Bayesian model selection for complex dynamic systems.

Time series generated by complex systems like financial markets and the earth's atmosphere often represent superstatistical random walks: on short time scales, the data follow a simple low-level model, but the model parameters are not constant and can fluctuate on longer time scales according to a high-level model. While the low-level model is often dictated by the type of the data, the high-level model, which describes how the parameters change, is unknown in most cases. Here we present a computationally efficient method to infer the time course of the parameter variations from time-series with short-range correlations. Importantly, this method evaluates the model evidence to objectively select between competing high-level models. We apply this method to detect anomalous price movements in financial markets, characterize cancer cell invasiveness, identify historical policies relevant for working safety in coal mines, and compare different climate change scenarios to forecast global warming.

Migration in Confined 3D Environments Is Determined by a Combination of Adhesiveness, Nuclear Volume, Contractility, and Cell Stiffness.

In cancer metastasis and other physiological processes, cells migrate through the three-dimensional (3D) extracellular matrix of connective tissue and must overcome the steric hindrance posed by pores that are smaller than the cells. It is currently assumed that low cell stiffness promotes cell migration through confined spaces, but other factors such as adhesion and traction forces may be equally important. To study 3D migration under confinement in a stiff (1.77 MPa) environment, we use soft lithography to fabricate polydimethylsiloxane (PDMS) devices consisting of linear channel segments with 20 µm length, 3.7 µm height, and a decreasing width from 11.2 to 1.7 µm. To study 3D migration in a soft (550 Pa) environment, we use self-assembled collagen networks with an average pore size of 3 µm. We then measure the ability of four different cancer cell lines to migrate through these 3D matrices, and correlate the results with cell physical properties including contractility, adhesiveness, cell stiffness, and nuclear volume. Furthermore, we alter cell adhesion by coating the channel walls with different amounts of adhesion proteins, and we increase cell stiffness by overexpression of the nuclear envelope protein lamin A. Although all cell lines are able to migrate through the smallest 1.7 µm channels, we find significant differences in the migration velocity. Cell migration is impeded in cell lines with larger nuclei, lower adhesiveness, and to a lesser degree also in cells with lower contractility and higher stiffness. Our data show that the ability to overcome the steric hindrance of the matrix cannot be attributed to a single cell property but instead arises from a combination of adhesiveness, nuclear volume, contractility, and cell stiffness.

Vinculin phosphorylation at residues Y100 and Y1065 is required for cellular force transmission.

The focal adhesion protein vinculin connects the actin cytoskeleton, through talin and integrins, with the extracellular matrix. Vinculin consists of a globular head and tail domain, which undergo conformational changes from a closed auto-inhibited conformation in the cytoplasm to an open conformation in focal adhesions. Src-mediated phosphorylation has been suggested to regulate this conformational switch. To explore the role of phosphorylation in vinculin activation, we used knock-out mouse embryonic fibroblasts re-expressing different vinculin mutants in traction microscopy, magnetic tweezer microrheology, FRAP and actin-binding assays. Compared to cells expressing wild-type or constitutively active vinculin, we found reduced tractions, cytoskeletal stiffness, adhesion strength, and increased vinculin dynamics in cells expressing constitutively inactive vinculin or vinculin where Src-mediated phosphorylation was blocked by replacing tyrosine at position 100 and/or 1065 with a non-phosphorylatable phenylalanine residue. Replacing tyrosine residues with phospho-mimicking glutamic acid residues restored cellular tractions, stiffness and adhesion strength, as well as vinculin dynamics, and facilitated vinculin-actin binding. These data demonstrate that Src-mediated phosphorylation is necessary for vinculin activation, and that phosphorylation controls cytoskeletal mechanics by regulating force transmission between the actin cytoskeleton and focal adhesion proteins.

Microconstriction arrays for high-throughput quantitative measurements of cell mechanical properties.

We describe a method for quantifying the mechanical properties of cells in suspension with a microfluidic device consisting of a parallel array of micron-sized constrictions. Using a high-speed charge-coupled device camera, we measure the flow speed, cell deformation, and entry time into the constrictions of several hundred cells per minute during their passage through the device. From the flow speed and the occupation state of the microconstriction array with cells, the driving pressure across each constriction is continuously computed. Cell entry times into microconstrictions decrease with increased driving pressure and decreased cell size according to a power law. From this power-law relationship, the cell elasticity and fluidity can be estimated. When cells are treated with drugs that depolymerize or stabilize the cytoskeleton or the nucleus, elasticity and fluidity data from all treatments collapse onto a master curve. Power-law rheology and collapse onto a master curve are predicted by the theory of soft glassy materials and have been previously shown to describe the mechanical behavior of cells adhering to a substrate. Our finding that this theory also applies to cells in suspension provides the foundation for a quantitative high-throughput measurement of cell mechanical properties with microfluidic devices.

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.

Biomembrane-mimicking lipid bilayer system as a mechanically tunable cell substrate.

Cell behavior such as cell adhesion, spreading, and contraction critically depends on the elastic properties of the extracellular matrix. It is not known, however, how cells respond to viscoelastic or plastic material properties that more closely resemble the mechanical environment cells encounter in the body. In this report, we employ viscoelastic and plastic biomembrane-mimicking cell substrates. The compliance of the substrates can be tuned by increasing the number of polymer-tethered bilayers. This leaves the density and conformation of adhesive ligands on the top bilayer unaltered. We then observe the response of fibroblasts to these property changes. For comparison, we also study the cells on soft polyacrylamide and hard glass surfaces. Cell morphology, motility, cell stiffness, contractile forces and adhesive contact size all decrease on more compliant matrices but are less sensitive to changes in matrix dissipative properties. These data suggest that cells are able to feel and respond predominantly to the effective matrix compliance, which arises as a combination of substrate and adhesive ligand mechanical properties.

CAS directly interacts with vinculin to control mechanosensing and focal adhesion dynamics.

Focal adhesions are cellular structures through which both mechanical forces and regulatory signals are transmitted. Two focal adhesion-associated proteins, Crk-associated substrate (CAS) and vinculin, were both independently shown to be crucial for the ability of cells to transmit mechanical forces and to regulate cytoskeletal tension. Here, we identify a novel, direct binding interaction between CAS and vinculin. This interaction is mediated by the CAS SRC homology 3 domain and a proline-rich sequence in the hinge region of vinculin. We show that CAS localization in focal adhesions is partially dependent on vinculin, and that CAS-vinculin coupling is required for stretch-induced activation of CAS at the Y410 phosphorylation site. Moreover, CAS-vinculin binding significantly affects the dynamics of CAS and vinculin within focal adhesions as well as the size of focal adhesions. Finally, disruption of CAS binding to vinculin reduces cell stiffness and traction force generation. Taken together, these findings strongly implicate a crucial role of CAS-vinculin interaction in mechanosensing and focal adhesion dynamics.

Identification of DAPK as a scaffold protein for the LIMK/cofilin complex in TNF-induced apoptosis.

The role of cytoskeleton-associated proteins during TNF-induced apoptosis is not fully understood. A potential candidate kinase that might connect TNF signaling to actin reorganization is the death-associated protein kinase (DAPK). To identify new DAPK interaction partners in TNF-induced apoptosis, we performed a peptide array screen. We show that TNF-treatment enhanced the phosphorylation of LIMK at threonine508 and its downstream target cofilin at serine3 (p-cofilin(Ser3)). Modulation of DAPK activity and expression by DAPK inhibitor treatment, siRNA knockdown, and overexpression affected the phosphorylation of both proteins. We propose a 3D structural model where DAPK functions as a scaffold for the LIMK/cofilin complex and triggers a closer interaction of both proteins under TNF stimulation. Upon TNF a striking redistribution of LIMK, DAPK, and cofilin to the perinuclear compartment was observed. The pro-apoptotic DAPK/LIMK/cofilin multiprotein complex was abrogated in detached cells, indicating that its signaling was no longer needed if cells committed to apoptosis. P-cofilin(Ser3) was strongly accumulated in cells with condensed chromatin, pronounced membrane blebs and Annexin V up-regulation. From studying different cofilin(Ser3) mutants we suggest that p-cofilin(Ser3) is an indicator of TNF-induced apoptosis. Collectively, our findings identify a novel molecular cytoskeleton-associated mechanism in TNF-induced DAPK-dependent apoptosis.

Biomechanical characterization of a desminopathy in primary human myoblasts.

Heterozygous mutations of the human desmin gene on chromosome 2q35 cause hereditary and sporadic myopathies and cardiomyopathies. The expression of mutant desmin brings about partial disruption of the extra sarcomeric desmin cytoskeleton and abnormal protein aggregation in the sarcoplasm of striated muscle cells. The precise molecular pathways and sequential steps that lead from a desmin gene defect to progressive muscle damage are still unclear. We tested whether mutant desmin changes the biomechanical properties and the intrinsic mechanical stress response of primary cultured myoblasts derived from a patient carrying a heterozygous R350P desmin mutation. Compared to wildtype controls, undifferentiated mutant desmin myoblasts revealed increased cell death and substrate detachment in response to cyclic stretch on flexible membranes. Moreover, magnetic tweezer microrheometry of myoblasts using fibronectin-coated beads showed increased stiffness of diseased cells. Our findings provide the first evidence that altered mechanical properties may contribute to the progressive striated muscle pathology in desminopathies. We postulate that the expression of mutant desmin leads to increased mechanical stiffness, which results in excessive mechanical stress in response to strain and consecutively to increased mechanical vulnerability and damage of muscle cells.

Inhibition of Rho kinases increases directional motility of microvascular endothelial cells.

Rho kinases are major regulators of actin cytoskeletal organization and cell motility. Depending on the model system, inhibitors of Rho kinases (ROCK) have been reported to increase or decrease endothelial cell migration. In the present study we investigated the effect of Rho kinase inhibitors on microvascular endothelial cell migration with a special focus on the isoform ROCK2. Migration of microvascular endothelial cells was analyzed in a wound-healing, a spheroid-on-collagen migration assay and in cells embedded in collagen-1 gels. The non-selective Rho kinase inhibitor H1152 was compared to the selective ROCK2 inhibitor SLX2119 and to siRNA knock down. Non-selective inhibition of Rho kinases decreased cell-spanning F-actin fibers, loosened cell-cell contacts visualized by VE cadherin staining, and reduced cell-matrix interactions as shown by reduced Hic-5 expression in focal contacts. Rho kinase inhibitors facilitated directed migration of endothelial cells away from spheroids on fibronectin-coated plates and in collagen-1 gels. By contrast, migration of firmly attached endothelial cells, resembling intact vessels, was not promoted by Rho kinase inhibition. Selective inhibition of ROCK2 mimicked the cytoskeletal effects of H1152 and also increased cell motility, although to a lesser extent. In summary, Rho kinase inhibition enhanced the migration and cytoskeletal restructuring preferentially in freshly attached endothelial cells. ROCK2 may be a potential target to manipulate endothelial cell migration after vessel injury.