Immune responses against multiple epitopes

Stability and Hopf bifurcation of an HIV infection model with two time delays

This work focuses on an HIV infection model with intracellular delay and immune response delay, in which the former delay refers to the time it takes for healthy cells to become infectious after infection, and the latter delay refers to the time when immune cells are activated and induced by infected cells. By investigating the properties of the associated characteristic equation, we derive sufficient criteria for the asymptotic stability of the equilibria and the existence of Hopf bifurcation to the delayed model. Based on normal form theory and center manifold theorem, the stability and the direction of the Hopf bifurcating periodic solutions are studied. The results reveal that the intracellular delay cannot affect the stability of the immunity-present equilibrium, but the immune response delay can destabilize the stable immunity-present equilibrium through the Hopf bifurcation. Numerical simulations are provided to support the theoretical results.

Role of CXCR5+ CD8+ T cells in human immunodeficiency virus-1 infection

Human immunodeficiency virus (HIV) infection can be effectively suppressed by life-long administration of combination antiretroviral therapy (cART). However, the viral rebound can occur upon cART cessation due to the long-term presence of HIV reservoirs, posing a considerable barrier to drug-free viral remission. Memory CD4⁺ T cell subsets, especially T follicular helper (T _FH ) cells that reside in B-cell follicles within lymphoid tissues, are regarded as the predominant cellular compartment of the HIV reservoir. Substantial evidence indicates that HIV-specific CD8⁺ T cell-mediated cellular immunity can sustain long-term disease-free and transmission-free HIV control in elite controllers. However, most HIV cure strategies that rely on expanded HIV-specific CD8⁺ T cells for virus control are likely to fail due to cellular exhaustion and T _FH reservoir-specialized anatomical structures that isolate HIV-specific CD8⁺ T cell entry into B-cell follicles. Loss of stem-like memory properties is a key feature of exhaustion. Recent studies have found that CXC chemokine receptor type 5 (CXCR5)-expressing HIV-specific CD8⁺ T cells are memory-like CD8⁺ T cells that can migrate into B-cell follicles to execute inhibition of viral replication. Furthermore, these unique CD8⁺ T cells can respond to immune checkpoint blockade (ICB) therapy. In this review, we discuss the functions of these CD8⁺ T cells as well as the translation of findings into viable HIV treatment and cure strategies.

Defining Kinetic Properties of HIV-Specific CD8⁺ T-Cell Responses in Acute Infection

Multiple lines of evidence indicate that CD8 + T cells are important in the control of HIV-1 (HIV) replication. However, CD8 + T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8 + T-cell responses induced during HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8 + T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8 + T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8 + T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8 + T cells in the chronic infection. The breadth of HIV-specific CD8 + T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8 + T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8 + T-cell responses and the presence of intra- and interclonal competition between multiple CD8 + T-cell responses; such competition may limit the magnitude of CD8 + T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8 + T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.

Global properties of nested network model with application to multi-epitope HIV/CTL dynamics

Mathematical modeling and analysis can provide insight on the dynamics of ecosystems which maintain biodiversity in the face of competitive and prey-predator interactions. Of primary interests are the underlying structure and features which stabilize diverse ecological networks. Recently Korytowski and Smith (Theor Ecol 8(1):111-120, 2015) proved that a perfectly nested infection network, along with appropriate life history trade-offs, leads to coexistence and persistence of bacteria-phage communities in a chemostat model. In this article, we generalize their model in order to apply it to the within-host dynamics virus and immune response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model can describe sequential viral escape from dominant immune responses and rise in subdominant immune responses, consistent with observed patterns of HIV/CTL evolution. We find a Lyapunov function for the system which leads to rigorous characterization of persistent viral and immune variants, along with informing upon equilibria stability and global dynamics. Results are interpreted in the context of within-host HIV/CTL evolution and numerical simulations are provided.

Single injection of CD8+ T lymphocytes derived from hematopoietic stem cells - Mathematical and numerical insights

Recently, hematopoietic stem cell (HSC) based therapy is being discussed as a possible treatment for HIV infection. The main advantage of this approach is that it limits the immune impairing effect of infection by introducing an independent influx of antigen-specific cytotoxic T lymphocytes (CTL). In this paper, we present a mathematical approach to predict the dynamics of HSC based therapy. We use a modification of a basic mathematical model for virus induced impairment of help to study how virus - immune system dynamics can be influenced by a single injection of CD8+ T lymphocytes derived from hematopoietic stem cells. Our mathematical and numerical results indicate that a single, large enough dose of genetically derived CTL may lead to restoration of the cellular immune response and result in long-term control of infection.

Mefenamic acid in combination with ribavirin shows significant effects in reducing chikungunya virus infection in vitro and in vivo

Chikungunya virus (CHIKV) infection is a persistent problem worldwide due to efficient adaptation of the viral vectors, Aedes aegypti and Aedes albopictus mosquitoes. Therefore, the absence of effective anti-CHIKV drugs to combat chikungunya outbreaks often leads to a significant impact on public health care. In this study, we investigated the antiviral activity of drugs that are used to alleviate infection symptoms, namely, the non-steroidal anti-inflammatory drugs (NSAIDs), on the premise that active compounds with potential antiviral and anti-inflammatory activities could be directly subjected for human use to treat CHIKV infections. Amongst the various NSAID compounds, Mefenamic acid (MEFE) and Meclofenamic acid (MECLO) showed considerable antiviral activity against viral replication individually or in combination with the common antiviral drug, Ribavirin (RIBA). The 50% effective concentration (EC50) was estimated to be 13 μM for MEFE, 18 μM for MECLO and 10 μM for RIBA, while MEFE + RIBA (1:1) exhibited an EC50 of 3 μM, and MECLO + RIBA (1:1) was 5 μM. Because MEFE is commercially available and its synthesis is easier compared with MECLO, MEFE was selected for further in vivo antiviral activity analysis. Treatment with MEFE + RIBA resulted in a significant reduction of hypertrophic effects by CHIKV on the mouse liver and spleen. Viral titre quantification in the blood of CHIKV-infected mice through the plaque formation assay revealed that treatment with MEFE + RIBA exhibited a 6.5-fold reduction compared with untreated controls. In conclusion, our study demonstrated that MEFE in combination with RIBA exhibited significant anti-CHIKV activity by impairing viral replication in vitro and in vivo. Indeed, this finding may lead to an even broader application of these combinatorial treatments against other viral infections.

Alloantibodies to therapeutic factor VIII in hemophilia A: the role of von Willebrand factor in regulating factor VIII immunogenicity

The rising incidence of neutralizing antibodies (inhibitors) against therapeutic factor VIII prompted the conduct of studies to answer the question as to whether this rise is related to the introduction of recombinant factor VIII products. The present article summarizes current opinions and results of non-clinical and clinical studies on the immunogenic potential of recombinant compared to plasma-derived factor VIII concentrates. Numerous studies provided circumstantial evidence that von Willebrand factor, the natural chaperone protein present in plasma-derived factor VIII products, plays an important role in protecting exogenous factor VIII from uptake by antigen presenting cells and from recognition by immune effectors. However, the definite contribution of von Willebrand factor in reducing the inhibitor risk and in the achievement of immune tolerance is still under debate.

Dynamics of stochastic mutation to immunodominance

Although a virus contains several epitopes that can be recognized by cytotoxic T lymphocytes (CTL), the immune responses against different epitopes are not uniform. Only a few CTLs (sometimes just one) will be immunodominant. Mutation of epitopes has been recognized as an important mechanism of immunodominance. Previous research has studied the influences of sporadic, discrete mutation events. In this work, we introduce a bounded noise term to account for the intrinsic stochastic nature of mutation. Monte Carlo simulations of the stochastic model show abounding complex phenomena, and patterns observed from the numerical simulations shed lights on long term trends of immunodomnance.

HIV evolution and progression of the infection to AIDS

In this paper, we propose and discuss a possible mechanism, which, via continuous mutations and evolution, eventually enables HIV to break from immune control. In order to investigate this mechanism, we employ a simple mathematical model, which describes the relationship between evolving HIV and the specific CTL response and explicitly takes into consideration the role of CD4(+)T cells (helper T cells) in the activation of the CTL response. Based on the assumption that HIV evolves towards higher replication rates, we quantitatively analyze the dynamical properties of this model. The model exhibits the existence of two thresholds, defined as the immune activation threshold and the immunodeficiency threshold, which are critical for the activation and persistence of the specific cell-mediated immune response: the specific CTL response can be established and is able to effectively control an infection when the virus replication rate is between these two thresholds. If the replication rate is below the immune activation threshold, then the specific immune response cannot be reliably established due to the shortage of antigen-presenting cells. Besides, the specific immune response cannot be established when the virus replication rate is above the immunodeficiency threshold due to low levels of CD4(+)T cells. The latter case implies the collapse of the immune system and beginning of AIDS. The interval between these two thresholds roughly corresponds to the asymptomatic stage of HIV infection. The model shows that the duration of the asymptomatic stage and progression of the disease are very sensitive to variations in the model parameters. In particularly, the rate of production of the naive lymphocytes appears to be crucial.

Infection of HIV-specific CD4 T helper cells and the clonal composition of the response

A hallmark of human immunodeficiency virus is its ability to infect CD4+ T helper cells, thus impairing helper cell responses and consequently effector responses whose maintenance depends on help (such as killer T cells and B cells). In particular, the virus has been shown to infect HIV-specific helper cells preferentially. Using mathematical models, we investigate the consequence of this assumption for the basic dynamics between HIV and its target cells, assuming the existence of two independently regulated helper cell clones, directed against different epitopes of the virus. In contrast to previous studies, we examine a relatively simple scenario, only concentrating on the interactions between the virus and its target cells, not taking into account any helper-dependent effector responses. Further, there is no direct competition for space or antigenic stimulation in the model. Yet, a set of interesting outcomes is observed that provide further insights into factors that shape helper cell responses. Despite the absence of competition, a stronger helper cell clone can still exclude a weaker one because the two clones are infected by the same pathogen, an ecological concept called "apparent competition". Moreover, we also observe "facilitation": if one of the helper cell clones is too weak to become established in isolation, the presence of a stronger clone can provide enhanced antigenic stimulation, thus allowing the weaker clone to persist. The dependencies of these outcomes on parameters is explored. Factors that reduce viral infectivity and increase the death rate of infected cells promote coexistence, which is in agreement with the observation that stronger immunity correlates with broader helper cell responses. The basic model is extended to explicitly take into account helper-dependent CTL responses and direct competition. This study sheds further light onto the factors that can influence the clonal composition of HIV-specific helper cell responses, which has implications for the overall pattern of disease progression.

Consequences of host heterogeneity, epitope immunodominance, and immune breadth for strain competition

Consumer-resource dynamics of hosts with their pathogens are modulated by complex interactions between various branches of hosts' immune systems and the imperfectly perceived pathogen. Multistrain SIR models tend to sweep competitive interaction terms between different pathogen strains into a single parameter representing cross-immunity. After reviewing several hypotheses about the generation of immune responses, we look into the consequences of assuming that hosts with identical immune repertoires respond to new pathogens identically. In particular, we vary the breadth of the typical immune response, or the average number of pathogen epitopes a host perceives, and the probability of perceiving a particular epitope. The latter quantity in our model is equivalent both to the degree of diversity in host responses at the population level and the relative immunodominance of different epitopes. We find that a sharp transition to strain coexistence occurs as host responses become narrow or skewed toward one epitope. Increasing the breadth of the immune response and the immunogenicity of different epitopes typically increases the range of cross-immunity values in which chaotic strain dynamics and competitive exclusion occur. Models attempting to predict the outcomes of strain competition should thus consider the potential diversity and specificity of hosts' responses to infection.

A model of host response to a multi-stage pathogen

We model the immune surveillance of a pathogen which passes through n immunologically distinct stages. The biological parameters of this system induce a partial order on the stages, and this, in turn, determines which stages will be subject to immune regulation. This corresponds to the system's unique asymptotically stable fixed point.

Does intra-individual major histocompatibility complex diversity keep a golden mean?

An adaptive immune response is usually initiated only if a major histocompatibility complex (MHC) molecule presents pathogen-derived peptides to T-cells. Every MHC molecule can present only peptides that match its peptide-binding groove. Thus, it seems advantageous for an individual to express many different MHC molecules to be able to resist many different pathogens. However, although MHC genes are the most polymorphic genes of vertebrates, each individual has only a very small subset of the diversity at the population level. This is an evolutionary paradox. We provide an overview of the current data on infection studies and mate-choice experiments and conclude that overall evidence suggests that intermediate intra-individual MHC diversity is optimal. Selective forces that may set an upper limit to intra-individual MHC diversity are discussed. An updated mathematical model based on recent findings on T-cell selection can predict the natural range of intra-individual MHC diversity. Thus, the aim of our review is to evaluate whether the number of MHC alleles usually present in individuals may be optimal to balance the advantages of presenting an increased range of peptides versus the disadvantages of an increased loss of T-cells.

BioLogic: A mathematical modeling framework for immunologists

The immune response to pathogens is a result of complex interactions among many cell types and a large number of molecular processes. As such it poses numerous challenges for modeling, simulation, and analysis. In this work we aim at addressing major issues regarding modeling of large biological systems with a special focus on the immune system. We address (1) the hierarchy in the system, from genes to organelles to cells to organs to organism, (2) the high variability due to experimentation, (3) the high variability among organisms, and (4) the need to bridge between immunologists/experimentalists and mathematicians/modelers. We provide an intuitive syntax to describe biological knowledge in terms of interactions (reactions) and objects (cells, organs, etc.) and illustrate how to use it in describing very complex systems. We describe the main elements of a simulation program that use that syntax to define models and to automatically simulate them. We restrict our discussion to modeling using logical network, although other modeling techniques, for example, differential equations and probabilistic/stochastic modeling, are also possible. Examples demonstrating the different features of the framework are given throughout the chapter.

Complete genetic linkage can subvert natural selection

The intricate adjustment of organisms to their environment demonstrates the effectiveness of natural selection. But Darwin himself recognized that certain biological features could limit this effectiveness, features that generally reduce the efficiency of natural selection or yield suboptimal adaptation. Genetic linkage is known to be one such feature, and here we show theoretically that it can introduce a more sinister flaw: when there is complete linkage between loci affecting fitness and loci affecting mutation rate, positive natural selection and recurrent mutation can drive mutation rates in an adapting population to intolerable levels. We discuss potential implications of this finding for the early establishment of recombination, the evolutionary fate of asexual populations, and immunological clearance of clonal pathogens.

Spatial models of virus-immune dynamics

To date, the majority of theoretical models describing the dynamics of infectious diseases in vivo are based on the assumption of well-mixed virus and cell populations. Because many infections take place in solid tissues, spatially structured models represent an important step forward in understanding what happens when the assumption of well-mixed populations is relaxed. Here, we explore models of virus and virus-immune dynamics where dispersal of virus and immune effector cells was constrained to occur locally. The stability properties of our spatial virus-immune dynamics models remained robust under almost all biologically plausible dispersal schemes, regardless of their complexity. The various spatial dynamics were compared to the basic non-spatial dynamics and important differences were identified: When space was assumed to be homogeneous, the dynamics generated by non-spatial and spatially structured models differed substantially at the peak of the infection. Thus, non-spatial models may lead to systematic errors in the estimates of parameters underlying acute infection dynamics. When space was assumed to be heterogeneous, spatial coupling not only changed the equilibrium properties of the uncoupled populations but also equalized the dynamics and thereby reduced the likelihood of dynamic elimination of the infection. In line with experimental and clinical observations, long-lasting oscillation periods were virtually absent. When source-sink dynamics were considered, the long-term outcome of the infection depended critically on the degree of spatial coupling. The infection collapsed when emigration from source sites became too large. Finally, we discuss the implications of spatially structured models on medical treatment of infectious diseases, and note that a huge gap exists in data accurately describing infection dynamics in solid tissues.

Some basic properties of immune selection

We analyze models for the evolutionary dynamics of viral or other infectious agents within a host. We study how the invasion of a new strain affects the composition and diversity of the viral population. We show that--under strain-specific immunity--the equilibrium abundance of uninfected cells declines during viral evolution. In addition, for cytotoxic immunity the absolute force of infection, and for non-cytotoxic immunity the absolute cellular virulence increases during viral evolution. We prove global stability by means of Lyapunov functions. These unidirectional trends of virus evolution under immune selection do not hold for general cross-reactive immune responses, which introduce frequency-dependent selection among viral strains. Therefore, appropriate cross-reactive immunity can lead to a viral evolution within a host which limits the extent of the disease.

Plasmodium falciparum genotypes, low complexity of infection, and resistance to subsequent malaria in participants in the Asembo Bay Cohort Project

To assess the relationship between the within-host diversity of malaria infections and the susceptibility of the host to subsequent infection, we genotyped 60 children's successive infections from birth through 3 years of life. MSP-1 Block2 genotypes were used to estimate the complexity of infection (COI). Malaria transmission and age were positively associated with the number of K1 and Mad20 alleles detected (COI(KM)) (P < 0.003). Controlling for previous parasitemia, transmission, drug treatment, parasite density, sickle cell, and age, COI(KM) was negatively correlated with resistance to parasitemia of > 500/microl (P < 0.0001). Parasitemias with the RO-genotype were more resistant than those without this genotype (P < 0.0000). The resistance in low COI(KM) infections was not genotype specific. We discuss the impact of genotype-transcending immunity to conserved antigenic determinants. We also propose a diversity-driven immunomodulation hypothesis that may explain the delayed development of natural immunity in the first few years of life and suggest that interventions that decrease the COI(KM) could facilitate the development of protective immunity.

Diversity and plasticity of the anti-DNA topoisomerase I autoantibody response in scleroderma

OBJECTIVE

To examine domain recognition by anti-DNA topoisomerase I (anti-DNA topo I, or anti-topo I) antibodies over time in scleroderma patients.

METHODS

Serial serum samples from scleroderma patients with known reactivity to Scl-70, a 70-kd topo I breakdown product, were tested by immunoblot for IgM, IgG, IgA, kappa, and lambda reactivity to Scl-70 and 8 overlapping recombinant peptide fragments (F1-F8) that span the human topo I molecule.

RESULTS

IgM, IgG, kappa, and lambda anti-topo I antibodies in both early-disease and late-disease serum samples preferentially recognized the Scl-70 molecule rather than the F1-F8 peptides, suggesting preferential recognition of conformational determinants on Scl-70 throughout the disease course. Amounts of both primary and secondary anti-topo I antibodies to Scl-70 varied over time, including increases in primary antibody responses late in the disease course. Striking variability in recognition of the F1-F8 peptides by IgM, IgG, IgA, kappa, and lambda anti-topo I antibodies was seen in serial samples. Most often, the change in FI-F8 recognition from one sample to the next was unpredictable, although occasionally patterns of antibody recognition were reciprocal in serial samples. Of note, in several patients, what could have been interpreted as domain spreading among F1-F8 in 2 successive samples was just a part of changing antibody reactivity to these peptides that again became more restricted in a third sample.

CONCLUSION

Titers and immunodominant domains recognized by both primary and secondary anti-topo I antibodies are highly variable over time. This suggests continual antigen presentation and regulation of the anti-topo I antibody response in scleroderma, even late in the disease course.

Immunological transitions in response to antigenic mutation during viral infection

Antigenic variation is an important factor in viral persistence and disease progression. We analyze immunological changes which occur in response to antigenic mutation during chronic viral infection. Using an established model of viral and immune system dynamics, we determine which qualitative shifts in the immune response can be elicited by the appearance of a new mutant. We find that antigenic mutation can cause dramatic shifts in the magnitude and type of anti-viral immune response. For example, the appearance of a mutant can elicit a new immune response which recognizes the original viral strain. We also find that novel strains of the virus which replicate more slowly than existing viral strains are able to invade and survive, even when the immune system is capable of mounting an immune response against the mutant.

Number of triplets in 16S rRNA gene related with pathogenicity of Bacillus spp. and Clostridium spp

The relation between the number of some trinucleotides in the sequence of 16S rRNA gene and pathogenicity of bacterial species from the genera of Bacillus and Clostridium was revealed. The species of genus Bacillus, which are pathogenic for humans, mammals and insects, have an increased number of AAA and TAT triplets in 16S rRNA gene. Theoretically, these species, B. anthracis and B. cereus for example, may be detected in the specimen by the higher ratio of AAA plus TAT triplets to the number of GGG triplet. Species of genus Clostridium, which are pathogenic for humans and mammals, have a maximum ratio of AAA and TAT triplet numbers. This ratio was higher than 2.6 for pathogenic species and lower than 2.2 for saprophytic ones. These theoretical data may open a new way for detecting pathogenic bacteria through the determination of triplet numbers in the sequences of 16S rRNA or rRNA. However, the mechanism of evolutionary relation between the number of AAA and TAT triplets in the sequence of 16S rRNA gene and the pathogenicity of bacterial species is not known.

A condition for successful escape of a mutant after primary HIV infection

Cytotoxic T lymphocytes (CTLs) vigorously restrict primary human immunodeficiency virus (HIV) infection. However, the frequently erroneous process of viral replication favors the creation of mutants not recognizable by primary CTLs. Variants that tolerate the mutations may have selective advantage and may increase in abundance, until the immune system reacts against them. Therefore, such variants represent a way of propagating the viremia. With the aid of a simple mathematical model, here we estimate the intensity of CTL cross-reactivity against different strains of HIV in a typical progressor. We show that below a critical intensity of cross-reactivity, the concentration of a mutant created at primary peak grows and causes a secondary peak in viremia. Above this critical intensity, such a mutant strain is prevented from reaching a detectable level. We speculate about how this result may contribute to the design of an anti-HIV vaccine.

Evolutionary dynamics of HIV-induced subversion of the immune response

Human immunodeficiency virus (HIV) disease progression is characterized by a slow but steady decline in the number of CD4+ T cells. It results in the development of AIDS when the immune response collapses and the virus grows uncontrolled. Pathogenicity of HIV may be due to viral escape from cellular immune responses as well as virus-induced immune impairment. Here we discuss how the dynamic interactions between the virus population and the immune response may lead to the development of AIDS. In particular we argue that in vivo evolution of HIV may be the driving force successively weakening the immune system. This may lead to increased levels of viraemia as well as to the evolution of more virulent phenotypes which indicate progression to AIDS. These insights are important for understanding the disease process itself and for designing effective treatment regimes.

Dynamics of T-cell antagonism: enhanced viral diversity and survival

In rapidly evolving viruses the detection of virally infected cells can possibly be subverted by the production of altered peptides. There are peptides with single amino acid changes that can dramatically change T-cell responses, e.g. a loss of cytotoxic activity. They are still recognized by the T cell, but the signals required for effector function are only partially delivered. Thus, altered peptide presenting cells can act as decoy targets for specific immune responses. The existence of altered peptides in vivo has been demonstrated in hepatitis B and HIV. Using a mathematical model we address the question of how these altered peptides can affect the virus-immune system dynamics, and demonstrate that virus survival is enhanced. If the mutation rate of the virus is sufficient, one observes complex dynamics in which the antagonism acts so as to maintain the viral diversity, possibly leading to the development of a mutually antagonistic network or a continual turnover of escape mutants. In either case the pathogen is able to outrun the immune system. Indeed, sometimes the enhancement is so great that a virus that would normally be cleared by the immune system is able to outrun it.

Gene therapy of T helper cells in HIV infection: mathematical model of the criteria for clinical effect

This paper presents a mathematical analysis of the criteria for gene therapy of T helper cells to have a clinical effect on HIV infection. The analysis indicates that for such a therapy to be successful, it must protect the transduced cells against HIV-induced death. The transduced cells will not survive as a population if the gene therapy only blocks the spread of virus from transduced cells that become infected. The analysis also suggests that the degree of protection against disease-related cell death provided by the gene therapy is more important than the fraction cells that is initially transduced. If only a small fraction of the cells can be transduced, transduction of T helper cells and transduction of haematopoietic progenitor cells will result in the same steady-state level of transduced T helper cells. For gene therapy to be efficient against HIV infection, our analysis suggests that a 100% protection against viral escape must be obtained. The study also suggests that a gene therapy against HIV infection should be designed to give the transduced cells a partial but not necessarily total protection against HIV-induced cell death, and to avoid the production of viral mutants insensitive to the gene therapy.

Evolutionary pattern of intra-host pathogen antigenic drift: effect of cross-reactivity in immune response

Several viruses are known to change their surface antigen types after infecting a host, thereby escaping the immune defence and ensuring persistent infection. In this paper, we theoretically study the pattern of intra-host micro-evolution of pathogen antigen variants under the antigen specific immune response. We assume that the antigen types of the pathogen can be indexed in one-dimensional space, and that a mutation can produce a new antigen variant that is one step distant from the parental type. We also assume that antibodies directed to a specific antigen can also neutralize similar antigen types with a decreased efficiency (cross-reactivity). The model reveals that the pattern of intra-host antigen evolution critically depends on the width of cross-reactivity. If the width of cross-reactivity is narrower than a certain threshold, antigen variants gradually evolve in antigen space as a travelling wave with a constant wave speed, and the total pathogen density approaches a constant. In contrast, if the width of cross-reactivity exceeds the threshold, the travelling wave loses stability and the distribution of antigen variants fluctuates both in time and in genotype space. In the latter case, the expected episodes after infection are a series of intermittent outbreaks of pathogen density, caused by distantly separated antigen types. The implication of the model to intra-host evolution of equine infectious anaemia virus and human immunodeficiency virus is discussed.

Mathematical and computational challenges in population biology and ecosystems science

Mathematical and computational approaches provide powerful tools in the study of problems in population biology and ecosystems science. The subject has a rich history intertwined with the development of statistics and dynamical systems theory, but recent analytical advances, coupled with the enhanced potential of high-speed computation, have opened up new vistas and presented new challenges. Key challenges involve ways to deal with the collective dynamics of heterogeneous ensembles of individuals, and to scale from small spatial regions to large ones. The central issues-understanding how detail at one scale makes its signature felt at other scales, and how to relate phenomena across scales-cut across scientific disciplines and go to the heart of algorithmic development of approaches to high-speed computation. Examples are given from ecology, genetics, epidemiology, and immunology.

Immunodominance, competition and evolution in immunological responses to helminth parasite antigens

The paper describes the development and analysis of a mathematical framework for the study of the within-host population dynamics of the interaction between macroparasites and the human immune system. Simple models of this interaction based on the proliferation of T cell clones specific to parasite antigen, and the impact of clonal expansion on parasite survival, capture the basic features of age-related changes in worm loads within human communities. The model is generalized to multiple epitopes on a single antigen, and reveals competitive exclusion amongst T cells, with a single clone becoming immunodominant in the absence of cross-reactive responses and genetic variation. The introduction of genetic heterogeneity and concomitant variability in the immunogenicity of specific epitopes induces additional complexity into the dynamical interaction. Most importantly, multiple epitope models with antigenic variation suggest that the immunodominant response may not necessarily be targeted at the epitope at which some strains show the greatest immunogenicity. High immunogenicity at a particular epitope can be masked by genetic variability even though many of the variants are more immunogenic at this epitope by comparison with the epitope to which the immunodominant immunological response is directed.

Recent developments in theories of pathogenesis of AIDS

Experimental and theoretical progress in HIV research includes an improved resolution of the spatial heterogeneity and the dynamics (time course and turnover rates) of virus and CD4+ cells. Some of these advances have resulted from the joint work of experimental and theoretical groups, demonstrating that interdisciplinary research can be fruitful.

Population dynamics of immune responses to persistent viruses

Mathematical models, which are based on a firm understanding of biological interactions, can provide nonintuitive insights into the dynamics of host responses to infectious agents and can suggest new avenues for experimentation. Here, a simple mathematical approach is developed to explore the relation between antiviral immune responses, virus load, and virus diversity. The model results are compared to data on cytotoxic T cell responses and viral diversity in infections with the human T cell leukemia virus (HTLV-1) and the human immunodeficiency virus (HIV-1).