Ultra-long-range force transmission in fiber networks enabled by multiaxial mechanical coupling

Force transmission in the extracellular matrix is crucial for cellular mechanosensing. This transmission is influenced by factors such as tension-compression asymmetric stiffness and the fiber alignment of fibrous materials. However, the role of the anomalous Poisson's ratio, intrinsic to fibrous materials, in force transmission remains underexplored. In this study, we utilize discrete fiber network simulations with different levels of connectivity to examine the stress decay of cell contraction in fibrous matrices. Our findings show that highly connected fiber networks exhibit reduced fiber alignment and atypical tensile hoop stress. This leads to an ultraslow decay of radial stress induced by isotropic contraction of spherical cells. Delving deeper, we discover that the increase of network connectivity corresponds to an enhanced Poisson's ratio, signifying a pronounced multiaxial coupling effect. To fully comprehend this multiaxial coupling, we develop a constitutive law for fibrous materials. This law considers the stiffening along the tensile direction and their significant transverse contraction. Theoretical analysis elucidates that the stress decay of cell contraction adheres to a scaling law, represented as sigma r similar to r n, with the decay exponent n ranging from 1.5 to 3. Notably, this finding diverges from prior predictions that n is more than 2. The combination of a high tension-to-compression stiffness ratio with strong multiaxial coupling leads to ultra-long-range force transmission in fibrous materials. This ultra-long-range force transmission is marked by a convergent diminishing n approximating 1.5. In summary, our study provides a quantitative framework for elucidating the maximum limit of the force transmission range and serves as a guideline for developing innovative biomimetic materials.