The Binding Landscape of Serum Antibodies: How Physical and Mathematical Concepts Can Advance Systems Immunology

Abstract

Antibodies constitute a major component of serum on protein mass basis. We also know that the structural diversity of these antibodies exceeds that of all other proteins in the body and they react with an immense number of molecular targets. What we still cannot quantitatively describe is how antibody abundance is related to affinity, specificity, and cross reactivity. This ignorance has important practical consequences: we also do not have proper biochemical units for characterizing polyclonal serum antibody binding. The solution requires both a theoretical foundation, a physical model of the system, and technology for the experimental confirmation of theory. Here we argue that the quantitative characterization of interactions between serum antibodies and their targets requires systems-level physical chemistry approach and generates results that should help create maps of antibody binding landscape.

Keywords: antibody; chemical potential; differential equation; logistic function; system.

Figure 1

Categorization of antibodies based on sensor and effector function. The two functional types of antibodies, two corresponding cell types and the mixed type are shown. BCR, B-cell receptor.

Figure 2

Immune responses displayed in configuration space of antibody interactions. Distance of the lines representing immune system boundary from the center corresponds to chemical potential.

Figure 3

Expansion and affinity maturation of germinal center B cells displayed in configuration space. Naive and memory sensor B cells seed an active response, being activated via BCR. Somatic hypermutations generate random shifts in configuration space (blue lines between purple nodes), a selection of higher affinity mutants produce lymphoblasts. Secretion of antibodies with higher affinity appears as a protrusion of the interaction space towards the targeted antigen. Following an active immune response, the system retracts leading to a steady state with new borders, corresponding to LLPC and MBC with an affinity higher than original.

Figure 4

Probing the configuration space with antigen. Configuration space (a,b) can be probed (brown arrow) by measuring the changes of chemical potential of serum antibodies with the antigen of interest, using an immunoassay. Using antigen microspot titration key parameters of interaction, such as standard chemical potential and limiting activity coefficient, can be modeled by the Richards curve (c,d) parameters, including the determination of inflection point (blue circle) position. During an active immune response (a,c), the apparent affinity increases, as reflected by a decreased average standard chemical potential, and changes in clonal composition alter the limiting coefficient ${\gamma }_{Ag}^{\infty }$. A memory response (b,d) is characterized by optimized affinity and clonal heterogeneity. [Ag]_i, antigen concentration at point of inflection.

Figure 5

Interpretation of the limiting activity coefficient of antigen. The limiting thermodynamic activity coefficient reflects the contribution of epitope to binding by all antibody structures or the epitope-paratope fit in other words. Only the outlines of the paratope surfaces are shown (circles) to allow the visualization of overlaps. (a) A monoclonal antibody paratope-epitope fit is shown for comparison. Memory formation (b) reduces surviving clones to minimal optimal binders, while during an active immune response (c) several structurally distinct antibodies co-exist and compete for binding.