Parameter inference for a stochastic kinetic model of expanded polyglutamine proteins

TL;DR

This paper develops a Gaussian process-based inference method to estimate parameters in a stochastic model of polyglutamine protein aggregation, providing new biological insights despite limited and noisy data.

Contribution

It introduces an efficient inference approach using Gaussian process emulators for a stochastic kinetic model of protein aggregation, addressing computational challenges and data uncertainty.

Findings

Identified key parameters influencing protein aggregation kinetics.

Demonstrated the effectiveness of Gaussian process emulators in inference.

Provided biological insights into the aggregation process.

Abstract

The presence of protein aggregates in cells is a known feature of many human age-related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutamine (PolyQ) proteins in cells have been used to gain a better understanding of the biological system, how to focus drug development and how to construct more efficient designs of future laboratory-based in vitro experiments. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly and so they are estimated within the inference algorithm by repeatedly simulating realisations from the model. In general such an approach is computationally very expensive and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by examining the fit of our model and highlight appropriate values of the model parameters leading to new insights into the underlying biological processes such as the kinetics of aggregation.