The in vivo measure and mathematical modeling of protein turnover in multiple biological compartments and across patient cohorts

Beyond the knowledge of protein abundance in various tissues, there is great interest in the turnover or dynamics of proteins. Protein turnover is the net rate at which proteins are produced or imported in a tissue, and simultaneously degraded or cleared. This complementary perspective to protein abundance is relevant in a number of applications. For example, abnormal turnover has been observed for specific proteins such as amyloid-β (Aβ), Tau, or sTREM2 in Alzheimer disease (AD) (Mawuenyega et al., 2010; Sato et al., 2018; Suárez-Calvet et al., 2016) or retinol-binding protein 4 (RBP4) in diabetes (Jourdan et al., 2009).

Turnover data are typically acquired by mass spectrometry (MS) after introducing isotopic tracers to label the newly synthesized proteins. The ratio of labeled versus unlabeled protein peptide abundances is called the relative isotope abundance (RIA). Summarized at the protein level, the variation of RIA over time provides turnover information. We have developed both targeted and genome-wide methods (Lehmann et al., 2015 & 2019) based on the stable isotope labeling kinetics (SILK) protocol relying on 13C6-Leu intravenous injection (Bateman et al., 2006). Injection lasts for 9 hours and serial proteome acquisitions are performed from time 0 to 24 hours or longer.

Here, applying concepts of population pharmacodynamics, we show how turnover data obtained from patient cerebrospinal fluid (CSF) and blood plasma can be modeled both at the cohort and individual levels. Data were obtained from 4 individuals in CSF and 7 in plasma (Fig. 1A). Mathematical modeling was based on differential equation coupled with Bayesian statistics. We discuss how such models can enable inter-cohort statistical tests to identify altered turnover.

Then, applying notions of pharmacokinetics, we modeled genome-wide turnover data obtained from plasma and CSF simultaneously from a same individual. The new mathematical model entails the modeling of a hidden central nervous system (CNS) compartment to properly model passages from blood to CSF and vice versa (Fig. 1B). We show that the observed dynamics in plasma and CSF can be similar or rather different, and in certain configurations this strongly constrain the dynamics in the CNS, i.e. we can accurately infer an average CNS turnover. In other configurations, the CNS contribution seems less crucial and hence the CNS turnover is vaguely inferred only (Fig. 1C).

Lastly, we will present unpublished turnover data of a cohort of Alzheimer patients modeled both at the cohort and 2-biological compartment levels.

Figure 1. (A) Population and individual dynamics in plasma for 7 patients. (B) Barriers between CSF, plasma and CNS. (C) Simultaneous dynamics in CSF and plasma along with inferred CNS dynamics (k_ij = rates of passage, k_i = clearance rate, l_i = amplitude).