Power laws in microrheology experiments on living cells: comparative analysis and modelling

We compare and synthesize the results of two microrheological experiments on the cytoskeleton of single cells. In the first one, the creep function J(t) of a cell stretched between two glass plates is measured after applying a constant force step. In the second one, a micrometric bead specifically bound to transmembrane receptors is driven by an oscillating optical trap, and the viscoelastic coefficient $G_e(\omega)$ is retrieved. Both $J(t)$ and $G_e(\omega)$ exhibit power law behavior: $J(t)= A(t/t_0)^\alpha$ and $\bar G_e(\omega)\bar = G_0 (\omega/\omega_0)^\alpha$, with the same exponent $\alpha\approx 0.2$. This power law behavior is very robust ; $\alpha$ is distributed over a narrow range, and shows almost no dependance on the cell type, on the nature of the protein complex which transmits the mechanical stress, nor on the typical length scale of the experiment. On the contrary, the prefactors $A_0$ and $G_0$appear very sensitive to these parameters. Whereas the exponents $\alpha$ are normally distributed over the cell population, the prefactors $A_0$ and $G_0$ follow a log-normal repartition. These results are compared with other data published in the litterature. We propose a global interpretation, based on a semi-phenomenological model, which involves a broad distribution of relaxation times in the system. The model predicts the power law behavior and the statistical repartition of the mechanical parameters, as experimentally observed for the cells. Moreover, it leads to an estimate of the largest response time in the cytoskeletal network: $\tau_m \approx 1000$ s.Comment: 47 pages, 14 figures // v2: PDF file is now Acrobat Reader 4 (and up) compatible // v3: Minor typos corrected - The presentation of the model have been substantially rewritten (p. 17-18), in order to give more details - Enhanced description of protocols // v4: Minor corrections in the text : the immersion angles are estimated and not measured // v5: Minor typos corrected. Two references were clarifie

Bistability in a Metabolic Network Underpins the De Novo Evolution of Colony Switching in Pseudomonas fluorescens

Phenotype switching is commonly observed in nature. This prevalence has allowed the elucidation of a number of underlying molecular mechanisms. However, little is known about how phenotypic switches arise and function in their early evolutionary stages. The first opportunity to provide empirical insight was delivered by an experiment in which populations of the bacterium Pseudomonas fluorescens SBW25 evolved, de novo, the ability to switch between two colony phenotypes. Here we unravel the molecular mechanism behind colony switching, revealing how a single nucleotide change in a gene enmeshed in central metabolism (carB) generates such a striking phenotype. We show that colony switching is underpinned by ON/OFF expression of capsules consisting of a colanic acid-like polymer. We use molecular genetics, biochemical analyses, and experimental evolution to establish that capsule switching results from perturbation of the pyrimidine biosynthetic pathway. Of central importance is a bifurcation point at which uracil triphosphate is partitioned towards either nucleotide metabolism or polymer production. This bifurcation marks a cell-fate decision point whereby cells with relatively high pyrimidine levels favour nucleotide metabolism (capsule OFF), while cells with lower pyrimidine levels divert resources towards polymer biosynthesis (capsule ON). This decision point is present and functional in the wild-type strain. Finally, we present a simple mathematical model demonstrating that the molecular components of the decision point are capable of producing switching. Despite its simple mutational cause, the connection between genotype and phenotype is complex and multidimensional, offering a rare glimpse of how noise in regulatory networks can provide opportunity for evolution

Rhéologie à l’échelle d’une cellule vivante

From epigenetics to mecanotransduction, there is increasing evidence that mechanical properties play a central role in the development and the survival of organisms. To determine the mechanical properties of isolated living cells, we built a single cell rheometer. Individual cells, of various types, were strained under constant stress (creep experiment). Their creep function always scaled with a power law of time (J(t) = At^(α)). The exponent gave a normal distribution around 0.25, whereas the distribution of the prefactor was log-normal. As the mechanical response was linear, we could compare our creep parameters to those observed previously by dynamical rheology (magnetocytometry, AFM). Thus we confirmed, qualitatively as well as quantitatively, results obtained with local and oscillating perturbations. In order to identify the contribution of cytoskeletal elements to the mechanical properties, we compared wild-type and vimentin-deficient fibroblasts. We found that vimentin had no effect on the form of the creep function, but was necessary to maintain mechanical integrity at high strain. In addition, we measured the force generated by a cell upon spreading between two glass microplates. Preliminary results indicated that myoblasts adapted the force they applied to the stiffness of the microplates.De l'épigénétique (méthylation de l'ADN) à la mécanotransduction, il y a un nombre croissant de preuves que les propriétés mécaniques jouent un rôle essentiel dans le développement et la survie des organismes. Pour sonder les propriétés mécaniques d'une cellule vivante, nous avons mis au point un véritable rhéomètre à cellule unique. Ainsi avons-nous pu montrer, pour la première fois à l'échelle de la cellule entière, que la fonction de fluage suivait une loi de puissance fonction du temps (J(t) = At^(α)) pour tous les types cellulaires sollicités. L'exposant est distribué normalement autour de 0, 25. Le préfacteur est, pour sa part, distribué de manière log-normale. Ayant déterminé le régime linéaire, nous avons pu comparer nos résultats de fluage aux mesures de rhéologie dynamique (magnétocytométrie, AFM). Nous avons ainsi confirmé, qualitativement et quantitativement, les résultats obtenus par des techniques où la sollicitation est locale et oscillante. Par ailleurs, en vue d'identifier la contribution des éléments du cytosquelette à la réponse mécanique d'une cellule, nous avons réalisé des mesures sur des fibroblastes n'exprimant pas la vimentine et sur des fibroblastes sauvages. Il a été mis en évidence que la vimentine n'avait pas d'incidence sur la forme de la fonction de fluage mais qu'elle était nécessaire au maintient de l'intégrité mécanique à grande déformation. Enfin nous avons pu mesurer la force exercée par une cellule lorsqu'elle s'étale entre les deux lamelles de verres. Des résultats préliminaires semblent indiquer que les myoblastes sont capables d'adapter leur force à la raideur des lamelles

Rhéologie à l' échelle d' une cellule vivante

PARIS7-Bibliothèque centrale (751132105) / SudocSudocFranceF

À la recherche des capteurs mécaniques moléculaires de la cellule

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Inferring epigenetic dynamics from kin correlations.

Populations of isogenic embryonic stem cells or clonal bacteria often exhibit extensive phenotypic heterogeneity that arises from intrinsic stochastic dynamics of cells. The phenotypic state of a cell can be transmitted epigenetically in cell division, leading to correlations in the states of cells related by descent. The extent of these correlations is determined by the rates of transitions between the phenotypic states. Therefore, a snapshot of the phenotypes of a collection of cells with known genealogical structure contains information on phenotypic dynamics. Here, we use a model of phenotypic dynamics on a genealogical tree to define an inference method that allows extraction of an approximate probabilistic description of the dynamics from observed phenotype correlations as a function of the degree of kinship. The approach is tested and validated on the example of Pyoverdine dynamics in Pseudomonas aeruginosa colonies. Interestingly, we find that correlations among pairs and triples of distant relatives have a simple but nontrivial structure indicating that observed phenotypic dynamics on the genealogical tree is approximately conformal--a symmetry characteristic of critical behavior in physical systems. The proposed inference method is sufficiently general to be applied in any system where lineage information is available

Inferring epigenetic dynamics from kin correlations

Populations of isogenic embryonic stem cells or clonal bacteria often exhibit extensive phenotypic heterogeneity which arises from stochastic intrinsic dynamics of cells. The internal state of the cell can be transmitted epigenetically in cell division, leading to correlations in the phenotypic states of cells related by descent. Therefore, a phenotypic snapshot of a collection of cells with known genealogical structure, contains information on phenotypic dynamics. Here we use a model of phenotypic dynamics on a genealogical tree to define an inference method which allows to extract an approximate probabilistic description of phenotypic dynamics based on measured correlations as a function of the degree of kinship. The approach is tested and validated on the example of Pyoverdine dynamics in P. aeruginosa colonies. Interestingly, we find that correlations among pairs and triples of distant relatives have a simple but non-trivial structure indicating that observed phenotypic dynamics on the genealogical tree is approximately conformal - a symmetry characteristic of critical behavior in physical systems. Proposed inference method is sufficiently general to be applied in any system where lineage information is available.Comment: 18 pages, 11 figure

Monitoring microbial population dynamics at low densities

We propose a new and simple method for the measurement of microbial concentrations in highly diluted cultures. This method is based on an analysis of the intensity fluctuations of light scattered by microbial cells under laser illumination. Two possible measurement strategies are identified and compared using simulations and measurements of the concentration of gold nanoparticles. Based on this comparison, we show that the concentration of Escherichia coli and Saccharomyces cerevisiae cultures can be easily measured in situ across a concentration range that spans five orders of magnitude. The lowest measurable concentration is three orders of magnitude (1000×) smaller than in current optical density measurements. We show further that this method can also be used to measure the concentration of fluorescent microbial cells. In practice, this new method is well suited to monitor the dynamics of population growth at early colonization of a liquid culture medium. The dynamic data thus obtained are particularly relevant for microbial ecology studies

Tissue deformation modulates Twist expression to determine anterior midgut differentiation in Drosophila embryos

International audienceMechanical deformations associated with embryonic morphogenetic movements have been suggested to actively participate in the signaling cascades regulating developmental gene expression. Here we develop an appropriate experimental approach to ascertain the existence and the physiological relevance of this phenomenon. By combining the use of magnetic tweezers with in vivo laser ablation, we locally control physiologically relevant deformations in wild-type Drosophila embryonic tissues. We demonstrate that the deformations caused by germ band extension upregulate Twist expression in the stomodeal primordium. We find that stomodeal compression triggers Src42A-dependent nuclear translocation of Armadillo/β-catenin, which is required for Twist mechanical induction in the stomodeum. Finally, stomodeal-specific RNAi-mediated silencing of Twist during compression impairs the differentiation of midgut cells, resulting in larval lethality. These experiments show that mechanically induced Twist upregulation in stomodeal cells is necessary for subsequent midgut differentiation. DEVBI

Contrast mechanisms in third-harmonic generation microscopy of cells and tissues

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