Gaussian Process Modeling of Protein Turnover

We describe a stochastic model to compute in vivo protein turnover rate constants from stable-isotope labeling and high-throughput liquid chromatography–mass spectrometry experiments. We show that the often-used one- and two-compartment nonstochastic models allow explicit solutions from the corresponding stochastic differential equations. The resulting stochastic process is a Gaussian processes with Ornstein–Uhlenbeck covariance matrix. We applied the stochastic model to a large-scale data set from 15N labeling and compared its performance metrics with those of the nonstochastic curve fitting. The comparison showed that for more than 99% of proteins, the stochastic model produced better fits to the experimental data (based on residual sum of squares). The model was used for extracting protein-decay rate constants from mouse brain (slow turnover) and liver (fast turnover) samples. We found that the most affected (compared to two-exponent curve fitting) results were those for liver proteins. The ratio of the median of degradation rate constants of liver proteins to those of brain proteins increased 4-fold in stochastic modeling compared to the two-exponent fitting. Stochastic modeling predicted stronger differences of protein turnover processes between mouse liver and brain than previously estimated. The model is independent of the labeling isotope. To show this, we also applied the model to protein turnover studied in induced heart failure in rats, in which metabolic labeling was achieved by administering heavy water. No changes in the model were necessary for adapting to heavy-water labeling. The approach has been implemented in a freely available R code.