Kill rates by immune cells: Ratio-dependent, or mass action?

We describe a cell-based fixed-lattice model to simulate immune cell and tumor cell interaction involving MHC recognition, and FasL vs perforin lysis. We are motivated by open questions about the mechanisms behind observed kill rates of tumor cells by different types of effector cells. These mechanisms play a big role in the effectiveness of many cancer immunotherapies.

Introduction of Plasmid to the Murine Gut via Consumption of an Carrier and Examining the Impact of Bacterial Dosing and Antibiotics on Persistence.

Purpose: We examine the impacts of dosing strategies of plasmids on bacterial communities in the murine gut by measuring the quantity of plasmids in mouse feces.

Methods: We fed mice carrier bacteria, , that contain plasmids with both a reporter gene and an antibiotic resistant gene. We varied the quantity of the plasmid-carrying bacteria and the length of time the mice consumed the bacteria.

Modeling the interaction of polymeric nanoparticles functionalized with cell penetrating peptides at the nano-bio interface.

The interaction of nanoparticles with Caco-2 monolayers in cell culture underpins our predictions of the uptake of nanoformulations in vivo for drug delivery. Cell-penetrating peptides (CPP), such as oligoarginine, are currently of interest to enhance cellular uptake of bioactives and nanoparticles. This paper assesses the cellular association of poly(ethyl-cyanoacrylate) nanoparticles functionalized with di-arginine-histidine (RRH) in a Caco-2 cell model.

Pairing food and drink: A physiological model of blood ethanol levels for a variety of drinking behaviors.

We present a blood ethanol concentration compartment model which utilizes an animal's ethanol intake, food intake, and weight to predict the animal's blood ethanol concentration at any given time. By incorporating the food digestion process into the model we can predict blood ethanol concentration levels over time for a variety of drinking and eating scenarios. The model is calibrated and validated using data from cohorts of male monkeys, and is able to capture blood ethanol concentration kinetics of the monkeys from a variety of drinking behavior classifications.

Predicting the impact of placing an overdose prevention site in Philadelphia: a mathematical modeling approach.

Background: Fatal overdoses from opioid use and substance disorders are increasing at an alarming rate. One proposed harm reduction strategy for reducing overdose fatalities is to place overdose prevention sites-commonly known as safe injection facilities-in proximity of locations with the highest rates of overdose. As urban centers in the USA are tackling legal hurdles and community skepticism around the introduction and location of these sites, it becomes increasingly important to assess the magnitude of the effect that these services might have on public health.

Increasing the speed of frequency-domain, homodyne thermoreflectance imaging.

Charge coupled device (CCD)-based thermoreflectance imaging using a "4-bucket" lock-in imaging algorithm is a well-established, powerful method for obtaining high spatial and thermal resolution two-dimensional thermal maps of optoelectronic, electronic, and micro-electro-mechanical systems devices. However, the technique is relatively slow, limiting broad commercial adoption. In this work, we examine the underlying limit on the image acquisition speed using the conventional "4-bucket" algorithm and show that the straightforward extension to an n-bucket technique by faster sampling does not address the underlying statistical bias in the data analysis and hence does not reduce the image acquisition time.

Time for a Drink? A Mathematical Model of Non-human Primate Alcohol Consumption.

We simulate a non-human primate's alcohol drinking pattern in order to better understand temporal patterning of alcoholic drinks that can lead to the excessive intakes associated with alcohol use disorder. A stochastic mathematical model of alcohol consumption pattern is developed, where model parameters are calibrated to an individual monkey's drinking history. The model predicts a time series that simulates a monkey's alcohol intake in time, and we analyze this drinking pattern to understand the variations in day and night drinking, the lengths of drinks (intake in 5 or more consecutive secs), and lengths of bouts (1 or more drinks per 5 min occasion).

Variability of Betweenness Centrality and Its Effect on Identifying Essential Genes.

This paper begins to build a theoretical framework that would enable the pharmaceutical industry to use network complexity measures as a way to identify drug targets. The variability of a betweenness measure for a network node is examined through different methods of network perturbation. Our results indicate a robustness of betweenness centrality in the identification of target genes.

Graph complexity analysis identifies an ETV5 tumor-specific network in human and murine low-grade glioma.

Conventional differential expression analyses have been successfully employed to identify genes whose levels change across experimental conditions. One limitation of this approach is the inability to discover central regulators that control gene expression networks. In addition, while methods for identifying central nodes in a network are widely implemented, the bioinformatics validation process and the theoretical error estimates that reflect the uncertainty in each step of the analysis are rarely considered.

Signaled drug delivery and transport across the blood-brain barrier.

We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound (US). Thereupon, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain barrier (BBB).

Accounting for unintended binding events in the analysis of quartz crystal microbalance kinetic data.

Previous methods for analyzing protein-ligand binding events using the quartz crystal microbalance with dissipation monitoring (QCM-D) fail to account for unintended binding that inevitably occurs during surface measurements and obscure kinetic information. In this article, we present a system of differential equations that accounts for both reversible and irreversible unintended interactions. This model is tested on three protein-ligand systems, each of which has different features, to establish the feasibility of using the QCM-D for protein binding analysis.

Dynamic pricing of network goods with boundedly rational consumers.

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational and unable either to pay immediate attention to each price change or to make accurate forecasts of the adoption of the network good. Our analysis shows that the seller's optimal price trajectory has the following structure: The price is low when the user base is below a target level, is high when the user base is above the target, and is set to keep the user base stationary once the target level has been attained.

A model of dendritic cell therapy for melanoma.

Dendritic cells are a promising immunotherapy tool for boosting an individual's antigen-specific immune response to cancer. We develop a mathematical model using differential and delay-differential equations to describe the interactions between dendritic cells, effector-immune cells, and tumor cells. We account for the trafficking of immune cells between lymph, blood, and tumor compartments.

A multiple time-scale computational model of a tumor and its micro environment.

Experimental evidence suggests that a tumor's environment may be critical to designing successful therapeutic protocols: Modeling interactions between a tumor and its environment could improve our understanding of tumor growth and inform approaches to treatment. This paper describes an efficient, flexible, hybrid cellular automaton-based implementation of numerical solutions to multiple time-scale reaction-diffusion equations, applied to a model of tumor proliferation. The growth and maintenance of cells in our simulation depend on the rate of cellular energy (ATP) metabolized from nearby nutrients such as glucose and oxygen.

Best practices in mathematical modeling.

Mathematical modeling is a vehicle that allows for explanation and prediction of natural phenomena. In this chapter we present guidelines and best practices for developing and implementing mathematical models, using cancer growth, chemotherapy, and immunotherapy modeling as examples.

Kinetics of bile salt binding to liposomes revealed by carboxyfluorescein release and mathematical modeling.

We propose a mathematical model for the release of carboxyfluorescein from liposomes whose membrane permeability is modified by the binding of different bile salts to the leaflets of the lipid bilayer. We find that the permeability of the liposomal bilayer depends on the difference in the concentrations of bile salt in the inner and outer leaflets and is only minimally influenced by the total concentration of bile salt in the bilayer. Deoxycholate and cholate are found to behave similarly in enhancing permeability for limited times, whereas the novel bile salt, 12-monoketocholate, flips from the outer to inner leaflet slowly, thereby enhancing membrane permeability for a prolonged time.

Team research at the biology-mathematics interface: project management perspectives.

The success of interdisciplinary research teams depends largely upon skills related to team performance. We evaluated student and team performance for undergraduate biology and mathematics students who participated in summer research projects conducted in off-campus laboratories. The student teams were composed of a student with a mathematics background and an experimentally oriented biology student.

A validated mathematical model of cell-mediated immune response to tumor growth.

Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynamics of immune-mediated tumor rejection. The model describes tumor-immune cell interactions using a system of differential equations.

A delay differential equation model for tumor growth.

We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle.