s12915-022-01279-2).

Ca2+ homeostasis in brain microvascular endothelial cells

Blood brain barrier (BBB) is formed by the brain microvascular endothelial cells (BMVECs) lining the wall of brain capillaries. Its integrity is regulated by multiple mechanisms, including up/downregulation of tight junction proteins or adhesion molecules, altered Ca²⁺ homeostasis, remodeling of cytoskeleton, that are confined at the level of BMVECs. Beside the contribution of BMVECs to BBB permeability changes, other cells, such as pericytes, astrocytes, microglia, leukocytes or neurons, etc. are also exerting direct or indirect modulatory effects on BBB. Alterations in BBB integrity play a key role in multiple brain pathologies, including neurological (e.g. epilepsy) and neurodegenerative disorders (e.g. Alzheimer's disease, Parkinson's disease, amyotrophic lateral sclerosis etc.). In this review, the principal Ca²⁺ signaling pathways in brain microvascular endothelial cells are discussed and their contribution to BBB integrity is emphasized. Improving the knowledge of Ca²⁺ homeostasis alterations in BMVECa is fundamental to identify new possible drug targets that diminish/prevent BBB permeabilization in neurological and neurodegenerative disorders.

Parameters controlling the strength of stochastic fibrous materials

Many materials of everyday use are fibrous and their strength is important in most applications. In this work we study the dependence of the strength of random fiber networks on structural parameters such as the network density, cross-link density, fiber tortuosity, and the strength of the inter-fiber cross-links. Athermal networks of cellular and fibrous type are considered. We conclude that the network strength scales linearly with the cross-link number density and with the cross-link strength for a broad range of network parameters, and for both types of networks considered. Network strength is independent of fiber material properties and of fiber tortuosity. This information can be used to design fiber networks for specified strength and, generally, to understand the mechanical behavior of fibrous materials.

Random Fiber Networks With Superior Properties Through Network Topology Control

In this work, we study the effect of network architecture on the nonlinear elastic behavior and strength of athermal random fiber networks of cellular type. We introduce a topology modification of Poisson-Voronoi (PV) networks with convex cells, leading to networks with stochastic nonconvex cells. Geometric measures are developed to characterize this new class of nonconvex Voronoi (NCV) networks. These are softer than the reference PV networks at the same nominal network parameters such as density, cross-link density, fiber diameter, and connectivity number. Their response is linear elastic over a broad range of strains, unlike PV networks that exhibit a gradual increase of the tangent stiffness starting from small strains. NCV networks exhibit much smaller Poisson contraction than any network of same nominal parameters. Interestingly, the strength of NCV networks increases continuously with an increasing degree of nonconvexity of the cells. These exceptional properties render this class of networks of interest in a variety of applications, such as tissue scaffolds, nonwovens, and protective clothing.

Mechanical effects of load speed on the human colon

The aim of this study was to examine the mechanical behavior of the colon using tensile tests under different loading speeds. Specimens were taken from different locations of the colonic frame from refrigerated cadavers. The specimens were submitted to uniaxial tensile tests after preconditioning using a dynamic load (1 m/s), intermediate load (10 cm/s), and quasi-static load (1 cm/s). A total of 336 specimens taken from 28 colons were tested. The stress-strain analysis for longitudinal specimens indicated a Young's modulus of 3.17 ± 2.05 MPa under dynamic loading (1 m/s), 1.74 ± 1.15 MPa under intermediate loading (10 cm/s), and 1.76 ± 1.21 MPa under quasi-static loading (1 cm/s) with p < 0.001. For the circumferential specimen, the stress-strain curves indicated a Young's modulus of 3.15 ± 1.73 MPa under dynamic loading (1 m/s), 2.14 ± 1.3 MPa under intermediate loading (10 cm/s), and 0.63 ± 1.25 MPa under quasi-static loading (1 cm/s) with p < 0.001. The curves reveal two types of behaviors of the colon: fast break behavior at high speed traction (1 m/s) and a lower break behavior for lower speeds (10 cm/s and 1 cm/s). The circumferential orientation required greater levels of stress and strain to obtain lesions than the longitudinal orientation. The presence of taeniae coli changed the mechanical response during low-speed loading. Colonic mechanical behavior varies with loading speeds with two different types of mechanical behavior: more fragile behavior under dynamic load and more elastic behavior for quasi-static load.

Implementing cell contractility in filament-based cytoskeletal models

Cells are known to respond over time to mechanical stimuli, even actively generating force at longer times. In this paper, a microstructural filament-based cytoskeletal network model is extended to incorporate this active response, and a computational study to assess the influence on relaxation behaviour was performed. The incorporation of an active response was achieved by including a strain energy function of contractile activity from the cross-linked actin filaments. A four-state chemical model and strain energy function was adopted, and generalisation to three dimensions and the macroscopic deformation field was performed by integration over the unit sphere. Computational results in MATLAB and ABAQUS/Explicit indicated an active cellular response over various time-scales, dependent on contractile parameters. Important features such as force generation and increasing cell stiffness due to prestress are qualitatively predicted. The work in this paper can easily be extended to encompass other filament-based cytoskeletal models as well.

Artificial Formation and Tuning of Glycoprotein Networks on Live Cell Membranes: A Single-Molecule Tracking Study

We present a method to artificially induce network formation of membrane glycoproteins and show the precise tuning of their interconnection on living cells. For this, membrane glycans are first metabolically labeled with azido sugars and then tagged with biotin by copper-free click chemistry. Finally, these biotin-tagged membrane proteins are interconnected with streptavidin (SA) to form an artificial protein network in analogy to a lectin-induced lattice. The degree of network formation can be controlled by the concentration of SA, its valency, and the concentration of biotin on membrane proteins. This was verified by investigation of the spatiotemporal dynamics of the SA-protein networks employing single-molecule tracking. It was also proven that this network formation strongly influences the biologically relevant process of endocytosis as it is known from natural lattices on the cell surface.

Experimental and computational assessment of F-actin influence in regulating cellular stiffness and relaxation behaviour of fibroblasts

In biomechanics, a complete understanding of the structures and mechanisms that regulate cellular stiffness at a molecular level remain elusive. In this paper, we have elucidated the role of filamentous actin (F-actin) in regulating elastic and viscous properties of the cytoplasm and the nucleus. Specifically, we performed colloidal-probe atomic force microscopy (AFM) on BjhTERT fibroblast cells incubated with Latrunculin B (LatB), which results in depolymerisation of F-actin, or DMSO control. We found that the treatment with LatB not only reduced cellular stiffness, but also greatly increased the relaxation rate for the cytoplasm in the peripheral region and in the vicinity of the nucleus. We thus conclude that F-actin is a major determinant in not only providing elastic stiffness to the cell, but also in regulating its viscous behaviour. To further investigate the interdependence of different cytoskeletal networks and cell shape, we provided a computational model in a finite element framework. The computational model is based on a split strain energy function of separate cellular constituents, here assumed to be cytoskeletal components, for which a composite strain energy function was defined. We found a significant influence of cell geometry on the predicted mechanical response. Importantly, the relaxation behaviour of the cell can be characterised by a material model with two time constants that have previously been found to predict mechanical behaviour of actin and intermediate filament networks. By merely tuning two effective stiffness parameters, the model predicts experimental results in cells with a partly depolymerised actin cytoskeleton as well as in untreated control. This indicates that actin and intermediate filament networks are instrumental in providing elastic stiffness in response to applied forces, as well as governing the relaxation behaviour over shorter and longer time-scales, respectively.

Geometrical and mechanical properties control actin filament organization

The different actin structures governing eukaryotic cell shape and movement are not only determined by the properties of the actin filaments and associated proteins, but also by geometrical constraints. We recently demonstrated that limiting nucleation to specific regions was sufficient to obtain actin networks with different organization. To further investigate how spatially constrained actin nucleation determines the emergent actin organization, we performed detailed simulations of the actin filament system using Cytosim. We first calibrated the steric interaction between filaments, by matching, in simulations and experiments, the bundled actin organization observed with a rectangular bar of nucleating factor. We then studied the overall organization of actin filaments generated by more complex pattern geometries used experimentally. We found that the fraction of parallel versus antiparallel bundles is determined by the mechanical properties of actin filament or bundles and the efficiency of nucleation. Thus nucleation geometry, actin filaments local interactions, bundle rigidity, and nucleation efficiency are the key parameters controlling the emergent actin architecture. We finally simulated more complex nucleation patterns and performed the corresponding experiments to confirm the predictive capabilities of the model.