This paper is devoted to the application of the pair torque interaction potential for the simulation of the elastic behavior of a promising two-dimensional material: single layer molybdenium disulphide (SLMoS2). It is demonstrated that both Mo–Mo and S–S interactions can be regarded as pair force interactions with sufficient accuracy. Using both experimental and calculated numerically elastic moduli, and also the phonon spectrum available in the literature, the parameters of the Morse potential are determined for Mo–Mo and S–S bonds, and the parameters of the pair torque potential are obtained for the Mo–S bond. As a result, a combination of force and torque pair potentials is proposed, which allows for the correct modelling of SLMoS2 mechanical behavior.

The extracellular matrix (ECM) is a fibrous network supporting biological cells and provides them a medium for interaction. Cells modify the ECM by applying traction forces, and these forces can propagate to long ranges and establish a mechanism of mechanical communication between neighboring cells. Previous studies have mainly focused on analysis of static force transmission across the ECM. In this study, we explore the plausibility of dynamic mechanical interaction, expressed as vibrations or abrupt fluctuations, giving rise to elastic waves propagating along ECM fibers. We use a numerical mass-spring model to simulate the longitudinal and transversal waves propagating along a single ECM fiber and across a 2D random fiber network. The elastic waves are induced by an active contracting cell (signaler) and received by a passive neighboring cell (receiver). We show that dynamic wave propagation may amplify the signal at the receiver end and support up to an order of magnitude stronger mechanical cues and longer-ranged communication relative to static transmission. Also, we report an optimal impulse duration corresponding to the most effective transmission, as well as extreme fast impulses, in which the waves are encaged around the active cell and do not reach the neighboring cell, possibly due to the Anderson localization effect. Finally, we also demonstrate that extracellular fluid viscosity reduces, but still allows, dynamic propagation along embedded ECM fibers. Our results motivate future biological experiments in mechanobiology to investigate, on the one hand, the mechanosensitivity of cells to dynamic forces traveling and guided by the ECM and, on the other hand, the impact of ECM architecture and remodeling on dynamic force transmission and its spectral filtering, dispersion, and decay.

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