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Dynamics and Bifurcation Analysis of the Heat-Shock Response In Eukaryotic Cells

Dimitrios I. Gerogiorgis, Department of Chemical Engineering, Massachusetts Institute of Technology (M.I.T.), 77 Massachusetts Avenue, Cambridge, MA 02139

The heat-shock response mechanism in eukaryotic cells is a vital and therefore ubiquitous molecular reaction to proteotoxicity resulting from the appearance of various classes of non-native (misfolded and damaged) proteins. The accumulation of such non-native protein species can result in the dangerous generation of protein aggregates. To handle this build-up of abnormal proteins, cells employ a complicated machinery of molecular chaperones: these species facilitate the refolding or degradation of misfolded polypeptides, prevent protein aggregation and play a role in formation of aggresome, a centrosome-associated body to which small cytoplasmic aggregates are transported. Protein folding and aggregates have been studied in the domain of neurochemistry and molecular neurobiology, and they are increasingly recognized as responsible for the progression of serious neurodegenerative diseases, which have a severe impact on progressively larger populations. These include Alzheimer's, Parkinson's and Huntington's diseases, and in addition Amyotrophic Lateral Sclerosis (Meriin and Sherman, 2005; Szilagyi, Kardos et al., 2007).

The heat-shock adaptation and survival mechanism is aimed at ensuring protein quality control and homeostasis. The transcriptional induction of genes encoding molecular chaperones and protein degradation mechanisms is a means of efficient management of misfolded and damaged proteins, against the likelihood of the latter persisting as proteotoxic species, protein aggregates, and inclusions. Computational analysis of a mathematical model of the heat-shock network, presented here, led to the identification of the elementary steps that may represent key determinants of network performance.

The central elements of this process are the heat-shock proteins (HSPs) that function as molecular chaperones. Upon sensing a stress signal, such as elevated temperatures, small toxic molecules, oxidants, or heavy metals, cells resort to transient molecular chaperone overexpression whose target is to meet the stress demand by high levels. Chaperones recognize and associate with exposed hydrophobic patches on unfolded polypeptides and conformational intermediates and sequester them uintil they reach their native confirmation by providing an environment for proper refolding, or act as an escort to the proteosomes for orderly degradation.

The importance and function of the heat-shock transcription factor-1 (HSF-1), which is central to the heat-shock response mechanism, has been studied extensively, as documented in numerous publications. Detailed network representations and dynamic mathematical models have been derived and tested in order to analyze quantitatively all species and their concentrations in the heat-shock response cycle. Furthermore, parameter estimation and sensitivity analysis have provided additional insight regarding the relative importance of a large number of kinetic parameters in the respective expression networks. This paper focuses on analyzing the importance of an uncertain, temperature-dependent parameter (bm,k) and conducting a bifurcation analysis with respect to an uncertain parameter, in order to evaluate multiplicity.

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