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The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our previous work (Huang and Yong, 2013) for simplifying the Fas signaling-induced apoptotic pathway identified by Hua et al. (2005) for human tumor T cells. The previous paper studied the downstream intracelluar-signaling subsystem, while the present one is concerned with the upstream death-inducing signaling complex (DISC) subsystem. Under the assumption that the bind of Fas-associated death domains and FLICE-inhibitory proteins to the DISC is much faster than that of the initiator procaspases, we greatly simplify the upstream subsystem from 35 reactions with 26 species to 6 reactions with 9 species by adopting the classical and recently justified partial equilibrium approximation method. Numerical simulations show that the simplified model is in an excellent agreement with the original model. Most importantly, the simplified model clearly reveals the key reactants and dominated pathways in the Fas signaling process, and thus provides new insights into the apoptosis. [ABSTRACT FROM AUTHOR]

Abstract: Immunodominance is a common phenomenon observed in multiple epitopes immune systems. Previous studies hypothesize that the competition among CD8+ T cell responses against different epitopes can be used to explain immunodominance. This paper proposes a mathematical model that describes the dynamics of CD8+ T cells primed by antigen-presenting dendritic cells (DCs) in the lymph nodes, and shows that the overall avidity of the interactions between peptide-specific T cells and cognate antigen-bearing DCs may determine the immunodominance. The model suggests the probability that a peptide-specific T cell be immunodominant is proportional to (1) the cognate T cell receptor (TCR) affinity, (2) the number of complexes of cognate peptide and major histocompatibility complex (pMHC) per DC, and (3) the half-life of cognate peptide-specific pMHC. The model predicts a threshold density of pMHC complexes for T cell activation. These observations from the mathematical model are consistent with experimental studies in the open literature. For DC-based vaccine design, the model suggests a strategy of immunotherapy based on the injection of cognate antigen-pulsed DCs. [Copyright &y& Elsevier]

Abstract: The limiting conditional probability distribution (LCD) has been much studied in the field of mathematical biology, particularly in the context of epidemiology and the persistence of epidemics. However, it has not yet been applied to the immune system. One of the characteristic features of the T cell repertoire is its diversity. This diversity declines in old age, whence the concepts of extinction and persistence are also relevant to the immune system. In this paper we model T cell repertoire maintenance by means of a continuous-time birth and death process on the positive integers, where the origin is an absorbing state. We show that eventual extinction is guaranteed. The late-time behaviour of the process before extinction takes place is modelled by the LCD, which we prove always exists for the process studied here. In most cases, analytic expressions for the LCD cannot be computed but the probability distribution may be approximated by means of the stationary probability distributions of two related processes. We show how these approximations are related to the LCD of the original process and use them to study the LCD in two special cases. We also make use of the large N expansion to derive a further approximation to the LCD. The accuracy of the various approximations is then analysed. [Copyright &y& Elsevier]

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator–prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator–prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1–12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of illustration we demonstrate an application of the models using real AIDS clinical trial data involving patients treated with a combination of anti-retroviral agents using a model which incorporates compliance data. [Copyright &y& Elsevier]