  Multimodal oncological strategies which combine chemotherapy or radiotherapy
with hyperthermia have a potential of improving the efficacy of the
non-surgical methods of cancer treatment. Hyperthermia engages the heat-shock
response mechanism (HSR), main component of which are heat-shock proteins
(HSP). Cancer cells have already partially activated HSR, thereby, hyperthermia
may be more toxic to them relative to normal cells. On the other hand, HSR
triggers thermotolerance, i.e. hyperthermia treated cells show an impairment in
their susceptibility to a subsequent heat-induced stress. This poses questions
about efficacy and optimal strategy of the anti-cancer therapy combined with
hyperthermia treatment.
  To address these questions, we adapt our previous HSR model and propose its
stochastic extension. We formalise the notion of a HSP-induced thermotolerance.
Next, we estimate the intensity and the duration of the thermotolerance.
Finally, we quantify the effect of a multimodal therapy based on hyperthermia
and a cytotoxic effect of bortezomib, a clinically approved proteasome
inhibitor. Consequently, we propose an optimal strategy for combining
hyperthermia and proteasome inhibition modalities.
  In summary, by a proof of concept mathematical analysis of HSR we are able to
support the common belief that the combination of cancer treatment strategies
increases therapy efficacy. thermotolerance.
