A second-order high-resolution finite difference scheme for a size-structured model for the spread of Mycobacterium marinum.

We present a second-order high-resolution finite difference scheme to approximate the solution of a mathematical model of the transmission dynamics of Mycobacterium marinum (Mm) in an aquatic environment. This work extends the numerical theory and continues the preliminary studies on the model first developed in Ackleh et al. [Structured models for the spread of Mycobacterium marinum: foundations for a numerical approximation scheme, Math. Biosci. Eng. 11 (2014), pp. 679-721]. Numerical simulations demonstrating the accuracy of the method are presented, and we compare this scheme to the first-order scheme developed in Ackleh et al. [Structured models for the spread of Mycobacterium marinum: foundations for a numerical approximation scheme, Math. Biosci. Eng. 11 (2014), pp. 679-721] to show that the first-order method requires significantly more computational time to provide solutions with a similar accuracy. We also demonstrated that the model can be a tool to understand surprising or nonintuitive phenomena regarding competitive advantage in the context of biologically realistic growth, birth and death rates.

Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations.

In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.

A new model for the estimation of cell proliferation dynamics using CFSE data.

CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al. (2009), Luzyanina et al. (2007), a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data.

Estimation of cell proliferation dynamics using CFSE data.

Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57-89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1-26, 2007) contain a mathematical model with fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Here, this model and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations suggest that the new decay/label loss and time dependent effective proliferation and death rates do indeed provide improved fits of the model to data. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics model should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences.

Label Structured Cell Proliferation Models.

We present a general class of cell population models that can be used to track the proliferation of cells which have been labeled with a fluorescent dye. The mathematical models employ fluorescence intensity as a structure variable to describe the evolution in time of the population density of proliferating cells. While cell division is a major component of changes in cellular fluorescence intensity, models developed here also address overall label degradation.

Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination.

The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods.

Public vaccination policy using an age-structured model of pneumococcal infection dynamics.

Public health professionals are charged with the task of designing prevention programs for the effective control of biologically intricate infectious diseases at a population level. The effective vaccination of a population for pneumococcal diseases (infections caused by Streptococcus pneumoniae) remains a relevant question in the scientific community. It is complicated by heterogeneity in individuals' responses to exposure to the bacterium and their responses to vaccination. Due to these complexities, most modelling efforts in this area have been on the cellular/bacteria level. Here, we introduce an age-structured SEIS-type model of pneumococcal diseases and their vaccination. We discuss the use of this framework in predicting the impact of vaccine strategies, with pneumococcal diseases as an example. Using parameter values reasonable for a developed country, we discuss the effects of targeting the colonization and/or infection stages on the age profiles of morbidity in a population.

Estimation of invasive pneumococcal disease dynamics parameters and the impact of conjugate vaccination in Australia.

Pneumococcal diseases, or infections from the etiological agent Streptococcus pneumoniae, have long been a major cause of morbidity and mortality worldwide. Recent advances in the development of vaccines for these infections have raised questions concerning their widespread and/or long-term use. In this work, we use surveillance data collected by the Australian National Notifiable Diseases Surveillance system to estimate parameters in a mathematical model of pneumococcal infection dynamics in a population with partial vaccination. The parameters obtained are of particular interest as they are not typically available in reported literature or measurable. The calibrated model is then used to assess the impact of the recent federally funded program that provides pneumococcal vaccines to large risk groups. The results presented here suggest the state of these infections may be changing in response to the programs, and warrants close quantitative monitoring.

Multiple receptor states are required to describe both kinetic binding and activation of neutrophils via N-formyl peptide receptor ligands.

It is well-established that the binding of N-formyl peptides to the N-formyl peptide receptor on neutrophils can be described by a kinetic scheme that involves two ligand-bound receptor states, both a low affinity ligand-receptor complex and a high affinity ligand-receptor complex, and that the rate constants describing ligand-receptor binding and receptor affinity state interconversion are ligand-specific. Here we examine whether differences due to these rate constants, i.e. differences in the numbers and lifetimes of particular receptor states, are correlated with neutrophil responses, namely actin polymerization and oxidant production. We find that an additional receptor state, one not discerned from kinetic binding assays, is required to account for these responses. This receptor state is interpreted as the number of low affinity bound receptors that are capable of activating G proteins; in other words, the accumulation of these active receptors correlates with the extent of both responses. Furthermore, this analysis allows for the quantification of a parameter that measures the relative strength of a ligand to bias the receptor into the active conformation. A model with this additional receptor state is sufficient to describe response data when two ligands (agonist/agonist or agonist/antagonist pairs) are added simultaneously, suggesting that cells respond to the accumulation of active receptors regardless of the identity of the ligand(s).

Receptor binding kinetics and cellular responses of six N-formyl peptide agonists in human neutrophils.

The goal of this study was to elucidate the relationships between early ligand binding/receptor processing events and cellular responses for the N-formyl peptide receptor system on human neutrophils as a model of a GPCR system in a physiologically relevant context. Binding kinetics of N-formyl-methionyl-leucyl-phenylalanyl-phenylalanyl-lysine-fluorescein and N-formyl-valyl-leucyl-phenylalanyl-lysine-fluorescein to the N-formyl peptide receptor on human neutrophils were characterized and combined with previously published binding data for four other ligands. Binding was best fit by an interconverting two-receptor state model that included a low affinity receptor state that converted to a high affinity state. Response behaviors elicited at 37 degrees C by the six different agonists for the N-formyl peptide receptor were measured. Dose response curves for oxidant production, actin polymerization, and G-protein activation were obtained for each ligand; whereas all ligands showed equal efficacy for all three responses, the ED(50) values varied as much as 7000-fold. The level of agonism and rank order of potencies of ligands for actin and oxidant responses were the same as for the G-protein activation assay, suggesting that the differences in abilities of ligands to mediate responses were determined upstream of G-protein activation at the level of ligand-receptor interactions. The rate constants governing ligand binding and receptor affinity conversion were ligand-dependent. Analysis of the forward and reverse rate constants governing binding to the proposed signaling receptor state showed that it was of a similar energy for all six ligands, suggesting the hypothesis that ligand efficacy is dictated by the energy state of this ligand-receptor complex. However, the interconverting two-receptor state model was not sufficient to predict response potency, suggesting the presence of receptor states not discriminated by the binding data.