Identification of Nascent Memory CD8 T Cells and Modeling of Their Ontogeny

Primary immune responses generate short-term effectors and long-term protective memory cells. The delineation of the genealogy linking naive, effector, and memory cells has been complicated by the lack of phenotypes discriminating effector from memory differentiation stages. Using transcriptomics and phenotypic analyses, we identify Bcl2 and Mki67 as a marker combination that enables the tracking of nascent memory cells within the effector phase. We then use a formal approach based on mathematical models describing the dynamics of population size evolution to test potential progeny links and demonstrate that most cells follow a linear naive→early effector→late effector→memory pathway. Moreover, our mathematical model allows long-term prediction of memory cell numbers from a few early experimental measurements. Our work thus provides a phenotypic means to identify effector and memory cells, as well as a mathematical framework to investigate their genealogy and to predict the outcome of immunization regimens in terms of memory cell numbers generated.

Integrating Evolutionary Game Theory into Mechanistic Genotype-Phenotype Mapping

Natural selection has shaped the evolution of organisms toward optimizing their structural and functional design. However, how this universal principle can enhance genotype-phenotype mapping of quantitative traits has remained unexplored. Here we show that the integration of this principle and functional mapping through evolutionary game theory gains new insight into the genetic architecture of complex traits. By viewing phenotype formation as an evolutionary system, we formulate mathematical equations to model the ecological mechanisms that drive the interaction and coordination of its constituent components toward population dynamics and stability. Functional mapping provides a procedure for estimating the genetic parameters that specify the dynamic relationship of competition and cooperation and predicting how genes mediate the evolution of this relationship during trait formation.

Structural and practical identifiability analysis of S-system

In the field of systems biology, biological reaction networks are usually modelled by ordinary differential equations. A sub-class, the S-systems representation, is a widely used form of modelling. Existing S-systems identification techniques assume that the system itself is always structurally identifiable. However, due to practical limitations, biological reaction networks are often only partially measured. In addition, the captured data only covers a limited trajectory, therefore data can only be considered as a local snapshot of the system responses with respect to the complete set of state trajectories over the entire state space. Hence the estimated model can only reflect partial system dynamics and may not be unique. To improve the identification quality, the structural and practical identifiablility of S-system are studied. The S-system is shown to be identifiable under a set of assumptions. Then, an application on yeast fermentation pathway was conducted. Two case studies were chosen; where the first case is based on a larger state trajectories and the second case is based on a smaller one. By expanding the dataset which span a relatively larger state space, the uncertainty of the estimated system can be reduced. The results indicated that initial concentration is related to the practical identifiablity.

Two-compartment model as a teaching tool for cholesterol homeostasis

Cholesterol is a vital structural and functional molecule in the human body that is only slightly soluble in water and therefore does not easily travels by itself in the bloodstream. To enable cholesterol's targeted delivery to cells and tissues, it is encapsulated by different fractions of lipoproteins, complex particles containing both proteins and lipids. Maintaining cholesterol homeostasis is a highly regulated process with multiple factors acting at both molecular and tissue levels. Furthermore, to regulate the circulatory transport of cholesterol in lipoproteins, the amount of cholesterol present depends on and is controlled by cholesterol dietary intake, de novo synthesis, usage, and excretion; abnormal and/or unbalanced cholesterol levels have been shown to lead to severe outcomes, e.g., cardiovascular diseases. To investigate cholesterol transport in the circulatory system, we have previously developed a two-compartment mathematical model. Here, we show how this model can be used as a teaching tool for cholesterol homeostasis. Using the model and a hands-on approach, students can familiarize themselves with the basic components and mechanisms behind balanced cholesterol circulatory transport as well as investigate the consequences of and countermeasures to abnormal cholesterol levels. Among others, various treatments of high blood cholesterol levels can be simulated, e.g., with commonly prescribed de novo cholesterol synthesis inhibitors.

Pedagogical view of model metabolic cycles

The main purpose of this study was to present a simplified view of model metabolic cycles. Although the models have been elaborated with the Mathematica Program, and using a system of differential equations, the main conclusions were presented in a rather intuitive way, easily understandable by students of general courses of Biochemistry, and without any need of mathematical support. A change in any kinetic constant (Km or Vmax) of only one enzyme affected the metabolic profile of all the substrates of the cycle. In addition, it is shown how an increase in the Km or a decrease in the Vmax values of any particular enzyme promoted an increase of its substrate; the contrary occurred decreasing the Km or increasing the Vmax values.

Multiscale model of a freeze-thaw process for tree sap exudation

Sap transport in trees has long fascinated scientists, and a vast literature exists on experimental and modelling studies of trees during the growing season when large negative stem pressures are generated by transpiration from leaves. Much less attention has been paid to winter months when trees are largely dormant but nonetheless continue to exhibit interesting flow behaviour. A prime example is sap exudation, which refers to the peculiar ability of sugar maple (Acer saccharum) and related species to generate positive stem pressure while in a leafless state. Experiments demonstrate that ambient temperatures must oscillate about the freezing point before significantly heightened stem pressures are observed, but the precise causes of exudation remain unresolved. The prevailing hypothesis attributes exudation to a physical process combining freeze-thaw and osmosis, which has some support from experimental studies but remains a subject of active debate. We address this knowledge gap by developing the first mathematical model for exudation, while also introducing several essential modifications to this hypothesis. We derive a multiscale model consisting of a nonlinear system of differential equations governing phase change and transport within wood cells, coupled to a suitably homogenized equation for temperature on the macroscale. Numerical simulations yield stem pressures that are consistent with experiments and provide convincing evidence that a purely physical mechanism is capable of capturing exudation.

Robust kinetics of an RNA virus: Transcription rates are set by genome levels

In order to persist in nature, RNA viruses have evolved strategies to grow in diverse host environments. To better understand how such strategies might work, we used qRT-PCR to measure viral RNA species during cellular infections by a model RNA virus, vesicular stomatitis virus (VSV). Absolute levels of the VSV major transcript and genome were measured for infections in BHK and PC3 cells, across different multiplicities of infection (MOI 1, 10, 100), in the absence or presence of protein synthesis, as well as in cells in an interferon-activated anti-viral state. While viral genome replication was delayed in more resistant host cells, kinetic modeling of these data revealed a simple linear relationship between the mRNA production rate and genome levels under all tested conditions. These results indicate that while viral transcription and genome replication both depend on the availability of the viral RNA-dependent RNA polymerase and host cellular resources, transcription proceeds without apparent limits on these resources.

Dynamic flux balance analysis for synthetic microbial communities

Dynamic flux balance analysis (DFBA) is an extension of classical flux balance analysis that allows the dynamic effects of the extracellular environment on microbial metabolism to be predicted and optimised. Recently this computational framework has been extended to microbial communities for which the individual species are known and genome-scale metabolic reconstructions are available. In this review, the authors provide an overview of the emerging DFBA approach with a focus on two case studies involving the conversion of mixed hexose/pentose sugar mixtures by synthetic microbial co-culture systems. These case studies illustrate the key requirements of the DFBA approach, including the incorporation of individual species metabolic reconstructions, formulation of extracellular mass balances, identification of substrate uptake kinetics, numerical solution of the coupled linear program/differential equations and model adaptation for common, suboptimal growth conditions and identified species interactions. The review concludes with a summary of progress to date and possible directions for future research.

Predicting future coexistence in a North American ant community

Global climate change will remodel ecological communities worldwide. However, as a consequence of biotic interactions, communities may respond to climate change in idiosyncratic ways. This makes predictive models that incorporate biotic interactions necessary. We show how such models can be constructed based on empirical studies in combination with predictions or assumptions regarding the abiotic consequences of climate change. Specifically, we consider a well-studied ant community in North America. First, we use historical data to parameterize a basic model for species coexistence. Using this model, we determine the importance of various factors, including thermal niches, food discovery rates, and food removal rates, to historical species coexistence. We then extend the model to predict how the community will restructure in response to several climate-related changes, such as increased temperature, shifts in species phenology, and altered resource availability. Interestingly, our mechanistic model suggests that increased temperature and shifts in species phenology can have contrasting effects. Nevertheless, for almost all scenarios considered, we find that the most subordinate ant species suffers most as a result of climate change. More generally, our analysis shows that community composition can respond to climate warming in nonintuitive ways. For example, in the context of a community, it is not necessarily the most heat-sensitive species that are most at risk. Our results demonstrate how models that account for niche partitioning and interspecific trade-offs among species can be used to predict the likely idiosyncratic responses of local communities to climate change.

Towards a comprehensive picture of the genetic landscape of complex traits

The formation of phenotypic traits, such as biomass production, tumor volume and viral abundance, undergoes a complex process in which interactions between genes and developmental stimuli take place at each level of biological organization from cells to organisms. Traditional studies emphasize the impact of genes by directly linking DNA-based markers with static phenotypic values. Functional mapping, derived to detect genes that control developmental processes using growth equations, has proven powerful for addressing questions about the roles of genes in development. By treating phenotypic formation as a cohesive system using differential equations, a different approach-systems mapping-dissects the system into interconnected elements and then map genes that determine a web of interactions among these elements, facilitating our understanding of the genetic machineries for phenotypic development. Here, we argue that genetic mapping can play a more important role in studying the genotype-phenotype relationship by filling the gaps in the biochemical and regulatory process from DNA to end-point phenotype. We describe a new framework, named network mapping, to study the genetic architecture of complex traits by integrating the regulatory networks that cause a high-order phenotype. Network mapping makes use of a system of differential equations to quantify the rule by which transcriptional, proteomic and metabolomic components interact with each other to organize into a functional whole. The synthesis of functional mapping, systems mapping and network mapping provides a novel avenue to decipher a comprehensive picture of the genetic landscape of complex phenotypes that underlie economically and biomedically important traits.

A Mathematic Model That Describes Modes of MdSGHV Transmission within House Fly Populations

In this paper it is proposed that one potential component by which the Musca domestica salivary gland hypertrophy virus (MdSGHV) infects individual flies is through cuticular damage. Breaks in the cuticle allow entry of the virus into the hemocoel causing the infection. Male flies typically have a higher rate of infection and a higher rate of cuticular damage than females. A model for the transmission of MdSGHV was formulated assuming several potential and recognized means of transmission. The model yields results that are in agreement with field data that measured the infection rate in house flies on dairy farms in Florida. The results from this model indicate that MdSGHV will be maintained at a stable rate within house fly populations and support the future use of MdSGHV as a birth control agent in house fly management.

Avidity and positive allosteric modulation/cooperativity act hand in hand to increase the residence time of bivalent receptor ligands

Bivalent ligands bear two target-binding pharmacophores. Their simultaneous binding increases their affinity (avidity) and residence time. They become 'bitopic' when the binding sites at the target permit the pharmacophores the exert allosteric modulation of each other's affinity and/or activity. Present simulations reveal that positive cooperativity exacerbates these phenomena, whereas negative cooperativity curtails them, irrespective of whether the association or dissociation rates of the individual pharmacophores are affected. Positive cooperativity delays the attainment of equilibrium binding, yielding 'hemi-equilibrium' conditions and only apparent affinity constants under usual experimental conditions. Monovalent ligands that bind to one of the target sites decrease the bitopic ligand's residence time concentration-wise; their potency depends on their association rate and thereon acting cooperativity rather than on affinity. This stems from the repetitive, very fast reformation of fully bound bitopic ligand-target complexes by rebinding of freshly dissociated pharmacophores. These studies deal with kinetic binding properties (of increasing interest in pharmacology) of bitopic ligands (a promising avenue in medicinal chemistry).

Delivering systems pharmacogenomics towards precision medicine through mathematics

The latest developments of pharmacology in the post-genomic era foster the emergence of new biomarkers that represent the future of drug targets. To identify these biomarkers, we need a major shift from traditional genomic analyses alone, moving the focus towards systems approaches to elucidating genetic variation in biochemical pathways of drug response. Is there any general model that can accelerate this shift via a merger of systems biology and pharmacogenomics? Here we describe a statistical framework for mapping dynamic genes that affect drug response by incorporating its pharmacokinetic and pharmacodynamic pathways. This framework is expanded to shed light on the mechanistic and therapeutic differences of drug response based on pharmacogenetic information, coupled with genomic, proteomic and metabolic data, allowing novel therapeutic targets and genetic biomarkers to be characterized and utilized for drug discovery.

A HIERARCHICAL FUNCTIONAL DATA ANALYTIC APPROACH FOR ANALYZING PHYSIOLOGICALLY BASED PHARMACOKINETIC MODELS

Ordinary differential equation (ODE) based models find application in a wide variety of biological and physiological phenomena. For instance, they arise in the description of gene regulatory networks, study of viral dynamics and other infectious diseases, etc. In the field of toxicology, they are used in physiologically based pharmacokinetic (PBPK) models for describing absorption, distribution, metabolism and excretion (ADME) of a chemical in-vivo. Knowledge about the model parameters is important for understanding the mechanism of action of a chemical and are often estimated using non-linear least squares methodology. However, there are several challenges associated with the usual methodology. Using functional data analytic methodology, in this article we develop a general framework for drawing inferences on parameters in models described by a system of differential equations. The proposed methodology takes into account variability between and within experimental units. The performance of the proposed methodology is evaluated using a simulation study and data obtained from a benzene inhalation study. We also describe a R-based software developed towards this purpose.

MATHEMATICAL MODELS OF SUBCUTANEOUS INJECTION OF INSULIN ANALOGUES: A MINI-REVIEW

In the last three decades, several models relevant to the subcutaneous injection of insulin analogues have appeared in the literature. Most of them model the absorption of insulin analogues in the injection depot and then compute the plasma insulin concentration. The most recent systemic models directly simulate the plasma insulin dynamics. These models have been and/or can be applied to the technology of the insulin pump or to the coming closed-loop systems, also known as the artificial pancreas. In this paper, we selectively review these models in detail and at point out that these models provide key building blocks for some important endeavors into physiological questions of insulin secretion and action. For example, it is not clear at this time whether or not picomolar doses of insulin are found near the islets and there is no experimental method to assess this in vivo. This is of interest because picomolar concentrations of insulin have been found to be effective at blocking beta-cell death and increasing beta-cell growth in recent cell culture experiments.

Mood Oscillations and Coupling Between Mood and Weather in Patients with Rapid Cycling Bipolar Disorder

Rapid Cycling Bipolar Disorder (RCBD) outpatients completed twice-daily mood self-ratings for 3 consecutive months. These ratings were matched with local measurements of atmospheric pressure, cloud cover, and temperature. Several alternative second order differential equation models were fit to the data in which mood oscillations in RCBD were allowed to be linearly coupled with daily weather patterns. The modeling results were consistent with an account of mood regulation that included intrinsic homeostatic regulation as well as coupling between weather and mood. Models were tested first in a nomothetic method where models were fit over all individuals and fit statistics of each model compared to one another. Since substantial individual differences in intrinsic dynamics were observed, the models were next fit using an ideographic method where each individual's data were fit separately and best-fitting models identified. The best-fitting within-individual model for the largest number of individuals was also the best-fitting nomothetic model: temperature and the first derivative of temperature coupled to mood and no effect of barometric pressure or cloud cover. But this model was not the best-fitting model for all individuals, suggesting that there may be substantial individual differences in the dynamic association between weather and mood in RCBD patients. Heterogeneity in the parameters of the differential equation model of homeostatic equilibrium as well as the coupling of mood to an inherently unpredictable (i.e., nonstationary) process such as weather provide an alternative account for reported broadband frequency spectra of daily mood in RCBD.

Exact Coefficients of the Limit Cycle in Van der Pol's Equation

A program generator to manipulate automatically Poisson series over the field of rational numbers is applied to develop the limit cycle of Van der Pol's equation in the powers of the small parameter. The results indicate that the recurrence relations in what Melvin calls the algorithm of the shifted phase are stable.

The Phase-Shifting Limit Cycles of the van der Pol Equation

The van der Pol limit cycles are generated at small amplitudes by the computer implementation of the Poincaré-Lindstedt method. The formal algebraic solution is accomplished by manipulations of Poisson series, and the FORTRAN programming of the inductive algorithm yields the phase-shifting limit cycles to graphical accuracy over the range 0 ≤ λ ≤ 1.5. This improves upon the method of Deprit and Rom in two ways. First, because the formal solution is carried out by hand, an algebraic processor is not necessary. Second, the standard solutions which they generated are only valid for 0 ≤ λ ≤ 1.2 whereas the phase-shifting limit cycles are still valid at λ = 1.5; that is, they do not exhibit the Gibbs phenomenon even at λ = 1.5.