A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile.

Background: One of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this article aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical intervention (NPI) strategies for the dynamics of any transmissible disease. Materials and methods: Epidemiological modeling of the present work relies on delay differential equations describing time variation and transitions between suitable compartments. The practical identifiability approach relies on parameter optimization, a parametric bootstrap technique, and data processing. We implemented a careful parameter optimization algorithm by searching for suitable initialization according to each processed dataset. In addition, we implemented a parametric bootstrap technique to accurately predict the ICU curve trend in the medium term and assess vaccination. Results: We show the framework's calibration capabilities for several processed COVID-19 datasets of different regions of Chile. We found a unique range of parameters that works well for every dataset and provides overall numerical stability and convergence for parameter optimization. Consequently, the framework produces outstanding results concerning quantitative tracking of COVID-19 dynamics. In addition, it allows us to accurately predict the ICU curve trend in the medium term and assess vaccination. Finally, it is reproducible since we provide open-source codes that consider parameter initialization standardized for every dataset. Conclusion: This work attempts to implement a holistic and general modeling framework for quantitative tracking of the dynamics of any transmissible disease, focusing on accurately predicting the ICU curve trend in the medium term and assessing vaccination. The scientific community could adapt it to evaluate the impact of combined vaccination and NPIs strategies for COVID-19 or any transmissible disease in any country and help visualize the potential effects of implemented plans by policymakers. In future work, we want to improve the computational cost of the parametric bootstrap technique or use another more efficient technique. The aim would be to reconstruct epidemiological curves to predict the combined NPIs and vaccination policies' impact on the ICU curve trend in real-time, providing scientific evidence to help anticipate policymakers' decisions.

Patient-Wise Methodology to Assess Glycemic Health Status: Applications to Quantify the Efficacy and Physiological Targets of Polyphenols on Glycemic Control.

A growing body of evidence indicates that dietary polyphenols could be used as an early intervention to treat glucose-insulin (G-I) dysregulation. However, studies report heterogeneous information, and the targets of the intervention remain largely elusive. In this work, we provide a general methodology to quantify the effects of any given polyphenol-rich food or formulae over glycemic regulation in a patient-wise manner using an Oral Glucose Tolerance Test (OGTT). We use a mathematical model to represent individual OGTT curves as the coordinated action of subsystems, each one described by a parameter with physiological interpretation. Using the parameter values calculated for a cohort of 1198 individuals, we propose a statistical model to calculate the risk of dysglycemia and the coordination among subsystems for each subject, thus providing a continuous and individual health assessment. This method allows identifying individuals at high risk of dysglycemia-which would have been missed with traditional binary diagnostic methods-enabling early nutritional intervention with a polyphenol-supplemented diet where it is most effective and desirable. Besides, the proposed methodology assesses the effectiveness of interventions over time when applied to the OGTT curves of a treated individual. We illustrate the use of this method in a case study to assess the dose-dependent effects of Delphinol® on reducing dysglycemia risk and improving the coordination between subsystems. Finally, this strategy enables, on the one hand, the use of low-cost, non-invasive methods in population-scale nutritional studies. On the other hand, it will help practitioners assess the effectiveness of an intervention based on individual vulnerabilities and adapt the treatment to manage dysglycemia and avoid its progression into disease.

Novel Symbiotic Genome-Scale Model Reveals Wolbachia's Arboviral Pathogen Blocking Mechanism in Aedes aegypti.

Wolbachia are endosymbiont bacteria known to infect arthropods causing different effects, such as cytoplasmic incompatibility and pathogen blocking in Aedes aegypti. Although several Wolbachia strains have been studied, there is little knowledge regarding the relationship between this bacterium and their hosts, particularly on their obligate endosymbiont nature and its pathogen blocking ability. Motivated by the potential applications on disease control, we developed a genome-scale model of two Wolbachia strains: wMel and the strongest Dengue blocking strain known to date: wMelPop. The obtained metabolic reconstructions exhibit an energy metabolism relying mainly on amino acids and lipid transport to support cell growth that is consistent with altered lipid and cholesterol metabolism in Wolbachia-infected mosquitoes. The obtained metabolic reconstruction was then coupled with a reconstructed mosquito model to retrieve a symbiotic genome-scale model accounting for 1,636 genes and 6,408 reactions of the Aedes aegypti-Wolbachia interaction system. Simulation of an arboviral infection in the obtained novel symbiotic model represents a metabolic scenario characterized by pathogen blocking in higher titer Wolbachia strains, showing that pathogen blocking by Wolbachia infection is consistent with competition for lipid and amino acid resources between arbovirus and this endosymbiotic bacteria. IMPORTANCE Arboviral diseases such as Zika and Dengue have been on the rise mainly due to climate change, and the development of new treatments and strategies to limit their spreading is needed. The use of Wolbachia as an approach for disease control has motivated new research related to the characterization of the mechanisms that underlie its pathogen-blocking properties. In this work, we propose a new approach for studying the metabolic interactions between Aedes aegypti and Wolbachia using genome-scale models, finding that pathogen blocking is mainly influenced by competition for the resources required for Wolbachia and viral replication.

A Novel Synthetic Model of the Glucose-Insulin System for Patient-Wise Inference of Physiological Parameters From Small-Size OGTT Data.

Existing mathematical models for the glucose-insulin (G-I) dynamics often involve variables that are not susceptible to direct measurement. Standard clinical tests for measuring G-I levels for diagnosing potential diseases are simple and relatively cheap, but seldom give enough information to allow the identification of model parameters within the range in which they have a biological meaning, thus generating a gap between mathematical modeling and any possible physiological explanation or clinical interpretation. In the present work, we present a synthetic mathematical model to represent the G-I dynamics in an Oral Glucose Tolerance Test (OGTT), which involves for the first time for OGTT-related models, Delay Differential Equations. Our model can represent the radically different behaviors observed in a studied cohort of 407 normoglycemic patients (the largest analyzed so far in parameter fitting experiments), all masked under the current threshold-based normality criteria. We also propose a novel approach to solve the parameter fitting inverse problem, involving the clustering of different G-I profiles, a simulation-based exploration of the feasible set, and the construction of an information function which reshapes it, based on the clinical records, experimental uncertainties, and physiological criteria. This method allowed an individual-wise recognition of the parameters of our model using small size OGTT data (5 measurements) directly, without modifying the routine procedures or requiring particular clinical setups. Therefore, our methodology can be easily applied to gain parametric insights to complement the existing tools for the diagnosis of G-I dysregulations. We tested the parameter stability and sensitivity for individual subjects, and an empirical relationship between such indexes and curve shapes was spotted. Since different G-I profiles, under the light of our model, are related to different physiological mechanisms, the present method offers a tool for personally-oriented diagnosis and treatment and to better define new health criteria.

A simultaneous blow-up problem arising in tumor modeling.

Although macrophages are part of the human immune system, it has been remarkably observed in laboratory experiments that decreasing its number can slow down the tumor progression. We analyze through a recently mathematical model proposed in the literature, necessary conditions for aggregation of tumor cells and macrophages. In order to do so, we prove the possibility of having blow-up in finite time. Next, we study if the aggregation of macrophages can occur when having a low density of tumor cells, and vice versa. With this purpose, we consider the problem of analyzing the existence or not of a simultaneous blow-up. We achieve this goal thanks to a novel process that allows us to compare the entropy functional associated with the density of each population, which turns out to be also a method to find enough conditions for having a simultaneous blow-up.

A systems biology approach for studying Wolbachia metabolism reveals points of interaction with its host in the context of arboviral infection.

Wolbachia are alpha-proteobacteria known to infect arthropods, which are of interest for disease control since they have been associated with improved resistance to viral infection. Although several genomes for different strains have been sequenced, there is little knowledge regarding the relationship between this bacterium and their hosts, particularly on their dependency for survival. Motivated by the potential applications on disease control, we developed genome-scale models of four Wolbachia strains known to infect arthropods: wAlbB (Aedes albopictus), wVitA (Nasonia vitripennis), wMel and wMelPop (Drosophila melanogaster). The obtained metabolic reconstructions exhibit a metabolism relying mainly on amino acids for energy production and biomass synthesis. A gap analysis was performed to detect metabolic candidates which could explain the endosymbiotic nature of this bacterium, finding that amino acids, requirements for ubiquinone precursors and provisioning of metabolites such as riboflavin could play a crucial role in this relationship. This work provides a systems biology perspective for studying the relationship of Wolbachia with its host and the development of new approaches for control of the spread of arboviral diseases. This approach, where metabolic gaps are key objects of study instead of just additions to complete a model, could be applied to other endosymbiotic bacteria of interest.

Parameter estimation and mathematical modeling for the quantitative description of therapy failure due to drug resistance in gastrointestinal stromal tumor metastasis to the liver.

In this work we develop a general mathematical model and devise a practical identifiability approach for gastrointestinal stromal tumor (GIST) metastasis to the liver, with the aim of quantitatively describing therapy failure due to drug resistance. To this end, we have modeled metastatic growth and therapy failure produced by resistance to two standard treatments based on tyrosine kinase inhibitors (Imatinib and Sunitinib) that have been observed clinically in patients with GIST metastasis to the liver. The parameter identification problem is difficult to solve, since there are no general results on this issue for models based on ordinary differential equations (ODE) like the ones studied here. We propose a general modeling framework based on ODE for GIST metastatic growth and therapy failure due to drug resistance and analyzed five different model variants, using medical image observations (CT scans) from patients that exhibit drug resistance. The associated parameter estimation problem was solved using the Nelder-Mead simplex algorithm, by adding a regularization term to the objective function to address model instability, and assessing the agreement of either an absolute or proportional error in the objective function. We compared the goodness of fit to data for the proposed model variants, as well as evaluated both error forms in order to improve parameter estimation results. From the model variants analyzed, we identified the one that provides the best fit to all the available patient data sets, as well as the best assumption in computing the objective function (absolute or proportional error). This is the first work that reports mathematical models capable of capturing and quantitatively describing therapy failure due to drug resistance based on clinical images in a patient-specific manner.

Proposal of a hybrid approach for tumor progression and tumor-induced angiogenesis.

One of the main challenges in cancer modelling is to improve the knowledge of tumor progression in areas related to tumor growth, tumor-induced angiogenesis and targeted therapies efficacy. For this purpose, incorporate the expertise from applied mathematicians, biologists and physicians is highly desirable. Despite the existence of a very wide range of models, involving many stages in cancer progression, few models have been proposed to take into account all relevant processes in tumor progression, in particular the effect of systemic treatments and angiogenesis. Composite biological experiments, both in vitro and in vivo, in addition with mathematical modelling can provide a better understanding of theses aspects. In this work we proposed that a rational experimental design associated with mathematical modelling could provide new insights into cancer progression. To accomplish this task, we reviewed mathematical models and cancer biology literature, describing in detail the basic principles of mathematical modelling. We also analyze how experimental data regarding tumor cells proliferation and angiogenesis in vitro may fit with mathematical modelling in order to reconstruct in vivo tumor evolution. Additionally, we explained the mathematical methodology in a comprehensible way in order to facilitate its future use by the scientific community.

Mathematical modeling of the dynamic storage of iron in ferritin.

BACKGROUND: Iron is essential for the maintenance of basic cellular processes. In the regulation of its cellular levels, ferritin acts as the main intracellular iron storage protein. In this work we present a mathematical model for the dynamics of iron storage in ferritin during the process of intestinal iron absorption. A set of differential equations were established considering kinetic expressions for the main reactions and mass balances for ferritin, iron and a discrete population of ferritin species defined by their respective iron content. RESULTS: Simulation results showing the evolution of ferritin iron content following a pulse of iron were compared with experimental data for ferritin iron distribution obtained with purified ferritin incubated in vitro with different iron levels. Distinctive features observed experimentally were successfully captured by the model, namely the distribution pattern of iron into ferritin protein nanocages with different iron content and the role of ferritin as a controller of the cytosolic labile iron pool (cLIP). Ferritin stabilizes the cLIP for a wide range of total intracellular iron concentrations, but the model predicts an exponential increment of the cLIP at an iron content > 2,500 Fe/ferritin protein cage, when the storage capacity of ferritin is exceeded. CONCLUSIONS: The results presented support the role of ferritin as an iron buffer in a cellular system. Moreover, the model predicts desirable characteristics for a buffer protein such as effective removal of excess iron, which keeps intracellular cLIP levels approximately constant even when large perturbations are introduced, and a freely available source of iron under iron starvation. In addition, the simulated dynamics of the iron removal process are extremely fast, with ferritin acting as a first defense against dangerous iron fluctuations and providing the time required by the cell to activate slower transcriptional regulation mechanisms and adapt to iron stress conditions. In summary, the model captures the complexity of the iron-ferritin equilibrium, and can be used for further theoretical exploration of the role of ferritin in the regulation of intracellular labile iron levels and, in particular, as a relevant regulator of transepithelial iron transport during the process of intestinal iron absorption.