Phenotypic spandrel: absolute discrimination and ligand antagonism

Abstract

We consider the general problem of sensitive and specific discrimination between biochemical species. An important instance is immune discrimination between self and not-self, where it is also observed experimentally that ligands just below the discrimination threshold negatively impact response, a phenomenon called antagonism. We characterize mathematically the generic properties of such discrimination, first relating it to biochemical adaptation. Then, based on basic biochemical rules, we establish that, surprisingly, antagonism is a generic consequence of any strictly specific discrimination made independently from ligand concentration. Thus antagonism constitutes a 'phenotypic spandrel': a phenotype existing as a necessary by-product of another phenotype. We exhibit a simple analytic model of discrimination displaying antagonism, where antagonism strength is linear in distance from the detection threshold. This contrasts with traditional proofreading based models where antagonism vanishes far from threshold and thus displays an inverted hierarchy of antagonism compared to simpler models. The phenotypic spandrel studied here is expected to structure many decision pathways such as immune detection mediated by TCRs and FCòRIs, as well as endocrine signalling/disruption.

Attack and defence in cellular decision-making: lessons from machine learning

“…Similar properties have been observed experimentally for ambiguous samples in immune recognition: maximally antagonizing ligands have a binding time just below the decision threshold [2]. We interpret this property as a consequence of the flat landscape far from the decision threshold leading to a steep gradient close to it [13,12].…”

“…However, underlying, low manifold descriptions could locally still combine higher level information in ways similar to parameter τ , so that the theory presented here could still apply once those directions are discovered. Coming back to biology, it was shown mathematically that for the classification problem of discriminating ligand quality irrespective of their quantity, one always gets antagonism close to the boundary [12]. This is precisely due to the necessary presence of a significant gradient in the direction of the decision-making.…”

“…To model cellular decision-making, we will use the general class of "adaptive sorting" or "adaptive proofreading", models, which account for many aspects of immune recognition [29,11], and can be shown to capture all relevant features of such cellular decision-making close to a decision threshold [12]. Mathematical details on the models are given in Appendix 1.…”

“…Different models have different antagonistic properties, based on the strength of the activation branch (N ) relative to the repression branch (m). More mathematical details on such models can be found in [29,11,12].…”

“…we take an output TN,m with N > m ≥ 1. Here, the output is no longer sensitive to the addition of many weakly bound self ligands, yielding an inversion of the antagonistic hierarchy where the strongest antagonizing ligands exist closer to threshold [12]. An extreme case has been proposed for immune recognition where the strongest antagonists are found just below the threshold of activation [2].…”