A mathematical model and CD4+ lymphocyte dynamics in HIV infection.

The paper presents a model of CD4 + lymphocyte dynamics in HIV-infected persons. The model incorporates a feedback mechanism regulating the production of T lymphocytes and simulates the dynamics of CD8 + lymphocytes, whose production is assumed to be closely linked to that of CD4 + cells. Because CD4 + lymphocyte counts are a good prognostic indicator of HIV infection, the model was used to simulate such therapeutic interventions as chemotherapy and active and passive immunization. The model also simulated the therapeutic administration of anti-CD8 antibodies; this intervention was assumed to activate T-cell production by activating a feedback mechanism blocked by the high numbers of CD8 + lymphocytes present in HIV-infected persons. The character and implications of the model are discussed in the context of other mathematical models used in HIV infection.

Mathematical modelling of HIV infection therapy.

The previously developed mathematical model simulates the CD4+ lymphocyte dynamics in HIV infection very well. As the number of these cells is a good indicator of the infection progression, it was used to evaluate the effectiveness of different therapeutic interventions. For chemotherapy simulation, both permanent and temporary zinovudine (AZT) administration were considered and the induced return of the CD4+ lymphocyte counts was analysed. Similar analysis was performed for active and passive immunotherapy. The model offers also the possibility of stimulating the CD4+ dynamics after depletion of CD8+ lymphocytes by antibodies. Even one simulated administration of anti-CD8 antibodies increases the CD4+ lymphocyte counts and prolongs the survival of the patient. However, if cells involved in protective immunity are assumed to belong to the CD8+ category, anti-CD8 antibodies accelerate the decrease of CD4- cells and thus shorten the patient's survival.

A mathematical model of CD8+ lymphocyte dynamics in HIV infection.

The previously developed mathematical model of CD4+ lymphocyte dynamics in HIV infection incorporated a homeostatic mechanism regulating production of both CD4+ and CD8+ lymphocytes. The model simulated the CD4+ lymphocyte dynamics well, but simulation of CD8+ lymphocyte values was not satisfactory, because simulated numbers of these cells increased even at later stages of infection, when no further increase was observed in infected individuals. Modifications of the model were attempted to obtain better simulation results assuming the influence of HIV infection on CD8+ lymphocyte maturation. Satisfactory results were obtained, if the influx of immature CD4+ and CD8+ lymphocytes was constrained by HIV infection. This modified version was then used for simulation of the anti-CD8 antibody administration effect in HIV-infected persons.

Effects of interferon gamma on the antibody response to Pseudomonas aeruginosa lipopolysaccharide in mice.

Different strains of mice were examined for the capacity to produce an Ig subclass-specific antibody response to purified Pseudomonas aeruginosa lipopolysaccharide (PALPS). With the exception of the AKR strain, the predominant isotype for most of the strains tested was IgG3 whereas the least frequent isotype expressed was either IgG2b or IgG1. AKR mice were unique in that the predominant isotype produced was IgG2a, rather than IgG3; however, the administration of anti-interferon gamma antibody, at the time of immunization with PALPS caused a substantial decrease in the IgG2a antibody response. Selected B10 congenic strains were used to assess the relationship between the antibody responses and the major histocompatibility complex (MHC) genes. Here, the isotype-patterns for the antibody responses were essentially the same regardless of the MHC haplotype. Interestingly, an increase in IgG2a, with a concomitant decrease in IgM and IgG1 antibody was noted when C3H mice were given interferon gamma at the time of immunization. These studies indicate that, in general, the antibody response to PALPS consists of IgG3 antibody as the predominant isotype, and that the antibody response can be modified by interferon gamma.

Molecular structures that influence the immunomodulatory properties of the lipid A and inner core region oligosaccharides of bacterial lipopolysaccharides.

The relationship between chain length as well as the position of fatty acyl groups to the ability of lipid A to abolish the expression of suppressor T-cell (Ts) activity was examined. Fatty acyl chain lengths of C12 to C14, as in the lipid A of Escherichia coli and Salmonella minnesota, appear to be optimal for this bioactivity, since lipid A preparations with fatty acyl groups of relatively short chain length (C10 to C12 for Pseudomonas aeruginosa and Chromobacterium violaceum) or predominantly long chain length (C18 for Helicobacter pylori) are without effect. The presence of an acyloxyacyl group of appropriate chain length at the 3' position of the glucosamine disaccharide backbone of lipid A also plays a decisive role. By contrast, the lipid A proximal inner core region oligosaccharides of some bacterial lipopolysaccharides increase the expression of Ts activity; this is due mainly to the capacity of such oligosaccharides, which are relatively conserved in structure among gram-negative bacteria, to enlarge or expand upon the population of CD8+ Ts generated during the course of a normal antibody response to unrelated microbial antigens. The minimal structure required for the expression of the added immunosuppression observed appears to be a hexasaccharide containing one 2-keto-3-deoxyoctonate residue, two glucose residues, and three heptose residues to which are attached two pyrophosphorylethanolamine groups. The relevance of these findings to virulence and to the pathogenesis of gram-negative infections is discussed.

Immunological properties of heterozygous nu/+ mice: changes in antibody response and inducibility of tolerance to protein antigens.

Heterozygous nu/+ mice are not fully identical in their immunological properties with the mice of wild +/+ genotype. A colony of nu/nu, nu/+ and +/+ mice from the same breeding nucleus was established and their immune reactivity to human serum albumin, inducibility of adult immune tolerance to hen egg lysozyme (HEL), sensitivity of their lymphoid cells to stimulation by mitogens and ratio of CD3, CD4 and CD8 positive cell populations was studied. Both the numbers of antibody-forming cells in regional lymph nodes and the antibody titres in sera of nu/+ mice were highly variable, between undetectable values of nu/nu and high values of +/+ homozygotes. Intravenous pretreatment with soluble HEL, leading in +/+ mice to a deep hyporeactivity to subsequent immunization with the same antigen, did not decrease the response of nu/+ mice significantly. These results indicate that the immunological alteration of nu/+ mice is not only quantitative and that T cell subpopulations might be differentially modified by the presence of nu allele. The finding of decreased CD4:CD8 ratio in nu/+ mice also supports this idea.

Mathematical modelling of chemotherapy in HIV infection.

A mathematical model of CD4+ lymphocyte depletion in HIV infection is used to simulate and analyse the effect of AZT treatment. In most cases, permanent administration of AZT is observed to stop the CD4+ lymphocyte count decline and to stimulate their increase up to a new steady-state level, which depends on the intensity of AZT treatment, i.e. AZT dose. Temporary administration of AZT leads only to a temporary increase in CD4+ lymphocyte count. After the treatment is terminated, the count starts to decline again. However, the resulting prolongation of patient's survival exceeds the time interval of AZT administration. Interestingly, the survival prolongation is greater, if the treatment is started at five than at two years after the infection and there is no striking increase in survival time if a dose of AZT inhibiting 75% of HIV proliferation is used instead of a lower one inducing 25% inhibition only.

Mathematical modelling of immunotherapy in HIV infection.

The effect of active or passive immunotherapy on HIV infection was simulated using a mathematical model of CD4+ lymphocyte depletion. Permanently effective active immunotherapy increased CD4+ lymphocyte counts to a steady-state level depending on the intensity of the therapy. Active HIV immunization effective for one or more years increased CD4+ lymphocyte counts during the treatment period and prolonged survival substantially; this prolongation exceeded the time interval of therapy duration. Intensive passive immunotherapy by anti-HIV antibodies led to a temporary increase of CD4+ lymphocyte numbers and an apparent prolongation of survival.

T-cell mediated immunosuppression and its implications for the development of protective immunity.

The mechanisms by which regulatory CD4- CD8+ suppressor T cells (Ts) and CD4+ CD8- amplifier T cells (Ta) influence the magnitude of the antibody response to the capsular polysaccharide antigen of type III Streptococcus pneumoniae are reviewed in detail. This represents the best-characterized experimental model system available for demonstrating how subsets of T cells act in a negative and positive manner to control the magnitude of an antibody response. The fact that transferred Ts and Ta elicit their effects in athymic immunized mice affirms, that such regulatory T cells are antigen-specific and act on immune B cells to produce the effects observed. The ability of the lipid A and the inner core-region oligosaccharide fractions of bacterial lipopolysaccharide to abolish and increase the expression of Ts function, respectively, is examined with respect to its immunomodulatory potential and its possible role in enhancing the virulence of Gram-negative bacteria.

The influence of monophosphoryl lipid A (MPL) on erythrocyte autoantibody formation.

The onset and the amount of erythrocyte autoantibodies induced by the injection of C57BL/6N mice with rat red blood cells (RRBC) were hastened and increased, respectively, after the administration of monophosphoryl lipid A (MPL); this was not the case for similarly treated BALB/cAnN mice, which make a lower autoantibody response after immunization with RRBC. The transfer of spleen cells from donor C57BL/6N mice immunized with RRBC suppressed autoantibody formation in recipient mice subsequently immunized with RRBC; however, treatment with MPL prevented neither the induction nor the expression of such suppression. This suggests that the increased autoantibody response in RRBC-immunized C57BL/6N mice treated with MPL is not due to the inactivation of suppressor cell activity which, in other studies, was found to be extremely sensitive to MPL.

Effects of IL-4 depletion on the antibody response to Pseudomonas aeruginosa lipopolysaccharide in mice.

These studies were done to examine the role of interleukin-4 (IL-4) in the generation of isotype specific antibody responses of mice to Pseudomonas aeruginosa lipopolysaccharide (PALPS) by neutralization of IL-4 in vivo using anti-IL-4 antibody (11B11). We found that the administration of anti-IL-4 antibody (11B11) 24 h before immunization with PALPS resulted in a decreased PALPS-specific antibody response for all isotypes examined (IgM, IgG1, IgG2a, IgG2b, IgG3). By contrast, we observed that the non-antigen-specific (polyclonal) IgM response of mice following treatment with 11B11 antibody and PALPS was increased while the polyclonal responses for the other isotypes were unaffected. When mice were given recombinant IL-10 at the time of immunization with PALPS there was a decrease in the PALPS-specific antibody response but an increase in the polyclonal IgM, IgG2a, IgG2b, IgG3 response whereas the polyclonal IgG1 response was decreased by a five-fold margin. The results of these studies suggest that both the antigen-specific and the polyclonal response can be influenced in a different manner by IL-4 or by IL-10.

Structural features that influence the ability of lipid A and its analogs to abolish expression of suppressor T cell activity.

Lipid A preparations derived from the lipopolysaccharides of several gram-negative bacteria, as well as chemically defined synthetic lipid A's and their analogs (both glucosamine mono- and disaccharides), were used to establish the chemical structures required for (i) abolishing the expression of suppressor T cell (Ts) function and (ii) inducing polyclonal activation of B cells. Salmonella minnesota R595 lipid A (diphosphoryl lipid A) possesses both of these activities. Decreasing the number of phosphate groups in lipid A from two to one (monophosphoryl lipid A) as well as decreasing the fatty acyl content, primarily by removing the residue at the 3 position, resulted in a progressive reduction in toxicity; however, these structural modifications did not influence its ability to abolish the expression of Ts function. Reducing the fatty acyl content from five to four (lipid A precursor IVA or Ia) eliminated the capacity to influence Ts function but not to induce polyclonal activation of B cells. None of the monosaccharide analogs of lipid A examined influenced the expression of Ts activity, although some were able to activate B cells polyclonally. Thus, in order to be able to abolish the expression of Ts function, lipid A (i) must be a glucosamine disaccharide, (ii) may have either one or two phosphate groups, and (iii) must have at least five fatty acyl groups. Also, the chain length of the nonhydroxylated fatty acid, as well as the location of acyloxyacyl groups (2' versus 3' position), may play an important role. These findings indicate that the chemical structures responsible for the toxicity of lipid A differ from those that influence its capacity to abolish the expression of Ts function and to induce polyclonal activation of B cells.

Model-based analysis of CD4+ lymphocyte dynamics in HIV-infected individuals. II. Evaluation of the model based on clinical observations.

The recently developed mathematical model of CD4+ lymphocyte depletion in HIV-infected individuals is evaluated using a comparison with available clinical data. The data used for such an evaluation are to be extrapolated from the published clinical observations as these data sets are not homogeneous covering only parts of HIV infection duration. An additional complication is due to the uncertainty of exact infection onset. Based on these considerations, several different reference data sets are generated from the available clinical data and the range of applicability of the mathematical model and its modifications is then investigated. As a result of such quantitative confrontation, it can be concluded that the appropriate setting of cell interaction parameters in the model can result in a fairly good coincidence of the simulated HIV infection dynamics with reference data sets. Perspectives and limitations of such an approach are also discussed.

Effect of a proline-rich polypeptide (PRP) on the development of hemolytic anemia and survival of New Zealand black (NZB) mice.

PRP, administered intraperitoneally into NZB mice, twice a week, at doses 0.01-1 microgram per mouse, significantly lowered the incidence of positive Coombs' reaction and prolonged the mean age of the mice. The effect of PRP on survival of mice was better when the treatment with PRP started early (in mice showing first signs of the disease). The results suggest that PRP may induce, from a precursor pool of cells, suppressor cells controlling development of the disease. In addition, the data indicate that PRP may have a therapeutical value in treatment of autoimmune disorders, e.g. the juvenile arthritis.

Influence of the cell interaction parameters on the simulated CD4+ lymphocyte depletion in HIV infection.

The previously suggested mathematical models of CD4+ lymphocyte depletion in HIV-infected individuals are analysed from the point of view of fundamental cell interaction mechanisms involved. Under the assumption of growth restriction of the HIV by cytotoxic lymphocytes, the intensity of the feedback mechanism increasing the influx of immature CD4+ lymphocytes and the intensity of the helper effect of CD4+ lymphocytes during the maturation of cytotoxic cells are evaluated and compared in a wide range of the respective model parameters. In this respect also the role of the proliferation rate of these cytotoxic lymphocytes under antigenic stimulation by HIV products is discussed. In addition, an alternative elimination mechanism of CD4+ lymphocytes is investigated, which assumes their destruction by cytotoxic lymphocytes. It is concluded that any of the considered cases of the influx amplification parameter, helper effect intensity parameter, and CD4+ lymphocyte elimination mechanism can be used for a qualitative adjustment of the model to clinical data.

Model-based analysis of CD4+ lymphocyte dynamics in HIV infected individuals.

The previously suggested mathematical model of CD4+ lymphocyte depletion in HIV-infected individuals is analyzed and further developed. The model assumes that CD4+ lymphocyte depletion is caused by HIV products. Fairly good simulation of CD4+ lymphocyte dynamics is obtained, when limitation of HIV growth by specific cytotoxic T cells is included in the model. As it is probable that the substantial decrease of CD4+ lymphocytes, this type of influx control mechanism is also included in the model. It is shown that the simulated CD4+ lymphocyte dynamics agree with the observed data, analogously as in the earlier considered case of the constant influx. Moreover, the depleting effect of HIV products on mature and/or immature CD4+ lymphocytes is analyzed by the model. Also, another modification of the model assuming that CD4+ lymphocyte depletion is due to their destruction by cytotoxic T cells specific for HIV antigens, gives simulation results comparable to those obtained by the original version of the model, where the mechanism of the depletion is not specified.

Immunoregulatory effect of a synthetic peptide corresponding to a region of protein p24 of HIV.

The effect of a synthetic peptide, corresponding to a sequence of HIV-1 p24 protein (amino acids 218-237), on in vitro immune responses was studied. The peptide inhibited in a dose-dependent manner the induction of an anti-SRC antibody response and of a PPD-specific proliferative response of human PBL. On the other hand, PHA-induced proliferation of human PBL and PPD-induced proliferation of a PPD-specific human T-cell line were not modified by comparable amounts of the peptide. These results suggest that structures from a protein (p24), present in the serum throughout the course of HIV infection, are able to interfere with the inductive stages of specific immune responses. These findings may help to unravel some of the pathogenic mechanisms of AIDS and may contribute to the development of vaccine strategies.

Mathematical model of CD4+ lymphocyte depletion in HIV infection.

The CD4+ lymphocyte depletion in human immunodeficiency virus (HIV)-infected persons seems to be affected by HIV products. As the dynamics of the concentration of HIV products is reciprocal to that of non-replicating antigen used for induction of tolerance, the mathematical model of immunological tolerance can be used to describe the dynamics of CD4+ lymphocyte depletion. To stimulate the clinically observed dynamics, it is necessary to include the limitation of HIV growth by the corresponding cytotoxic T cells and their dependence on the helper effect of CD4+ lymphocytes. Simulation analysis suggests that qualitatively similar results are obtained if immature, mature, or both categories of CD4+ lymphocytes considered in the model are depleted by the HIV products.

Increase by bacterial lipopolysaccharide of antibody production in mice rendered hyporesponsive to lysozyme.

The effect of bacterial lipopolysaccharide (LPS) on the immune response of adult mice to hen egg lysozyme (HEL) was studied under conditions in which hyporesponsiveness to HEL was induced by: (i) the intravenous injection of syngeneic spleen cells incubated with HEL; (ii) the intravenous administration of soluble HEL, and (iii) the intraperitoneal injection of HEL in IFA. In all cases, mice were immunized by footpad injection of HEL, with or without LPS. The antibody response produced was measured by the number of indirect anti-HEL plaque forming cells (PFC) detected in popliteal lymph nodes. The incorporation of LPS in the immunizing dose of HEL had little effect on the response of controls; however, it resulted in an appreciable increase in the antibody response of all three groups of hyporesponsive mice. Although, after treatment with LPS, the number of PFC detected in mice made tolerant by spleen cell injection approached those of the controls, lower increases in the antibody response were noted for the remaining two groups of hyporesponsive mice.