Sparse polynomial surrogates for F-actin networks with compliant crosslinkers

Filamentous actin (F-actin) constitutes the primary contributor to cell elasticity and structural integrity, forming dynamic, crosslinked networks in the actin cortex. Existing mechanical models for F-actin and crosslinked filament networks successfully describe filament- and network-level behavior, but are often limited in accounting for biological dynamic processes and inherent material uncertainty and variability. We develop a stochastic modeling framework that integrates Polynomial Chaos Expansion (PCE) surrogates using the Finite Element Method (FEM). These surrogates replace filament-scale equations for compliant crosslinked F-actin networks, efficiently enabling uncertainty quantification and sensitivity analysis of key material parameters. The first and second statistical moments from the PCE are incorporated into a micro-sphere network model and implemented via a user-defined material subroutine. Validation was performed against 10 000 Monte Carlo simulations (MCS) for each of four FEM test cases: three simple deformation modes applied to a unit length cubic element, and a thin gel layer under shear mimicking a parallel plate rheology setup. In every test, the surrogate predicts the expected value of relevant stress quantities at maximum deformation with under 1% relative error versus the MCS reference. Moreover, the surrogate captures the network's variability as measured by second-order moments, demonstrating its ability to deliver rapid, statistically faithful predictions of both mean response and standard deviation in simple element tests and experimentally relevant rheology geometries. The proposed methodology provides a scalable route for incorporating intrinsic material variability into F-actin mechanical modeling, with implications for studying cell motility, division, and pathologies related to cytoskeletal remodeling.