Topics
Speculation space
Synopsis of the speculative topics in the IgOme project, with links to more detailed notes. The topics contain established results, working hypotheses under active scrutiny as well as outlook to potential future projects.
Specificity as a distribution
The conventional picture treats an antibody as specific for one epitope. A physics-flavoured alternative describes it by the distribution of binding free energies it realises across the whole space of epitopes. Specificity then becomes a property of that distribution’s shape — how peaked, how heavy-tailed.
\[ p(\varepsilon) \;=\; \frac{1}{Z}\, e^{-\beta\, E(\varepsilon)}, \qquad Z = \sum_{\varepsilon} e^{-\beta E(\varepsilon)} \]
A sharply specific antibody has a distribution dominated by a few low-energy epitopes; a polyreactive one spreads its weight broadly. Read the note →
Mimotope spaces
Peptide mimotopes selected on whole repertoires sample the functional binding landscape of the immunoglobulins in the blood as opposed to sequencing of the B cell receptors. The two approaches look at the antibody repertoire from non-overlapping viewpoints with nothing to bridge them yet. A library of mimotopes is a finite, noisy sample from a much larger reactivity space; the questions are how densely it covers that space and how to compare two such samples.
Key tools: phage display selection, NGS readout, representative sub-libraries, and string-distance metrics over the peptide alphabet. Read the note →
Graph representations
We represent the repertoire of reactivities as a graph: mimotope sequences are nodes, edges connect sequences sharing a common subsequence (e.g. 5 of 7 residues), or microarray reactivities linked by cross-reactivity. The graph’s community structure, spectral embedding, and topology then become measurable features.
\[ L \;=\; D - A, \qquad L\,\mathbf{v}_k = \lambda_k\, \mathbf{v}_k \]
Methods in rotation: modularity and CPM community detection, the Leiden algorithm, spectral graph analysis, and UMAP for visualization as well as non-negative matrix factorization for direct analysis of the binding data.
Repertoire physics
If individual antibodies are affinity distributions, the repertoire is an ensemble of such distributions. This invites questions framed in statistical mechanics: what is the “temperature” of a repertoire, what conserved quantities constrain it, and can anti-idiotypic structure emerge as a self-consistency condition on the ensemble?
This is the most speculative topic here — a working hypothesis under active scrutiny, not an established result. The field has been developed partially by Jozsef Prechl(1).
Does evolution ‘care’ about idiotypy?
IgOme maps show changes associated with autoimmune pathology with two recurrent features:
Loss of public IgM reactivities and
Non-random association with idiotypic reactivity.
Could we have a new tool at our disposal to study idiotypy in a more systematic way?