Multiscale mechanobiology: computational models for integrating molecules to multicellular systems

Abstract

Mechanical signals exist throughout the biological landscape. Across all scales, these signals, in the form of force, stiffness, and deformations, are generated and processed, resulting in an active mechanobiological circuit that controls many fundamental aspects of life, from protein unfolding and cytoskeletal remodeling to collective cell motions. The multiple scales and complex feedback involved present a challenge for fully understanding the nature of this circuit, particularly in development and disease in which it has been implicated. Computational models that accurately predict and are based on experimental data enable a means to integrate basic principles and explore fine details of mechanosensing and mechanotransduction in and across all levels of biological systems. Here we review recent advances in these models along with supporting and emerging experimental findings.

Fig. 1

Mechanobiology simulations from molecular to multicellular scales. Coarse graining of simulation elements or reduction in system interactions is required to simulate larger scales due to computational cost. (a) Steered molecular dynamics simulation of a stretching force applied to the H1–H12 rod of talin, adapted from ref. . Talin has five vinculin binding helices (H4, H6, H9, H11, H12) in its rod domain. As the molecule is stretched by a 300 pN force distributed across its cross section (as indicated), the amount of buried surface area of the vinculin binding sites is reduced, suggesting increased binding affinity for vinculin. ΔL corresponds to the increase in length of the domain as compared to its equilibrium length, which is 3.2 nm. (b) Brownian dynamics simulations of actin (teal) networks connected via actin crosslinking proteins ACPs (red), adapted from ref. . (left) A prestrain is applied to this network in the x direction, inducing stress on ACPs and actin. This model predicts that a supportive framework emerges in this network that bears the majority of the stress, such that removal of large fractions of ACPs and actin still enables most of the stress to be sustained when identical oscillatory strain is applied (right). Simulation results provide insights that different mechanisms, such as ACP and actin bending and extension, dictate network viscoelasticity depending on prestrain. (c) A single-cell migration model with focal adhesions, stress fibers, protrusions, and a nucleus, adapted from ref. 110. The cell can adhere to a micropatterned surface and generate spatial profiles of traction forces comparable to experimental studies. Focal adhesions adhere to the substrate and stress fibers can connect to adhesion sites and the nucleus. 3D force balance calculations are performed at each integrin node. This model provides a platform for investigating how prominent intracellular components interact with each other and respond to environmental constraints to generate an integrated cell response. It also implicates the nucleus as a cause for asymmetry in leading and trailing edge adhesion dynamics. (d) Hybrid Potts and finite element model of endothelial networks, adapted from ref. 13. (top) Endothelial cells generate forces and deform a soft substrate. Neighboring cells respond to substrate strains and undergo durotaxis, leading to the formation of networks from single cells that resemble experimental observations (bottom). This model provides indications of how force signals can lead to endothelial morphogenesis.

Fig. 2

Schematics of molecular-level mechanotransduction. (a) When myosin II motors are inactive, cells exhibit reduced tension, causing mechanosensitive protein complexes to assume inactive forms. Inactive talin and filamin have cryptic binding sites, which are unavailable for binding with affiliated molecules. (b) When myosin motors are active or external tension is applied, mechanosensitive proteins become stretched, making accessible previously hidden binding sites. Downstream signaling proteins, such as vinculin, can then bind and activate signaling cascades that promote adhesion, migration, and other physiological functions. Increased force can also alter the binding kinetics and adhesion dynamics of mechanosensitive complexes.

Fig. 3

Schematic illustrating mechanical properties of crosslinked filament networks and the impact on mechanotransduction. Crosslinked actin networks exhibit stiffening and enhanced elasticity under an appropriate, intermediate level of strain or stress, which can be induced by external application or internal motors. Crosslinker and filament kinetics and mechanics determine the appropriate range. Elastic networks, where forces are not rapidly dissipated, that exhibit fibrillar alignment enable longer range transmission and transduction of mechanical signals.

Fig. 4

Mechanical signals, in the form of force and spatial distortions, are generated by cells and molecular motors. The soft, fibrillar ECM and cytoskeleton are the mechanical wiring networks in which these signals are transmitted, and adhesion complexes enable bidirectional transduction between the two environments. The cell nucleus is also directly connected to this mechanical circuit. (a) Single cells and cell aggregates exert contractile forces on the ECM, propagating signals to distant cells and generating matrix alignment. (b) Expanded view of two connected cells illustrates the connections between a cell and its neighbor and the ECM via adhesion complexes, which act to transmit mechanical signals both inside-out and outside-in. Inside the cell, molecular motors such as myosin II contract the intracellular matrix made of crosslinked actin filaments. The actin cytoskeleton is further connected to the nucleus via the LINC-complex, enabling direct force transmission to the nucleus.