A generalized quantitative antibody homeostasis model: antigen saturation, natural antibodies and a quantitative antibody network

Abstract

In a pair of articles, we present a generalized quantitative model for the homeostatic function of clonal humoral immune system. In this second paper, we describe how antibody production controls the saturation of antigens and the network of antibody interactions that emerges in the epitome space with the establishment of the immune system. Efficient control of antigens, be it self or foreign, requires the maintenance of antibody concentrations that saturate antigen to relevant levels. Simple calculations suggest that the observed diverse recognition of antigens by natural antibodies is only possible by cross-reactivity whereby particular clones of antibodies bind to diverse targets and shared recognition of particular antigens by multiple antibody clones contribute to the maintenance of antigen control. We also argue that natural antibodies are none else than the result of thymus-independent responses against immunological self. We interpret and explain antibody production and function in a virtual molecular interaction space and as a network of interactions. Indeed, the general quantitative (GQM) model we propose is in agreement with earlier models, confirms some assumptions and presumably provides the theoretical basis for the construction of a real antibody network using the sequence and interaction database data.

Figure 1

Outlines of the GQM for regulation of antibody production. (a) Antibodies will saturate antigen by increasing their concentration or by increasing apparent affinity. (b) Low concentrations of low-affinity antibodies do not bind antigen at relevant extent, antigen concentrations can be best controlled at around 50% saturation, while elimination is achieved by increasing saturation further. (c) ASC produce antibodies to increase concentration, while prior differentiation account for increased affinity or ability to remove antigen. Immune complexes are removed by different cells and silent or proinflammatory events.

Figure 2

Balance of Ab and Ag achieved by different humoral immune responses. The epitope-antibody interaction landscape as defined by free antibody concentration and affinity. Second signals required by B cells for becoming antibody-secreting cells are listed next to the type of immune response. The range of total serum immunoglobulin concentration and the concentration achieved by a single ASC clone are indicated. B_m, memory B-cell; btk, Bruton's tyrosine kinase; NKT, NK T cells; PRR, pattern recognition receptors; TD, thymus dependen; T_FH, follicular helper T cells; Th, helper T-cell; TI, thymus independent.

Figure 3

Thymus-independent- and thymus-dependent antibody responses in the interaction landscape. Relative concentration of epitopes, antibodies and affinity of the interactions define natural and thymus-dependent antibodies.

Figure 4

Layers of interactions of antibodies with immunological self and non-self. mutBCR, BCR with somatic hypermutation.

Figure 5

Definitions of the antibody network. (a) Antibody Ab_i reacts with epitope A and cross-reacts with epitope B. Ab_j reacts with epitope A and cross-reacts with epitope B. Distances, expressed as negative logarithm of K_D are averaged to get the distance in the epitope space, providing an edge in the network. (b) Free antibody concentration divided by K_D reflects antigen-binding capacity. This value is displayed as the radius of the node. Changes in antigen concentration will trigger changes in node radius. New antigens entering the system may react with higher affinity with a given antibody and thereby change its position in the epitope space.

Figure 6

Simplified schematic representation of the antibody-epitome interaction network. Only nodes of the network are shown, edges are not drawn for the sake of simplicity but are represented as internodal distances. Blue nodes are natural antibody interactions, purple nodes are interactions with the accepted environment, red nodes are TD interactions in the epitope space. Green area represents B cells in the quiescent state, not producing antibodies but presenting themselves in the epitome space. Immunological self is a superconnected central component, while epitopes marked for elimination are extruded and disconnected.