Mathematical Biology: Expand, Expose, and Educate!

Mathematical biology has made significant contributions and advancements in the biological sciences. Recruitment efforts focus on encouraging students, especially those who are underrepresented and underserved, to pursue the field of mathematical biology, regardless of their undergraduate institution type, and raise awareness about the countless professional and academic possibilities provided by this specialized training. This article examines the need to expand, expose, and educate others about mathematical biology. To support field expansion, we give several recommendations of ways to integrate mathematics applied curricula to attract broader student interest. With this exposure-whether it is led by an individual, a department, a university, or researchers in mathematical biology-each can help to promote a base knowledge and appreciation of the field. In order to encourage the next generation of researchers to consider mathematical biology, we highlight current interdisciplinary programs, share popular mathematical tools, and present some thoughts on ways to support a thriving and inclusive mathematical biology community for years to come.

Little Cigars are More Toxic than Cigarettes and Uniquely Change the Airway Gene and Protein Expression.

Little cigars (LCs) are regulated differently than cigarettes, allowing them to be potentially targeted at youth/young adults. We exposed human bronchial epithelial cultures (HBECs) to air or whole tobacco smoke from cigarettes vs. LCs. Chronic smoke exposure increased the number of dead cells, lactate dehydrogenase release, and interleukin-8 (IL-8) secretion and decreased apical cilia, cystic fibrosis transmembrane conductance regulator (CFTR) protein levels, and transepithelial resistance. These adverse effects were significantly greater in LC-exposed HBECs than cigarette exposed cultures. LC-exposure also elicited unique gene expression changes and altered the proteomic profiles of airway apical secretions compared to cigarette-exposed HBECs. Gas chromatography-mass spectrometry (GC-MS) analysis indicated that LCs produced more chemicals than cigarettes, suggesting that the increased chemical load of LCs may be the cause of the greater toxicity. This is the first study of the biological effects of LCs on pulmonary epithelia and our observations strongly suggest that LCs pose a more severe danger to human health than cigarettes.

Flavored e-cigarette liquids reduce proliferation and viability in the CALU3 airway epithelial cell line.

E-cigarettes are generally thought of as a safer smoking alternative to traditional cigarettes. However, little is known about the effects of e-cigarette liquids (e-liquids) on the lung. Since over 7,000 unique flavors have been identified for purchase in the United States, our goal was to conduct a screen that would test whether different flavored e-liquids exhibited different toxicant profiles. We tested the effects of 13 different flavored e-liquids [with nicotine and propylene glycol/vegetable glycerin (PG/VG) serving as controls] on a lung epithelial cell line (CALU3). Using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay as an indicator of cell proliferation/viability, we demonstrated a dose-dependent decrease of MTT metabolism by all flavors tested. However, a group of four flavors consistently showed significantly greater toxicity compared with the PG/VG control, indicating the potential for some flavors to elicit more harmful effects than others. We also tested the aerosolized "vapor" from select e-liquids on cells and found similar dose-dependent trends, suggesting that direct e-liquid exposures are a justifiable first-pass screening approach for determining relative e-liquid toxicity. We then identified individual chemical constituents for all 13 flavors using gas chromatography-mass spectrometry. These data revealed that beyond nicotine and PG/VG, the 13 flavored e-liquids have diverse chemical constituents. Since all of the flavors exhibited some degree of toxicity and a diverse array of chemical constituents with little inhalation toxicity available, we conclude that flavored e-liquids should be extensively tested on a case-by-case basis to determine the potential for toxicity in the lung and elsewhere.

The Cystic Fibrosis Transmembrane Conductance Regulator (CFTR) Uses its C-Terminus to Regulate the A2B Adenosine Receptor.

CFTR is an apical membrane anion channel that regulates fluid homeostasis in many organs including the airways, colon, pancreas and sweat glands. In cystic fibrosis, CFTR dysfunction causes significant morbidity/mortality. Whilst CFTR's function as an ion channel has been well described, its ability to regulate other proteins is less understood. We have previously shown that plasma membrane CFTR increases the surface density of the adenosine 2B receptor (A2BR), but not of the ß2 adrenergic receptor (ß2AR), leading to an enhanced, adenosine-induced cAMP response in the presence of CFTR. In this study, we have found that the C-terminal PDZ-domain of both A2BR and CFTR were crucial for this interaction, and that replacing the C-terminus of A2BR with that of ß2AR removed this CFTR-dependency. This observation extended to intact epithelia and disruption of the actin cytoskeleton prevented A2BR-induced but not ß2AR-induced airway surface liquid (ASL) secretion. We also found that CFTR expression altered the organization of the actin cytoskeleton and PDZ-binding proteins in both HEK293T cells and in well-differentiated human bronchial epithelia. Furthermore, removal of CFTR's PDZ binding motif (ΔTRL) prevented actin rearrangement, suggesting that CFTR insertion in the plasma membrane results in local reorganization of actin, PDZ binding proteins and certain GPCRs.

A Mathematical Model of Human Papillomavirus (HPV) in the United States and its Impact on Cervical Cancer.

BACKGROUND: Mathematical models can be useful tools in exploring disease trends and health consequences of interventions in a population over time. Most cancers, in particular cervical cancer, have long incubation periods. The time from acquisition of HPV infection to development of invasive cancer can be up to two decades or more. Mathematical models can be used to translate short-term findings from prevention and mitigations trials into predictions of long-term health outcomes. The main objective of this paper is to develop a mathematical model of HPV for African American women (AAW) in the United States and give quantitative insight into current U.S. prevention and mitigations against cervical cancer. METHODS: A compartmental mathematical model of the cycle of HPV that includes the choices individuals make once they become infected; treatment versus no treatment, was developed. Using this mathematical model we evaluated the impact of human papillomavirus (HPV) on a given population and determined what could decrease the rate at which AAW become infected. All state equations in the model were approximated using the Runge-Kutta 4(th) order numerical approximation method using MatLab software. RESULTS: In this paper we found that the basic reproductive number R(OU) is directly proportional to the rate of infectivity of HPV and the contact rate in which a human infects another human with HPV. The R(OU) was indirectly proportional to the recovery rate plus the mortality by natural causes and the disease. The second R(OT) is also directly proportional to the rate of infectivity of HPV and contact rate in which humans infect another human with HPV and indirectly proportional to the recovery rate plus the mortality from HPV related cause and natural causes. Based on the data of AAW for the parameters; we found that R(OU) and R(OT)were 0.519798 and 0.070249 respectively. As both of these basic reproductive numbers are less than one, infection cannot therefore get started in a fully susceptible population, however, if mitigation is to be implemented effectively it should focus on the HPV untreated population as R(OT)is greater than 0.5. CONCLUSION: Mathematical models, from individual and population perspectives, will help decision makers to evaluate different prevention and mitigation measures of HPV and deploy synergistically to improve cancer outcomes. Integrating the best-available epidemiologic data, computer-based mathematical models used in a decision-analytic framework can identify those factors most likely to influence outcomes and can help in formulating decisions that need to be made amidst considerable lack of data and uncertainty. Specifically, the model provides a tool that can accommodate new information, and can be modified as needed, to iteratively assess the expected benefits, costs, and cost-effectiveness of different policies in the United States. This model can help show the direct relationship between HPV and cervical cancer. If any of the rates change it will greatly impact the graphs. These graphs can be used to discover new methods of treatment that will decrease the rate of infectivity of HPV and Cervical cancer with time.