Buckling-Fracture Transition and the Geometrical Charge of a Crack.

We present a unifying approach that describes both surface bending and fracture in the same geometrical framework. An immediate outcome of this view is a prediction for a new mechanical transition: the buckling-fracture transition. Using responsive gel strips that are subjected to nonuniform osmotic stress, we show the existence of the transition: Thin plates do not fracture. Instead, they release energy via buckling, even at strains that can be orders of magnitude larger than the Griffith fracture criterion. The analysis of the system reveals the dependence of the transition on system's parameters and agrees well with experimental results. Finally, we suggest a new description of a mode I crack as a line distribution of Gaussian curvature. It is thus exchangeable with extrinsic generation of curvature via buckling. The work opens the way for the study of mechanical problems within a single nonlinear framework. It suggests that fracture driven by internal stresses can be completely avoided by a proper geometrical design.

Variability and memory of protein levels in human cells.

Protein expression is a stochastic process that leads to phenotypic variation among cells. The cell-cell distribution of protein levels in microorganisms has been well characterized but little is known about such variability in human cells. Here, we studied the variability of protein levels in human cells, as well as the temporal dynamics of this variability, and addressed whether cells with higher than average protein levels eventually have lower than average levels, and if so, over what timescale does this mixing occur. We measured fluctuations over time in the levels of 20 endogenous proteins in living human cells, tagged by the gene for yellow fluorescent protein at their chromosomal loci. We found variability with a standard deviation that ranged, for different proteins, from about 15% to 30% of the mean. Mixing between high and low levels occurred for all proteins, but the mixing time was longer than two cell generations (more than 40 h) for many proteins. We also tagged pairs of proteins with two colours, and found that the levels of proteins in the same biological pathway were far more correlated than those of proteins in different pathways. The persistent memory for protein levels that we found might underlie individuality in cell behaviour and could set a timescale needed for signals to affect fully every member of a cell population.

Experimental study of shape transitions and energy scaling in thin non-Euclidean plates.

We present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, K(tar). We vary the disks' thickness t(0) and measure the dependence of configurations, surface curvature, and energy content on t(0). For K(tar)<0, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as t(0)→0, and to a slow decay of both bending and stretching energies. Both vary like t(0)(2), compared with t(0)(3) of the bending energy in disks with K(tar)>0.

Shaping of elastic sheets by prescription of non-Euclidean metrics.

The connection between a surface's metric and its Gaussian curvature (Gauss theorem) provides the base for a shaping principle of locally growing or shrinking elastic sheets. We constructed thin gel sheets that undergo laterally nonuniform shrinkage. This differential shrinkage prescribes non-Euclidean metrics on the sheets. To minimize their elastic energy, the free sheets form three-dimensional structures that follow the imposed metric. We show how both large-scale buckling and multiscale wrinkling structures appeared, depending on the nature of possible embeddings of the prescribed metrics. We further suggest guidelines for how to generate each type of feature.

Dynamic proteomics in individual human cells uncovers widespread cell-cycle dependence of nuclear proteins.

We examined cell cycle-dependent changes in the proteome of human cells by systematically measuring protein dynamics in individual living cells. We used time-lapse microscopy to measure the dynamics of a random subset of 20 nuclear proteins, each tagged with yellow fluorescent protein (YFP) at its endogenous chromosomal location. We synchronized the cells in silico by aligning protein dynamics in each cell between consecutive divisions. We observed widespread (40%) cell-cycle dependence of nuclear protein levels and detected previously unknown cell cycle-dependent localization changes. This approach to dynamic proteomics can aid in discovery and accurate quantification of the extensive regulation of protein concentration and localization in individual living cells.