Quantification of fluorophore copy number from intrinsic fluctuations during fluorescence photobleaching

We present a theoretical technique for quantifying the cellular copy-number of fluorophores that relies on the random nature of the photobleaching process. Our approach does not require single-molecule sensitivity, and therefore can be used with commonly used epifluorescence microscopes. Fluctuations arising from photobleaching can be used to estimate the proportionality between fluorescence intensity and copy-number, which can then be used with subsequent intensity measurements to estimate copy-number. We calculate the statistical errors of our approach and verify them with stochastic simulations. By using fluctuations over the entire photobleaching process, we obtain significantly smaller errors than previous approaches that have used fluctuations arising from cytoplasmic proteins partitioning during cellular division. From the time-dependence of the fluctuations as photobleaching proceeds, we can discriminate between desired photobleach fluctuations and background noise or photon shot noise. Our approach does not require cellular division and the photobleaching rate sets a timescale that is adjustable with respect to cellular processes. We hope that our approach will now be applied experimentally.     

Dark proteins: effect of inclusion body formation on quantification of protein expression

Plasmid-borne gene expression systems have found wide application in the emerging fields of systems biology and synthetic biology, where plasmids are used to implement simple network architectures, either to test systems biology hypotheses about issues such as gene expression noise or as a means of exerting artificial control over a cell's dynamics. In both these cases, fluorescent proteins are commonly applied as a means of monitoring the expression of genes in the living cell, and efforts have been made to quantify protein expression levels through fluorescence intensity calibration and by monitoring the partitioning of proteins among the two daughter cells after division; such quantification is important in formulating the predictive models desired in systems and synthetic biology research. A potential pitfall of using plasmid-based gene expression systems is that the high protein levels associated with expression from plasmids can lead to the formation of inclusion bodies, insoluble aggregates of misfolded, nonfunctional proteins that will not generate fluorescence output; proteins caught in these inclusion bodies are thus "dark" to fluorescence-based detection methods. If significant numbers of proteins are incorporated into inclusion bodies rather than becoming biologically active, quantitative results obtained by fluorescent measurements will be skewed; we investigate this phenomenon here. We have created two plasmid constructs with differing average copy numbers, both incorporating an unregulated promoter (P(LtetO-1) in the absence of TetR) expressing the GFP derivative enhanced green fluorescent protein (EGFP), and inserted them into Escherichia coli bacterial cells (a common model organism for work on the dynamics of prokaryotic gene expression). We extracted the inclusion bodies, denatured them, and refolded them to render them active, obtaining a measurement of the average number of EGFP per cell locked into these aggregates; at the same time, we used calibrated fluorescent intensity measurements to determine the average number of active EGFP present per cell. Both measurements were carried out as a function of cellular doubling time, over a range of 45-75 min. We found that the ratio of inclusion body EGFP to active EGFP varied strongly as a function of the cellular growth rate, and that the number of "dark" proteins in the aggregates could in fact be substantial, reaching ratios as high as approximately five proteins locked into inclusion bodies for every active protein (at the fastest growth rate), and dropping to ratios well below 1 (for the slowest growth rate). Our results suggest that efforts to compare computational models to protein numbers derived from fluorescence measurements should take inclusion body loss into account, especially when working with rapidly growing cells.     

Real-Time Monitoring of Transferrin-Induced Endocytic Vesicle Formation by Mid-Infrared Surface Plasmon Resonance

We report on the application of surface plasmon resonance (SPR), based on Fourier transform infrared spectroscopy in the mid-infrared wavelength range, for real-time and label-free sensing of transferrin-induced endocytic processes in human melanoma cells. The evanescent field of the mid-infrared surface plasmon penetrates deep into the cell, allowing highly sensitive SPR measurements of dynamic processes occurring at significant cellular depths. We monitored in real-time, infrared reflectivity spectra in the SPR regime from living cells exposed to human transferrin (Tfn). We show that although fluorescence microscopy measures primarily Tfn accumulation in recycling endosomes located deep in the cell's cytoplasm, the SPR technique measures mainly Tfn-mediated formation of early endocytic organelles located in close proximity to the plasma membrane. Our SPR and fluorescence data are very well described by a kinetic model of Tfn endocytosis, suggested previously in similar cell systems. Hence, our SPR data provide further support to the rather controversial ability of Tfn to stimulate its own endocytosis. Our analysis also yields what we believe is novel information on the role of membrane cholesterol in modulating the kinetics of endocytic vesicle biogenesis and consumption.     

Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell.     

Algorithms to Model Single Gene,Single Chromosome,and Whole Genome Copy Number Changes Jointly in Tumor Phylogenetics

We present methods to construct phylogenetic models of tumor progression at the cellular level that include copy number changes at the scale of single genes, entire chromosomes, and the whole genome. The methods are designed for data collected by fluorescence in situ hybridization (FISH), an experimental technique especially well suited to characterizing intratumor heterogeneity using counts of probes to genetic regions frequently gained or lost in tumor development. Here, we develop new provably optimal methods for computing an edit distance between the copy number states of two cells given evolution by copy number changes of single probes, all probes on a chromosome, or all probes in the genome. We then apply this theory to develop a practical heuristic algorithm, implemented in publicly available software, for inferring tumor phylogenies on data from potentially hundreds of single cells by this evolutionary model. We demonstrate and validate the methods on simulated data and published FISH data from cervical cancers and breast cancers. Our computational experiments show that the new model and algorithm lead to more parsimonious trees than prior methods for single-tumor phylogenetics and to improved performance on various classification tasks, such as distinguishing primary tumors from metastases obtained from the same patient population.     

Multidimensional detection and analysis of Ca2+ sparks in cardiac myocytes

Examining calcium spark morphology and its relationship to the structure of the cardiac myocyte offers a direct means of understanding excitation-contraction coupling mechanisms. Traditional confocal line scanning achieves excellent temporal spark resolution but at the cost of spatial information in the perpendicular dimension. To address this, we developed a methodology to identify and analyze sparks obtained via two-dimensional confocal or charge-coupled device microscopy. The technique consists of nonlinearly subtracting the background fluorescence, thresholding the data on the basis of noise level, and then localizing the spark peaks via a generalized extrema test, while taking care to detect and separate adjacent peaks. In this article, we describe the algorithm, compare its performance to a previously validated spark detection algorithm, and demonstrate it by applying it to both a synthetic replica and an experimental preparation of a two-dimensional isotropic myocyte monolayer exhibiting sparks during a calcium transient. We find that our multidimensional algorithm provides better sensitivity than the conventional method under conditions of temporally heterogeneous background fluorescence, and the inclusion of peak segmentation reduces false negative rates when spark density is high. Our algorithm is robust and can be effectively used with different imaging modalities and allows spark identification and quantification in subcellular, cellular, and tissue preparations.     

Stochastic Measurement Models for Quantifying Lymphocyte Responses Using Flow Cytometry

Adaptive immune responses are complex dynamic processes whereby B and T cells undergo division and differentiation triggered by pathogenic stimuli. Deregulation of the response can lead to severe consequences for the host organism ranging from immune deficiencies to autoimmunity. Tracking cell division and differentiation by flow cytometry using fluorescent probes is a major method for measuring progression of lymphocyte responses, both in vitro and in vivo. In turn, mathematical modeling of cell numbers derived from such measurements has led to significant biological discoveries, and plays an increasingly important role in lymphocyte research. Fitting an appropriate parameterized model to such data is the goal of these studies but significant challenges are presented by the variability in measurements. This variation results from the sum of experimental noise and intrinsic probabilistic differences in cells and is difficult to characterize analytically. Current model fitting methods adopt different simplifying assumptions to describe the distribution of such measurements and these assumptions have not been tested directly. To help inform the choice and application of appropriate methods of model fitting to such data we studied the errors associated with flow cytometry measurements from a wide variety of experiments. We found that the mean and variance of the noise were related by a power law with an exponent between 1.3 and 1.8 for different datasets. This violated the assumptions inherent to commonly used least squares, linear variance scaling and log-transformation based methods. As a result of these findings we propose a new measurement model that we justify both theoretically, from the maximum entropy standpoint, and empirically using collected data. Our evaluation suggests that the new model can be reliably used for model fitting across a variety of conditions. Our work provides a foundation for modeling measurements in flow cytometry experiments thus facilitating progress in quantitative studies of lymphocyte responses.     

Non‐invasive,whole‐plant imaging of chloroplast movement and chlorophyll fluorescence reveals photosynthetic phenotypes independent of chloroplast photorelocation defects in chloroplast division mutants

Leaf chloroplast movement is thought to optimize light capture and to minimize photodamage. To better understand the impact of chloroplast movement on photosynthesis, we developed a technique based on the imaging of reflectance from leaf surfaces that enables continuous, high‐sensitivity, non‐invasive measurements of chloroplast movement in multiple intact plants under white actinic light. We validated the method by measuring photorelocation responses in Arabidopsis chloroplast division mutants with drastically enlarged chloroplasts, and in phototropin mutants with impaired photorelocation but normal chloroplast morphology, under different light regimes. Additionally, we expanded our platform to permit simultaneous image‐based measurements of chlorophyll fluorescence and chloroplast movement. We show that chloroplast division mutants with enlarged, less‐mobile chloroplasts exhibit greater photosystem II photodamage than is observed in the wild type, particularly under fluctuating high levels of light. Comparison between division mutants and the severe photorelocation mutant phot1‐5 phot2‐1 showed that these effects are not entirely attributable to diminished photorelocation responses, as previously hypothesized, implying that altered chloroplast morphology affects other photosynthetic processes. Our dual‐imaging platform also allowed us to develop a straightforward approach to correct non‐photochemical quenching (NPQ) calculations for interference from chloroplast movement. This correction method should be generally useful when fluorescence and reflectance are measured in the same experiments. The corrected data indicate that the energy‐dependent (qE) and photoinhibitory (qI) components of NPQ contribute differentially to the NPQ phenotypes of the chloroplast division and photorelocation mutants. This imaging technology thus provides a platform for analyzing the contributions of chloroplast movement, chloroplast morphology and other phenotypic attributes to the overall photosynthetic performance of higher plants.     

Two-color fluorescence analysis of individual virions determines the distribution of the copy number of proteins in herpes simplex virus particles

We present a single virion method to determine absolute distributions of copy number in the protein composition of viruses and apply it to herpes simplex virus type 1. Using two-color coincidence fluorescence spectroscopy, we determine the virion-to-virion variability in copy numbers of fluorescently labeled tegument and envelope proteins relative to a capsid protein by analyzing fluorescence intensity ratios for ensembles of individual dual-labeled virions and fitting the resulting histogram of ratios. Using EYFP-tagged capsid protein VP26 as a reference for fluorescence intensity, we are able to calculate the mean and also, for the first time to our knowledge, the variation in numbers of gD, VP16, and VP22 tegument. The measurement of the number of glycoprotein D molecules was in good agreement with independent measurements of average numbers of these glycoproteins in bulk virus preparations, validating the method. The accuracy, straightforward data processing, and high throughput of this technique make it widely applicable to the analysis of the molecular composition of large complexes in general, and it is particularly suited to providing insights into virus structure, assembly, and infectivity.     

An Algorithm to Automate Yeast Segmentation and Tracking

Our understanding of dynamic cellular processes has been greatly enhanced by rapid advances in quantitative fluorescence microscopy. Imaging single cells has emphasized the prevalence of phenomena that can be difficult to infer from population measurements, such as all-or-none cellular decisions, cell-to-cell variability, and oscillations. Examination of these phenomena requires segmenting and tracking individual cells over long periods of time. However, accurate segmentation and tracking of cells is difficult and is often the rate-limiting step in an experimental pipeline. Here, we present an algorithm that accomplishes fully automated segmentation and tracking of budding yeast cells within growing colonies. The algorithm incorporates prior information of yeast-specific traits, such as immobility and growth rate, to segment an image using a set of threshold values rather than one specific optimized threshold. Results from the entire set of thresholds are then used to perform a robust final segmentation.     

Local and global analysis of endocytic patch dynamics in fission yeast using a new “temporal superresolution” realignment method

Quantitative microscopy is a valuable tool for inferring molecular mechanisms of cellular processes such as clathrin-mediated endocytosis, but, for quantitative microscopy to reach its potential, both data collection and analysis needed improvement. We introduce new tools to track and count endocytic patches in fission yeast to increase the quality of the data extracted from quantitative microscopy movies. We present a universal method to achieve “temporal superresolution” by aligning temporal data sets with higher temporal resolution than the measurement intervals. These methods allowed us to extract new information about endocytic actin patches in wild-type cells from measurements of the fluorescence of fimbrin-mEGFP. We show that the time course of actin assembly and disassembly varies <600 ms between patches. Actin polymerizes during vesicle formation, but we show that polymerization does not participate in vesicle movement other than to limit the complex diffusive motions of newly formed endocytic vesicles, which move faster as the surrounding actin meshwork decreases in size over time. Our methods also show that the number of patches in fission yeast is proportional to cell length and that the variability in the repartition of patches between the tips of interphase cells has been underestimated.     

Cellular growth and division in the Gillespie algorithm

Recent experimental studies elucidating the importance of noise in gene regulation have ignited widespread interest in Gillespie's stochastic simulation technique for biochemical networks. We formulate modifications to the Gillespie algorithm which are necessary to correctly simulate chemical reactions with time-dependent reaction rates. We concentrate on time dependence of kinetic rates arising from the periodic process of growth and division of the cellular volume, and demonstrate that a careful re-derivation of the Gillespie algorithm is important when all stochastically simulated reactions have rates slower or comparable to the cellular growth rate. For an unregulated single-gene system, we illustrate our findings using recently proposed hybrid simulation techniques, and systematically compare our algorithm with analytic results obtained from the chemical master equation.     

Z-scan fluorescence profile deconvolution of cytosolic and membrane-associated protein populations

This study introduces a technique that characterizes the spatial distribution of peripheral membrane proteins that associate reversibly with the plasma membrane. An axial scan through the cell generates a z-scan intensity profile of a fluorescently labeled peripheral membrane protein. This profile is analytically separated into membrane and cytoplasmic components by accounting for both the cell geometry and the point spread function. We experimentally validated the technique and characterized both the resolvability and stability of z-scan measurements. Furthermore, using the cellular brightness of green fluorescent protein, we were able to convert the fluorescence intensities into concentrations at the membrane and in the cytoplasm. We applied the technique to study the translocation of the pleckstrin homology domain of phospholipase C delta 1 labeled with green fluorescent protein on ionomycin treatment. Analysis of the z-scan fluorescence profiles revealed protein-specific cell height changes and allowed for comparison between the observed fluorescence changes and predictions based on the cellular surface area-to-volume ratio. The quantitative capability of z-scan fluorescence profile deconvolution offers opportunities for investigating peripheral membrane proteins in the living cell that were previously not accessible.     

Measuring DNA content in live cells by fluorescence microscopy

Background

Live-cell fluorescence microscopy (LCFM) is a powerful tool used to investigate cellular dynamics in real time. However, the capacity to simultaneously measure DNA content in cells being tracked over time remains challenged by dye-associated toxicities. The ability to measure DNA content in single cells by means of LCFM would allow cellular stage and ploidy to be coupled with a variety of imaging directed analyses. Here we describe a widely applicable nontoxic approach for measuring DNA content in live cells by fluorescence microscopy. This method relies on introducing a live-cell membrane-permeant DNA fluorophore, such as Hoechst 33342, into the culture medium of cells at the end of any live-cell imaging experiment and measuring each cell’s integrated nuclear fluorescence to quantify DNA content. Importantly, our method overcomes the toxicity and induction of DNA damage typically caused by live-cell dyes through strategic timing of adding the dye to the cultures; allowing unperturbed cells to be imaged for any interval of time before quantifying their DNA content. We assess the performance of our method empirically and discuss adaptations that can be implemented using this technique.

Results

Presented in conjunction with cells expressing a histone 2B-GFP fusion protein (H2B-GFP), we demonstrated how this method enabled chromosomal segregation errors to be tracked in cells as they progressed through cellular division that were later identified as either diploid or polyploid. We also describe and provide an automated Matlab-derived algorithm that measures the integrated nuclear fluorescence in each cell and subsequently plots these measurements into a cell cycle histogram for each frame imaged. The algorithm’s accurate assessment of DNA content was validated by parallel flow cytometric studies.

Conclusions

This method allows the examination of single-cell dynamics to be correlated with cellular stage and ploidy in a high-throughput fashion. The approach is suitable for any standard epifluorescence microscope equipped with a stable illumination source and either a stage-top incubator or an enclosed live-cell incubation chamber. Collectively, we anticipate that this method will allow high-resolution microscopic analysis of cellular processes involving cell cycle progression, such as checkpoint activation, DNA replication, and cellular division.

     

An algorithm combining discrete and continuous methods for optical mapping.

Optical mapping is a novel technique for generating the restriction map of a DNA molecule by observing many single, partially digested copies of it, using fluorescence microscopy. The real-life problem is complicated by numerous factors: false positive and false negative cut observations, inaccurate location measurements, unknown orientations, and faulty molecules. We present an algorithm for solving the real-life problem. The algorithm combines continuous optimization and combinatorial algorithms applied to a nonuniform discretization of the data. We present encouraging results on real experimental data and on simulated data.     

Colored extrinsic fluctuations and stochastic gene expression

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise’, is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored’). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high‐throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.     

Amines of the mucosal mast cell of the gut in normal and nematode infected rats

Infection with the nematode N. brasiliensis is accompanied by a marked increase of the number of mucosal mast cells (MMC) and the mucosal content of histamine and 5-hydroxytryptamine (5-HT). We compared amine levels, determined by ion exchange and high performance liquid chromatography (HPLC) with numbers of MMC and enterochromaffin cells (ECC). Furthermore, we measured 5-HT cytofluorometrically in individual MMC and ECC. The cellular distribution of 5-HT was studied immunohistochemically. Our results corroborate previous findings that histamine is stored in MMC. Quotients between histamine content and numbers of MMC decreased throughout the period of worm expulsion, followed by a recovery, suggesting a histamine release during this defense reaction. The HPLC analysis gave no evidence for a storage of dopamine in MMC. ECC and MMC of normal and infected rats showed a formaldehyde induced fluorescence and 5-HT immunoreactivity. The formaldehyde induced fluorescence of MMC from normal rats was about 10% that of ECC, but MMC exceeded ECC three times by numbers. These findings suggest that a considerable proportion of the intestinal 5-HT in the normal rat is stored in MMC. ECC numbers did not change during the infection and their content of 5-HT was unchanged, as judged by cytofluorometry. The cytofluorometric measurements showed that the intensity of the monoamine fluorescence from the MMC of infected animals was about three times as high as that of controls. It was concluded that the increased tissue levels of 5-HT was due to both an increase in MMC numbers and an increase in the 5-HT content of individual MMC. The results suggest a different role for histamine and 5-HT in the defense reaction towards the nematode infection.     

Dimerization of MT1-MMP during cellular invasion detected by fluorescence resonance energy transfer

Homodimerization of the membrane-bound collagenase MT1-MMP [membrane-type 1 MMP (matrix metalloproteinase)] is crucial for its collagenolytic activity. However, it is not clear whether this dimerization is regulated during cellular invasion into three-dimensional collagen matrices. To address this question, we established a fluorescence resonance energy transfer system to detect MT1-MMP dimerization and analysed the process in cells invading through three-dimensional collagen. Our data indicate that dimerization occurs dynamically and constantly at the leading edge of migrating cells, but not the trailing edge. We found that polarized dimerization was not due to ECM (extracellular matrix) attachment, but was rather controlled by reorganization of the actin cytoskeleton by the small GTPases, Cdc42 (cell division cycle 42) and Rac1. Our data indicate that cell-surface collagenolytic activity is regulated co-ordinately with cell migration events to enable penetration of the matrix physical barrier.