Effects of Fracture Characteristics of Cross-Linking Proteins on the Mechanical Responses of Actin-Microtubule Composite Networks

GONG Bo; LIU Yuanjia; YUAN Liren; XU Wei

doi:10.21656/1000-0887.470001

Volume 47 Issue 6

Jun. 2026

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(6): 736-749

GONG Bo, LIU Yuanjia, YUAN Liren, XU Wei. Effects of Fracture Characteristics of Cross-Linking Proteins on the Mechanical Responses of Actin-Microtubule Composite Networks[J]. Applied Mathematics and Mechanics, 2026, 47(6): 736-749. doi: 10.21656/1000-0887.470001

Citation:

PDF( 4544 KB)

Effects of Fracture Characteristics of Cross-Linking Proteins on the Mechanical Responses of Actin-Microtubule Composite Networks

doi: 10.21656/1000-0887.470001

Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, P.R. China

Received Date: 2025-12-31
Rev Recd Date: 2026-02-03
Publish Date: 2026-06-01

Abstract

Abstract

The mechanical properties of the cytoskeleton are crucial for maintaining cell morphology and enabling life processes such as cell movement and division. Actin filaments and microtubules, as core components of the cytoskeleton, are interconnected by cross-linking proteins to form a complex polymer network structure, of which the macroscopic mechanical behavior is closely related to the physical properties of cross-linking proteins. Based on a coarse-grained actin-microtubule composite network model, the effects of 2 key parameters of cross-linking proteins: the fracture distance threshold and the formation distance threshold, on the network's mechanical properties were systematically investigated. The simulation results show that, the fracture distance threshold of microtubule cross-linking proteins plays a dominant role in the network's mechanical responses: reducing this threshold leads to an overall downward shift of the stress-strain curve and a decrease in structural loading-bearing capacity. In contrast, changes in the fracture distance threshold of actin filament cross-linking proteins have a weak impact on the macroscopic mechanical behavior, and the formation distance threshold of cross-linking proteins has no significant effect on the network's mechanical properties. This study reveals that the macroscopic mechanical properties of the actin-microtubule composite network are mainly dependent on the fracture distance threshold of cross-linking proteins while being insensitive to the formation distance threshold, providing a new sight for understanding the role of dynamic cross-linking in the mechanical stability of the cytoskeleton.
- composite actin-microtubule network,
- dynamic cross-linking,
- fracture distance,
- formation distance

FullText(HTML)

References(43)

References

[1]	DOGTEROM M, KOENDERINK G H. Actin-microtubule crosstalk in cell biology[J]. Nature Reviews Molecular Cell Biology, 2019, 20(1): 38-54 doi: 10.1038/s41580-018-0067-1
[2]	WEN Q, JANMEY P A. Polymer physics of the cytoskeleton[J]. Current Opinion in Solid State and Materials Science, 2011, 15(5): 177-182. doi: 10.1016/j.cossms.2011.05.002
[3]	HUBER F, BOIRE A, LÓPEZ M P, et al. Cytoskeletal crosstalk: when three different personalities team up[J]. Current Opinion in Cell Biology, 2015, 32: 39-47. doi: 10.1016/j.ceb.2014.10.005
[4]	LEE W. The cytoskeleton and its binding proteins as mechanosensors, transducers, and functional regulators of cells[J]. International Journal of Molecular Sciences, 2023, 25(1): 172. doi: 10.3390/ijms25010172
[5]	HANG J T, XU G K. Stiffening and softening in the power-law rheological behaviors of cells[J]. Journal of the Mechanics and Physics of Solids, 2022, 167: 104989. doi: 10.1016/j.jmps.2022.104989
[6]	WANG H, HANG J T, CHANG Z, et al. Static and dynamic mechanics of cell monolayers: a multi-scale structural model[J]. Acta Mechanica Sinica, 2022, 38(5): 222006. doi: 10.1007/s10409-022-22006-x
[7]	HANG J T, KANG Y, XU G K, et al. A hierarchical cellular structural model to unravel the universal power-law rheological behavior of living cells[J]. Nature Communications, 2021, 12: 6067. doi: 10.1038/s41467-021-26283-y
[8]	MCGARRY J G, PRENDERGAST P J. A three-dimensional finite element model of an adherent eukaryotic cell[J]. European Cells and Materials, 2004, 7: 27-34. doi: 10.22203/eCM.v007a03
[9]	WANG L, WANG L, XU L, et al. Finite element modelling of single cell based on atomic force microscope indentation method[J]. Computational and Mathematical Methods in Medicine, 2019, 2019(1): 7895061.
[10]	ZHANG L Y, LI Y, CAO Y P, et al. Stiffness matrix based form-finding method of tensegrity structures[J]. Engineering Structures, 2014, 58: 36-48. doi: 10.1016/j.engstruct.2013.10.014
[11]	LIN Y C, KOENDERINK G H, MACKINTOSH F C, et al. Control of non-linear elasticity in F-actin networks with microtubules[J]. Soft Matter, 2011, 7(3): 902-906. doi: 10.1039/C0SM00478B
[12]	LIANG D, HANG J T, XU G K. A structure-based cellular model reveals power-law rheology and stiffening of living cells under shear stress[J]. Acta Mechanica Sinica, 2023, 39(10): 623129. doi: 10.1007/s10409-023-23129-x
[13]	KIM T, HWANG W, KAMM R D. Dynamic role of cross-linking proteins in actin rheology[J]. Biophysical Journal, 2011, 101(7): 1597-1603. doi: 10.1016/j.bpj.2011.08.033
[14]	KOLE T P, TSENG Y, JIANG I, et al. Intracellular mechanics of migrating fibroblasts[J]. Molecular Biology of the Cell, 2005, 16(1): 328-338. doi: 10.1091/mbc.e04-06-0485
[15]	FISCHER-FRIEDRICH E, TOYODA Y, CATTIN C J, et al. Rheology of the active cell cortex in mitosis[J]. Biophysical Journal, 2016, 111(3): 589-600. doi: 10.1016/j.bpj.2016.06.008
[16]	CHAUBET L, CHAUDHARY A R, HERIS H K, et al. Dynamic actin cross-linking governs the cytoplasm's transition to fluid-like behavior[J]. Molecular Biology of the Cell, 2020, 31(16): 1744-1752. doi: 10.1091/mbc.E19-09-0504
[17]	KUČERA O, GAILLARD J, GUÉRIN C, et al. Actin-microtubule dynamic composite forms responsive active matter with memory[J]. Proceedings of the National Academy of Sciences of the United States of America, 2022, 119(31): e2209522119.
[18]	HANG J T, WANG H, WANG B C, et al. Anisotropic power-law viscoelasticity of living cells is dominated by cytoskeletal network structure[J]. Acta Biomaterialia, 2024, 180: 197-205. doi: 10.1016/j.actbio.2024.04.002
[19]	LI S H, XU G K. Topological mechanism in the nonlinear power-law relaxation of cell cortex[J]. Physical Review E, 2023, 108(6): 064408.
[20]	ZHOU W H, YIN X, XIE S J, et al. A tensegrity-based mechanochemical model for capturing cell oscillation and reorientation[J]. Journal of Applied Physics, 2024, 136(7): 074701. doi: 10.1063/5.0226910
[21]	RICKETTS S N, FRANCIS M L, FARHADI L, et al. Varying crosslinking motifs drive the mesoscale mechanics of actin-microtubule composites[J]. Scientific Reports, 2019, 9: 12831. doi: 10.1038/s41598-019-49236-4
[22]	RICKETTS S N, ROSS J L, ROBERTSON-ANDERSON R M. Co-entangled actin-microtubule composites exhibit tunable stiffness and power-law stress relaxation[J]. Biophysical Journal, 2018, 115(6): 1055-1067. doi: 10.1016/j.bpj.2018.08.010
[23]	FRANCIS M L, RICKETTS S N, FARHADIL, et al. Non-monotonic dependence of stiffness on actin crosslinking in cytoskeleton composites[J]. Soft Matter, 2019, 15(44): 9056-9065. doi: 10.1039/C9SM01550G
[24]	DWYER M E, ROBERTSON-ANDERSON R M, GURMESSA B J. Nonlinear microscale mechanics of actin networks governed by coupling of filament crosslinking and stabilization[J]. Polymers, 2022, 14(22): 4980. doi: 10.3390/polym14224980
[25]	MAXIAN O, PELÁEZ R P, MOGILNER A, et al. Simulations of dynamically cross-linked actin networks: morphology, rheology, and hydrodynamic interactions[J]. PLoS Computational Biology, 2021, 17(12): e1009240. doi: 10.1371/journal.pcbi.1009240
[26]	ZHANG B, GONG Z, ZHAO L, et al. Decoding protein dynamics in cells using chemicalcross-linking and hierarchical analysis[J]. Angewandte Chemie International Edition, 2023, 62(35): e202301345. doi: 10.1002/anie.202301345
[27]	LI L, HOU Z. Crosslink-induced conformation change of intrinsically disordered proteins have a nontrivial effect on phase separation dynamics and thermodynamics[J]. The Journal of Physical Chemistry B, 2023, 127(22): 5018-5026. doi: 10.1021/acs.jpcb.3c01728
[28]	XU J, WIRTZ D, POLLARD T D. Dynamic cross-linking by α-actinin determines the mechanical properties of actin filament networks[J]. Journal of Biological Chemistry, 1998, 273(16): 9570-9576. doi: 10.1074/jbc.273.16.9570
[29]	FREEDMAN S L, BANERJEE S, HOCKY G M, et al. A versatile framework for simulating the dynamic mechanical structure of cytoskeletal networks[J]. Biophysical Journal, 2017, 113(2): 448-460. doi: 10.1016/j.bpj.2017.06.003
[30]	ZHA J, ZHANG Y, XIA K, et al. Coarse-grained simulation of mechanical properties of single microtubules with micrometer length[J]. Frontiers in Molecular Biosciences, 2021, 7: 632122. doi: 10.3389/fmolb.2020.632122
[31]	CHU J W, VOTH G A. Coarse-grained modeling of the actin filament derived from atomistic-scale simulations[J]. Biophysical Journal, 2006, 90(5): 1572-1582. doi: 10.1529/biophysj.105.073924
[32]	WANG Z, YUAN L, XU W, et al. Mechanical behaviors of actin-microtubule composite network: a coarse-grained Langevin dynamics study[J]. Acta Mechanica Sinica, 2025, 42(4): 624674.
[33]	STUKOWSKI A. Visualization and analysis of atomistic simulation data with OVITO: the open visualization tool[J]. Modelling and Simulation in Materials Science and Engineering, 2010, 18(1): 015012. doi: 10.1088/0965-0393/18/1/015012
[34]	BRANGWYNNE C P, MACKINTOSH F C, KUMAR S, et al. Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement[J]. The Journal of Cell Biology, 2006, 173(5): 733-741. doi: 10.1083/jcb.200601060
[35]	GARDEL M L, NAKAMURA F, HARTWIG J, et al. Stress-dependent elasticity of composite actin networks as a model for cell behavior[J]. Physical Review Letters, 2006, 96(8): 088102. doi: 10.1103/PhysRevLett.96.088102
[36]	POLLARD T D. Actin and actin-binding proteins[J]. Cold Spring Harbor Perspectives in Biology, 2016, 8(8): a018226. doi: 10.1101/cshperspect.a018226
[37]	LIELEG O, SCHMOLLER K M, CLAESSENS M M A E, et al. Cytoskeletal polymer networks: viscoelastic properties are determined by the microscopic interaction potential of cross-links[J]. Biophysical Journal, 2009, 96(11): 4725-4732. doi: 10.1016/j.bpj.2009.03.038
[38]	SEMMRICH C, LARSEN R J, BAUSCH A R. Nonlinear mechanics of entangled F-actin solutions[J]. Soft Matter, 2008, 4(8): 1675-1680. doi: 10.1039/b800989a
[39]	TANG B, SUN F, WEI X, et al. Defect size and cross-linkerproperties controlled fracture of biopolymer networks[J]. Extreme Mechanics Letters, 2022, 54: 101743. doi: 10.1016/j.eml.2022.101743
[40]	WEI X, FANG C, GONG B, et al. Viscoelasticity of 3D actin networks dictated by the mechanochemical characteristics of cross-linkers[J]. Soft Matter, 2021, 17(45): 10177-10185. doi: 10.1039/D0SM01558J
[41]	HUISMAN E M, VAN DILLEN T, ONCK P R, et al. Three-dimensional cross-linked F-actin networks: relation between network architecture and mechanical behavior[J]. Physical Review Letters, 2007, 99(20): 208103. doi: 10.1103/PhysRevLett.99.208103
[42]	WEI X, FANG C, GONG B, et al. Time-dependent response of bio-polymer networks regulated by catch and slip bond-like kinetics of cross-linkers[J]. Journal of the Mechanics and Physics of Solids, 2021, 147: 104267. doi: 10.1016/j.jmps.2020.104267
[43]	LI S H, GAO H, XU G K. Network dynamics of the nonlinear power-law relaxation of cell cortex[J]. Biophysical Journal, 2022, 121(21): 4091-4098. doi: 10.1016/j.bpj.2022.09.035