Now showing 1 - 8 of 8
  • Publication
    Nonlinear signalling networks and cell-to-cell variability transform external signals into broadly distributed or bimodal responses
    We show theoretically and experimentally a mechanism behind the emergence of wide or bimodal protein distributions in biochemical networks with nonlinear input–output characteristics (the dose–response curve) and variability in protein abundance. Large cell-to-cell variation in the nonlinear dose–response characteristics can be beneficial to facilitate two distinct groups of response levels as opposed to a graded response. Under the circumstances that we quantify mathematically, the two distinct responses can coexist within a cellular population, leading to the emergence of a bimodal protein distribution. Using flow cytometry, we demonstrate the appearance of wide distributions in the hypoxia-inducible factor-mediated response network in HCT116 cells. With help of our theoretical framework, we perform a novel calculation of the magnitude of cell-to-cell heterogeneity in the dose–response obtained experimentally.
      385Scopus© Citations 18
  • Publication
    ERK2 drives tumour cell migration in three-dimensional microenvironments by suppressing expression of Rab17 and liprin-β2
    (The Company of Biologists, 2012-02-10) ; ; ;
    Upregulation of the extracellular signal-regulated kinase (ERK) pathway has been shown to contribute to tumour invasion and progression. Because the two predominant ERK isoforms (ERK1 and ERK2, also known as MAPK3 and MAPK1, respectively) are highly homologous and have indistinguishable kinase activities in vitro, both enzymes were believed to be redundant and interchangeable. To challenge this view, we show that ERK2 silencing inhibits invasive migration of MDA-MB-231 cells, and re-expression of ERK2 but not ERK1 restores the normal invasive phenotype. A detailed quantitative analysis of cell movement on 3D matrices indicates that ERK2 knockdown impairs cellular motility by decreasing the migration velocity as well as increasing the time that cells spend not moving. Using gene expression arrays we found that the expression of the genes for Rab17 and liprin-β2 was increased by knockdown of ERK2 and restored to normal levels following re-expression of ERK2, but not ERK1. Both play inhibitory roles in the invasive behaviour of three independent cancer cell lines. Importantly, knockdown of either Rab17 or liprin-β2 restores invasiveness of ERK2-depleted cells, indicating that ERK2 drives invasion of MDA-MB-231 cells by suppressing expression of these genes.
      140Scopus© Citations 54
  • Publication
    Linear Approaches to Intramolecular Förster Resonance Energy Transfer Probe Measurements for Quantitative Modeling
    Numerous unimolecular, genetically-encoded Förster Resonance Energy Transfer (FRET) probes for monitoring biochemical activities in live cells have been developed over the past decade. As these probes allow for collection of high frequency, spatially resolved data on signaling events in live cells and tissues, they are an attractive technology for obtaining data to develop quantitative, mathematical models of spatiotemporal signaling dynamics. However, to be useful for such purposes the observed FRET from such probes should be related to a biological quantity of interest through a defined mathematical relationship, which is straightforward when this relationship is linear, and can be difficult otherwise. First, we show that only in rare circumstances is the observed FRET linearly proportional to a biochemical activity. Therefore in most cases FRET measurements should only be compared either to explicitly modeled probes or to concentrations of products of the biochemical activity, but not to activities themselves. Importantly, we find that FRET measured by standard intensity-based, ratiometric methods is inherently non-linear with respect to the fraction of probes undergoing FRET. Alternatively, we find that quantifying FRET either via (1) fluorescence lifetime imaging (FLIM) or (2) ratiometric methods where the donor emission intensity is divided by the directly-excited acceptor emission intensity (denoted Ralt) is linear with respect to the fraction of probes undergoing FRET. This linearity property allows one to calculate the fraction of active probes based on the FRET measurement. Thus, our results suggest that either FLIM or ratiometric methods based on Ralt are the preferred techniques for obtaining quantitative data from FRET probe experiments for mathematical modeling purposes.
      189Scopus© Citations 11
  • Publication
    Biology using engineering tools: The negative feedback amplifier
    (Landes Bioscience, 2011-07-01) ;
    Negative feedback is an ubiquitous feature of biological networks. Recent work from Sturm and colleaguespresents experimental evidence that biological negative feedback can serve the same function as it does for engineered systems: robustness to perturbations within the feedback loop. Such behavior has important implications for how to attack deregulated signaling networks containing negative feedback in diseases such as cancer.
      105Scopus© Citations 14
  • Publication
    Emergence of bimodal cell population responses from the interplay between analog single-cell signaling and protein expression noise
    (Springer (Biomed Central Ltd.), 2012) ; ; ;
    Background: Cell-to-cell variability in protein expression can be large, and its propagation through signaling networks affects biological outcomes. Here, we apply deterministic and probabilistic models and biochemical measurements to study how network topologies and cell-to-cell protein abundance variations interact to shape signaling responses. Results: We observe bimodal distributions of extracellular signal-regulated kinase (ERK) responses to epidermal growth factor (EGF) stimulation, which are generally thought to indicate bistable or ultrasensitive signaling behavior in single cells. Surprisingly, we find that a simple MAPK/ERK-cascade model with negative feedback that displays graded, analog ERK responses at a single cell level can explain the experimentally observed bimodality at the cell population level. Model analysis suggests that a conversion of graded input–output responses in single cells to digital responses at the population level is caused by a broad distribution of ERK pathway activation thesholds brought about by cell-to-cell variability in protein expression. Conclusions: Our results show that bimodal signaling response distributions do not necessarily imply digital (ultrasensitive or bistable) single cell signaling, and the interplay between protein expression noise and network topologies can bring about digital population responses from analog single cell dose responses. Thus, cells can retain the benefits of robustness arising from negative feedback, while simultaneously generating population-level on/off responses that are thought to be critical for regulating cell fate decisions.
      260Scopus© Citations 57
  • Publication
    Evaluating Strategies to Normalise Biological Replicates of Western Blot Data
    Western blot data are widely used in quantitative applications such as statistical testing and mathematical modelling. To ensure accurate quantitation and comparability between experiments, Western blot replicates must be normalised, but it is unclear how the available methods affect statistical properties of the data. Here we evaluate three commonly used normalisation strategies: (i) by fixed normalisation point or control; (ii) by sum of all data points in a replicate; and (iii) by optimal alignment of the replicates. We consider how these different strategies affect the coefficient of variation (CV) and the results of hypothesis testing with the normalised data. Normalisation by fixed point tends to increase the mean CV of normalised data in a manner that naturally depends on the choice of the normalisation point. Thus, in the context of hypothesis testing, normalisation by fixed point reduces false positives and increases false negatives. Analysis of published experimental data shows that choosing normalisation points with low quantified intensities results in a high normalised data CV and should thus be avoided. Normalisation by sum or by optimal alignment redistributes the raw data uncertainty in a mean-dependent manner, reducing the CV of high intensity points and increasing the CV of low intensity points. This causes the effect of normalisations by sum or optimal alignment on hypothesis testing to depend on the mean of the data tested; for high intensity points, false positives are increased and false negatives are decreased, while for low intensity points, false positives are decreased and false negatives are increased. These results will aid users of Western blotting to choose a suitable normalisation strategy and also understand the implications of this normalisation for subsequent hypothesis testing.
      300Scopus© Citations 134
  • Publication
    Endocytosis and signalling: A meeting with mathematics
    Although endocytosis has traditionally been understood as a signal attenuation mechanism, an emerging view considers endocytosis as an integral part of signal propagation and processing. On the short time scale, trafficking of endocytic vesicles contributes to signal propagation from the surface to distant targets, with bi-directional communication between signalling and trafficking. Mathematical modelling helps combine the mechanistic, molecular knowledge with rigorous analysis of the complex output dynamics of endocytosis in time and space. Simulations reveal novel roles for endocytosis, including the control of cell polarity, enhancing the spatial signal propagation, and controlling the signal magnitudes, kinetics, and synchronization with stimulus dynamics.
      273Scopus© Citations 27
  • Publication
    Mammalian protein expression noise: scaling principles and the implications for knockdown experiments
    The abundance of a particular protein varies both over time within a single mammalian cell and between cells of a genetically identical population. Here, we investigate the properties of such noisy protein expression in mammalian cells by combining theoretical and experimental approaches. The gamma distribution model is well-known to describe cell-to-cell variability in protein expression in a variety of common scenarios. This model predicts, and experiments show, that when protein levels are manipulated by altering transcription rates or mRNA half-life, protein expression noise, defined as the squared coefficient of variation, is constant. In contrast, we also demonstrate that when protein levels are manipulated by changing protein half-life, as mean levels increase, noise decreases. Thus, in mammalian cells, the scaling relationship between mean protein levels and expression noise depends on how mean levels are perturbed. Therefore it may be important to consider how common experimental manipulations of pro in expression affect not only mean levels, but also noise levels. In the context of knockdown experiments, natural cell-tocell variability in protein expression implies that a particular cell from the knockdown population may have higher protein levels than a cell from the control population. Simulations and experimental data suggest that approximately three-fold knockdown in mean expression levels can reduce such so-called “overlap probability” to less than ~10%. This has implications for the interpretation of knockdown experiments when the readout is a single cell measure.
      382Scopus© Citations 10