Effect of environmental stress on regulation of gene expression in the yeast

• Transcriptional responses to external stimuli are modeled using ODE with an unknown forcing term.
• Hyperparameters are estimated using Gaussian Process priors and type II maximum likelihood.
• State-space trajectories representing signature responses to different environmental stimuli are generated.

Several mathematical models have been proposed to predict the activation state of a transcription factor (TF) from the expression levels of its target genes. This inference problem is complicated however due to the fact that different genes may be regulated by different activation schemes (linear, exponential, sigmoidal, etc.). In addition to transcription regulation, the rate of gene expression at any instantaneous point in time is also determined by the independent rates of baseline production and degradation. Consequently, the set of solutions to any model equations describe an infinite number of trajectories in probability space, thus rendering the problem NP-hard. In the current study we used a Gaussian process (GP) approach to address this inverse problem. Experimental gene expression data were modeled by a putative linear activation scheme and discrepancy between theory and experiment was modeled by a GP. Model hyperparameters were calculated using maximum likelihood estimates to generate continuous TF state-space profiles. Identifiability of model parameters was optimized by obtaining TF state-space functions for multiple genes simultaneously. We found that model parameters were sensitive to environmental stress conditions, producing different state-space profiles for different stresses.