Cells both actively generate and sensitively react to forces through their mechanical framework, the cytoskeleton, which is a nonequilibrium composite material including polymers and motor proteins. We measured the dynamics and mechanical properties of a simple three-component model system consisting of myosin II, actin filaments, and cross-linkers. In this system, stresses arising from motor activity controlled the cytoskeletal network mechanics, increasing stiffness by a factor of nearly 100 and qualitatively changing the viscoelastic response of the network in an adenosine triphosphate-dependent manner. We present a quantitative theoretical model connecting the large-scale properties of this active gel to molecular force generation.

Quantitatively measuring the mechanical properties of soft matter over a wide range of length and time scales, especially if a sample is as complex as typical biological materials, remains challenging. Living cells present a further complication because forces are generated within these nonequilibrium materials that can change material properties. We have here developed high-bandwidth techniques for active one-and two-particle microrheology to tackle these issues. By combining active micromanipulation of probe particles with an optical trap with high-resolution tracking of thermal motions of the very same particles by laser interferometry, we can both measure the mechanical properties of and, at the same time, identify nonequilibrium forces in soft materials. In both simple liquids and equilibrium cytoskeletal actin networks, active microrheology (AMR) proves to be less noise sensitive than and offers extended bandwidth (0.1-100 kHz) compared to passive microrheology (PMR), which merely tracks thermal motions. We confirm high-frequency power-law dynamics in equilibrium actin networks with two-particle AMR and also discuss low-frequency local mechanical response near probe particles which shows up in one-particle AMR. The combination of AMR and PMR allowed us to quantify nonthermal force fluctuations in actin networks driven by myosin motor proteins. Our approach offers a new direct way to investigate the nonequilibrium dynamics of living materials.

Dynamic networks designed to model the cell cytoskeleton can be reconstituted from filamentous actin, the motor protein myosin and a permanent cross-linker. They are driven out of equilibrium when the molecular motors are active. This gives rise to athermal fluctuations that can be recorded by tracking probe particles that are dispersed in the network. We have here probed athermal fluctuations in such "active gels" using video microrheology. We have measured the full 10 distribution of probe displacements, also known as the van Hove correlation function. The dominant influence of thermal or athermal fluctuations can be detected by varying the lag time over which the displacements are measured. We argue that the exponential tails of the distribution derive from single motors close to the probes, and we extract an estimate of the velocity of motor heads along the actin filaments. The distribution exhibits a central Gaussian region which we 15 assume derives from the action of many independent motor proteins far from the probe particles when athermal fluctuations dominate. Recording the whole distribution rather than just the typically measured second moment of probe fluctuations (mean-squared displacement) thus allowed us to differentiate between the effect of individual motors and the collective action of many motors.

Nonequilibrium energetics of single molecule translational motor kinesin was investigated by measuring heat dissipation from the violation of the fluctuation-response relation of a probe attached to the motor using optical tweezers. The sum of the dissipation and work did not amount to the input free energy change, indicating large hidden dissipation exists. Possible sources of the hidden dissipation were explored by analyzing the Langevin dynamics of the probe, which incorporates the two-state Markov stepper as a kinesin model. We conclude that internal dissipation is dominant.Kinesin-1 (hereafter called kinesin) is a molecular motor that transports various cargos along microtubules throughout the cell [1,2]. Single molecule kinesin takes 8 nm steps [3] per ATP hydrolysis [4,5] on a microtubule rail and generates ≈7 pN maximum force [6][7][8]. The two catalytic sites (heads) hydrolyze ATP in a "hand-over-hand" manner that mimics bipedal walking [9-11] by alternating its two heads in coordination with different nucleotide/microtubule binding states [12]. Kinesin shows backward steps occasionally at no load and frequently at high loads [13][14][15]. Recent experiments indicate that the biased unidirectional motion is achieved by regulating selective binding/unbinding of the head to/from the appropriate binding site [16][17][18][19][20]. Contrary to the molecular mechanism of the motility, the thermodynamic energetics of the motor is poorly understood due to kinesin's stochastic and nonequilibrium behavior.The energetics of single-molecule motors were historically discussed when their stall forces were measured [21]. Kinesin's stall force of ≈7 pN indicates that maximum work per 8-nm step (≈56 pN•nm) is smaller than the physiological free energy change per ATP hydrolysis (≈85 pN•nm). This is in contrast to rotary motor F 1 -ATPase, whose stall force explains all input free energy [22]. Kinesin's inefficient work at stall has been regarded as an "open problem" [23]. However, it may not be appropriate to evaluate kinesin efficiency from the stall force for two reasons. First, it is believed that kinesin consumes ATP at backsteps instead of synthesizing ATP [13][14][15], indicating that the stall condition is not thermodynamically (quasi-)static. Second, the physiological role of kinesin is to carry vesicles against viscous media, meaning that the input energy is dissipated as "heat" rather than "work." Thus, measuring the "dissipation" from the motor is essential when discussing kinesin's nonequilibrium energetics in physiologically relevant conditions.The Harada-Sasa equality is best suited for this purpose [24,25] :Here, J x is total heat dissipation per unit time from the system through specific degrees of freedom indicated with subscript x. γ is viscous drag, and x  v is mean velocity, where  denotes the ensemble average. () Cf , with frequency f, is a Fourier transform of the correlation function of velocity fluctuations,is a Fourier transform of the velocity response function, and the prime indicates the re...

Physiological processes in cells are performed efficiently without getting jammed although cytoplasm is highly crowded with various macromolecules. Elucidating the physical machinery is challenging because the interior of a cell is so complex and driven far from equilibrium by metabolic activities. Here, we studied the mechanics of in vitro and living cytoplasm using the particle-tracking and manipulation technique. The molecular crowding effect on cytoplasmic mechanics was selectively studied by preparing simple in vitro models of cytoplasm from which both the metabolism and cytoskeletons were removed. We obtained direct evidence of the cytoplasmic glass transition; a dramatic increase in viscosity upon crowding quantitatively conformed to the super-Arrhenius formula, which is typical for fragile colloidal suspensions close to jamming. Furthermore, the glass-forming behaviors were found to be universally conserved in all the cytoplasm samples that originated from different species and developmental stages; they showed the same tendency for diverging at the macromolecule concentrations relevant for living cells. Notably, such fragile behavior disappeared in metabolically active living cells whose viscosity showed a genuine Arrhenius increase as in typical strong glass formers. Being actively driven by metabolism, the living cytoplasm forms glass that is fundamentally different from that of its non-living counterpart.