Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. Results We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. Conclusion The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods

Dynamic analysis of stochastic transcription cycles

In individual mammalian cells the expression of some genes such as prolactin is highly variable over time and has been suggested to occur in stochastic pulses. To investigate the origins of this behavior and to understand its functional relevance, we quantitatively analyzed this variability using new mathematical tools that allowed us to reconstruct dynamic transcription rates of different reporter genes controlled by identical promoters in the same living cell. Quantitative microscopic analysis of two reporter genes, firefly luciferase and destabilized EGFP, was used to analyze the dynamics of prolactin promoter-directed gene expression in living individual clonal and primary pituitary cells over periods of up to 25 h. We quantified the time-dependence and cyclicity of the transcription pulses and estimated the length and variation of active and inactive transcription phases. We showed an average cycle period of approximately 11 h and demonstrated that while the measured time distribution of active phases agreed with commonly accepted models of transcription, the inactive phases were differently distributed and showed strong memory, with a refractory period of transcriptional inactivation close to 3 h. Cycles in transcription occurred at two distinct prolactin-promoter controlled reporter genes in the same individual clonal or primary cells. However, the timing of the cycles was independent and out-of-phase. For the first time, we have analyzed transcription dynamics from two equivalent loci in real-time in single cells. In unstimulated conditions, cells showed independent transcription dynamics at each locus. A key result from these analyses was the evidence for a minimum refractory period in the inactive-phase of transcription. The response to acute signals and the result of manipulation of histone acetylation was consistent with the hypothesis that this refractory period corresponded to a phase of chromatin remodeling which significantly increased the cyclicity. Stochastically timed bursts of transcription in an apparently random subset of cells in a tissue may thus produce an overall coordinated but heterogeneous phenotype capable of acute responses to stimuli

Extracting fluorescent reporter time courses of cell lineages from high-throughput microscopy at low temporal resolution

The extraction of fluorescence time course data is a major bottleneck in high-throughput live-cell microscopy. Here we present an extendible framework based on the open-source image analysis software ImageJ, which aims in particular at analyzing the expression of fluorescent reporters through cell divisions. The ability to track individual cell lineages is essential for the analysis of gene regulatory factors involved in the control of cell fate and identity decisions. In our approach, cell nuclei are identified using Hoechst, and a characteristic drop in Hoechst fluorescence helps to detect dividing cells. We first compare the efficiency and accuracy of different segmentation methods and then present a statistical scoring algorithm for cell tracking, which draws on the combination of various features, such as nuclear intensity, area or shape, and importantly, dynamic changes thereof. Principal component analysis is used to determine the most significant features, and a global parameter search is performed to determine the weighting of individual features. Our algorithm has been optimized to cope with large cell movements, and we were able to semi-automatically extract cell trajectories across three cell generations. Based on the MTrackJ plugin for ImageJ, we have developed tools to efficiently validate tracks and manually correct them by connecting broken trajectories and reassigning falsely connected cell positions. A gold standard consisting of two time-series with 15,000 validated positions will be released as a valuable resource for benchmarking. We demonstrate how our method can be applied to analyze fluorescence distributions generated from mouse stem cells transfected with reporter constructs containing transcriptional control elements of the Msx1 gene, a regulator of pluripotency, in mother and daughter cells. Furthermore, we show by tracking zebrafish PAC2 cells expressing FUCCI cell cycle markers, our framework can be easily adapted to different cell types and fluorescent markers

Adult Pituitary Data1

GFP fluorescence measured from single cells in adult pituitary tissue and subsequent modelling of transcription activity using a stochastic switch model