Statistical lower bounds on protein copy number from fluorescence expression images

Variance reducing and noise correction in protein quantification by measuring fluctuations in fluorescence due to photobleaching

Quantifying the absolute protein number using the ratio between the variance and the mean of the protein Fluorescence intensity is a straightforward method for microscopy imaging. Recently, this method has been expanded to fluorescence decaying processes due to photobleaching with binomial distribution. The article examines the method proposed and shows how it can be adapted to the case of variance in the initial number of proteins between the cells. The article shows that the method can be improved by the implementation of the information processing of each frame independently from other frames. By doing so, the variance in determining the protein number can be reduced. In addition, the article examines the management of unwanted noises in the measurement, offers a solution for the shot noise and background noise, examines the expected error caused by the decay constant inaccuracy, and analyzes the expected difficulties in conducting a practical experiment, which includes a non-exponential decay and variance in the photobleaching rate of the cells. The method can be applied to any superposition of n_0 discrete decaying processes. However, the evaluation of expected errors in quantification is essential for early planning of the experimental conditions and evaluation of the error.

Resolving fluorescent species by their brightness and diffusion using correlated photon-counting histograms

Fluorescence fluctuation spectroscopy (FFS) refers to techniques that analyze fluctuations in the fluorescence emitted by fluorophores diffusing in a small volume and can be used to distinguish between populations of molecules that exhibit differences in brightness or diffusion. For example, fluorescence correlation spectroscopy (FCS) resolves species through their diffusion by analyzing correlations in the fluorescence over time; photon counting histograms (PCH) and related methods based on moment analysis resolve species through their brightness by analyzing fluctuations in the photon counts. Here we introduce correlated photon counting histograms (cPCH), which uses both types of information to simultaneously resolve fluorescent species by their brightness and diffusion. We define the cPCH distribution by the probability to detect both a particular number of photons at the current time and another number at a later time. FCS and moment analysis are special cases of the moments of the cPCH distribution, and PCH is obtained by summing over the photon counts in either channel. cPCH is inherently a dual channel technique, and the expressions we develop apply to the dual colour case. Using simulations, we demonstrate that two species differing in both their diffusion and brightness can be better resolved with cPCH than with either FCS or PCH. Further, we show that cPCH can be extended both to longer dwell times to improve the signal-to-noise and to the analysis of images. By better exploiting the information available in fluorescence fluctuation spectroscopy, cPCH will be an enabling methodology for quantitative biology.

Estimating numbers of intracellular molecules through analysing fluctuations in photobleaching

The impact of fluorescence microscopy has been limited by the difficulties of expressing measurements of fluorescent proteins in numbers of molecules. Absolute numbers enable the integration of results from different laboratories, empower mathematical modelling, and are the bedrock for a quantitative, predictive biology. Here we propose an estimator to infer numbers of molecules from fluctuations in the photobleaching of proteins tagged with Green Fluorescent Protein. Performing experiments in budding yeast, we show that our estimates of numbers agree, within an order of magnitude, with published biochemical measurements, for all six proteins tested. The experiments we require are straightforward and use only a wide-field fluorescence microscope. As such, our approach has the potential to become standard for those practising quantitative fluorescence microscopy.

Mid-embryo patterning and precision in Drosophila segmentation: Krüppel dual regulation of hunchback

In early development, genes are expressed in spatial patterns which later define cellular identities and tissue locations. The mechanisms of such pattern formation have been studied extensively in early Drosophila (fruit fly) embryos. The gap gene hunchback (hb) is one of the earliest genes to be expressed in anterior-posterior (AP) body segmentation. As a transcriptional regulator for a number of downstream genes, the spatial precision of hb expression can have significant effects in the development of the body plan. To investigate the factors contributing to hb precision, we used fine spatial and temporal resolution data to develop a quantitative model for the regulation of hb expression in the mid-embryo. In particular, modelling hb pattern refinement in mid nuclear cleavage cycle 14 (NC14) reveals some of the regulatory contributions of simultaneously-expressed gap genes. Matching the model to recent data from wild-type (WT) embryos and mutants of the gap gene Krüppel (Kr) indicates that a mid-embryo Hb concentration peak important in thoracic development (at parasegment 4, PS4) is regulated in a dual manner by Kr, with low Kr concentration activating hb and high Kr concentration repressing hb. The processes of gene expression (transcription, translation, transport) are intrinsically random. We used stochastic simulations to characterize the noise generated in hb expression. We find that Kr regulation can limit the positional variability of the Hb mid-embryo border. This has been recently corroborated in experimental comparisons of WT and Kr- mutant embryos. Further, Kr regulation can decrease uncertainty in mid-embryo hb expression (i.e. contribute to a smooth Hb boundary) and decrease between-copy transcriptional variability within nuclei. Since many tissue boundaries are first established by interactions between neighbouring gene expression domains, these properties of Hb-Kr dynamics to diminish the effects of intrinsic expression noise may represent a general mechanism contributing to robustness in early development.

Estimating binding properties of transcription factors from genome-wide binding profiles

The binding of transcription factors (TFs) is essential for gene expression. One important characteristic is the actual occupancy of a putative binding site in the genome. In this study, we propose an analytical model to predict genomic occupancy that incorporates the preferred target sequence of a TF in the form of a position weight matrix (PWM), DNA accessibility data (in the case of eukaryotes), the number of TF molecules expected to be bound specifically to the DNA and a parameter that modulates the specificity of the TF. Given actual occupancy data in the form of ChIP-seq profiles, we backwards inferred copy number and specificity for five Drosophila TFs during early embryonic development: Bicoid, Caudal, Giant, Hunchback and Kruppel. Our results suggest that these TFs display thousands of molecules that are specifically bound to the DNA and that whilst Bicoid and Caudal display a higher specificity, the other three TFs (Giant, Hunchback and Kruppel) display lower specificity in their binding (despite having PWMs with higher information content). This study gives further weight to earlier investigations into TF copy numbers that suggest a significant proportion of molecules are not bound specifically to the DNA.

Measuring gene expression noise in early Drosophila embryos: nucleus-to-nucleus variability

In recent years the analysis of noise in gene expression has widely attracted the attention of experimentalists and theoreticians. Experimentally, the approaches based on in vivo fluorescent reporters in single cells appear to be straightforward and effective tools for bacteria and yeast. However, transferring these approaches to multicellular organisms presents many methodological problems. Here we describe our approach to measure between-nucleus variability (noise) in the primary morphogenetic gradient of Bicoid (Bcd) in the precellular blastoderm stage of fruit fly (Drosophila) embryos. The approach is based on the comparison of results for fixed immunostained embryos with observations of live embryos carrying fluorescent Bcd (Bcd-GFP). We measure the noise using two-dimensional Singular Spectrum Analysis (2D SSA). We have found that the nucleus-to-nucleus noise in Bcd intensity, both for live (Bcd-GFP) and for fixed immunstained embryos, tends to be signal-independent. In addition, the character of the noise is sensitive to the nuclear masking technique used to extract quantitative intensities. Further, the method of decomposing the raw quantitative expression data into a signal (expression surface) and residual noise affects the character of the residual noise. We find that careful masking of confocal images and use of appropriate computational tools to decompose raw expression data into trend and noise makes it possible to extract and study the biological noise of gene expression.

Gene expression noise in spatial patterning: hunchback promoter structure affects noise amplitude and distribution in Drosophila segmentation

Positional information in developing embryos is specified by spatial gradients of transcriptional regulators. One of the classic systems for studying this is the activation of the hunchback (hb) gene in early fruit fly (Drosophila) segmentation by the maternally-derived gradient of the Bicoid (Bcd) protein. Gene regulation is subject to intrinsic noise which can produce variable expression. This variability must be constrained in the highly reproducible and coordinated events of development. We identify means by which noise is controlled during gene expression by characterizing the dependence of hb mRNA and protein output noise on hb promoter structure and transcriptional dynamics. We use a stochastic model of the hb promoter in which the number and strength of Bcd and Hb (self-regulatory) binding sites can be varied. Model parameters are fit to data from WT embryos, the self-regulation mutant hb(14F), and lacZ reporter constructs using different portions of the hb promoter. We have corroborated model noise predictions experimentally. The results indicate that WT (self-regulatory) Hb output noise is predominantly dependent on the transcription and translation dynamics of its own expression, rather than on Bcd fluctuations. The constructs and mutant, which lack self-regulation, indicate that the multiple Bcd binding sites in the hb promoter (and their strengths) also play a role in buffering noise. The model is robust to the variation in Bcd binding site number across a number of fly species. This study identifies particular ways in which promoter structure and regulatory dynamics reduce hb output noise. Insofar as many of these are common features of genes (e.g. multiple regulatory sites, cooperativity, self-feedback), the current results contribute to the general understanding of the reproducibility and determinacy of spatial patterning in early development.