Predictability analysis in stochastic reaction networks is typically challenged by intrinsic noise. We utilize non-intrusive spectral expansions to efficiently propagate input parametric uncertainties in the presence of intrinsic stochasticity. To address the curse of dimensionality, orthogonal spectral projections are performed using a sparse quadrature approach that is shown to perform better than High Dimensional Model Representation (HDMR) for the benchmark problem. The methodology is illustrated for the gene regulation network of the Bacillus Subtilis bacterium.