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.