Backward bifurcation in a model for HTLV-I infection of CD4+ T cells

Human T-cell Lymphotropic Virus Type I (HTLV-I) primarily infects CD4⁺ helper T cells. HTLV-I infection is clinically linked to the development of Adult T-cell Leukemia/Lymphoma and of HTLV-I Associated Myelopathy/Tropical Spastic Paraparesis, among other illnesses. HTLV-I transmission can be either horizontal through cell-to-cell contact, or vertical through mitotic division of infected CD4⁺ T cells. It has been observed that HTLV-I infection has a high proviral load but a low rate of proviral genetic variation. This suggests that vertical transmission through mitotic division of infected cells may play an important role.We consider and analyze a mathematical model for HTLV-I infection of CD4⁺ T cells that incorporates both horizontal and vertical transmission. Among interesting dynamical behaviors of the model is a backward bifurcation which raises many new challenges to effective infection control.     

Anti-tumor immunity in adult T-cell leukemia

Adult T-cell leukemia (ATL) occurs in a small population of human T-cell leukemia virus type I (HTLV-I)-infected individuals. It has been noted that ATL is incidentally associated with mother-to-child infection which occurs mainly through breast-feeding, elevated levels of proviral load, and insufficiency in HTLV-I-specific cytotoxic T lymphocyte (CTL) responses. Among these, anti-tumor potentials of HTLV-I-specific CTL have been shown in ex vivo analysis of human HTLV-I-infected individuals and also in vivo experiments by using rat models of HTLV-I-infected lymphomas. In another rat model of HTLV-I-infection, orally infected rats showed significantly higher HTLV-I proviral load but lower HTLV-I-specific cellular immune responses than in intraperitoneally infected rats. As a result, persistent viral load was inversely correlated with levels of virus-specific T-cell responses. HTLV-I-specific T-cell responses in orally infected rats recovered by re-immunization. Conversion of Tax-specific T-cell responses from low to high levels was also observed in an ATL patient who obtained complete remission after hematopoietic stem cell transplantation. These findings suggest that HTLV-I-specific immune unresponsiveness associated with oral HTLV-I infection may be a potential risk factor for development of ATL, allowing expansion of the infected cell reservoir in vivo, and that immunological strategies targeting Tax may potentially reduce the risk of ATL and induce therapeutic effects on ATL.     

Multistability in a Model for CTL Response to HTLV-I Infection and Its Implications to HAM/TSP Development and Prevention

Human T-cell leukaemia/lymphoma virus type I (HTLV-I) is a retrovirus that has been identified as the causative agent of HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP) and other illnesses. HTLV-I infects primarily CD4⁺ T cells and the transmission occurs through direct cell-to-cell contact. HAM/TSP patients harbor higher proviral loads in peripheral blood lymphocytes than asymptomatic carriers. Also, HAM/TSP patients exhibit a remarkably high number of circulating HTLV-I-specific CD8⁺ cytotoxic T lymphocytes (CTLs) in the peripheral blood. While CTLs have a protective role by killing the infected cells and lowering the proviral load, a high level of CTLs and their cytotoxicity are believed to be a main cause of the development of HAM/TSP. A mathematical model for HTLV-I infection of CD4⁺ T cells that incorporates the CD8⁺ cytotoxic T-cell (CTL) response is investigated. Our mathematical analysis reveals that the system can stabilize at a carrier steady-state with persistent viral infection but no CTL response, or at a HAM/TSP steady-state at which both the viral infection and CTL response are persistent. We also establish two threshold parameters R ₀ and R ₁, the basic reproduction numbers for viral persistence and for CTL response, respectively. We show that the parameter R ₁ can be used to distinguish asymptomatic carriers from HAM/TSP patients, and as an important control parameter for preventing the development of HAM/TSP.     

Genetic control and dynamics of the cellular immune response to the human T-cell leukaemia virus, HTLV-I.

About 1% of people infected with the human T-cell leukaemia virus, type 1 (HTLV-I) develop a disabling chronic inflammatory disease of the central nervous system known as HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP). Patients with HAM/TSP have a vigorous immune response to HTLV-I, and it has been widely suggested that this immune response, particularly the HTLV-I-specific cytotoxic T-lymphocyte (CTL) response, causes the tissue damage that is seen in HAM/TSP. In this paper we summarize recent evidence that a strong CTL response to HTLV-I does in fact protect against HAM/TSP by reducing the proviral load of HTLV-I. We conclude that HTLV-I is persistently replicating at a high level, despite the relative constancy of its genome sequence. These results imply that antiretroviral drugs could reduce the risk of HAM/TSP by reducing the viral load, and that an effective anti-HTLV-I vaccine should elicit a strong CTL response to the virus. The dynamic nature of the infection also has implications for the epidemiology and the evolution of HTLV-I.     

Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression

Mathematical analysis is carried out that completely determines the global dynamics of a mathematical model for the transmission of human T-cell lymphotropic virus I (HTLV-I) infection and the development of adult T-cell leukemia (ATL). HTLV-I infection of healthy CD4(+) T cells takes place through cell-to-cell contact with infected T cells. The infected T cells can remain latent and harbor virus for several years before virus production occurs. Actively infected T cells can infect other T cells and can convert to ATL cells, whose growth is assumed to follow a classical logistic growth function. Our analysis establishes that the global dynamics of T cells are completely determined by a basic reproduction number R(0). If R(0)< or =1, infected T cells always die out. If R(0)>1, HTLV-I infection becomes chronic, and a unique endemic equilibrium is globally stable in the interior of the feasible region. We also show that the equilibrium level of ATL-cell proliferation is higher when the HTLV-I infection of T cells is chronic than when it is acute.     

Persistence of viral infections on the population level explained by an immunoepidemiological model

We consider a mathematical model of viral spread in a population based on an immune response model embedded in an epidemic network model. The immune response model includes virus load and effector and memory T cells with two possible outcomes depending on parameters: (a) virus clearance and establishment of immune memory and (b) establishment of a non-zero viral presence characterized with increased T-cell concentrations. Isolated individuals can have different immune system parameters and, after a primary infection, can either return to the infection-free state or develop persistent or chronic infection. When individuals are connected in the network, they can reinfect each other. We show that the virus can persist in the epidemic network for indefinite time even if the whole population consists of individuals that are able to clear the virus when isolated from the network. In this case a few individuals with a relatively weak immune response can maintain the infection in the whole population. These results are in contrast to implications of classical epidemiological models that a viral epidemic will end if there is no influx of new susceptibles and if individuals can become immune after infection.     

Modelling the Role of Tax Expression in HTLV-I Persistence in vivo

Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterized by life-long infection and risk of developing HAM/TSP, a progressive neurological and inflammatory disease, and adult T-cell leukemia (ATL). Chronically infected individuals often harbor high proviral loads despite maintaining a persistently activated immune response. Based on a new hypothesis for the persistence of HTLV-I infection, a three-dimensional compartmental model is constructed that describes the dynamic interactions among latently infected target cells, target-cell activation, and immune responses to HTLV-I, with an emphasis on understanding the role of Tax expression in the persistence of HTLV-I.     

Immunological risks of adult T-cell leukemia at primary HTLV-I infection

A small percentage of human T-cell leukemia virus type-I (HTLV-I)-infected individuals develop adult T-cell leukemia (ATL). In animal experiments, inoculation of HTLV-I via the oral route, which is the main route of mother-to-child viral transmission in humans as a result of breastfeeding, induced host HTLV-I-specific T-cell unresponsiveness and resulted in increased viral load. This strongly suggested that the known epidemiological risk factors for ATL (i.e. vertical HTLV-I infection and elevated viral load) are linked by an insufficient HTLV-I-specific T-cell response. Recent findings on the anti-tumor effects of Tax-targeted vaccination in rats and the reactivation of Tax-specific T cells in ATL patients as a result of hematopoietic stem cell transplantation imply promising immunological approaches for the prophylaxis and therapy of ATL.     

The genetic background as a determinant of human T-cell leukemia virus type 1 proviral load

Human T-cell leukemia virus type 1 (HTLV-1) is etiologically linked with HTLV-1-associated diseases. HTLV-1 proviral load is higher in persons with adult T-cell leukemia and HTLV-1-associated myelopathy/tropical spastic paraparesis than in asymptomatic carriers. However there are little data available on the factors controlling HTLV-1 proviral load in carriers. To study the effect of genetic background on HTLV-1 proviral load, we employed a mouse model of HTLV-1 infection that we had established. Here we analyzed nine strains of mice and found there is a great variation of proviral load among mouse strains that is not necessarily dependent on major histocompatibility complex. The antibody response is also different among these strains. To our knowledge, this is the first demonstration of the importance of the genetic background other than major histocompatibility complex controlling the HTLV-1 proviral load.     

The role of CTLs in persistent viral infection: cytolytic gene expression in CD8+ lymphocytes distinguishes between individuals with a high or low proviral load of human T cell lymphotropic virus type 1

The proviral load in human T cell lymphotropic virus type 1 (HTLV-1) infection is typically constant in each infected host, but varies by >1000-fold between hosts and is strongly correlated with the risk of HTLV-1-associated inflammatory disease. However, the factors that determine an individual's HTLV-1 proviral load remain uncertain. Experimental evidence from studies of host genetics, viral genetics, and lymphocyte function and theoretical considerations suggest that a major determinant of the equilibrium proviral load is the CD8+ T cell response to HTLV-1. In this study, we tested the hypothesis that the gene expression profile in circulating CD8+ and CD4+ lymphocytes distinguishes between individuals with a low proviral load of HTLV-1 and those with a high proviral load. We show that circulating CD8+ lymphocytes from individuals with a low HTLV-1 proviral load overexpressed a core group of nine genes with strong functional coherence: eight of the nine genes encode granzymes or other proteins involved in cell-mediated lysis or Ag recognition. We conclude that successful suppression of the HTLV-1 proviral load is associated with strong cytotoxic CD8+ lymphocyte activity in the peripheral blood.     

Human T cell leukemia virus type I and neurologic disease: events in bone marrow, peripheral blood, and central nervous system during normal immune surveillance and neuroinflammation.

Human T cell lymphotropic/leukemia virus type I (HTLV-I) has been identified as the causative agent of both adult T cell leukemia (ATL) and HTLV-I-associated myelopathy/tropical spastic paraparesis (HAM/TSP). Although the exact sequence of events that occur during the early stages of infection are not known in detail, the initial route of infection may predetermine, along with host, environmental, and viral factors, the subset of target cells and/or the primary immune response encountered by HTLV-I, and whether an HTLV-I-infected individual will remain asymptomatic, develop ATL, or progress to the neuroinflammatory disease, HAM/TSP. Although a large number of studies have indicated that CD4(+) T cells represent an important target for HTLV-I infection in the peripheral blood (PB), additional evidence has accumulated over the past several years demonstrating that HTLV-I can infect several additional cellular compartments in vivo, including CD8(+) T lymphocytes, PB monocytes, dendritic cells, B lymphocytes, and resident central nervous system (CNS) astrocytes. More importantly, extensive latent viral infection of the bone marrow, including cells likely to be hematopoietic progenitor cells, has been observed in individuals with HAM/TSP as well as some asymptomatic carriers, but to a much lesser extent in individuals with ATL. Furthermore, HTLV-I(+) CD34(+) hematopoietic progenitor cells can maintain the intact proviral genome and initiate viral gene expression during the differentiation process. Introduction of HTLV-I-infected bone marrow progenitor cells into the PB, followed by genomic activation and low level viral gene expression may lead to an increase in proviral DNA load in the PB, resulting in a progressive state of immune dysregulation including the generation of a detrimental cytotoxic Tax-specific CD8(+) T cell population, anti-HTLV-I antibodies, and neurotoxic cytokines involved in disruption of myelin-producing cells and neuronal degradation characteristic of HAM/TSP.     

Polymerase chain reaction analysis of defective human T-cell leukemia virus type I proviral genomes in leukemic cells of patients with adult T-cell leukemia.

Human T-cell leukemia virus type I (HTLV-I) is the etiologic agent of adult T-cell leukemia, and the clonally derived leukemic cells all contain proviral genomes. Polymerase chain reaction with a variety of primers which span the HTLV-I genome was used to determine that a significant fraction of patients (at least 32%) carry deleted viral genomes in their leukemic cells. The pX region of the HTLV-I genome encoding the regulatory genes tax and rex was preferentially retained. The fact that the tax coding region was retained provides supporting evidence that the tax protein contributes to leukemogenesis in vivo. The reasonably high fraction of patients with adult T-cell leukemia carrying deleted genomes in their tumor cells suggests that the deletions have a role in leukemogenesis.     

The cytotoxic T-lymphocyte response to HTLV-I: the main determinant of disease?

There is a powerful, chronically activated cytotoxic T-lymphocyte (CTL) response to the Tax protein of human T-cell leukaemia virus type I (HTLV-I) in most people infected with the virus. The CTL select variant sequences of Tax which escape immune recognition and interfere with recognition of the wild-type protein. This positive selection process is more efficient in healthy HTLV-I carriers than in patients with tropical spastic paraparesis, an inflammatory neurological disease associated with HTLV-I. The mean virus load is more than 10-fold greater in patients with this neurological disease than in healthy carriers of HTLV-I. We conclude that anti-Tax CTL play an important part in limiting the rate of replication of HTLV-I. We suggest that the outcome of infection with HTLV-I is primarily determined by the CTL response of the individual: low CTL responders to HTLV-I develop a high virus load, resulting in widespread chronic activation of T cells. The activated T cells then invade the tissues and cause bystander tissue damage, probably by releasing cytokines and other soluble substances. An efficient CTL response to HTLV-I limits the equilibrium virus load, and so reduces the chance of developing inflammatory disease.     

Quantifying HTLV-I dynamics

Despite significant advances in our understanding of the immune response to persistent viruses like human T-cell lymphotropic virus type I (HTLV-I), many important questions remain unanswered. Mathematical modelling enables us to interpret and synthesise diverse experimental data in new ways and thus can contribute to our understanding. Here, we review recent advances in mathematical modelling of HTLV-I infection and illustrate how mathematics has enabled us to identify factors that determine an individual's viral burden and risk of developing HTLV-I-associated diseases.     

Multiple Stable Periodic Oscillations in a Mathematical Model of CTL Response to HTLV-I Infection

Stable periodic oscillations have been shown to exist in mathematical models for the CTL response to HTLV-I infection. These periodic oscillations can be the result of mitosis of infected target CD4⁺ cells, of a general form of response function, or of time delays in the CTL response. In this study, we show through a simple mathematical model that time delays in the CTL response process to HTLV-I infection can lead to the coexistence of multiple stable periodic solutions, which differ in amplitude and period, with their own basins of attraction. Our results imply that the dynamic interactions between the CTL immune response and HTLV-I infection are very complex, and that multi-stability in CTL response dynamics can exist in the form of coexisting stable oscillations instead of stable equilibria. Biologically, our findings imply that different routes or initial dosages of the viral infection may lead to quantitatively and qualitatively different outcomes.     

Neuraminidase enhances the initial steps of human T-cell leukemia virus type 1 replication

Human T-cell leukemia virus type 1 (HTLV-1) infection is involved in the development of adult T-cell leukemia and HTLV-1-associated myelopathy/tropical spastic paraparesis. A high HTLV-1 proviral load in circulating lymphocytes of HTLV-1 carriers is a risk factor for HTLV-1-related diseases. The virus–cell interaction is linked to viral tropism and pathogenesis. Characterization of the factors that affect HTLV-1 infection is important for preventing HTLV-1 infection. HTLV-1 virions are believed to be weakly infectious under cell culture conditions; however, we found that the treatment of HTLV-1 virions with microbial neuraminidase, an enzyme catalyzing the removal of sialic acid residues from various glycoconjugates, enhanced the number of proviral DNAs in infected cells in a dose-dependent manner. Neuraminidase treatment of virions, but not target cells, enhanced viral binding and entry into cells and viral infectivity; treatment of target cells prior to infection had no effect. Moreover, the number of HTLV-1-mediated syncytia was higher in the presence of neuraminidase. Our results suggest a possible contribution of microbial agents carrying neuraminidase activity to HTLV-1 pathogenesis.     

Evolutionary Dynamics of HTLV-I

Using mathematical models to describe the in vivo dynamics of HTLV-I infection, an explanation is offered for the slow rate of evolution of HTLV-I relative to HIV-1. In agreement with experimental findings, it is assumed that cell activation is required for successful replication in T helper cells and that HTLV-I induces a significant degree of bystander activation. It is found that the rate of evolution of HTLV-I is limited by the restricted availability of activated uninfected T cells, both at high and low proviral loads. This limits the within-host sequence diversity of HTLV-I and may therefore account for the slow rate of evolution of the virus in the population. Specific differences in the in vivo dynamics of HTLV-I and HIV-1 are identified which may account for the discrepancy in the rate of evolution of these two retroviruses. Received: 7 September 1999 / Accepted: 6 December 1999