Stochastic simulation platform for visualization and estimation of transcriptional kinetics
TL;DR: An implementation of the Gillespie algorithm that simulates the stochastic kinetics of nascent and mature RNA, which includes two-state gene regulation, RNA synthesis initiation and stepwise elongation, release to the cytoplasm, andstepwise degradation, is presented.
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Abstract: We present an implementation of the Gillespie algorithm that simulates the stochastic kinetics of nascent and mature RNA. Our model includes two-state gene regulation, RNA synthesis initiation and stepwise elongation, release to the cytoplasm, and stepwise degradation, a granular description currently tractable only by simulation. To facilitate comparison with experimental data, the algorithm predicts fluorescent probe signals measurable by single-cell RNA imaging. We approach the inverse problem of estimating underlying parameters in a five-dimensional parameter space and suggest optimization heuristics that successfully recover known reaction rates from simulated gene expression turn-on data. The simulation framework includes a graphical user interface, available as a MATLAB app at https://data.caltech.edu/records/1287.
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Figures
Fig 2. Parameter estimation process and performance. A: Parallelized calculation of the search objective 140 function for a set of trial parameters (ΔMean: mean squared error, ΔCDF: Wasserstein distance, Objective: 141 error function value). B: Convergence of the genetic algorithm (red: ground truth target, gray: population 142 of parameter estimates). C: Final trial parameter population from B (red: ground truth target, histogram: 143 
Fig 1. Model and simulation platform. A: Model schematic and probe parameterization (gold: probe 94 coverage, 𝑃3: 3’-most edge of the probe, 𝑃5: 5′-most edge of the probe) B: Time-dependent molecule-level 95 visualizations available through the GUI. Trajectory generated using 𝑘𝑖𝑛𝑖 = 100 min -1, 𝑘𝑜𝑛 = 3 min
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