A novel logical model of COVID-19 intracellular infection to support therapies development

In this paper, a logical-based mathematical model of the cellular pathways involved in the COVID-19 infection has been developed to study various drug treatments (single or in combination), in different illness scenarios, providing insights into their mechanisms of action. Drug simulations suggest that the effects of single drugs are limited, or depending on the scenario counterproductive, whereas better results appear combining different treatments. Specifically, the combination of the anti-inflammatory Baricitinib and the anti-viral Remdesivir showed significant benefits while a stronger efficacy emerged from the triple combination of Baricitinib, Remdesivir, and the corticosteroid Dexamethasone. Together with a sensitivity analysis, we performed an analysis of the mechanisms of the drugs to reveal their impact on molecular pathways.

The paper introduces a logical-based mathematical model of the cellular pathways involved in the COVID-19 infection. The aim of the model is to study, in a qualitative but comprehensive way, the cellular mechanisms developed during the virus infection with the principal focus on drug treatments. The model is able to reproduce various illness scenarios: from the early infection stages to the late illness stages characterized by strong immune reaction usually evolving in the so-called cytokine storm. Different drug effects have been tested singularly and in combination treatments. Computational sensitivity analysis was performed on the model along with the analysis of the mechanisms of the drugs to reveal their impact on molecular pathways. The results show that the effect of single drugs may be limited or counterproductive, depending on the illness stage. The highest predicted efficacy is obtained by combining three different treatments: the anti-inflammatory Baricitinib, the anti-viral Remdesivir and the corticosteroid Dexamethasone. This triple combination therapy has been analyzed not only in terms of global cellular effect but also in function of the involved internal pathways, suggesting the rational mechanisms for its successfulness.

Effects of mutations and immunogenicity on outcomes of anti-cancer therapies for secondary lesions

Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised. By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects on final outcomes for secondary lesions are also investigated, showing that actions on primary lesions could sometimes result in unexpected clearances of secondary tumours. This outcome is strongly dependent on the clonal composition of the primary and secondary masses and is shown to allow, in some cases, the control of the disease for years.

Combination therapies and intra-tumoral competition: Insights from mathematical modeling

Drug resistance is one of the major obstacles to a successful treatment of cancer and, in turn, has been recognized to be linked to intratumoral heterogeneity, which increases the probability of the emergence of cancer clones refractory to treatment. Combination therapies have been introduced to overcome resistance, but the design of successful combined protocols is still an open problem. In order to provide some indications on the effectiveness of medical treatments, a mathematical model is proposed, comprising two cancer populations competing for resources and with different susceptibilities to the action of immune system cells and therapies: the focus is on the effects of chemotherapy and immunotherapy, used singularly or in combination. First, numerical predictions of the model have been tested with experimental data from the literature and next therapeutic protocols with different doses and temporal order have been simulated. Finally the role of competitive interactions has been also investigated, to provide some insights on the role of competitive interactions among cancer clones in determining treatment outcomes.

Irreversibility of the two-dimensional enstrophy cascade

We study the time irreversibility of the direct cascade in two-dimensional turbulence by looking at the time derivative of the square vorticity along Lagrangian trajectories, a quantity called metenstrophy. By means of extensive direct numerical simulations we measure the time irreversibility from the asymmetry of the probability density function of the metenstrophy and we find that it increases with the Reynolds number of the cascade, similarly to what is found in three-dimensional turbulence. A detailed analysis of the different contributions to the enstrophy budget reveals a remarkable difference with respect to what is observed for the energy cascade, in particular the role of the statistics of the forcing to determine the degree of irreversibility.