Gaussian process regression (GPR) has been extensively used for modelling and differential testing of biological time-series measurements due to its robustness and interpretability. However, the standard gaussian process assumes stationary model dynamics and is a poor fit for common perturbation experiments, where we expect to see rapid changes after the perturbation and diminishing rate of state change as the cell returns back to a stable state. A common application of time-series measurements is the testing of significant difference between two time-serie profiles. The currently used two-sample differential tests, based on gaussian processes, focus on comparing model likelihoods over a subset of measured time-points, and hence necessitate dense measurements to cover the time axis. We address these problems by proposing time-dependent extensions to both gaussian process regression and significance analysis between time-series. We propose a time-dependent noise model and time-dependent covariance priors, suitable for perturbation experiments. We utilise a novel model inference criteria for sparse measurements, which results in more informative models along time. We propose two novel differential tests for time-series, that both allow significance testing at non-observed time-points. We apply the extended GPR model for analysis of differential expression of irradiated human umbilical vein endothelial cell (HUVEC) transcriptomics dataset.