Receptor crosstalk improves concentration sensing of multiple ligands

Abstract

Cells need to reliably sense external ligand concentrations to achieve various biological functions such as chemotaxis or signaling. The molecular recognition of ligands by surface receptors is degenerate in many systems leading to crosstalk between different receptors. Crosstalk is often thought of as a deviation from optimal specific recognition, as the binding of non-cognate ligands can interfere with the detection of the receptor's cognate ligand, possibly leading to a false triggering of a downstream signaling pathway. Here we quantify the optimal precision of sensing the concentrations of multiple ligands by a collection of promiscuous receptors. We demonstrate that crosstalk can improve precision in concentration sensing and discrimination tasks. To achieve superior precision, the additional information about ligand concentrations contained in short binding events of the noncognate ligand should be exploited. We present a proofreading scheme to realize an approximate estimation of multiple ligand concentrations that reaches a precision close to the derived optimal bounds. Our results help rationalize the observed ubiquity of receptor crosstalk in molecular sensing. * These authors are listed alphabetically † Corresponding authors derstanding the limits in cellular sensing for single receptors with spatial [10-14] and temporal gradients [15,16], for multiple receptors [17][18][19] and even for cells that can communicate [20][21][22]. The thermodynamic cost [23][24][25][26][27] and the trade-offs between different resources for sensing [28][29][30] has also been explored at large.

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“…While the drift is linear in the above sum (so that the average of the sum can be treated as shown above), the diffusivity depends on the square of the sum. The diffusivity involves then the correlation of times and ratios ( Carballo-Pacheco et al, 2019 ), which is harder to obtain as it depends a priori on the details of the binding site model (see the subsection ’Equality between drift and diffusivity’ and the subsection ’When are correlations between the times of events leading to decision important?’ of Appendix 3 for details).…”

“…We have shown in the subsection ’Expansion of the drift for small concentration differences’ of Appendix 3 that the first non-vanishing term in the expansion of the drift is of order 2 in and is given by Equation 16 . An integral formula for the second moment of the log -likelihood is given in Equation A15 of Carballo-Pacheco et al, 2019 from which we get that the diffusivity of the log ratio is the sum of four terms. The first term is given by is proportional to and so is of order .…”

“…And so we recover that for small concentration differences, . In the case of one binding site with ON rate and OFF rate ν we check that the formula from Carballo-Pacheco et al, 2019 gives the exact expression computed in Siggia and Vergassola, 2013 Replacing L 2 with L in Equation 26 and expanding in we have We identify the drift computed for the one binding site example in the paragraph ’Mean decision time : connecting drift-diffusion and Wald’s approaches’ of the main text and find that at first order drift and diffusivity are equal.

Appendix 3—figure 1.

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“…Following the arguments in Carballo-Pacheco et al, 2019 , let us consider the following generating function for the cumulants of the log-likelihood difference at a given time T assuming hypothesis i is true ( or 2) : where is the log -likelihood of hypothesis , n is the number of ON-OFF cycles and and are respectively the ON and OFF waiting times. This is not exactly what appears in Carballo-Pacheco et al, 2019 , but it is sufficient to grasp the consequences of the correlations introduced by a global constraint on the duration of the process, that is, the function. Note that such constraint breaks the statistical independence of the various cycles, and introduces dependencies even though the and factorize.…”

Energy consumption and cooperation for optimal sensing

“…Limited sensor-signal specificity places an additional constraint on sensing performance 24 (but see, ref. 25 ). Previous works have shown that kinetic proofreading schemes 3 can mitigate this problem for isolated chemoreceptors that bind to correct and incorrect ligands 26,27 .…”