Heat Shock Response In Eukaryotes Research Articles

Abstract LB234: Activation of the integrated stress response by the developmental HSF1 pathway inhibitor NXP800

Abstract HSF1 is a stress-inducible transcription factor that regulates the eukaryotic heat shock response (HSR). HSF1 activation induces the expression of multiple proteins needed for cellular recovery from stress. HSF1 also plays a key role in tumorigenesis and regulates the expression of a cancer-specific gene signature which is unique to malignant cells and distinct from that activated during the HSR. We discovered NXP800, the first-in-class orally active HSF1 pathway inhibitor which is now undergoing Phase 1 clinical trial, based on a phenotypic pathway screen. Here we employed various techniques to investigate the mechanism of action of NXP800. Using RNAseq in a panel of human carcinoma cell lines, we identified overlapping gene expression changes in response to NXP800. These included genes regulated by HSF1 and interestingly also genes associated with activation of the integrated stress response (ISR). In contrast, we found no evidence for activation of the unfolded protein response. Consistent with the observed NXP800-induced phosphorylation of eIF2α which is a critical regulator of the ISR, NXP800 increased the protein expression of downstream ISR markers ATF4, CHOP and CHAC1, both in human tumor cells in vitro and in human tumor xenograft models in vivo. Induction of the ISR is controlled by four stress-activated protein kinases (PKs) that phosphorylate eIF2α. To further explore these kinases in the mechanism of action of NXP800 we used genetic knockdown by siRNA and inhibition by small-molecule tool compounds. Silencing each of the ISR-regulatory PKs revealed that GCN2 was required for ISR activation by NXP800. This was confirmed using two GCN2 inhibitors from different chemical series. Global phospho-proteome analysis showed that altered protein phosphorylation following NXP800 exposure was reversed upon co-treatment with a GCN2 inhibitor. We also demonstrated that activation of the ISR caused inhibition of HSF1 activation when stimulated with an HSF1 activator, thus confirming the link between ISR induction and inhibition of HSF1 activation. Activation of GCN2 and the ISR can occur in response to a variety of stimuli including amino acid deprivation. However, we did not detect a difference in the uptake of amino acids following exposure to NXP800, indicating that NXP800 does not directly impair amino acid uptake. Using an siRNA approach to determine if activation of the ISR components was contributing to growth inhibition following NXP800 exposure, we found that blocking the induction of ATF4 reduced the response of NXP800-sensitive SK-OV-3 human ovarian carcinoma cells to NXP800 treatment. In summary, NXP800 acts on cancer cells to induce activation of the ISR pathway via GCN2, which then leads to inhibition of HSF1 activation. Further studies are underway to determine the precise molecular target of NXP800 and the mechanism of HSF1 pathway inhibition. Citation Format: Marissa V. Powers, Swee Y. Sharp, Eirini-Maria Lampraki, Toby Roe, Loredana Pellegrino, Maria Taskinen, Robert te Poele, Florence Raynaud, Suzanne Eccles, Matthew Cheeseman, Keith Jones, Paul A. Clarke, Paul Workman. Activation of the integrated stress response by the developmental HSF1 pathway inhibitor NXP800 [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 2 (Clinical Trials and Late-Breaking Research); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(8_Suppl):Abstract nr LB234.

98 (PB088) - Discovery and validation of biomarkers to support clinical development of NXP800: A first-in-class orally active, small-molecule HSF1 pathway inhibitor

Background: Heat Shock Factor (HSF1) is a stress-inducible transcription factor that plays a key role in the activation of the eukaryotic heat shock response. HSF1 is hijacked by cancer cells to activate a set of genes that overlap with, but are not identical to, the classical heat shock response. Whereas the HSF1 pathway has been shown to play a key role in oncogenesis and multiple hallmark features of malignancy in experimental cancers, and its amplification/expression/activity correlates with poor clinical outcome, knockout of HSF1 does not impair viability in model organisms – suggesting a potential therapeutic window.

Abstract ND08: NXP800: A first-in-class orally active, small-molecule HSF1 pathway inhibitor

Abstract We report the discovery of NXP800 — a first-in-class orally active HSF1 pathway inhibitor identified in our academic laboratory at the Institute of Cancer Research, London — and its progression into Phase I clinical trials in collaboration with our partner Nuvectis Pharma. HSF1 (Heat Shock Factor 1) is an ancient stress-inducible transcription factor that plays a key role in the transcriptional activation of the eukaryotic heat shock response. This leads to expression of many heat shock proteins, including molecular chaperones, and through this HSF1 acts as a master transcriptional regulator of proteostasis. Importantly, HSF1 is hijacked by cancer cells to activate a set of genes that overlaps with, but is not identical to, the classical heat shock response. The HSF1 pathway has been shown to play a key role in oncogenesis and the hallmark features of malignancy and is important in the initiation and progression of many experimental cancer models. Importantly, while HSF1 has been demonstrated to be important in mouse models of oncogenesis, knockout of the homologue of HSF1 has only modest effects in mice and flies under non-stressed laboratory conditions – supporting the potential for a therapeutic window. In addition, gene amplification, expression and activation of HSF1 has been shown to predict clinical outcome in many human cancers. Despite strong scientific rationale and pre-clinical validation, pharmaceutical exploitation has been limited because analysis of the available molecular structures of HSF1 shows it to be very difficult to drug. Because of this, we set out to discover inhibitors of the HSF1 pathway using an initial phenotypic screen that reports on the activation of the HSF1-regulated gene HSP72. This identified the bisamide series that was followed up by a detailed understanding of structure-activity relationships and medicinal chemistry optimization, particularly to improve pharmaceutical properties, leading to the selection of NXP800 (CCT361814) as the development candidate. NXP800 has good pharmacokinetic properties in mice, including oral bioavailability; also, pharmacodynamic studies show modulation of biomarkers of the HSF1 pathway and stress response in human tumour xenograft models. NXP800 exhibits striking therapeutic activity in xenografts of human ovarian clear cell ovarian cancer (OCCC) and endometrioid ovarian cancer, two serious conditions of high unmet medical need with limited treatment options – including prolonged tumour growth inhibition and regression at doses that show good toleration. The efficacy and tolerability data indicate a clear therapeutic window, supported by selectivity and safety profiting in pharmacology and kinome panels. In addition, we identified deficiency in ARID1A, a component of the SWI/SNF chromatin remodelling complex, as indicative of greater therapeutic responsiveness. This was confirmed through broader evaluation in human cancer cell line panels that also indicates therapeutic potential for NXP800 in additional cancer types. Studies to support mechanism of action and identify patient selection biomarkers will be described. A Phase 1 trial of NXP800 is now open, incorporating validated predictive, pharmacokinetic and pharmacodynamic biomarkers that provide a robust Pharmacological Audit Trail and support the prediction of dose-to-human. Citation Format: Paul Workman. NXP800: A first-in-class orally active, small-molecule HSF1 pathway inhibitor [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr ND08.

Scalable reaction network modeling with automatic validation of consistency in Event-B

Constructing a large biological model is a difficult, error-prone process. Small errors in writing a part of the model cascade to the system level and their sources are difficult to trace back. In this paper we extend a recent approach based on Event-B, a state-based formal method with refinement as its central ingredient, allowing us to validate for model consistency step-by-step in an automated way. We demonstrate this approach on a model of the heat shock response in eukaryotes and its scalability on a model of the mathsf {ErbB} signaling pathway. All consistency properties of the model were proved automatically with computer support.

Transient intracellular acidification regulates the core transcriptional heat shock response.

Heat shock induces a conserved transcriptional program regulated by heat shock factor 1 (Hsf1) in eukaryotic cells. Activation of this heat shock response is triggered by heat-induced misfolding of newly synthesized polypeptides, and so has been thought to depend on ongoing protein synthesis. Here, using the budding yeast Saccharomyces cerevisiae, we report the discovery that Hsf1 can be robustly activated when protein synthesis is inhibited, so long as cells undergo cytosolic acidification. Heat shock has long been known to cause transient intracellular acidification which, for reasons which have remained unclear, is associated with increased stress resistance in eukaryotes. We demonstrate that acidification is required for heat shock response induction in translationally inhibited cells, and specifically affects Hsf1 activation. Physiological heat-triggered acidification also increases population fitness and promotes cell cycle reentry following heat shock. Our results uncover a previously unknown adaptive dimension of the well-studied eukaryotic heat shock response.

HSF1: Primary Factor in Molecular Chaperone Expression and a Major Contributor to Cancer Morbidity.

Heat shock factor 1 (HSF1) is the primary component for initiation of the powerful heat shock response (HSR) in eukaryotes. The HSR is an evolutionarily conserved mechanism for responding to proteotoxic stress and involves the rapid expression of heat shock protein (HSP) molecular chaperones that promote cell viability by facilitating proteostasis. HSF1 activity is amplified in many tumor contexts in a manner that resembles a chronic state of stress, characterized by high levels of HSP gene expression as well as HSF1-mediated non-HSP gene regulation. HSF1 and its gene targets are essential for tumorigenesis across several experimental tumor models, and facilitate metastatic and resistant properties within cancer cells. Recent studies have suggested the significant potential of HSF1 as a therapeutic target and have motivated research efforts to understand the mechanisms of HSF1 regulation and develop methods for pharmacological intervention. We review what is currently known regarding the contribution of HSF1 activity to cancer pathology, its regulation and expression across human cancers, and strategies to target HSF1 for cancer therapy.

Hsf1 and Hsp70 constitute a two-component feedback loop that regulates the yeast heat shock response.

Models for regulation of the eukaryotic heat shock response typically invoke a negative feedback loop consisting of the transcriptional activator Hsf1 and a molecular chaperone. Previously we identified Hsp70 as the chaperone responsible for Hsf1 repression and constructed a mathematical model that recapitulated the yeast heat shock response (Zheng et al., 2016). The model was based on two assumptions: dissociation of Hsp70 activates Hsf1, and transcriptional induction of Hsp70 deactivates Hsf1. Here we validate these assumptions. First, we severed the feedback loop by uncoupling Hsp70 expression from Hsf1 regulation. As predicted by the model, Hsf1 was unable to efficiently deactivate in the absence of Hsp70 transcriptional induction. Next, we mapped a discrete Hsp70 binding site on Hsf1 to a C-terminal segment known as conserved element 2 (CE2). In vitro, CE2 binds to Hsp70 with low affinity (9 µM), in agreement with model requirements. In cells, removal of CE2 resulted in increased basal Hsf1 activity and delayed deactivation during heat shock, while tandem repeats of CE2 sped up Hsf1 deactivation. Finally, we uncovered a role for the N-terminal domain of Hsf1 in negatively regulating DNA binding. These results reveal the quantitative control mechanisms underlying the heat shock response.

Transcriptional Regulation of the Ambient Temperature Response by H2A.Z Nucleosomes and HSF1 Transcription Factors in Arabidopsis

Temperature influences the distribution, range, and phenology of plants. The key transcriptional activators of heat shock response in eukaryotes, the heat shock factors (HSFs), have undergone large-scale gene amplification in plants. While HSFs are central in heat stress responses, their role in the response to ambient temperature changes is less well understood. We show here that the warm ambient temperature transcriptome is dependent upon the HSFA1 clade of Arabidopsis HSFs, which cause a rapid and dynamic eviction of H2A.Z nucleosomes at target genes. A transcriptional cascade results in the activation of multiple downstream stress-responsive transcription factors, triggering large-scale changes to the transcriptome in response to elevated temperature. H2A.Z nucleosomes are enriched at temperature-responsive genes at non-inducible temperature, and thus likely confer inducibility of gene expression and higher responsive dynamics. We propose that the antagonistic effects of H2A.Z and HSF1 provide a mechanism to activate gene expression rapidly and precisely in response to temperature, while preventing leaky transcription in the absence of an activation signal.

Cellular thermotolerance is independent of HSF 1 expression in zebu and crossbred non-lactating cattle.

Heat stress is an important domain of research in livestock due to its negative impact on production and disease resistance. The augmentation of stress in the body stimulates the antioxidative activity comprising various enzymes (viz., catalase, superoxide dismutase), metabolites (reduced glutathione, etc.), vitamins, minerals, etc. to combat the situation. The major key players involved in regulation of heat shock response in eukaryotes are the transcription factors, called as heat shock factors (HSF). They activate the heat shock protein (HSP) genes by binding to their promoters. Lymphocytes are considered to be the best model to evaluate the immunity in any living body as it contains plethora of white blood cells (WBCs).In this study, the peripheral blood mononuclear cells (PBMC) obtained from non-lactating Sahiwal vis-à-vis crossbred (Holstein Friesian × Sahiwal) cattle with 75% or more exotic inheritance were subjected to heat shock at 39, 41, and 43°C in three different incubators, in vitro. The cell count and viability test of pre and post heat stress of concerned PBMCs indicated that the crossbreeds are more prone to heat stress as compared to Sahiwal. The reverse transcription PCR (qRT-PCR) expression data revealed an increment in HSF1 expression at 41°C which subsequently declined (non-significantly) at 43°C in both breeds post 1h heat shock. However, the association between the HSF 1 expression and antioxidative activity through correlation analysis was found to be non-significant (P<0.05), though enzymatic activity appeared to behave in a similar fashion in both breeds at 5% level of significance (P<0.05). This rule out the role of HSF1 expression level on the activity of enzymes involved in oxidative stress in vitro in zebu and crossbred cattle.

Heat Shock RNA 1, Known as a Eukaryotic Temperature-Sensing Noncoding RNA, Is of Bacterial Origin

Heat shock RNA 1 (HSR1) is described as a "eukaryotic heat-sensing noncoding RNA" that regulates heat shock response in human and other eukaryotic cells. Highly conserved HSR1 sequences have been identified from humans, hamsters, Drosophila, Caenorhabditis elegans, and Arabidopsis. In a previous study, however, it was suggested that HSR1 had originated from a bacterial genome. HSR1 showed no detectible nucleotide sequence similarity to any eukaryotic sequences but harbored a protein coding region that showed amino-acid sequence similarity to bacterial voltage-gated chloride channel proteins. The bacterial origin of HSR1 was not convincible because the nucleotide sequence similarity was marginal. In this study, we have found that a genomic contig sequence of Comamonas testosteroni strain JL14 contained a sequence virtually identical to that of HSR1, decisively confirming the bacterial origin of HSR1. Thus, HSR1 is an exogenous RNA, which can ectopically trigger heat shock response in eukaryotes. Therefore, it is no longer appropriate to cite HSR1 as a "eukaryotic functional noncoding RNA."

FBXW7 modulates cellular stress response and metastatic potential through ​HSF1 post-translational modification.

Heat-shock factor 1 (HSF1) orchestrates the heat-shock response in eukaryotes. Although this pathway has been evolved to help cells adapt in the presence of challenging conditions, it is co-opted in cancer to support malignancy. However, the mechanisms that regulate HSF1 and thus cellular stress response are poorly understood. Here we show that the ubiquitin ligase FBXW7 α interacts with HSF1 through a conserved motif phosphorylated by GSK3β and ERK1. FBXW7α ubiquitylates HSF1 and loss of FBXW7α results in impaired degradation of nuclear HSF1 and defective heat-shock response attenuation. FBXW7α is either mutated or transcriptionally downregulated in melanoma and HSF1 nuclear stabilization correlates with increased metastatic potential and disease progression. FBXW7α deficiency and subsequent HSF1 accumulation activates an invasion-supportive transcriptional program and enhances the metastatic potential of human melanoma cells. These findings identify a post-translational mechanism of regulation of the HSF1 transcriptional program both in the presence of exogenous stress and in cancer.

Genome-wide analysis of the Hsf family in soybean and functional identification of GmHsf-34 involvement in drought and heat stresses.

BackgroundHigh temperature affects organism growth and metabolic activity. Heat shock transcription factors (Hsfs) are key regulators in heat shock response in eukaryotes and prokaryotes. Under high temperature conditions, Hsfs activate heat shock proteins (Hsps) by combining with heat stress elements (HSEs) in their promoters, leading to defense of heat stress. Since the first plant Hsf gene was identified in tomato, several plant Hsf family genes have been thoroughly characterized. Although soybean (Glycine max), an important oilseed crops, genome sequences have been available, the Hsf family genes in soybean have not been characterized accurately.ResultWe analyzed the Hsf genetic structures and protein function domains using the GSDS, Pfam, SMART, PredictNLS, and NetNES online tools. The genome scanning of dicots (soybean and Arabidopsis) and monocots (rice and maize) revealed that the whole-genome replication occurred twice in soybean evolution. The plant Hsfs were classified into 3 classes and 16 subclasses according to protein structure domains. The A8 and B3 subclasses existed only in dicots and the A9 and C2 occurred only in monocots. Thirty eight soybean Hsfs were systematically identified and grouped into 3 classes and 12 subclasses, and located on 15 soybean chromosomes. The promoter regions of the soybean Hsfs contained cis-elements that likely participate in drought, low temperature, and ABA stress responses. There were large differences among Hsfs based on transcriptional levels under the stress conditions. The transcriptional levels of the A1 and A2 subclass genes were extraordinarily high. In addition, differences in the expression levels occurred for each gene in the different organs and at the different developmental stages. Several genes were chosen to determine their subcellular localizations and functions. The subcellular localization results revealed that GmHsf-04, GmHsf-33, and GmHsf-34 were located in the nucleus. Overexpression of the GmHsf-34 gene improved the tolerances to drought and heat stresses in Arabidopsis plants.ConclusionsThis present investigation of the quantity, structural features, expression characteristics, subcellular localizations, and functional roles provides a scientific basis for further research on soybean Hsf functions.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2164-15-1009) contains supplementary material, which is available to authorized users.

Function of Hsf1 in SV40 T-antigen-transformed HEK293T cells

Heat shock factor 1 (HSF1), a main regulator of the heat shock response in eukaryotes, increases cell survival in numerous pathophysiological conditions. The aim of the present study was to o bserve the function of defective HSF1 expression in HEK293T cells. shRNA of human HSF1 was constructed into the retroviral vector pLTHR generating pLTHR‑shRNA‑HSF1. The shRNA was transiently transfected into HEK293T cells to silence the expression of the HSF1 gene. Cell colony formation, MTT and cell cycle assays were used to analyze the SV40 T‑antigen (Ag)‑transformed cell proliferation rate. Immunoblotting was used to study the protein expression of HSF1, SV40 T‑Ag, p53, p21, heat shock protein 90 (Hsp90), Hsp70 and Hsp25. The results revealed that a deficiency in HSF1 expression inhibited cellular growth. Defective HSF1 upregulated the protein expression of p53, retinoblastoma protein (Rb) and SV40 T‑Ag, and reduced the association between SV40 T‑Ag and p53/Rb, which resulted in growth inhibition of SV40 T‑Ag‑transformed cells. In conclusion, HSF1 is involved in the regulation of SV40 T‑Ag‑induced cell growth and modulates the expression of p53 and Rb proteins.

Biology of the Heat Shock Response and Protein Chaperones: Budding Yeast (Saccharomyces cerevisiae) as a Model System

The eukaryotic heat shock response is an ancient and highly conserved transcriptional program that results in the immediate synthesis of a battery of cytoprotective genes in the presence of thermal and other environmental stresses. Many of these genes encode molecular chaperones, powerful protein remodelers with the capacity to shield, fold, or unfold substrates in a context-dependent manner. The budding yeast Saccharomyces cerevisiae continues to be an invaluable model for driving the discovery of regulatory features of this fundamental stress response. In addition, budding yeast has been an outstanding model system to elucidate the cell biology of protein chaperones and their organization into functional networks. In this review, we evaluate our understanding of the multifaceted response to heat shock. In addition, the chaperone complement of the cytosol is compared to those of mitochondria and the endoplasmic reticulum, organelles with their own unique protein homeostasis milieus. Finally, we examine recent advances in the understanding of the roles of protein chaperones and the heat shock response in pathogenic fungi, which is being accelerated by the wealth of information gained for budding yeast.

Quantitative Model Refinement as a Solution to the Combinatorial Size Explosion of Biomodels

Building a large system through a systematic, step-by-step refinement of an initial abstract specification is a well established technique in software engineering, not yet much explored in systems biology. In the case of systems biology, one starts from an abstract, high-level model of a biological system and aims to add more and more details about its reactants and/or reactions, through a number of consecutive refinement steps. The refinement should be done in a quantitatively correct way, so that (some of) the numerical properties of the model (such as the experimental fit and validation) are preserved. In this study, we focus on the data-refinement mechanism where the aim is to increase the level of details of some of the reactants of a given model. That is, we analyse the case when a model is refined by substituting a given species by several types of subspecies. We show in this paper how the refined model can be systematically obtained from the original one. As a case study for this methodology we choose a recently introduced model for the eukaryotic heat shock response, [I. Petre, A. Mizera, C. L. Hyder, A. Meinander, A. Mikhailov, R.I. Morimoto, L. Sistonen, J. E. Eriksson, R.-J. Back, A simple mass-action model for the eukaryotic heat shock response and its mathematical validation, Natural Computing, 10(1), 595–612, 2011.]. We refine this model by including details about the acetylation of the heat shock factors and its influence on the heat shock response. The refined model has a significantly higher number of kinetic parameters and variables. However, we show that our methodology allows us to preserve the experimental fit/validation of the model with minimal computational effort.

A Boolean Approach for Disentangling the Roles of Submodules to the Global Properties of a Biomodel

To disentangle the numerical contribution of modules to the system-level behavior of a given biomodel, one often considers knock-out mutant models, investigating the change in the model behavior when modules are systematically included and excluded from the model architecture in all possible ways. We propose in this paper a Boolean approach for extracting conclusions about the role of each module from the systematic comparison of the numerical behavior of all knock-out mutants. We associate a Boolean variable to each module, expressing when the module is included in the architecture and when it is not. We can then express the satisfiability of system-level properties of the full model, such as efficiency, or economical use of resources, in terms of a Boolean formula expressing in a compact way which model architectures, i.e., which combinations of modules, give rise to the desired property. We demonstrate this method on a recently proposed computational model for the heat shock response in eukaryotes. We describe the contribution of each of its three feedback loops towards achieving an economical and effective heat shock response.

Methods for Biochemical Model Decomposition and Quantitative Submodel Comparison

AbstractComparing alternative models for a given biochemical system is in general a very difficult problem: the models may focus on different aspects of the same system and may consist of very different species and reactions. The numerical setups of the models also play a crucial role in the quantitative comparison. When the alternative designs are submodels of a reference model, for example, knockdown mutants of a model, the problem of comparing them becomes simpler: they all have very similar, although not identical, underlying reaction networks, and the biological constraints are given by those in the reference model. In the first part of our study, we review several known methods for model decomposition and for quantitative comparison of submodels. We describe knockdown mutants, elementary flux modes, control‐based decomposition, mathematically controlled comparison and its extension, local submodel comparison and a discrete approach for comparing continuous submodels. In the second part of the paper we present a new statistical method for comparing submodels, which complements the methods presented in the review. The main difference between our approach and the known methods is related to the important question of how to chose the numerical setup in which to perform the comparison. In the case of the reviewed methods, the comparison is made in the numerical context of the reference model, i.e., in each of the alternative models both the kinetics of the reactions and the initial values of all variables are chosen to be identical to those from the reference model. We propose in this paper a different approach, better suited for response networks, where each alternative model is assumed to start from its own steady state under basal conditions. We demonstrate our approach with a case study focusing on the heat shock response in eukaryotes.

A simple mass-action model for the eukaryotic heat shock response and its mathematical validation

The heat shock response is a primordial defense mechanism against cell stress and protein misfolding. It proceeds with the minimum number of mechanisms that any regulatory network must include, a stress-induced activation and a feedback regulation, and can thus be regarded as the archetype for a cellular regulatory process. We propose here a simple mechanistic model for the eukaryotic heat shock response, including its mathematical validation. Based on numerical predictions of the model and on its sensitivity analysis, we minimize the model by identifying the reactions with marginal contribution to the heat shock response. As the heat shock response is a very basic and conserved regulatory network, our analysis of the network provides a useful foundation for modeling strategies of more complex cellular processes.

Modelling of ultrasound therapeutic heating and numerical study of the dynamics of the induced heat shock response

In this presentation we consider hyperthermia, a procedure of raising the temperature above 43 °C, as a treatment modality. To this purpose, a numerical model of in vivo soft tissue ultrasound heating is proposed by extending a previously presented in vitro model. Based on the numerical simulations, a heating scheme satisfying some constraints related to potential clinical applications is established, and the resulting temperature time-course profile is composed with the temperature-dependent protein denaturation formula of a recently published mathematical model for the eukaryotic heat shock response. The obtained simulation results of the combined models are discussed in view of potential application of ultrasound soft tissue heating in clinical treatment.

Stochastic modelling of the eukaryotic heat shock response

The heat shock response (HSR) is a highly evolutionarily conserved defence mechanism allowing the cell to promptly react to elevated temperature conditions and other forms of stress. It has been subject to intense research for at least two main reasons. First, it is considered a promising candidate for deciphering the engineering principles underlying regulatory networks. Second, heat shock proteins (main actors of the HSR) play crucial role in many fundamental cellular processes. Therefore, profound understanding of the heat shock response would have far-reaching ramifications for the cell biology.Recently, a new deterministic model of the eukaryotic heat shock response has been proposed in the literature. It is very attractive since it consists of only the minimum number of components required by any functional regulatory network, while yet being capable of biological validation. However, it admits small molecule populations of some of the considered metabolites. In this paper a stochastic model corresponding to the deterministic one is constructed and the outcomes of these two models are confronted. The aim with this comparison is to show that, in the case of the heat shock response, the approximation of a discrete system with a continuous model is a reasonable approach. This is not always the truth, especially when the numbers of molecules of the considered species are small. By making the effort of performing and analysing 1000 stochastic simulations, we investigate the range of behaviour the stochastic model is likely to exhibit. We demonstrate that the obtained results agree well with the dynamics displayed by the continuous model, which strengthens the trust in the deterministic description. A proof of the existence and uniqueness of the stationary distribution of the Markov chain underlying the stochastic model is given. Moreover, the obtained view of the stochastic dynamics and the performed comparison to the outcome of the continuous formulation provide more insight into the dynamics of the heat shock response mechanism.