Alessio Paris (1), Pranami Bora (1), Silvia Parolo (1), Michael Monine (2), Xiao Tong (2), Satish Eraly (2), Alex McCampbell (2), Danielle Graham (2), Toby Ferguson (2), Enrico Domenici (1,3), Ivan Nestorov (2), Luca Marchetti (1)
(1) Fondazione The Microsoft Research - University of Trento Centre for Computational and Systems Biology (COSBI), (2) Biogen, Inc., Cambridge, Massachusetts, USA, (3) University of Trento, Department of Cellular, Computational and Integrative Biology - CIBIO
Objectives: Neurofilaments (NFs) are cytoskeletal proteins of the neurons present mainly in the axons. Following axonal injury, NFs are released into the surrounding interstitial fluid and they can be detected in the periphery, thus serving as potential biomarkers of neuronal damage [1]. The objective of this work was to develop a mathematical model of NF trafficking from the nervous system to the periphery in healthy subjects, providing a base framework for the investigation of NF dynamics in neurodegenerative diseases.
Methods: The model was implemented based on three distinct modules, one for each NF subunit: NF light (NFL), medium (NFM) and heavy (NFH). Each module consists of 7 Ordinary Differential Equations (ODEs) describing the evolution in time of the NF concentration in the different compartments: central nervous system neurons, peripheral nervous system neurons, interstitial fluid (ISF), endoneurial fluid, cranial cerebrospinal fluid (CSF), spinal CSF and blood. While a set of model reaction rates was assumed to be identical for all the three NF subunits (for example, the transport of NFs from the ISF to the CSF and from CSF to blood), other reactions, such as the leakage of NFs from the neurons and the clearance of NFs in blood, were assumed to have a different rate among the NFs subunits. We estimated these previously unknown parameters as mass-action rate constants by fitting at steady state the CSF and blood NF concentrations derived from literature [2-5]. Dependence on age was also explicitly considered in the model by including in the equations the formula introduced in [2] and by checking the capability of the model in reproducing the experimental data on the NF levels in the CSF at different ages provided in the same paper. The final model has been then deeply analyzed by simulation and global sensitivity analysis. The ODE system and all the analyses were implemented as a collection of R scripts, using R libraries for numerical integration and analysis [6].
Results: The calibration of the model at steady state allowed us to estimate the parameters of the model that could not be recovered from literature. We then performed a global sensitivity analysis to highlight the factors that mostly affect the dynamics at steady state. This analysis allowed us to rank the parameters according to their sensitivity values and to identify a set of them critical for the entire system, such as the synthesis and degradation reactions of NFs in neurons. Conversely, other parameters, such as the NF blood clearance, demonstrated to affect the NF dynamics only in specific model compartments. Model sensitivity analysis also highlighted the importance of the age-dependence of NF levels in the periphery. In addition to the steady-state global sensitivity analysis, we also investigated the effect of single parameter variations on the overall model dynamics. Our results showed that some parameters have only a transient effect on NF concentrations, while others, upon perturbation, take the biological system to a new steady state. To assess the impact on the NF dynamics of the uncertainty in parameter estimates, we finally computed the percentage variation of the NF concentration in each model compartment as a function of the percentage of parameter perturbation. In this way, we were able to classify the model parameters into three groups, according to their predicted quantitative effect on the model dynamics (strong/weak/negligible). This classification can be potentially used to prioritize wet lab experiments to decrease the estimation uncertainty of the more critical parameters.
Conclusions: The NF platform described here provides a deterministic mathematical model of NF trafficking in healthy subjects. The model links neuron-specific processes to NF levels in peripheral compartments, especially in blood, where NFs can be easily measured. This implementation serves as a base framework that will be extended to investigate the role of NFs as biomarkers of disease-associated neurodegeneration.
References:
[1] Khalil M et al. Nat Rev Neurol.14:577-589, 2018
[2] Yilmaz A et al. Expert Review of Molecular Diagnostics 17 (8): 761-70, 2017
[3] Martínez-Morillo e et al. Clinical Chemistry and Laboratory Medicine (CCLM) 53 (10): 1575-84, 2015
[4] De Schaepdryver M et al. Journal of Neurology, Neurosurgery & Psychiatry 89 (4): 367-73, 2016
[5] Disanto G et al. Journal of Neurology, Neurosurgery, and Psychiatry 87 (2): 126-9. 2016
[6] Soetaert K https://cran.r-project.org/web/packages/rootSolve/vignettes/rootSolve.pdf (2014).
Reference: PAGE () Abstr 9240 [www.page-meeting.org/?abstract=9240]
Poster: Oral: Methodology - New Modelling Approaches