An explicit model to extract viscoelastic properties of cells from AFM force-indentation curves

Atomic force microscopy (AFM) is widely used for quantifying the mechanical properties of soft materials such as cells. AFM force-indentation curves are conventionally fitted with a Hertzian model to extract elastic properties. These properties solely are, however, insufficient to describe the mechanical properties of cells. Here, we expand the analysis capabilities to describe the viscoelastic behavior while using the same force-indentation curves. Our model gives an explicit relation of force and indentation and extracts physically meaningful mechanical parameters. We first validated the model on simulated force-indentation curves. Then, we applied the fitting model to the force-indentation curves of two hydrogels with different crosslinking mechanisms. Finally, we characterized HeLa cells in two cell cycle phases, interphase and mitosis, and showed that mitotic cells have a higher apparent elasticity and a lower apparent viscosity. Our study provides a simple method, which can be directly integrated into the standard AFM framework for extracting the viscoelastic properties of materials

Confluence reduction for Markov automata

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude

Modelling and analysis of Markov reward automata

Costs and rewards are important ingredients for many types of systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating rewards (or costs) in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Rewards come in two flavours: action rewards, acquired instantaneously when taking a transition; and state rewards, acquired while residing in a state. We present algorithms to optimise three reward functions: the expected cumulative reward until a goal is reached, the expected cumulative reward until a certain time bound, and the long-run average reward. We have implemented these algorithms in the SCOOP/IMCA tool chain and show their feasibility via several case studies

DFTCalc: a tool for efficient fault tree analysis

Effective risk management is a key to ensure that our nuclear power plants, medical equipment, and power grids are dependable; and it is often required by law. Fault Tree Analysis (FTA) is a widely used methodology here, computing important dependability measures like system reliability. This paper presents DFTCalc, a powerful tool for FTA, providing (1) efficient fault tree modelling via compact representations; (2) effective analysis, allowing a wide range of dependability properties to be analysed (3) efficient analysis, via state-of-the-art stochastic techniques; and (4) a flexible and extensible framework, where gates can easily be changed or added. Technically, DFTCalc is realised via stochastic model checking, an innovative technique offering a wide plethora of powerful analysis techniques, including aggressive compression techniques to keep the underlying state space small

Matrix stiffness mechanosensing modulates the expression and distribution of transcription factors in Schwann cells

After peripheral nerve injury, mature Schwann cells (SCs) de-differentiate and undergo cell reprogramming to convert into a specialized cell repair phenotype that promotes nerve regeneration. Reprogramming of SCs into the repair phenotype is tightly controlled at the genome level and includes downregulation of pro-myelinating genes and activation of nerve repair-associated genes. Nerve injuries induce not only biochemical but also mechanical changes in the tissue architecture which impact SCs. Recently, we showed that SCs mechanically sense the stiffness of the extracellular matrix and that SC mechanosensitivity modulates their morphology and migratory behavior. Here, we explore the expression levels of key transcription factors and myelin-associated genes in SCs, and the outgrowth of primary dorsal root ganglion (DRG) neurites, in response to changes in the stiffness of generated matrices. The selected stiffness range matches the physiological conditions of both utilized cell types as determined in our previous investigations. We find that stiffer matrices induce upregulation of the expression of transcription factors Sox2, Oct6, and Krox20, and concomitantly reduce the expression of the repair-associated transcription factor c-Jun, suggesting a link between SC substrate mechanosensing and gene expression regulation. Likewise, DRG neurite outgrowth correlates with substrate stiffness. The remarkable intrinsic physiological plasticity of SCs, and the mechanosensitivity of SCs and neurites, may be exploited in the design of bioengineered scaffolds that promote nerve regeneration upon injury

A comparison of microfluidic methods for high-throughput cell deformability measurements

The mechanical phenotype of a cell is an inherent biophysical marker of its state and function, with many applications in basic and applied biological research. Microfluidics-based methods have enabled single-cell mechanophenotyping at throughputs comparable to those of flow cytometry. Here, we present a standardized cross-laboratory study comparing three microfluidics-based approaches for measuring cell mechanical phenotype: constriction-based deformability cytometry (cDC), shear flow deformability cytometry (sDC) and extensional flow deformability cytometry (xDC). All three methods detect cell deformability changes induced by exposure to altered osmolarity. However, a dose-dependent deformability increase upon latrunculin B-induced actin disassembly was detected only with cDC and sDC, which suggests that when exposing cells to the higher strain rate imposed by xDC, cellular components other than the actin cytoskeleton dominate the response. The direct comparison presented here furthers our understanding of the applicability of the different deformability cytometry methods and provides context for the interpretation of deformability measurements performed using different platforms. This Analysis compares microfluidics-based methods for assessing mechanical properties of cells in high throughput

Compositional Verification and Optimization of Interactive Markov Chains

Interactive Markov chains (IMC) are compositional behavioural models extending labelled transition systems and continuous-time Markov chains. We provide a framework and algorithms for compositional verification and optimization of IMC with respect to time-bounded properties. Firstly, we give a specification formalism for IMC. Secondly, given a time-bounded property, an IMC component and the assumption that its unknown environment satisfies a given specification, we synthesize a scheduler for the component optimizing the probability that the property is satisfied in any such environment

Stretching and heating cells with light-nonlinear photothermal cell rheology

Stretching and heating are everyday experiences for skin and tissue cells. They are also standard procedures to reduce the risk for injuries in physical exercise and to relieve muscle spasms in physiotherapy. Here, we ask which immediate and long-term mechanical effects of such treatments are quantitatively detectable on the level of individual living cells. Combining versatile optical stretcher techniques with a well-tested mathematical model for viscoelastic polymer networks, we investigate the thermomechanical properties of suspended cells with a photothermal rheometric protocol that can disentangle fast transient and slow 'inelastic' components in the nonlinear mechanical response. We find that a certain minimum strength and duration of combined stretching and heating is required to induce long-lived alterations of the mechanical state of the cells, which then respond qualitatively differently to mechanical tests than after weaker/shorter treatments or merely mechanical preconditioning alone. Our results suggest a viable protocol to search for intracellular biomolecular signatures of the mathematically detected dissimilar mechanical response modes

DFTCalc: reliability centered maintenance via fault tree analysis (tool paper)

Reliability, availability, maintenance and safety (RAMS) analysis is essential in the evaluation of safety critical systems like nuclear power plants and the railway infrastructure. A widely used methodology within RAMS analysis are fault trees, representing failure propagations throughout a system. We present DFTCalc, a tool-set to conduct quantitative analysis on dynamic fault trees including the effect of a maintenance strategy on the system dependability