Power-law creep behavior of a semiflexible chain

Nonlinear stress relaxation of transiently crosslinked biopolymer networks

A long-standing puzzle in the rheology of living cells is the origin of the experimentally observed long-time stress relaxation. The mechanics of the cell is largely dictated by the cytoskeleton, which is a biopolymer network consisting of transient crosslinkers, allowing for stress relaxation over time. Moreover, these networks are internally stressed due to the presence of molecular motors. In this work we propose a theoretical model that uses a mode-dependent mobility to describe the stress relaxation of such prestressed transient networks. Our theoretical predictions agree favorably with experimental data of reconstituted cytoskeletal networks and may provide an explanation for the slow stress relaxation observed in cells.

Transport cycle of Escherichia coli lactose permease in a nonhomogeneous random walk model

We present Monte Carlo simulations for the transport cycle of Escherichia coli lactose permease (LacY), using as a starting point the model proposed by Kaback et al. [Nat. Rev. Mol. Cell Biol. 2, 610 (2001)NRMCBP1471-007210.1038/35085077], which is based on functional properties of mutants and x-ray structures. Kaback's model suggests the existence of six states for the whole cycle of lactose-H^{+} symport. However, the free-energy differences between these states have not yet been reported in the literature. Here, we analyzed the biochemical structure of each state and determined a range of possible values for each one of the five free-energy variations. Then, using the Metropolis algorithm in a nonhomogeneous random walk model, we tested all the possible combinations with these values to find the free-energy curve that best reproduces the dynamics of LacY. The agreement between our model predictions and the experimental data suggests that our free-energy curve is appropriate for describing the lactose-H^{+} symport. We found not only this curve, but also the time of occupancy of the permease at each conformation. In addition, we paved the way in this work to solve an open question related to this transport mechanism, which is the importance of protonation for lactose binding.

Time course of isotonic shortening and the underlying contraction mechanism in airway smooth muscle

Although the structure of the contractile unit in smooth muscle is poorly understood, some of the mechanical properties of the muscle suggest that a sliding-filament mechanism, similar to that in striated muscle, is also operative in smooth muscle. To test the applicability of this mechanism to smooth muscle function, we have constructed a mathematical model based on a hypothetical structure of the smooth muscle contractile unit: a side-polar myosin filament sandwiched by actin filaments, each attached to the equivalent of a Z disk. Model prediction of isotonic shortening as a function of time was compared with data from experiments using ovine tracheal smooth muscle. After equilibration and establishment of in situ length, the muscle was stimulated with ACh (100 μM) until force reached a plateau. The muscle was then allowed to shorten isotonically against various loads. From the experimental records, length-force and force-velocity relationships were obtained. Integration of the hyperbolic force-velocity relationship and the linear length-force relationship yielded an exponential function that approximated the time course of isotonic shortening generated by the modeled sliding-filament mechanism. However, to obtain an accurate fit, it was necessary to incorporate a viscoelastic element in series with the sliding-filament mechanism. The results suggest that a large portion of the shortening is due to filament sliding associated with muscle activation and that a small portion is due to continued deformation associated with an element that shows viscoelastic or power-law creep after a step change in force.

Stress transmission within the cell

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. During past decades, it has become evident that the deformable cytoskeleton (CSK), an intracellular network of various filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical responses. To understand how mechanical forces regulate cellular functions, it is necessary to first understand how the CSK develops mechanical stresses in response to applied forces, and how those stresses are propagated through the CSK where various signaling molecules are immobilized. New experimental techniques have been developed to quantify cytoskeletal mechanics, which together with new computational approaches have given rise to new theories and models for describing mechanics of living cells. In this article, we discuss current understanding of cell biomechanics by focusing on the biophysical mechanisms that are responsible for the development and transmission of mechanical stresses in the cell and their effect on cellular functions. We compare and contrast various theories and models of cytoskeletal mechanics, emphasizing common mechanisms that those theories are built upon, while not ignoring irreconcilable differences. We highlight most recent advances in the understanding of mechanotransduction in the cytoplasm of living cells and the central role of the cytoskeletal prestress in propagating mechanical forces along the cytoskeletal filaments to activate cytoplasmic enzymes. It is anticipated that advances in cell mechanics will help developing novel therapeutics to treat pulmonary diseases like asthma, pulmonary fibrosis, and chronic obstructive pulmonary disease.

A continuous-binding cross-linker model for passive airway smooth muscle

Although the active properties of airway smooth muscle (ASM) have garnered much modeling attention, the passive mechanical properties are not as well studied. In particular, there are important dynamic effects observed in passive ASM, particularly strain-induced fluidization, which have been observed both experimentally and in models; however, to date these models have left an incomplete picture of the biophysical, mechanistic basis for these behaviors. The well-known Huxley cross-bridge model has for many years successfully described many of the active behaviors of smooth muscle using sliding filament theory; here, we propose to extend this theory to passive biological soft tissue, particularly ASM, using as a basis the attachment and detachment of cross-linker proteins at a continuum of cross-linker binding sites. The resulting mathematical model exhibits strain-induced fluidization, as well as several types of force recovery, at the same time suggesting a new mechanistic basis for the behavior. The model is validated by comparison to new data from experimental preparations of rat tracheal airway smooth muscle. Furthermore, experiments in noncontractile tissue show qualitatively similar behavior, suggesting support for the protein-filament theory as a biomechanical basis for the behavior.

Cell mechanics: dissecting the physical responses of cells to force

It is now widely appreciated that normal tissue morphology and function rely upon cells' ability to sense and generate forces appropriate to their correct tissue context. Although the effects of forces on cells have been studied for decades, our understanding of how those forces propagate through and act on different cell substructures remains at an early stage. The past decade has seen a resurgence of interest, with a variety of different micromechanical methods in current use that probe cells' dynamic deformation in response to a time-varying force. The ability of researchers to carefully measure the mechanical properties of cells subjected to a variety of pharmacological and genetic interventions, however, currently outstrips our ability to quantitatively interpret the data in many cases. Despite these challenges, the stage is now set for the development of detailed models for cell deformability, motility, and mechanosensing that are rooted at the molecular level.

Tension dynamics and viscoelasticity of extensible wormlike chains

The dynamic response of prestressed semiflexible biopolymers is characterized by the propagation and relaxation of tension, which arises due to the near inextensibility of a stiff backbone. It is coupled to the dynamics of contour length stored in thermal undulations but also to the local relaxation of elongational strain. We present a systematic theory of tension dynamics for stiff yet extensible wormlike chains. Our results show that even moderate prestress gives rise to distinct Rouse-like extensibility signatures in the high-frequency viscoelastic response.

Thermodynamic origin of cooperativity in actomyosin interactions: the coupling of short-range interactions with actin bending stiffness in an Ising-like model

We present Monte Carlo simulations for a molecular motor system found in virtually all eukaryotic cells, the acto-myosin motor system, composed of a group of organic macromolecules. Cell motors were mapped to an Ising-like model, where the interaction field is transmitted through a tropomyosin polymer chain. The presence of Ca2+ induces tropomyosin to block or unblock binding sites of the myosin motor leading to its activation or deactivation. We used the Metropolis algorithm to find the transient and the equilibrium states of the acto-myosin system composed of solvent, actin, tropomyosin, troponin, Ca2+, and myosin-S1 at a given temperature, including the spatial configuration of tropomyosin on the actin filament surface. Our model describes the short- and long-range cooperativity during actin-myosin binding which emerges from the bending stiffness of the tropomyosin complex. We found all transition rates between the states only using the interaction energy of the constituents. The agreement between our model and experimental data also supports the recent theory of flexible tropomyosin.