Mechanism and computer simulation of immune complex formation, opsonization, and clearance

Mathematical modeling in autoimmune diseases: from theory to clinical application

The research & development (R&D) of novel therapeutic agents for the treatment of autoimmune diseases is challenged by highly complex pathogenesis and multiple etiologies of these conditions. The number of targeted therapies available on the market is limited, whereas the prevalence of autoimmune conditions in the global population continues to rise. Mathematical modeling of biological systems is an essential tool which may be applied in support of decision-making across R&D drug programs to improve the probability of success in the development of novel medicines. Over the past decades, multiple models of autoimmune diseases have been developed. Models differ in the spectra of quantitative data used in their development and mathematical methods, as well as in the level of "mechanistic granularity" chosen to describe the underlying biology. Yet, all models strive towards the same goal: to quantitatively describe various aspects of the immune response. The aim of this review was to conduct a systematic review and analysis of mathematical models of autoimmune diseases focused on the mechanistic description of the immune system, to consolidate existing quantitative knowledge on autoimmune processes, and to outline potential directions of interest for future model-based analyses. Following a systematic literature review, 38 models describing the onset, progression, and/or the effect of treatment in 13 systemic and organ-specific autoimmune conditions were identified, most models developed for inflammatory bowel disease, multiple sclerosis, and lupus (5 models each). ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others - as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. Despite covering a relatively wide range of diseases, most models described the same components of the immune system, such as T-cell response, cytokine influence, or the involvement of macrophages in autoimmune processes. All models were thoroughly analyzed with an emphasis on assumptions, limitations, and their potential applications in the development of novel medicines.

Spatiotemporal dynamics of complement C5a production within bacterial extracellular polymeric substance

Opsonization and anaphylatoxin production are early events in the innate response to bacterial pathogens. Opsonization alone is frequently not lethal and production of anaphy-latoxins, especially C5a, allows for recruitment of cellular defenses. Complement biochemistry is extensively studied and computational models have been reported previously. However, a critical feature of complement-mediated attack is its spatial dependence: diffusion of mediators into and away from a bacterium is central to understanding C5a generation. Spatial dependence is especially important in biofilms, where diffusion limitation is crucial to bacterial counterdefense. Here we develop a model of opsonization and C5a production in the presence of a common blood-borne pathogen, Staphylococcus epidermidis. Our results indicate that when complement attacks a single cell, diffusion into the extracellular polymeric substance (EPS) is complete within 10 ms and that production of C5a peaks over the next 15 min. When longer diffusion lengths (as in an EPS-rich biofilm) are incorporated, diffusion limitation appears such that the intensity and duration of C5a production is increased. However, the amount of C5a produced under several likely clinical scenarios where single cells or sparse biofilms are present is below the kD of the C5a receptor suggesting that complement activation by a single bacterium may be difficult to detect when diffusion is taken into account.

Modelling the within-host dynamics of the foot-and-mouth disease virus in cattle

In this paper we investigate the within-host dynamics of the foot-and-mouth disease virus (FMDV) in cattle using previously published data for 8 experimentally infected cows. An 8-compartment, 14-parameter differential equation model was fitted to data collected from each cow every 24 h over the course of an infection on: (i) the concentration of FMDV genomes in the blood, (ii) the concentration of infectious virus in the blood, (iii) antibody levels, and (iv) interferon levels. Model parameters were estimated using maximum-likelihood methods. The likelihood surface was sampled using Markov chain Monte Carlo methods giving credible intervals for each of the model parameters. The model was able to capture the within-host dynamics well for 6 of the infections, with both the innate (type 1 interferon) and antibody responses playing key roles in determining the height and duration of peak levels of virus. There was considerable variation between virus dynamics in individual cattle which was only partly accounted for by inferred differences in the dose of virus received. A better understanding of the within-host dynamics also provides insights into the dynamics of infectiousness and the transmission of virus to new hosts.

Investigating the role of T-cell avidity and killing efficacy in relation to type 1 diabetes prediction

During the progression of the clinical onset of Type 1 Diabetes (T1D), high-risk individuals exhibit multiple islet autoantibodies and high-avidity T cells which progressively destroy beta cells causing overt T1D. In particular, novel autoantibodies, such as those against IA-2 epitopes (aa1-577), had a predictive rate of 100% in a 10-year follow up (rapid progressors), unlike conventional autoantibodies that required 15 years of follow up for a 74% predictive rate (slow progressors). The discrepancy between these two groups is thought to be associated with T-cell avidity, including CD8 and/or CD4 T cells. For this purpose, we build a series of mathematical models incorporating first one clone then multiple clones of islet-specific and pathogenic CD8 and/or CD4 T cells, together with B lymphocytes, to investigate the interaction of T-cell avidity with autoantibodies in predicting disease onset. These models are instrumental in examining several experimental observations associated with T-cell avidity, including the phenomenon of avidity maturation (increased average T-cell avidity over time), based on intra- and cross-clonal competition between T cells in high-risk human subjects. The model shows that the level and persistence of autoantibodies depends not only on the avidity of T cells, but also on the killing efficacy of these cells. Quantification and modeling of autoreactive T-cell avidities can thus determine the level of risk associated with each type of autoantibodies and the timing of T1D disease onset in individuals that have been tested positive for these autoantibodies. Such studies may lead to early diagnosis of the disease in high-risk individuals and thus potentially serve as a means of staging patients for clinical trials of preventive or interventional therapies far before disease onset.

Modeling immune complex-mediated autoimmune inflammation

A number of autoimmune diseases are thought to feature a particular type of self-sustaining inflammation, caused by the deposition of immune complexes (IC) in the inflamed tissue and a consequent activation of local effector cells. The persistence of this inflammation is due to a positive feedback loop, where autoantigen particles released as part of the tissue damage caused by the inflammation stimulate autoreactive B cells, leading to the formation of further immune complexes and their subsequent deposition. We present a mathematical model for the exploration of IC-mediated autoimmune inflammation and its clinical implications. We characterize the possible differences between normal individuals and those susceptible to such inflammation, and show that both random perturbations and bifurcations can lead to disease onset. Our model explains how defects in the mechanisms responsible for cellular debris clearance contribute to the development of disease, in agreement with empirical evidence. Moreover, we show that parameters governing the dynamics of immune complexes, such as their clearance rate, have an even stronger effect in determining the behavior of the system. We demonstrate the existence of hysteresis, implying that once IC-mediated autoimmune inflammation is triggered, its long-term suppression may be difficult to achieve. Our results can serve to guide the development of novel therapies to autoimmune diseases involving this type of inflammation.

Antibodies as drug carriers III: design of oligonucleotides with enhanced binding affinity for immunoglobulin G

PURPOSE

To understand the structural requirements in designing epitope-bearing oligonucleotides with high antibody-binding affinity.

METHODS

Binding affinity (KA) and stoichiometry (n) of dinitrophenyl (DNP)-derivatized model 27-mer oligonucleotides (ODNs), GGG(AAA)7GGG, to monoclonal anti-trinitrophenyl (TNP) antibodies were determined using isothermal titration calorimetry (ITC). Structural variations were made in the ODNs to assess the effects of antigenic valence, epitope density, inter-epitope linker length, and linker flexibility. Binding isotherms were fitted with a single binding-site model to obtain K(A) and n, from which changes in Gibbs free energy (deltaG(0)), entropy (deltaS(0)), and enthalpy (deltaH(0)) were derived.

RESULTS

As expected, ligands displaying increased epitope density showed increases in K(A): for example, K(A) for (DNP)2-Cys is 3.3-fold greater than that for DNP-Lys. Introduction of multiple DNP groups via long and flexible linkers to one end of the 27-mer ODN resulted in a bivalent behavior with n value of 1. A bivalent ligand, derivatized at both ends with a long and flexible linker, failed to form an immune complex when hybridized to its antisense strand, presumably due to intercalation of the DNP moiety to the double strand. ODNs derivatized with flexible linkers exhibited a higher K(A) than those with a rigid linker. Ligands with flexible inter-epitope linkers measuring distances of 110, 60, and 40 angstroms yielded 13-, 30-, and 13-fold increases in K(A), respectively. The combination of these factors; namely, bivalence, flexible inter-epitope linkers, and optimal inter-epitope distance, resulted in an overall 66-fold increase in K(A). Thermodynamic analysis of binding indicates that the formation of high-affinity ODN-IgG complexes was a spontaneous and exothermic event, characterized by large negative deltaS degrees, deltaH degrees, and deltaG degrees values.

CONCLUSIONS

All four strategies tested during this investigation, namely bivalence, epitope density, inter-epitope linker flexibility, and optimal inter-epitope distance, proved to be useful in improving the binding affinity of DNP-labeled ODNs to anti-TNP IgG. The final ODN design incorporating these strategies will be used in testing the systemic pharmacokinetic advantage gained from complexing such ODNs to IgG.

Anti-drug antibodies as drug carriers. I. For small molecules

PURPOSE

To better understand the pharmacokinetics of drugs compounds that bind endogenous antibodies

METHODS

Three groups of mice with differing anti-fluorescein (FL) titers were established by empirically developed immunization protocols. These with two control groups were given intravenously [3H]-ethanolamine conjugate of FL (FL-EA). The latter was synthesized using isothiocyanate chemistry. Radioactivity in the circulation, and occasionally in peritoneal ascites, was monitored for 7 days. A group of mice was immunized with eosin Y and given FL-EA. Conversely, eosin Y conjugate of radiolabeled EA (EY-EA) was given to mice immunized with FL. These two groups represented animals of low affinity to probe haptens. The affinity was assessed by a precipitation procedure, while titer was determined by a standard ELISA. Dose of FL-EA varied over a 100-fold.

RESULTS

On average, the three immunized groups showed a 1:13:85 ratio of anti-FL titer, with remarkably consistent levels within each group. Elimination rates of FL-EA from the serum of very high-titer mice and high-titer mice were similar, however, were substantially lower than that found in low-titer mice. The latter was in turn lower than that found in non- or mock-immunized mice. Serum of mice immunized with FL showed approximately 200-fold lower affinity towards EY-EA than FL-EA. In these mice and in mice immunized with eosin Y and given FL-EA, the elimination of the probe haptens was again fast, reminiscent of low-titer mice. Mice of either low titer or low affinity showed more rapid redistribution of the conjugate between serum and peritoneal fluid. In a group of mice with comparable anti-FL titer, elimination from serum was independent of dose over a 100-fold difference. The bi-phasic concentration-time profile observed was accommodated by a physiologically meaningful pharmacokinetic model incorporating two compartments in which antibody binding can occur.

CONCLUSIONS

Monovalent antigenic substance cannot trigger immune clearance. As such, endogenous antibodies that recognize the molecule can serve as a carrier to result in a substantial decrease in clearance.

Antibodies as carrier proteins

Pre-existing antibodies against a drug substance can significantly alter the pharmacokinetic profile of the drug in the circulation. Rapid clearance, mediated by complement or Fc receptors, occurs for crosslinked immune complexes, but not for complexes containing only one or two antibodies. With antibodies functioning as carrier proteins, monovalent antigens may enjoy a prolonged circulatory half-life, as observed in the case of digoxin, insulin, and various interleukins. While such an effect should be highly sensitive to fluctuations in antibody affinity and titer, it may present a means of extending the circulation of potent but rapidly cleared therapeutic agents. This mini-review attempts to delineate the causal relation between the factors influencing antibody binding and the circulatory life of a therapeutic agent, be it a small drug or a macromolecule.