A mathematical model for the investigation of the Th1 immune response to Chlamydia trachomatis

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Abstract

Chlamydia are bacterial pathogens of humans and animals causing the important human diseases trachoma, sexually transmitted chlamydial disease and pneumonia. Of the human chlamydial diseases, sexually transmitted disease caused by Chlamydia trachomatis is a major public health concern. Chlamydia trachomatis replicates intracellularly and is characterised by a complex developmental cycle. Chlamydia is susceptible to humoral and cell-mediated immunity. Here we investigate the Th1 cell-mediated immune response against Chlamydia-infected cells as the response changes over the chlamydial developmental cycle. We suggest a form for the immune response over one developmental cycle by modelling the change in the number of intracellular chlamydial particles and assume peptides are presented in proportion to the number of replicating forms of chlamydial particles. We predict, perhaps non-intuitively, that persistent Chlamydia should be induced and forced not to return to the lytic cycle. We also suggest that extending the length of the time of the lytic cycle will effectively decrease the required efficacy of the Th1 response to eliminate the pathogen. We produce plots of active disease progression, control and clearance for varying levels of Th1 effectiveness.

Introduction

Chlamydiae are obligate intracellular parasites that develop and multiply within a host cell’s vacuole (termed an inclusion). They are bacterial pathogens of humans and animals and cause the important human diseases trachoma, sexually transmitted chlamydial disease and pneumonia. Of the four chlamydial species, Chlamydia trachomatis and C. pneumoniae are primarily human pathogens, while all species, but particularly C. caviae (previously named C. psittaci [1]) and C. pecorum are found in animals.

Infection with the chlamydial species, C. trachomatis results in the most common sexually transmitted disease worldwide [2]. It can lead to serious outcomes such as infertility and ectopic pregnancy if left untreated. Chlamydia trachomatis is also the major cause of preventable blindness in the world with over 500 million people blinded as a result of trachoma due to this pathogen. There are currently no vaccines available for either of these major diseases. Chlamydia infections can be effectively treated with a course of antibiotics although the majority of people that are infected do not show evidence of symptoms and many infections go undetected, undiagnosed, and consequently, untreated. Untreated Chlamydia infections are able to persist and establish a long lasting, chronic infection, that can increase the risk of acquiring or transmitting HIV, the virus that causes AIDS, and in women can also spread into the pelvic area and infect the uterus, fallopian tubes, and ovaries leading to pelvic inflammatory disease.

All chlamydiae share a common biology [3]. Chlamydia has a unique biphasic life cycle which is initiated when an infectious, relatively durable, extracellular transmission body, termed the elementary body (EB), attaches to a susceptible host cell, promoting entry into a host cell-derived phagocytic vesicle. The Chlamydia lytic developmental cycle begins when extracellular Chlamydia EBs attach to host cells (Fig. 1). This attachment may be blocked by antibodies. The host cells internalize the EBs, where, once inside the host cell, the EBs are no longer accessible to antibodies. The metabolically inert EB undergoes morphological changes, reorganizing inside cellular vacuoles to the larger reticulate body (RB). At this stage, they lose their infectivity and change their physical attributes, becoming a replicative form so that after reorganisation the RBs multiply 200–500 fold. Lymphokines such as IFN-γ from CD4 and CD8 cells, attracted to the infection site can destroy intracellular Chlamydia at the RB stage [4].

Although most RB multiplication occurs within 10–20 h after infection, it can occur throughout the entire developmental cycle, resulting in asynchronous growth. At 20–25 h after infection, infectious EBs appear as the EB to RB conversion process is reversed. RBs continue to divide and reorganise into EBs until the host cell cannot support the Chlamydia multiplication any longer. The host cell bursts, releasing infectious EBs, thereby initiating new cycles of infection. Depending on the Chlamydia strain, the developmental cycle takes between 40 and 72 h.

Section snippets

Cellular immune response to the invading chlamydial pathogen

It has been suggested that Th1 CD4 T cell-mediated, not humoral, immune responses, play the dominant role in protective immunity [5]. It is known that efficient Th1 responses will often successfully clear infection [6], [7]. Humoral immunity, and in particular pre-existing major outer membrane protein antibody, appear to provide a preventative role against initial infection, whilst cell-mediated immunity is necesary for the removal of established infection once the organisms become

Modelling cell-mediated immunity to Chlamydia

As the developmental cycle progresses, the parasite presents more antigens to the host, making itself more of a target for the immune system. Presumably this is reflected in the immune response to the host. We assume that when a RB begins to replicate an immune response is initiated and this response is most effective when the number of intracellular RBs is largest. We assume that chlamydial peptides presented to immune cells are in proportion to the number of intracellular RBs [4]. Therefore,

Modelling the chlamydial developmental cycle

The mathematical model we present uses a deterministic approach to understand the cell-mediated response to chlamydial inclusions for controlling the disease by investigating its responsiveness over Chlamydia’s developmental cycle. We assume that the immune cytotoxic response rate is directly proportional to the number of RBs inside the infected cell. It seems reasonable to track the number of cells of varying maturation levels in the developmental cycle with a continuous variable, r.

The

Basic reproduction ratio

The basic reproduction ratio is a fundamental concept in epidemiology and microepidemiology [22], [23]. We define the basic reproduction ratio as the expected number of secondary cases produced, in a completely susceptible population, by one typical infected individual/cell during its entire period of infectiousness. The basic reproduction ratio is evaluated when abundance of uninfected cells is at pre-infection level. We obtain the following expression for the basic reproductive ratio from our

Numerical solution of the model equations

When the system is solved numerically the critical behaviour depends on the basic reproduction ratio. If the basic reproduction ratio is greater than unity then all species will increase without bound with time (what we term active disease). However, if the basic reproduction ratio is less than unity then the infection will be cleared for large times as the population levels tend to zero. If the basic reproduction ratio is equal to one, an equilibrium is set up, whereby the average source of

Secondary memory-induced Th1 immune response

The immune system recognises and responds to subtle chemical differences that distinguish one foreign pathogen from another. Once an antigen has been recognised, the immune system enlists the participation of a variety of cells and molecules to mount an appropriate response, called an effector response, to eliminate or neutrolise the organism. Later exposure to the same foreign organism induces a memory response, characterised by more rapid and heightened immune reaction that serves to

Discussion and conclusions

We have developed a model of the Chlamydia developmental cycle with emphasis on exploring the Th1 immune impact against Chlamydia-infected cells over the developmental cycle. We developed an age-structured PDE as the tool to investigate the infected cell maturation and corresponding immune action against a cell of given maturity. Our model incorporates age-structured components and we generalise to maturation not necessarily time. The assumed form for the immune response, over the developmental

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