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The main purpose of this work is to provide an extensive, simulation-based comparison of robustness of PID and MPC algorithms in control of blood glucose levels in patients with type 1 diabetes and thus answer the question of their safety. Cohort testing, with 1000 simulated, randomized patients allowed to analyze specific control quality indicators, such as number of hypoglycemic events, and length of hypo- and hyperglycemia periods. Results show that both algorithms provide a reasonable safety level, taking into account natural changes of patients’ physiological parameters. At the same time, we point out drawbacks of each solution, as well as general problems arising in close-loop control of blood glucose level.

Immune cells fine tune their responses to infection and inflammatory cues. Here, using live-cell confocal microscopy and mathematical modelling, we investigate interferon-induced JAK-STAT signalling in innate immune macrophages. We demonstrate that transient exposure to IFN-γ stimulation induces a long-term desensitisation of STAT1 signalling and gene expression responses, revealing a dose- and time-dependent regulatory feedback that controls JAK-STAT responses upon re-exposure to stimulus. We show that IFN-α/β1 elicit different level of desensitisation from IFN-γ, where cells refractory to IFN-α/β1 are sensitive to IFN-γ, but not vice versa. We experimentally demonstrate that the underlying feedback mechanism involves regulation of STAT1 phosphorylation but is independent of new mRNA synthesis and cognate receptor expression. A new feedback model of the protein tyrosine phosphatase activity recapitulates experimental data and demonstrates JAK-STAT network’s ability to decode relative changes of dose, timing, and type of temporal interferon stimulation. These findings reveal that STAT desensitisation renders cells with signalling memory of type I and II interferon stimulation, which in the future may improve administration of interferon therapy.

Abstract Background Ability to adapt to temperature changes trough the Heat Shock Response (HSR) pathways is one of the most fundamental and clinically relevant cellular response systems. Heat Shock (HS) affects the signalling and gene expression responses of the Nuclear Factor κB (NF-κB) transcription factor, a critical regulator of proliferation and inflammation, however, our quantitative understanding of how cells sense and adapt to temperature changes is limited. Methods We used live-cell time-lapse microscopy and mathematical modelling to understand the signalling of the NF-κB system in the human MCF7 breast adenocarcinoma cells in response to pro-inflammatory Interleukin 1β (IL1β) and Tumour Necrosis Factor α (TNFα) cytokines, following exposure to a 37–43 °C range of physiological and clinical temperatures. Results We show that exposure to 43 °C 1 h HS inhibits the immediate NF-κB signalling response to TNFα and IL1β stimulation although uptake of cytokines is not impaired. Within 4 h after HS treatment IL1β-induced NF-κB responses return to normal levels, but the recovery of the TNFα-induced responses is still affected. Using siRNA knock-down of Heat Shock Factor 1 (HSF1) we show that this stimulus-specificity is conferred via the Inhibitory κB kinase (IKK) signalosome where HSF1-dependent feedback regulates TNFα, but not IL1β-mediated IKK recovery post HS. Furthermore, we demonstrate that through the temperature-dependent denaturation and recovery of IKK, TNFα and IL1β-mediated signalling exhibit different temperature sensitivity and adaptation to repeated HS when exposed to a 37–43 °C temperature range. Specifically, IL1β-mediated NF-κB responses are more robust to temperature changes in comparison to those induced by TNFα treatment. Conclusions We demonstrate that the kinetics of the NF-κB system following temperature stress is cytokine specific and exhibit differential adaptation to temperature changes. We propose that this differential temperature sensitivity is mediated via the IKK signalosome, which acts as a bona fide temperature sensor trough the HSR cross-talk. This novel quantitative understanding of NF-κB and HSR interactions is fundamentally important for the potential optimization of therapeutic hyperthermia protocols. Video Abstract

Numerous studies have proven that both stimulation and blockade of 5-HT1A and the blockade of 5-HT7 receptors might cause the anxiolytic-like effects. Biased agonists selectively activate specific signaling pathways. Therefore, they might offer novel treatment strategies. In this study, we investigated the anxiolytic-like activity, as well as the possible mechanism of action of 1-[(2,5-dimethylphenoxy)propyl]-4-(2-methoxyphenyl)piperazine hydrochloride (HBK-17). In our previous experiments, HBK-17 showed high affinity for 5-HT1A and 5-HT7 receptors and antidepressant-like properties. We performed the four plate test and the elevated plus maze test to determine anxiolytic-like activity. Toward a better understanding of the pharmacological properties of HBK-17 we used various functional assays to determine its intrinsic activity at 5-HT1A, 5-HT2A, 5-HT7, and D2 receptors and UHPLC-MS/MS method to evaluate its pharmacokinetic profile. We observed the anxiolytic-like activity of HBK-17 in both behavioral tests and the effect was reversed by the pretreatment with WAY-100635, which proves that 5-HT1A receptor activation was essential for the anxiolytic-like effect. Moreover, the compound moderately antagonized D2, weakly 5-HT7 and very weakly 5-HT2A receptors. We demonstrated that HBK-17 preferentially activated ß-arrestin signaling after binding to the 5-HT1A receptor. HBK-17 was rapidly absorbed after intraperitoneal administration and had a half-life of about 150 min. HBK-17 slightly penetrated the peripheral compartment and showed bioavailability of approximately 45%. The unique pharmacological profile of HBK-17 encourages further experiments to understand its mechanism of action fully.

Elevated temperature induces the heat shock (HS) response, which modulates cell proliferation, apoptosis, the immune and inflammatory responses. However, specific mechanisms linking the HS response pathways to major cellular signaling systems are not fully understood. Here we used integrated computational and experimental approaches to quantitatively analyze the crosstalk mechanisms between the HS-response and a master regulator of inflammation, cell proliferation, and apoptosis the Nuclear Factor κB (NF-κB) system. We found that populations of human osteosarcoma cells, exposed to a clinically relevant 43°C HS had an attenuated NF-κB p65 response to Tumor Necrosis Factor α (TNFα) treatment. The degree of inhibition of the NF-κB response depended on the HS exposure time. Mathematical modeling of single cells indicated that individual crosstalk mechanisms differentially encode HS-mediated NF-κB responses while being consistent with the observed population-level responses. In particular "all-or-nothing" encoding mechanisms were involved in the HS-dependent regulation of the IKK activity and IκBα phosphorylation, while others involving transport were "analogue". In order to discriminate between these mechanisms, we used live-cell imaging of nuclear translocations of the NF-κB p65 subunit. The single cell responses exhibited "all-or-nothing" encoding. While most cells did not respond to TNFα stimulation after a 60 min HS, 27% showed responses similar to those not receiving HS. We further demonstrated experimentally and theoretically that the predicted inhibition of IKK activity was consistent with the observed HS-dependent depletion of the IKKα and IKKβ subunits in whole cell lysates. However, a combination of "all-or-nothing" crosstalk mechanisms was required to completely recapitulate the single cell data. We postulate therefore that the heterogeneity of the single cell responses might be explained by the cell-intrinsic variability of HS-modulated IKK signaling. In summary, we show that high temperature modulates NF-κB responses in single cells in a complex and unintuitive manner, which needs to be considered in hyperthermia-based treatment strategies.

Studies proved that among all α1-adrenoceptors, cardiac myocytes functionally express only α1A- and α1B-subtype. Scientists indicated that α1A-subtype blockade might be beneficial in restoring normal heart rhythm. Therefore, we aimed to determine the role of α1-adrenoceptors subtypes (i.e. α1A and α1B) in antiarrhythmic effect of six structurally similar derivatives of 2-methoxyphenylpiperazine. We compared the activity of studied compounds with carvedilol, which is β1- and α1-adrenoceptors blocker with antioxidant properties.To evaluate the affinity for adrenergic receptors, we used radioligand methods. We investigated selectivity at α1-adrenoceptors subtypes using functional bioassays. We tested antiarrhythmic activity in adrenaline-induced (20 µg/kg i.v.), calcium chloride-induced (140 and 25 mg/kg i.v.) and barium chloride-induced (32 and 10 mg/kg i.v.) arrhythmia models in rats. We also evaluated the influence of studied compounds on blood pressure in rats, as well as lipid peroxidation. All studied compounds showed high affinity towards α1-adrenoceptors but no affinity for β1 receptors. Biofunctional studies revealed that the tested compounds blocked α1A- stronger than α1B-adrenoceptors, but except for HBK-19 they antagonized α1A-adrenoceptor weaker than α1D-subtype. HBK-19 showed the greatest difference in pA2 values - it blocked α1A-adrenoceptors around sevenfold stronger than α1B subtype. All compounds showed prophylactic antiarrhythmic properties in adrenaline-induced arrhythmia, but only the activity of HBK-16, HBK-17, HBK-18 and HBK-19 (ED50=0.18-0.21) was comparable to that of carvedilol (ED50=0.36). All compounds reduced mortality in adrenaline-induced arrhythmia. HBK-16, HBK-17, HBK-18 and HBK-19 showed therapeutic antiarrhythmic properties in adrenaline-induced arrhythmia. None of the compounds showed activity in calcium chloride- or barium chloride-induced arrhythmias. HBK-16, HBK-17, HBK-18 and HBK-19 decreased heart rhythm at ED84. All compounds significantly lowered blood pressure in normotensive rats. HBK-18 showed the strongest hypotensive properties (the lowest active dose: 0.01 mg/kg). HBK-19 was the only compound in the group, which did not show hypotensive effect at antiarrhythmic doses. HBK-16, HBK-17, HBK-18, HBK-19 showed weak antioxidant properties.Our results indicate that the studied 2-methoxyphenylpiperazine derivatives that possessed stronger α1A-adrenolytic properties (i.e. HBK-16, HBK-17, HBK-18 and HBK-19) were the most compounds in adrenaline-induced arrhythmia. Thus, we suggest that the potent blockade of α1A-receptor subtype is essential to attenuate adrenaline-induced arrhythmia.

Regulatory networks structure and signaling pathways dynamics are uncovered in time- and resource consuming experimental work. However, it is increasingly supported by modeling, analytical and computational techniques as well as discrete mathematics and artificial intelligence applied to to extract knowledge from existing databases. This review is focused on mathematical modeling used to analyze dynamics and robustness of these networks. This paper presents a review of selected modeling methods that facilitate advances in molecular biology.

Abstract Intracellular processes are cascades of biochemical reactions, triggered in response to various types of stimuli. Mathematical models describing their dynamics have become increasingly popular in recent years, as tools supporting experimental work in analysis of pathways and regulatory networks. Not only do they provide insights into general properties of these systems, but also help in specific tasks, such as search for drug molecular targets or treatment protocols. Different tools and methods are used to model complex biological systems. In this work, we focus on ordinary differential equations (ODEs) and Petri nets. We consider specific methods of analysis of such models, i.e., sensitivity analysis (SA) and significance analysis. So far, they have been applied separately, with different goals. In this paper, we show that they can complement each other, combining the sensitivity of ODE models and the significance analysis of Petri nets. The former is used to find parameters, whose change results in the greatest quantitative and qualitative changes in the model response, while the latter is a structural analysis and allows indicating the most important subprocesses in terms of information flow in Petri net. Ultimately, both methods facilitate finding the essential processes in a given signaling pathway or regulatory network and may be used to support medical therapy development. In the paper, the use of dual modeling is illustrated with an example of ATM/p53/NF- $$\kappa$$ κ B pathway. Each method was applied to analyze this system, resulting in finding different subsets of important processes that might be prospective targets for changing this system behavior. While some of the processes were indicated in each of the approaches, others were found by one method only and would be missed if only that method was applied. This leads to the conclusion about the complementarity of the methods under investigation. The dual modeling approach of comprehensive structural and parametric analysis yields results that would not be possible if these two modeling approaches were applied separately. The combined approach, proposed in this paper, facilitates finding not only key processes, with which significant parameters are associated, but also significant modules, corresponding to subsystems of regulatory networks. The results provide broader insight into therapy targets in diseases in which the natural control of intracellular processes is disturbed, leading to the development of more effective therapies in medicine.

This paper deals with development of signaling pathways models and using plasmid-based experiments to support parameter estimation. We show that if cells transfected with plasmids are used in experiments, the models should include additional components that describe explicitly effects induced by plasmids. Otherwise, when the model is used to analyze responses of wild type, i.e. non-transfected cells, it may not capture their dynamics properly or even lead to false conclusions. In order to illustrate this, an original mathematical model of miRNA-mediated control of gene expression in the NF$\kappa$B pathway is presented. The paper shows what artifacts might appear due to experimental procedures and how to develop the models in order to avoid pursuing these artifacts instead of real kinetics.

This paper presents analysis and biomedical implications of a certain class of bilinear systems that can be applied in modeling of cancer chemotherapy. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy in their different aspects. The methodology of analysis of such models, based on system decomposition, is discussed. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the second one is infinite-dimensional and tridiagonal. Then the optimal control problem is defined in $l^1$ space. To derive necessary conditions for optimal control, the model description is transformed into an integrodifferential one.