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 FCϵRIs, as well as endocrine signalling/disruption.
Highlights
Recent works in quantitative evolution combined to mathematical modelling have shown that evolution of biological networks is constrained by selected phenotypes in strong unexpected ways
Numerical experiments of in silico evolution of phenotypic models of gene networks [3] have further shown that, surprisingly, selection of complex phenotypes leads to apparition of complex traits that have not been explicitly selected for
We could show that the main effect of kinetic proofreading in this system is to lower antagonism [18], but is it possible to construct an absolute discrimination system without any antagonism ? In the following, we show from general arguments how ligand antagonism is a necessary consequence of absolute discrimination, qualifying as a “phenotypic spandrel”
Summary
Recent works in quantitative evolution combined to mathematical modelling have shown that evolution of biological networks is constrained by selected phenotypes in strong unexpected ways. In kinetic proofreading proposed in [23], each receptor contributes additively to signalling once it is bound, so that more ligands, or with longer binding time, necessarily gives stronger signal In such models, starting from a critical ligand concentration L1 triggering response, any addition of ligands L2 gives higher output T value, and if response is based on thresholding of T , response is maintained. “Life-time dogma” [8] posits that immune recognition is an almost absolute discrimination process where the quality of ligand μ is encoded by binding time of ligands τ [17] This notion first came from a series of experimental data suggesting that the typical ligand concentration to trigger response falls by at least 4 to 5 orders of magnitude with a moderate change of binding time τ [31, 12]. Various theoretical and experimental studies of this behaviour have led authors to propose that kinetic proofreading should be complemented with combinations of internal positive/negative feedbacks to explain such observed high specificity in τ [20, 8, 16]
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