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Following recent work [e.g., J. Park et al., J. Rheol. 56, 1057–1082 (2012); T. Yaoita et al., Macromolecules 45, 2773–2782 (2012); and G. Ianniruberto et al., Macromolecules 45, 8058–8066 (2012)], we introduce the idea of a configuration dependent friction coefficient (CDFC) based on the relative orientation of Kuhn bonds of the test and surrounding matrix chains. We incorporate CDFC into the “toy” model of Mead et al. [Macromolecules 31, 7895–7914 (1998)] in a manner akin to Yaoita et al. [Nihon Reoroji Gakkaishi 42, 207–213 (2014)]. Additionally, we incorporate entanglement dynamics (ED) of discrete entanglement pairs into the new Mead–Banerjee–Park (MBP) model in a way similar to Ianniruberto and Marrucci [J. Rheol. 58, 89–102 (2014)]. The MBP model predicts a deformation dependent entanglement microstructure which is physically reflected in a reduced modulus that heals slowly following cessation of deformation. Incorporating ED into the model allows “shear modification” to be qualitatively captured. The MBP model is tested against experimental data in steady and transient extensional and shear flows. The MBP model captures the monotonic thinning of the extensional flow curve of entangled monodisperse polystyrene (PS) melts [A. Bach et al., Macromolecules 36, 5174–5179 (2003)] while simultaneously predicting the extension hardening found in PS semidilute solutions where CDFC is diluted out [P. K. Bhattacharjee et al., Macromolecules 35, 10131–10148 (2002)]. The simulation results also show that the rheological properties in nonlinear extensional flows of PS melts are sensitive to CDFC but not to convective constraint release (CCR) while those for shear flows are influenced more by CCR. The monodisperse MBP toy model is generalized to arbitrary polydispersity.

We reviewed numerical/analytical models for describing rheological properties and mechanical behaviors of biopolymer networks with a focus on the cytoskeleton, a major component of a living cell. The cytoskeleton models are classified into three categories: the cell-scale continuum-based model, the structure-based model, and the polymerbased model, according to the length scales of the phenomena of interest. The criteria for classification of the models are modified and extended from those used by Mofrad [M. R. K. Mofrad, Annual Rev. Fluid Mech. 41, 433 (2009)]. The main principles and characteristics of each model are summarized and discussed by comparison with each other.Since the stress-deformation relation of cytoskeleton is dependent on the length scale of stress elements, our model classification helps systematic understanding of biopolymer network modeling.

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