A quantitative modelling approach for DNA repair on a population scale

Abstract

The great advances of sequencing technologies allow the in vivo measurement of nuclear processes-such as DNA repair after UV exposure-over entire cell populations. However, data sets usually contain only a few samples over several hours, missing possibly important information in between time points. We developed a data-driven approach to analyse CPD repair kinetics over time in Saccharomyces cerevisiae. In contrast to other studies that consider sequencing signals as an average behaviour, we understand them as the superposition of signals from independent cells. By motivating repair as a stochastic process, we derive a minimal model for which the parameters can be conveniently estimated. We correlate repair parameters to a variety of genomic features that are assumed to influence repair, including transcription rate and nucleosome density. The clearest link was found for the transcription unit length, which has been unreported for budding yeast to our knowledge. The framework hence allows a comprehensive analysis of nuclear processes on a population scale.

Fig 1. Schematic representation of the Process.

(A) The repair proteins’ search process (purple with arrow) to the lesion (red) can be understood as a Brownian motion. Repair happens after association with some delay, which we assume to be another random variable (waiting time). (B) If we could repeatedly measure the repair times for one position in a single cell individually, we could distribute the measurements over a timeline. This can be analysed by a stochastic point process. Binning the timeline should correspond to the observable change of CPDs in a given window. (C) We presume that this stochastic repair process happens independently in each cell. Therefore, CPD-seq data can be understood as an accumulation of several experiments. This allows an understanding of the signal as a two-dimensional grid. Since there can be only one lesion per position per cell, we understand the amplitude of the signal as a surrogate for the number of cells that contain a lesion at this locus (marked in green).

Fig 2. Comparing XR-seq data with model predictions.

The values at 5 minutes are given in blue, 20 minutes are coloured yellow, and 60 minutes are green. The plots show that the distance correlation between prediction and XR-seq data is even higher than for the CPD-seq data. (A) Predicted repair rates with respect to the XR-seq data exhibit a considerably strong correlation (DC = 0.441). Predictions are given as the square root of the model prediction. This reduces the effect of increasing variance with larger derivatives. (B) The repair rates derive from the data as a function of XR-seq values shows a weaker correlation (DC = 0.209).

Fig 3. Collective behaviour of genomic regions can recover mutual effect of TCR and GGR.

Dashed lines give the mean whereas the shaded areas show the standard deviation. Blue and orange represent the repair fraction and the repair rate (derivative of the repair fraction), respectively. (A) The start of TCR regions is repaired early after irradiation, demonstrating the effect of TCR. (B) At the centre of TCR areas, we can observe the mutual effect of TCR (first peak) and GGR (second peak). (C) GGR’s contribution increases whilst the impact of TCR becomes less important towards the end of the gene. (D) Non-TCR regions are solely repaired by GGR. Therefore, repair is expected at later time points during the process.

Fig 4. The parameter distribution is coloured with respect to different genomic properties.

The x and y-axis give the values of m and θ, respectively. The size of the circles show 1/τ: the larger the circle, the shorter the characteristic time. Significant interrelationships are marked with a red frame. (A) and (B) are coloured with respect to NET-seq data (pink/low to green/high) for the centre of TS and NTS; (C) and (D) indicate the nucleosome density (turquoise/low to brown/high) for non-TCR regions and the NTS centre; (E) and (F) show the distribution with respect to the TU length (red/small to blue/big) for the centre of TS and NTS.