Predicting the dynamics of antiviral cytotoxic T-cell memory in response to different stimuli: cell population structure and protective function

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Understanding Experimental LCMV Infection of Mice: The Role of Mathematical Models

Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl), that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.

Enhanced reactivity of peripheral blood immune cells to HSV-1 in primary achalasia

OBJECTIVE

Achalasia is the best characterized oesophageal motor disorder but the etiology is unknown. The pathology is characterized by a decrease in nitric oxide-producing neurons and the presence of an activated T-cell inflammatory infiltrate in the myenteric plexus that are reactive to HSV-1 viral antigens. These findings are not present in normal controls. The current study compared the reactivity of peripheral blood mononuclear cells (PBMCs) between patients with primary achalasia and normal controls to determine if PBMCs of patients exhibit a similar heightened reactivity to the virus.

MATERIAL AND METHODS

Whole blood culture experiments were conducted with heparinized peripheral venous blood obtained from 151 patients with primary achalasia and 118 healthy controls. Whole blood was cultured in the presence of ultraviolet inactivated HSV-1 or conditioned cell culture media. Reactivity of mononuclear cells to viral antigens was quantified by measuring expression of the cytokine gene interferon-gamma using Taqman real-time polymerase chain reaction. Data are expressed as cytokine fold change corresponding to ratio of interferon-gamma messenger RNA copies produced in antigen stimulated versus unstimulated cells.

RESULTS

The interferon-gamma fold change was higher in cases 61.33 (20.54-217.00) than controls 49.67 (10.05-157.05). Mean fold change difference between cases and controls was 1.66 times (95% confidence interval 1.17-2.34, p = 0.004).

CONCLUSIONS

These results indicate that the PBMCs of patients with primary achalasia show an enhanced immune response to HSV-1 antigens. The data suggest that there is persistent stimulation of immune cells by herpes simplex virus type 1 (HSV-1) or HSV-1 like antigen moieties.

Discriminating between different pathways of memory CD8+ T cell differentiation

Despite the rapid accumulation of quantitative data on the dynamics of CD8(+) T cell responses following acute viral or bacterial infections of mice, the pathways of differentiation of naive CD8(+) T cells into memory during an immune response remain controversial. Currently, three models have been proposed. In the "stem cell-associated differentiation" model, following activation, naive T cells differentiate into stem cell-like memory cells, which then convert into terminally differentiated short-lived effector cells. In the "linear differentiation" model, following activation, naive T cells first differentiate into effectors, and after Ag clearance, effectors convert into memory cells. Finally, in the "progressive differentiation" model, naive T cells differentiate into memory or effector cells depending on the amount of specific stimulation received, with weaker stimulation resulting in formation of memory cells. This study investigates whether the mathematical models formulated from these hypotheses are consistent with the data on the dynamics of the CD8(+) T cell response to lymphocytic choriomeningitis virus during acute infection of mice. Findings indicate that two models, the stem cell-associated differentiation model and the progressive differentiation model, in which differentiation of cells is strongly linked to the number of cell divisions, fail to describe the data at biologically reasonable parameter values. This work suggests additional experimental tests that may allow for further discrimination between different models of CD8(+) T cell differentiation in acute infections.

Maintenance of HIV-specific central and effector memory CD4 and CD8 T cells requires antigen persistence

The HIV-specific central and effector CD4 and CD8 memory T cell populations disappear from the peripheral blood of infected individuals under highly active antiretroviral therapy (HAART) with a mean half-life of 6.0 and 7.7 months, respectively. By contrast, cytomegalovirus (CMV)-specific responses are stable or increase. The striking quantitative differences between T cell memory to two persistent viral infections are instructive as to how antigen dosage contributes to the maintenance of antigen-specific memory T cell responses in humans.

Impact of gene-modified T cells on HIV infection dynamics

Previous clinical trials in HIV-infected patients involving infusion of T cells protected by an antiviral gene have failed to show any therapeutic benefit. The value of such a treatment approach is thus still highly controversial. In this study, the anticipated effects of gene-modified cells on virus and T-cell kinetics are analysed by mathematical modeling. Because technically only a small fraction of all T cells in a patient can be manipulated ex vivo, therapeutic success will depend on the accumulation of gene-modified cells after infusion into the patient by in vivo selection. Our simulations predict that a significant therapeutic benefit is conferred only by antiviral genes that inhibit HIV replication before virus integration (class I genes). Genes that inhibit viral protein expression (class II, used in previous clinical trials), require a much higher inhibitory activity than class I genes to promote the regeneration of T cells and reduce the viral load. Inhibition of virus assembly and release alone (class III) confers no selective advantage to the T cell and is therefore ineffective unless combined with class I (or, possibly, class II) genes. Also crucial in determining the clinical outcome are the regenerative capacity of the gene-modified cells and the level of HIV replication in the patient. These results can be important for guiding future strategies in the field of gene therapy for HIV infection.

Modelling the dynamics of LCMV infection in mice: II. Compartmental structure and immunopathology

In this study, we develop a mathematical model for analysis of the compartmental aspects and immunopathology of lymphocytic choriomeningitis virus (LCMV) infection in mice. We used sets of original and published data on systemic (extrasplenic) virus distribution to estimate the parameters of virus growth and elimination for spleen and other anatomical compartments, such as the liver, kidney, thymus and lung as well as transfer rates between blood and the above organs. A mathematical model quantitatively integrating the virus distribution kinetics in the host, the specific cytotoxic T lymphocyte (CTL) response in spleen and the re-circulation of effector CTL between spleen, blood and liver is advanced to describe the CTL-mediated immunopathology (hepatitis) in mice infected with LCMV. For intravenous and "peripheral" routes of infection we examine the severity of the liver disease, as a function of the virus dose and the host's immune status characterized by the numbers of precursor and/or cytolytic effector CTL. The model is used to predict the efficacy of protection against virus persistence and disease in a localized viral infection as a function of the composition of CTL population. The modelling analysis suggests quantitative demands to CTL memory for maximal protection against a wide range of doses of infection with a primarily peripheral site of virus replication without the risk of favoring immunopathology. It specifies objectives for CTL vaccination to ensure virus elimination with minimal immunopathology vs. vaccination for disease.

Computational immunology: The coming of age

The explosive growth in biotechnology combined with major advances in information technology has the potential to radically transform immunology in the postgenomics era. Not only do we now have ready access to vast quantities of existing data, but new data with relevance to immunology are being accumulated at an exponential rate. Resources for computational immunology include biological databases and methods for data extraction, comparison, analysis and interpretation. Publicly accessible biological databases of relevance to immunologists number in the hundreds and are growing daily. The ability to efficiently extract and analyse information from these databases is vital for efficient immunology research. Most importantly, a new generation of computational immunology tools enables modelling of peptide transport by the transporter associated with antigen processing (TAP), modelling of antibody binding sites, identification of allergenic motifs and modelling of T-cell receptor serial triggering.

Cellular immune responses against hepatitis C virus: the evidence base 2002

Hepatitis C virus (HCV) is an RNA virus which is estimated to persistently infect about 170 million people worldwide. After acute infection, there is an initial period during which long-term outcome is decided. There is strong evidence that the cellular immune responses, involving both CD4+ and CD8+ T lymphocytes, are involved at this stage and it is their effectiveness which determines outcome. What is not understood is what determines their effectiveness. The most important component of this is likely to be some aspect of epitope selection, itself dictated by host MHC. Thus, to understand host immunity to HCV, we need to have a detailed understanding of the peptides involved in T lymphocyte responses. In this review, we discuss the peptide epitopes that have been identified so far, and their potential significance. We relate this to a scheme of host defence which may be useful for understanding natural and vaccine-induced immunity.

Low level viral persistence after infection with LCMV: a quantitative insight through numerical bifurcation analysis

Many important viruses persist at very low levels in the body in the face of host immunity, and may influence the maintenance of this state of 'infection immunity'. To analyse low level viral persistence in quantitative terms, we use a mathematical model of antiviral cytotoxic T lymphocyte (CTL) response to lymphocytic choriomeningitis virus (LCMV). This model, described by a non-linear system of delay differential equations (DDEs), is studied using numerical bifurcation analysis techniques for DDEs. Domains where low level LCMV coexistence with CTL memory is possible, either as an equilibrium state or an oscillatory pattern, are identified in spaces of the model parameters characterising the interaction between virus and CTL populations. Our analysis suggests that the coexistence of replication competent virus below the conventional detection limit (of about 100 pfu per spleen) in the immune host as an equilibrium state requires the per day relative growth rate of the virus population to decrease at least 5-fold compared to the acute phase of infection. Oscillatory patterns in the dynamics of persisting LCMV and CTL memory, with virus population varying between 1 and 100 pfu per spleen, are possible within quite narrow intervals of the rates of virus growth and precursor CTL population death. Whereas the virus replication rate appears to determine the stability of the low level virus persistence, it does not affect the steady-state level of the viral population, except for very low values.