Simple model of cytoskeletal fluctuations

Actin crosslinking by α-actinin averts viscous dissipation of myosin force transmission in stress fibers

Contractile force generated in actomyosin stress fibers (SFs) is transmitted along SFs to the extracellular matrix (ECM), which contributes to cell migration and sensing of ECM rigidity. In this study, we show that efficient force transmission along SFs relies on actin crosslinking by α-actinin. Upon reduction of α-actinin-mediated crosslinks, the myosin II activity induced flows of actin filaments and myosin II along SFs, leading to a decrease in traction force exertion to ECM. The fluidized SFs maintained their cable integrity probably through enhanced actin polymerization throughout SFs. A computational modeling analysis suggested that lowering the density of actin crosslinks caused viscous slippage of actin filaments in SFs and, thereby, dissipated myosin-generated force transmitting along SFs. As a cellular scale outcome, α-actinin depletion attenuated the ECM-rigidity-dependent difference in cell migration speed, which suggested that α-actinin-modulated SF mechanics is involved in the cellular response to ECM rigidity.

Hypermethylation of mitochondrial DNA in vascular smooth muscle cells impairs cell contractility

Vascular smooth muscle cell (SMC) from arterial stenotic-occlusive diseases is featured with deficiency in mitochondrial respiration and loss of cell contractility. However, the regulatory mechanism of mitochondrial genes and mitochondrial energy metabolism in SMC remains elusive. Here, we described that DNA methyltransferase 1 (DNMT1) translocated to the mitochondria and catalyzed D-loop methylation of mitochondrial DNA in vascular SMCs in response to platelet-derived growth factor-BB (PDGF-BB). Mitochondrial-specific expression of DNMT1 repressed mitochondrial gene expression, caused functional damage, and reduced SMC contractility. Hypermethylation of mitochondrial D-loop regions were detected in the intima-media layer of mouse carotid arteries subjected to either cessation of blood flow or mechanical endothelial injury, and also in vessel specimens from patients with carotid occlusive diseases. Likewise, the ligated mouse arteries exhibited an enhanced mitochondrial binding of DNMT1, repressed mitochondrial gene expression, defects in mitochondrial respiration, and impaired contractility. The impaired contractility of a ligated vessel could be restored by ex vivo transplantation of DNMT1-deleted mitochondria. In summary, we discovered the function of DNMT1-mediated mitochondrial D-loop methylation in the regulation of mitochondrial gene transcription. Methylation of mitochondrial D-loop in vascular SMCs contributes to impaired mitochondrial function and loss of contractile phenotype in vascular occlusive disease.

Distribution of active forces in the cell cortex

In this work, we study in detail the distribution of stochastic forces generated by the molecular motors activity, in the actin cortex of pre-muscular cells. By combining active and passive rheology experiments, performed on the same micro-bead bound to the actin network through membrane adhesive receptors, we measure the auto-correlation function C_ff(τ) of the average force pulling on the bead. As for any out-of-equilibrium system, the force distribution differs from the thermodynamical equilibrium one, especially at long time scale τ⪆ 1 s where the bead motion becomes partially directed. Thus the fluctuation-dissipation theorem does not apply and one can measure the distance from equilibrium through its violation. We investigate the influence of different parameters on the force distribution, focusing particularly on the role of ligand density: a detailed study shows how the amplitude of active forces increases when the bead is more tightly attached to the cortex. We introduce and study a model, which takes into account the number of bonds between the bead and the cytoskeleton, as well as the viscoelastic properties of the medium. This model faithfully accounts for the experimental observations. Also, it is shown that the amplitude of active forces increases with temperature. Finally, our data confirm that ATP depletion in the cell, or partial inhibition of the actomyosin activity, leads to a decrease of the amplitude of the force distribution. Altogether, we propose a consistent and quantitative description for the motion of a micrometric probe interacting with the actin network, and for the amplitude of the stochastic forces generated by molecular motors in the cortex surrounding this probe.

Nonmotile Single-Cell Migration as a Random Walk in Nonuniformity: The "Extreme Dumping Limit" for Cell-to-Cell Communications

In the present work, we model single-cell movement as a random walk in an external potential observed within the extreme dumping limit, which we define herein as the extreme nonuniform behavior observed for cell responses and cell-to-cell communications. Starting from the Newton–Langevin equation of motion, we solve the corresponding Fokker–Planck equation to compute higher moments of the displacement of the cell, and then we build certain quantities that can be measurable experimentally. We show that, each time, the dynamics depend on the external force applied, leading to predictions distinct from the standard results of a free Brownian particle. Our findings demonstrate that cell migration viewed as a stochastic process is still compatible with biological and experimental observations without the need to rely on more complicated or sophisticated models proposed previously in the literature.

Epithelia migration: a spatiotemporal interplay between contraction and adhesion

Epithelial tissues represent 60% of the cells that form the human body and where more than 90% of all cancers derived. Epithelia transformation and migration involve altered cell contractile mechanics powered by an actomyosin-based cytoskeleton and influenced by cell-cell and cell-extracellular matrix interactions. A balance between contractile and adhesive forces regulates a large number of cellular and tissue properties crucial for epithelia migration and tumorigenesis. In this review, the forces driving normal epithelia transformation into highly motile and invasive cells and tissues will be discussed.

Superstatistical analysis and modelling of heterogeneous random walks

Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.

Conventional methods to quantify the migratory behaviour of cells assume that underlying parameters are constant. Mark et al. apply a superstatistical approach to extract time-dependent parameters of motile cells, and demonstrate an enhanced ability to distinguish between different migration strategies.

LMX1B is essential for the maintenance of differentiated podocytes in adult kidneys

Mutations of the LMX1B gene cause nail-patella syndrome, a rare autosomal-dominant disorder affecting the development of the limbs, eyes, brain, and kidneys. The characterization of conventional Lmx1b knockout mice has shown that LMX1B regulates the development of podocyte foot processes and slit diaphragms, but studies using podocyte-specific Lmx1b knockout mice have yielded conflicting results regarding the importance of LMX1B for maintaining podocyte structures. In order to address this question, we generated inducible podocyte-specific Lmx1b knockout mice. One week of Lmx1b inactivation in adult mice resulted in proteinuria with only minimal foot process effacement. Notably, expression levels of slit diaphragm and basement membrane proteins remained stable at this time point, and basement membrane charge properties also did not change, suggesting that alternative mechanisms mediate the development of proteinuria in these mice. Cell biological and biophysical experiments with primary podocytes isolated after 1 week of Lmx1b inactivation indicated dysregulation of actin cytoskeleton organization, and time-resolved DNA microarray analysis identified the genes encoding actin cytoskeleton-associated proteins, including Abra and Arl4c, as putative LMX1B targets. Chromatin immunoprecipitation experiments in conditionally immortalized human podocytes and gel shift assays showed that LMX1B recognizes AT-rich binding sites (FLAT elements) in the promoter regions of ABRA and ARL4C, and knockdown experiments in zebrafish support a model in which LMX1B and ABRA act in a common pathway during pronephros development. Our report establishes the importance of LMX1B in fully differentiated podocytes and argues that LMX1B is essential for the maintenance of an appropriately structured actin cytoskeleton in podocytes.

Cell and tissue mechanics in cell migration

Migrating cells generate traction forces to counteract the movement-resisting forces arising from cell-internal stresses and matrix adhesions. In the case of collective migration in a cell colony, or in the case of 3-dimensional migration through connective tissue, movement-resisting forces arise also from external stresses. Although the deformation of a stiffer cell or matrix causes larger movement-resisting forces, at the same time a larger stiffness can also promote cell migration due to a feedback between forces, deformations, and deformation speed that is mediated by the acto-myosin contractile machinery of cells. This mechanical feedback is also important for stiffness sensing, durotaxis, plithotaxis, and collective migration in cell colonies.

Integrin adhesion and force coupling are independently regulated by localized PtdIns(4,5)2 synthesis

The 90-kDa isoform of the lipid kinase PIP kinase Type I γ (PIPKIγ) localizes to focal adhesions (FAs), where it provides a local source of phosphatidylinositol 4,5-bisphosphate (PtdIns(4,5)P(2)). Although PtdIns(4,5)P(2) regulates the function of several FA-associated molecules, the role of the FA-specific pool of PtdIns(4,5)P(2) is not known. We report that the genetic ablation of PIPKIγ specifically from FAs results in defective integrin-mediated adhesion and force coupling. Adhesion defects in cells deficient in FAPtdIns(4,5)P(2) synthesis are corrected within minutes while integrin-actin force coupling remains defective over a longer period. Talin and vinculin, but not kindlin, are less efficiently recruited to new adhesions in these cells. These data demonstrate that the specific depletion of PtdIns(4,5)P(2) from FAs temporally separates integrin-ligand binding from integrin-actin force coupling by regulating talin and vinculin recruitment. Furthermore, it suggests that force coupling relies heavily on locally generated PtdIns(4,5)P(2) rather than bulk membrane PtdIns(4,5)P(2).

Non-Markovian models for migration-proliferation dichotomy of cancer cells: anomalous switching and spreading rate

Proliferation and migration dichotomy of the tumor cell invasion is examined within two non-Markovian models. We consider the tumor spheroid, which consists of the tumor core with a high density of cells and the outer invasive zone. We distinguish two different regions of the outer invasive zone and develop models for both zones. In model I we analyze the near-core-outer region, where biased migration away from the tumor spheroid core takes place. We suggest non-Markovian switching between the migrating and proliferating phenotypes of tumor cells. Nonlinear master equations for mean densities of cancer cells of both phenotypes are derived. In anomalous switching case we estimate the average size of the near-core-outer region that corresponds to sublinear growth (r(t)) ~ t(μ) for 0 < μ < 1. In model II we consider the outer zone, where the density of cancer cells is very low. We suggest an integrodifferential equation for the total density of cancer cells. For proliferation rate we use the classical logistic growth, while the migration of cells is subdiffusive. The exact formulas for the overall spreading rate of cancer cells are obtained by a hyperbolic scaling and Hamilton-Jacobi techniques.

Superdiffusion induced by a long-correlated external random force

We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize the deviation from the internal equilibrium situation. Using a power-law force autocorrelation function, the mean-square displacement and the velocity autocorrelation function are analytically obtained in terms of Mittag-Leffler functions. In this case, we show that the present model exhibits a superdiffusive regime as a consequence of the competition between passive and active processes.

Role of fluctuations in membrane models: thermal versus nonthermal

We study the comparative importance of thermal to nonthermal fluctuations for membrane-based models in the linear regime. Our results, both in 1+1 and 2+1 dimensions, suggest that nonthermal fluctuations dominate thermal ones only when the relaxation time τ is large. For moderate to small values of τ, the dynamics is defined by a competition between these two forces. The results are expected to act as a quantitative benchmark for biological modeling in systems involving cytoskeletal and other nonthermal fluctuations.

Fluctuations of cytoskeleton-bound microbeads--the effect of bead-receptor binding dynamics

The cytoskeleton (CSK) of living cells is a crosslinked fiber network, subject to ongoing biochemical remodeling processes that can be visualized by tracking the spontaneous motion of CSK-bound microbeads. The bead motion is characterized by anomalous diffusion with a power-law time evolution of the mean square displacement (MSD), and can be described as a stochastic transport process with apparent diffusivity D and power-law exponent β: MSD ∼ D (t/t(0))(β). Here we studied whether D and β change with the time that has passed after the initial bead-cell contact, and whether they are sensitive to bead coating (fibronectin, integrin antibodies, poly-L-lysine, albumin) and bead size (0.5-4.5 µm). The measurements are interpreted in the framework of a simple model that describes the bead as an overdamped particle coupled to the fluctuating CSK network by an elastic spring. The viscous damping coefficient characterizes the degree of bead internalization into the cell, and the spring constant characterizes the strength of the binding of the bead to the CSK. The model predicts distinctive signatures of the MSD that change with time as the bead couples more tightly to the CSK and becomes internalized. Experimental data show that the transition from the unbound to the tightly bound state occurs in an all-or-nothing manner. The time point of this transition shows considerable variability between individual cells (2-30 min) and depends on the bead size and bead coating. On average, this transition occurs later for smaller beads and beads coated with ligands that trigger the formation of adhesion complexes (fibronectin, integrin antibodies). Once the bead is linked to the CSK, however, the ligand type and bead size have little effect on the MSD. On longer timescales of several hours after bead addition, smaller beads are internalized into the cell more readily, leading to characteristic changes in the MSD that are consistent with increased viscous damping by the cytoplasm and reduced binding strength.

Effect of extreme data loss on long-range correlated and anticorrelated signals quantified by detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations. To better identify the intrinsic correlation properties of real-world signals where a large amount of data is missing or removed due to artifacts, we investigate how extreme data loss affects the scaling behavior of long-range power-law correlated and anticorrelated signals. We introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long-range correlations. The surrogate signals we generate are characterized by four parameters: (i) the DFA scaling exponent alpha of the original correlated signal u(i) , (ii) the percentage p of the data removed from u(i) , (iii) the average length mu of the removed (or remaining) data segments, and (iv) the functional form P(l) of the distribution of the length l of the removed (or remaining) data segments. We find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90%. In contrast, the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost. These observations are confirmed on two examples of real-world signals: human gait and commodity price fluctuations. We further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales. We find that for anticorrelated signals even 10% of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior. In contrast, positively correlated signals show no observable changes in the local scaling for up to 65% of data loss, while for larger percentage of data loss, the local scaling shows overestimated regions (with higher local exponent) at small scales, followed by underestimated regions (with lower local exponent) at large scales. Finally, we investigate how the scaling is affected by the average length, probability distribution, and percentage of the remaining data segments in comparison to the removed segments. We find that the average length mu_{r} of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value. Interestingly, the scales where the maximum deviation occurs follow a power-law relationship with mu_{r} . Whereas the percentage of data loss determines the extent of the deviation. The results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss.

Subdiffusive behavior in a trapping potential: mean square displacement and velocity autocorrelation function

A theoretical framework for analyzing stochastic data from single-particle tracking in viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation, we found analytical expressions for the two-time dynamics of a particle subjected to a harmonic potential. The mean-square displacement and the velocity autocorrelation function of the diffusing particle are given in terms of the time lag. In particular, we investigate the subdiffusive case. Using a power-law memory kernel, exact expressions for the mean-square displacement and the velocity autocorrelation function are obtained in terms of Mittag-Leffler functions and their derivatives. The behaviors for short-, intermediate-, and long-time lags are investigated in terms of the involved parameters. Finally, the validity of usual approximations is examined.

Transition to superdiffusive behavior in intracellular actin-based transport mediated by molecular motors

Intracellular transport of large cargoes, such as organelles, vesicles, or large proteins, is a complex dynamical process that involves the interplay of adenosine triphosphate-consuming molecular motors, cytoskeleton filaments, and the viscoelastic cytoplasm. In this work we investigate the motion of pigment organelles (melanosomes) driven by myosin-V motors in Xenopus laevis melanocytes using a high-spatio-temporal resolution tracking technique. By analyzing the obtained trajectories, we show that the melanosomes mean-square displacement undergoes a transition from a subdiffusive to a superdiffusive behavior. A stochastic theoretical model, which explicitly considers the collective action of the molecular motors, is introduced to generalize the interpretation of our data. Starting from a generalized Langevin equation, we derive an analytical expression for the mean square displacement, which also takes into account the experimental noise. By fitting theoretical expressions to experimental data we were able to discriminate the exponents that characterize the passive and active contributions to the dynamics and to estimate the "global" motor forces correctly. Then, our model gives a quantitative description of active transport in living cells with a reduced number of parameters.

Mechano-coupling and regulation of contractility by the vinculin tail domain

Vinculin binds to multiple focal adhesion and cytoskeletal proteins and has been implicated in transmitting mechanical forces between the actin cytoskeleton and integrins or cadherins. It remains unclear to what extent the mechano-coupling function of vinculin also involves signaling mechanisms. We report the effect of vinculin and its head and tail domains on force transfer across cell adhesions and the generation of contractile forces. The creep modulus and the adhesion forces of F9 mouse embryonic carcinoma cells (wild-type), vinculin knock-out cells (vinculin −/−), and vinculin −/− cells expressing either the vinculin head domain, tail domain, or full-length vinculin (rescue) were measured using magnetic tweezers on fibronectin-coated super-paramagnetic beads. Forces of up to 10 nN were applied to the beads. Vinculin −/− cells and tail cells showed a slightly higher incidence of bead detachment at large forces. Compared to wild-type, cell stiffness was reduced in vinculin −/− and head cells and was restored in tail and rescue cells. In all cell lines, the cell stiffness increased by a factor of 1.3 for each doubling in force. The power-law exponent of the creep modulus was force-independent and did not differ between cell lines. Importantly, cell tractions due to contractile forces were suppressed markedly in vinculin −/− and head cells, whereas tail cells generated tractions similar to the wild-type and rescue cells. These data demonstrate that vinculin contributes to the mechanical stability under large external forces by regulating contractile stress generation. Furthermore, the regulatory function resides in the tail domain of vinculin containing the paxillin-binding site.