Asymmetric response emerges between creation and disintegration of force-bearing subcellular structures as revealed by percolation analysis.

Cells dynamically remodel their internal structures by modulating the arrangement of actin filaments (AFs). In this process, individual AFs exhibit stochastic behavior without knowing the macroscopic higher-order structures they are meant to create or disintegrate, but the mechanism allowing for such stochastic process-driven remodeling of subcellular structures remains incompletely understood. Here we employ percolation theory to explore how AFs interacting only with neighboring ones without recognizing the overall configuration can nonetheless create a substantial structure referred to as stress fibers (SFs) at particular locations. We determined the interaction probabilities of AFs undergoing cellular tensional homeostasis, a fundamental property maintaining intracellular tension. We showed that the duration required for the creation of SFs is shortened by the increased amount of preexisting actin meshwork, while the disintegration occurs independently of the presence of actin meshwork, suggesting that the coexistence of tension-bearing and non-bearing elements allows cells to promptly transition to new states in accordance with transient environmental changes. The origin of this asymmetry between creation and disintegration, consistently observed in actual cells, is elucidated through a minimal model analysis by examining the intrinsic nature of mechano-signal transmission. Specifically, unlike the symmetric case involving biochemical communication, physical communication to sense environmental changes is facilitated via AFs under tension, while other free AFs dissociated from tension-bearing structures exhibit stochastic behavior. Thus, both the numerical and minimal models demonstrate the essence of intracellular percolation, in which macroscopic asymmetry observed at the cellular level emerges not from microscopic asymmetry in the interaction probabilities of individual molecules, but rather only as a consequence of the manner of the mechano-signal transmission. These results provide novel insights into the role of the mutual interplay between distinct subcellular structures with and without tension-bearing capability. Insight: Cells continuously remodel their internal elements or structural proteins in response to environmental changes. Despite the stochastic behavior of individual structural proteins, which lack awareness of the larger subcellular structures they are meant to create or disintegrate, this self-assembly process somehow occurs to enable adaptation to the environment. Here we demonstrated through percolation simulations and minimal model analyses that there is an asymmetry in the response between the creation and disintegration of subcellular structures, which can aid environmental adaptation. This asymmetry inherently arises from the nature of mechano-signal transmission through structural proteins, namely tension-mediated information exchange within cells, despite the stochastic behavior of individual proteins lacking asymmetric characters in themselves.

Emergence of multiple set-points of cellular homeostatic tension.

Stress fibers (SFs), a contractile actin bundle in nonmuscle mesenchymal cells, are known to intrinsically sustain a constant level of tension or tensional stress, a process called cellular tensional homeostasis. Malfunction in this homeostatic process has been implicated in many diseases such atherosclerosis, but its mechanisms remain incompletely understood. Interestingly, the homeostatic stress in individual SFs is altered upon recruitment of α-smooth muscle actin in particular cellular contexts to reinforce the preexisting SFs. While this transition of the set-point stress is somewhat a universal process observed across different cell types, no clear explanation has been provided as to why cells end up possessing different stable stresses. To address the underlying physics, here we describe that imposing a realistic assumption on the nature of SFs yields the presence of multiple set-points of the homeostatic stress, which transition among them depending on the magnitude of the cellular tension. We analytically derive non-dimensional parameters that characterize the extent of the transition and predict that SFs tend to acquire secondary stable stresses if they are subject to as large a change in stiffness as possible or to as immediate a transition as possible upon increasing the tension. This is a minimal and simple explanation, but given the frequent emergence of force-dependent transformation of various subcellular structures in addition to that of SFs, the theoretical concept presented here would offer an essential guide to addressing potential common mechanisms governing complicated cellular mechanobiological responses.

A statistical mechanics model for determining the length distribution of actin filaments under cellular tensional homeostasis.

Tensional homeostasis is a cellular process whereby nonmuscle cells such as fibroblasts keep a constant level of intracellular tension and signaling activities. Cells are allowed thanks to tensional homeostasis to adapt to mechanical stress, but the detailed mechanism remains unclear. Here we address from a theoretical point of view what is required for maintaining cellular tensional homeostasis. A constrained optimization problem is formulated to analytically determine the probability function of the length of individual actin filaments (AFs) responsible for sustaining cellular tension. An objective function composed of two entropic quantities measuring the extent of formation and dispersion of AFs within cells is optimized under two constraint functions dictating a constant amount of actin molecules and tension that are arguably the two most salient features of tensional homeostasis. We then derive a specific probability function of AFs that is qualitatively consistent with previous experimental observations, in which short AF populations preferably appear. Regarding the underlying mechanism, our analyses suggest that the constraint for keeping the constant tension level makes long AF populations smaller in number because long AFs have a higher chance to be involved in bearing larger forces. The specific length distribution of AFs is thus required for achieving the constrained objectives, by which individual cells are endowed with the ability to stably maintain a homeostatic tension throughout the cell, thereby potentially allowing cells to locally detect deviation in the tension, keep resulting biological functions, and hence enable subsequent adaptation to mechanical stress. Although minimal essential factors are included given the actual complexity of cells, our approach would provide a theoretical basis for understanding complicated homeostatic and adaptive behavior of the cell.