Developing a Mathematical Model of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in Esophageal Cancer.

Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers, such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted therapy for patients with EGFR mutation-positive cancers. While preclinical studies and clinical trials have shown that afatinib has benefits for esophageal cancer patients, it is not known whether a combination of afatinib and RP4010 could achieve better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human esophageal squamous cell carcinoma cell line, using both experimental and mathematical simulations. Our mathematical simulation of Ca2+ oscillations could fit well with experimental data responding to afatinib or RP4010, both separately or in combination. Guided by simulation, we were able to identify a proper ratio of afatinib and RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect evidence by experimental measurement of intracellular Ca2+ and cell proliferation. This intracellular Ca2+ dynamic-based mathematical simulation approach could be useful for a rapid and cost-effective evaluation of combined targeting therapy drugs.

Impact of Population Recruitment on the HIV Epidemics and the Effectiveness of HIV Prevention Interventions.

Mechanistic mathematical models are increasingly used to evaluate the effectiveness of different interventions for HIV prevention and to inform public health decisions. By focusing exclusively on the impact of the interventions, the importance of the demographic processes in these studies is often underestimated. In this paper, we use simple deterministic models to assess the effectiveness of pre-exposure prophylaxis in reducing the HIV transmission and to explore the influence of the recruitment mechanisms on the epidemic and effectiveness projections. We employ three commonly used formulas that correspond to constant, proportional and logistic recruitment and compare the dynamical properties of the resulting models. Our analysis exposes substantial differences in the transient and asymptotic behavior of the models which result in 47 % variation in population size and more than 6 percentage points variation in HIV prevalence over 40 years between models using different recruitment mechanisms. We outline the strong influence of recruitment assumptions on the impact of HIV prevention interventions and conclude that detailed demographic data should be used to inform the integration of recruitment processes in the models before HIV prevention is considered.

Using models to advance medicine: mathematical modeling of post-myocardial infarction left ventricular remodeling.

The heart is an organ with limited capacity for regeneration and repair. The irreversible cell death and corresponding diminished ability of the heart to repair after myocardial infarction (MI), is a leading cause of morbidity and mortality worldwide. In this paper, a new mathematical model is presented to study the left ventricular (LV) remodeling and associated events after MI. The model accurately describes and predicts the interactions among heart cells and the immune system post-MI in the absence of medical interventions. The resulting system of nonlinear ordinary differential equations is studied both analytically and numerically in order to demonstrate the functionality and performance of the new model. To the best of our knowledge, this model is the only one of its kind to consider and correctly apply all of the known factors in diseased heart LV modeling. This model has the potential to provide researchers with a predictive computational tool to better understand the MI pathology and develop various cell-based treatment options, with benefits of lowering the cost and reducing the development time.

A simple model of immune and muscle cell crosstalk during muscle regeneration.

Muscle injury during aging predisposes skeletal muscles to increased damage due to reduced regenerative capacity. Some of the common causes of muscle injury are strains, while other causes are more complex muscle myopathies and other illnesses, and even excessive exercise can lead to muscle damage. We develop a new mathematical model based on ordinary differential equations of muscle regeneration. It includes the interactions between the immune system, healthy and damaged myonuclei as well as satellite cells. Our new mathematical model expands beyond previous ones by accounting for 21 specific parameters, including those parameters that deal with the interactions between the damaged and dead myonuclei, the immune system, and the satellite cells. An important assumption of our model is the replacement of only damaged parts of the muscle fibers and the dead myonuclei. We conduce systematic sensitivity analysis to determine which parameters have larger effects on the model and therefore are more influential for the muscle regeneration process. We propose additional validation for these parameters. We further demonstrate that these simulations are species-, muscle-, and age-dependent. In addition, the knowledge of these parameters and their interactions, may suggest targeting or selecting these interactions for treatments that accelerate the muscle regeneration process.

Impact of socio-economic conditions on the incidence of visceral leishmaniasis in Bihar, India.

Visceral leishmaniasis (VL) is one of the world's worst parasitic killers, second only to Malaria, claiming thousands of lives every year. More than three fifths of the world's VL cases occur in the Indian state of Bihar alone. While some research has been conducted with emphasis on the effects of climatic variables on the VL incidence rate, rigorous analysis of the effects of socio-economic variables is still lacking. In this paper a regression model is developed that describes the relationship between VL incidence rate and a variety of socio-economic factors. It uses data from 2005 and explains 92% of the observed variance. In addition, a stepwise regression model is also used to identify the most important factors that facilitate the prevalence of the VL disease. A discussion on how to most effectively distribute Bihar's limited resources on various control measures to decrease the incidence of VL is also presented.

Ionic silicon improves endothelial cells' survival under toxic oxidative stress by overexpressing angiogenic markers and antioxidant enzymes.

Oxidative stress, induced by harmful levels of reactive oxygen species, is a common occurrence that impairs proper bone defect vascular healing through the impairment of endothelial cell function. Ionic silicon released from silica-based biomaterials, can upregulate hypoxia-inducible factor-1α (HIF-1α). Yet it is unclear whether ionic Si can restore endothelial cell function under oxidative stress conditions. Therefore, we hypothesized that ionic silicon can help improve human umbilical vein endothelial cells' (HUVECs') survival under toxic oxidative stress. In this study, we evaluated the ionic jsilicon effect on HUVECs viability, proliferation, migration, gene expression, and capillary tube formation under normal conditions and under harmful hydrogen peroxide levels. We demonstrated that 0.5-mM Si4+ significantly enhanced angiogenesis in HUVECs under normal condition (p < 0.05). HUVECs exposed to 0.5-mM Si4+ presented a morphological change, even without the bed of Matrigel, and formed significantly more tube-like structures than the control (p < 0.001). In addition, 0.5-mM Si4+ enhanced cell viability in HUVECs under harmful H2 O2 levels. HIF-1α, vascular endothelial growth factor-A, and vascular endothelial growth factor receptor-2 were overexpressed more than twofold in silicon-treated HUVECs, under normal and toxic H2 O2 conditions. Moreover, the HUVECs were treated with 0.5-mM Si4+ overexpressed superoxide dismutase-1 (SOD-1), catalase-1 (Cat-1), and nitric oxide synthase-3 (NOS3) under normal and oxidative stress environment (p < 0.01). A computational model was used for explaining the antioxidant effect of Si4+ in endothelial cells and human periosteum cells by SOD-1 enhancement. In conclusion, we demonstrated that 0.5-mM Si4+ can recover the HUVECs' viability under oxidative stress conditions by reducing cell death and upregulating expression of angiogenic and antioxidant factors.

The Freter model: a simple model of biofilm formation.

A simple, conceptual model of biofilm formation, due to R. Freter et al. (1983), is studied analytically and numerically in both CSTR and PFR. Two steady state regimes are identified, namely, the complete washout of the microbes from the reactor and the successful colonization of both the wall and bulk fluid. One of these is stable for any particular set of parameter values and sharp and explicit conditions are given for the stability of each. The effects of adding an anti-microbial agent to the CSTR are examined.