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 polyglutaime (PolyQ) proteins in cells have been used to gain a better understanding of the biological system. 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 measurementerror. 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 realizations 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 highlighting appropriate values of the model parameters leading to new insights into the underlying biologicalprocesses.
Highlights
One of the main aims of modelling biological systems is to describe and understand the temporal evolution of the system taking account of the potentially complex inter-relationships between components within the system
Models can be used to facilitate in silico experiments in which virtual experiments are performed on a computer. These in silico experiments have an advantage over laboratory-based experiments as, in general, they are much cheaper and faster to conduct. This can lead to a better understanding of, for example, the biological system, how to focus drug development and how to construct more efficient designs of future laboratory-based in vitro experiments
A method for determining the posterior distribution for model quantities is described in Section 5 and, because a standard simulation-based MCMC solution is prohibitively expensive, we develop Gaussian process emulators in Section 6 which facilitate timely generation of realisations from the posterior distribution
Summary
One of the main aims of modelling biological systems is to describe and understand the temporal evolution of the system taking account of the potentially complex inter-relationships between components within the system. There has been considerable controversy over which stage of the aggregation process is most toxic to cells, and it has been suggested that the formation of large inclusion bodies may be protective as they sequester misfolded proteins and prevent the overload of protein degradation pathways (Ross and Poirier 2004) This has been shown experimentally in cell culture (Arrasate, Mitra et al 2004). The controversy regarding cytoxicity of PolyQ proteins is largely due to insufficient understanding of the molecular mechanisms involved This motivated our previous study which used live cell imaging with fluorescent reporter systems to examine the relationship between PolyQ protein, activation of the stress kinase p38MAPK (MAPK14; HGNC:6876 ), reactive oxygen species (ROS) generation, inhibition of the proteasome (a protein complex which degrades cellular proteins), and formation of PolyQ nuclear inclusions (Tang, Proctor et al 2010). Approaches which replace the continuous-time stochastic model with a discrete-time approximation include tau-leaping (Gillespie, 2001; Cao et al, 2006) and the chemical Langevin equation (Gillespie, 2000; van Kampen, 2001)
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