Rigidity generation by nonthermal fluctuations

Abstract

Active stabilization in systems with zero or negative stiffness is an essential element of a wide variety of biological processes. We study a prototypical example of this phenomenon at a microscale and show how active rigidity, interpreted as a formation of a pseudo-well in the effective energy landscape, can be generated in an overdamped ratchet-type stochastic system. We link the transition from negative to positive rigidity with correlations in the noise and show that subtle differences in out-of-equilibrium driving may compromise the emergence of a pseudo-well. The response of a living system to mechanical loading depends not only on the properties of the constituents and their connectivity, but also on the presence of nonthermal endogenous driving [1]. Thus, molecular motors can either stiffen the cytoskeleton through actively generated pre-stress [2] or fluidize it by facilitating remodeling [3]. Powered by ATP hydrolysis, living systems can also operate in mechanical regimes with negative passive stiffness as in the case of hair cells [4,5] and muscle halfsarcomeres [6,7]. In those cases metabolic resources are used to modify the mechanical susceptibility of the system and stabilize the apparently unstable states [8][9][10].At the structural level, active rigidity may be the outcome of tensegrity tightening [11], connectivity change [12], steric interactions [13], or the prestress exploiting strong nonlinearity of the passive response [14,15]. ATP induced stiffening can even take place at the level of individual structural elements as in the case of the Frank-Starling effect in cardiac muscles that cannot be explained by a simple filament overlap change [16].In this Letter we show that active rigidity can also emerge at the micro-scale level through resonant nonthermal excitation of molecular degrees of freedom as in the case of an inverted pendulum [17]. Following this inertial prototype, we construct an example of a mechanically unstable overdamped system where stabilization and creation of a new pseudo-well in the effective energy landscape can be induced by a colored noise. The proposed mechanism of rigidity generation requires a finite distance from equilibrium and is therefore different from the more conventional entropic stabilization [18]. The possibility of actively tunable rigidity opens interesting prospects not only in biomechanics [19] but also in engineering design incorporating negative stiffness [20] or aiming at synthetic materials stabilized dynamically [21,22].We illustrate our idea on a simple bi-stable mechanical system described by a single collective variable: the negative stiffness is viewed as a result of coarse-graining in a microscopic system with domineering long range interactions [23]. We assume that this 'snap-spring' is exposed to both thermal and correlated noises and acts against a linear spring which qualifies it as a molecular motor operating in stall conditions [24]. Instead of the conventional focus on active force, we study in this Letter a possibility of generating ...

Equilibrium unzipping at finite temperature

“…One of our important observations is that the discontinuous unzipping in such systems can be induced by tuning the overall rigidity. As it has been recently shown, in biological systems this kind of tuning can be achieved actively [57]. Our study then suggests that active rigidity manipulation may be an important factor controlling cell adhesion and may even facilitate filamental cross-linking during the reorganization of the cytoskeleton.…”

“…11c. For this behavior, which may be of a particular interest in biological applications, e.g., [56,57], to be relevant the temperature of the system must be, of course, sufficiently low.…”

Passive viscoelastic response of striated muscles

“…We also assume that the potential V (x) is asymmetric, which allows the system to generate (stall) force in the physiological regime of isometric contractions. While this asymmetry is maintained actively [34], we can still interpret the short time response in such system as passive. The active response involving detachment of the cross-bridges becomes dominant at time-scales of the order of 40 ms [35].…”

Stabilization in the Eye of a Cyclone

“…Applications vary from the induced force on probes in contact with biological tissue or filaments to the motion of dust in atmospheric dynamics. While the context of probes in contact with nonequilibrium media is clearly physically interesting there are very few mathematical treatments and even less rigorous results [1][2][3][4][5][6][7][8][9]. The present paper presents a mathematical study about the stabilization of a probe (the slow particle) which interacts with (fast) medium particles that are subject to a vortex-shaped force-field.…”