Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.Comment: 23 pages, 5 figures; The final publication is available at http://www.springerlink.com http://dx.doi.org/10.1007/s00285-011-0495-

On the dynamical generation of the Maxwell term and scale invariance

Gauge theories with no Maxwell term are investigated in various setups. The dynamical generation of the Maxwell term is correlated to the scale invariance properties of the system. This is discussed mainly in the cases where the gauge coupling carries dimensions. The term is generated when the theory contains a scale explicitly, when it is asymptotically free and in particular also when the scale invariance is spontaneously broken. The terms are not generated when the scale invariance is maintained. Examples studied include the large $N$ limit of the $CP^{N-1}$ model in $(2+\epsilon)$ dimensions, a 3D gauged $\phi^6$ vector model and its supersymmetric extension. In the latter case the generation of the Maxwell term at a fixed point is explored. The phase structure of the $d=3$ case is investigated in the presence of a Chern-Simons term as well. In the supersymmetric $\phi^6$ model the emergence of the Maxwell term is accompanied by the dynamical generation of the Chern-Simons term and its multiplet and dynamical breaking of the parity symmetry. In some of the phases long range forces emerge which may result in logarithmic confinement. These include a dilaton exchange which plays a role also in the case when the theory has no gauge symmetry. Gauged Lagrangian realizations of the 2D coset models do not lead to emergent Maxwell terms. We discuss a case where the gauge symmetry is anomalous.Comment: 38 pages, 4 figures; v2 slightly improved, typos fixed, references added, published versio

Cell-cycle-dependent transcriptional and translational DNA-damage response of 2 ribonucleotide reductase genes in S. cerevisiae

The ribonucleotide reductase (RNR) enzyme catalyzes an essential step in the production of deoxyribonucleotide triphosphates (dNTPs) in cells. Bulk biochemical measurements in synchronized Saccharomyces cerevisiae cells suggest that RNR mRNA production is maximal in late G1 and S phases; however, damaged DNA induces RNR transcription throughout the cell cycle. But such en masse measurements reveal neither cell-to-cell heterogeneity in responses nor direct correlations between transcript and protein expression or localization in single cells which may be central to function. We overcame these limitations by simultaneous detection of single RNR transcripts and also Rnr proteins in the same individual asynchronous S. cerevisiae cells, with and without DNA damage by methyl methanesulfonate (MMS). Surprisingly, RNR subunit mRNA levels were comparably low in both damaged and undamaged G1 cells and highly induced in damaged S/G2 cells. Transcript numbers became correlated with both protein levels and localization only upon DNA damage in a cell cycle-dependent manner. Further, we showed that the differential RNR response to DNA damage correlated with variable Mec1 kinase activity in the cell cycle in single cells. The transcription of RNR genes was found to be noisy and non-Poissonian in nature. Our results provide vital insight into cell cycle-dependent RNR regulation under conditions of genotoxic stress.Massachusetts Institute of Technology. Center for Environmental Health Sciences (deriving from NIH P30-ES002109)National Institutes of Health (U.S.) (grant R01-CA055042)National Institutes of Health (U.S.) (grant DP1-OD006422)Massachusetts Institute of Technology (CSBi Merck-MIT Fellowship

A Density-Dependent Switch Drives Stochastic Clustering and Polarization of Signaling Molecules

Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered “off” state is desired? And, what limits the spread of clusters when an “on” state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the “neutral drift polarity model.” Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization

AI-powered transmitted light microscopy for functional analysis of live cells

Transmitted light microscopy can readily visualize the morphology of living cells. Here, we introduce artificial-intelligence-powered transmitted light microscopy (AIM) for subcellular structure identification and labeling-free functional analysis of live cells. AIM provides accurate images of subcellular organelles; allows identification of cellular and functional characteristics (cell type, viability, and maturation stage); and facilitates live cell tracking and multimodality analysis of immune cells in their native form without labeling

Early In Vitro Differentiation of Mouse Definitive Endoderm Is Not Correlated with Progressive Maturation of Nuclear DNA Methylation Patterns

The genome organization in pluripotent cells undergoing the first steps of differentiation is highly relevant to the reprogramming process in differentiation. Considering this fact, chromatin texture patterns that identify cells at the very early stage of lineage commitment could serve as valuable tools in the selection of optimal cell phenotypes for regenerative medicine applications. Here we report on the first-time use of high-resolution three-dimensional fluorescence imaging and comprehensive topological cell-by-cell analyses with a novel image-cytometrical approach towards the identification of in situ global nuclear DNA methylation patterns in early endodermal differentiation of mouse ES cells (up to day 6), and the correlations of these patterns with a set of putative markers for pluripotency and endodermal commitment, and the epithelial and mesenchymal character of cells. Utilizing this in vitro cell system as a model for assessing the relationship between differentiation and nuclear DNA methylation patterns, we found that differentiating cell populations display an increasing number of cells with a gain in DNA methylation load: first within their euchromatin, then extending into heterochromatic areas of the nucleus, which also results in significant changes of methylcytosine/global DNA codistribution patterns. We were also able to co-visualize and quantify the concomitant stochastic marker expression on a per-cell basis, for which we did not measure any correlation to methylcytosine loads or distribution patterns. We observe that the progression of global DNA methylation is not correlated with the standard transcription factors associated with endodermal development. Further studies are needed to determine whether the progression of global methylation could represent a useful signature of cellular differentiation. This concept of tracking epigenetic progression may prove useful in the selection of cell phenotypes for future regenerative medicine applications

Current warming will reduce yields unless maize breeding and seed systems adapt immediately

The development of crop varieties that are better suited to new climatic conditions is vital for future food production1, 2. Increases in mean temperature accelerate crop development, resulting in shorter crop durations and reduced time to accumulate biomass and yield3, 4. The process of breeding, delivery and adoption (BDA) of new maize varieties can take up to 30 years. Here, we assess for the first time the implications of warming during the BDA process by using five bias-corrected global climate models and four representative concentration pathways with realistic scenarios of maize BDA times in Africa. The results show that the projected difference in temperature between the start and end of the maize BDA cycle results in shorter crop durations that are outside current variability. Both adaptation and mitigation can reduce duration loss. In particular, climate projections have the potential to provide target elevated temperatures for breeding. Whilst options for reducing BDA time are highly context dependent, common threads include improved recording and sharing of data across regions for the whole BDA cycle, streamlining of regulation, and capacity building. Finally, we show that the results have implications for maize across the tropics, where similar shortening of duration is projected

Reconstruction of one-dimensional chaotic maps from sequences of probability density functions

In many practical situations, it is impossible to measure the individual trajectories generated by an unknown chaotic system, but we can observe the evolution of probability density functions generated by such a system. The paper proposes for the first time a matrix-based approach to solve the generalized inverse Frobenius–Perron problem, that is, to reconstruct an unknown one-dimensional chaotic transformation, based on a temporal sequence of probability density functions generated by the transformation. Numerical examples are used to demonstrate the applicability of the proposed approach and evaluate its robustness with respect to constantly applied stochastic perturbations

Microfabricated Physical Spatial Gradients for Investigating Cell Migration and Invasion Dynamics

We devise a novel assay that introduces micro-architectures into highly confining microchannels to probe the decision making processes of migrating cells. The conditions are meant to mimic the tight spaces in the physiological environment that cancer cells encounter during metastasis within the matrix dense stroma and during intravasation and extravasation through the vascular wall. In this study we use the assay to investigate the relative probabilities of a cell 1) permeating and 2) repolarizing (turning around) when it migrates into a spatially confining region. We observe the existence of both states even within a single cell line, indicating phenotypic heterogeneity in cell migration invasiveness and persistence. We also show that varying the spatial gradient of the taper can induce behavioral changes in cells, and different cell types respond differently to spatial changes. Particularly, for bovine aortic endothelial cells (BAECs), higher spatial gradients induce more cells to permeate (60%) than lower gradients (12%). Furthermore, highly metastatic breast cancer cells (MDA-MB-231) demonstrate a more invasive and permeative nature (87%) than non-metastatic breast epithelial cells (MCF-10A) (25%). We examine the migration dynamics of cells in the tapered region and derive characteristic constants that quantify this transition process. Our data indicate that cell response to physical spatial gradients is both cell-type specific and heterogeneous within a cell population, analogous to the behaviors reported to occur during tumor progression. Incorporation of micro-architectures in confined channels enables the probing of migration behaviors specific to defined geometries that mimic in vivo microenvironments