How probable are antibody cross-reactions?

Antibodies to polypeptides are increasingly being used in research. Their specificity and tight but reversible binding make them ideal for applications such as identification of proteins, immunological quantification or purification, and peptide mapping. Antibodies are also used in medicine to deliver loads to specific sites in tissues, and in electron microscopy as heavy metal conjugates to locate antigens in thin sections. While these techniques depend on specificity of antibody binding, it is occasionally observed that cross-reactions occur. These cross-reactions are attributed to the existence of one or more antibody binding sites common to both polypeptides. It is important to know whether these cross-reactions are expected due to chance alone, or if they are improbable and likely due to some causative agent. Examples of such causative agents might include gene duplication events or convergence due to functional constraints. At the present time, good methods for predicting the probability and therefore the frequency of cross-reactions are unavailable. In this paper we apply some recently reported mathematical results to address the following questions: (1) What is the probability that polyclonal or monoclonal antibodies raised against a given polypeptide will cross-react with another polypeptide due to chance alone? (2) What is the probability that polyclonal or monoclonal antibodies raised against a given polypeptide will cross-react with one or more polypeptides in a pool of polypeptides? Approximate answers to these questions are presented for cases where amino acid compositions of linear polypeptides are known or unknown, but the amino acid sequence of one or more of the polypeptides is not known. Implications of the results for antibody use in protein research are discussed.