title: The Berg-Purcell limit revisited.
abstract: Biological systems often have to measure extremely low concentrations of chemicals with high precision. When dealing with such small numbers of molecules, the inevitable randomness of physical transport processes and binding reactions will limit the precision with which measurements can be made. An important question is what the lower bound on the noise would be in such measurements. Using the theory of diffusion-influenced reactions, we derive an analytical expression for the precision of concentration estimates that are obtained by monitoring the state of a receptor to which a diffusing ligand can bind. The variance in the estimate consists of two terms, one resulting from the intrinsic binding kinetics and the other from the diffusive arrival of ligand at the receptor. The latter term is identical to the fundamental limit derived by Berg and Purcell (Biophys. J., 1977), but disagrees with a more recent expression by Bialek and Setayeshgar. Comparing the theoretical predictions against results from particle-based simulations confirms the accuracy of the resulting expression and reaffirms the fundamental limit established by Berg and Purcell.
authors.affiliation: RIKEN Quantitative Biology Center (QBIC), RIKEN, 6-2-3 Furuedai, Suita, Osaka 565-0874, Japan.
authors.forename: Kazunari
authors.initials: K
authors.lastname: Kaizu
authors.affiliation: FOM Institute AMOLF, Science Park 104, 1098 XG, Amsterdam, The Netherlands.
authors.forename: Wiet
authors.initials: W
authors.lastname: de Ronde
authors.affiliation: FOM Institute AMOLF, Science Park 104, 1098 XG, Amsterdam, The Netherlands.
authors.forename: Joris
authors.initials: J
authors.lastname: Paijmans
authors.affiliation: RIKEN Quantitative Biology Center (QBIC), RIKEN, 6-2-3 Furuedai, Suita, Osaka 565-0874, Japan.
authors.forename: Koichi
authors.initials: K
authors.lastname: Takahashi
authors.affiliation: FOM Institute AMOLF, Science Park 104, 1098 XG, Amsterdam, The Netherlands.
authors.forename: Filipe
authors.initials: F
authors.lastname: Tostevin
authors.affiliation: FOM Institute AMOLF, Science Park 104, 1098 XG, Amsterdam, The Netherlands. Electronic address: tenwolde@amolf.nl.
authors.forename: Pieter Rein
authors.initials: PR
authors.lastname: ten Wolde
mesh_terms: D004058:Diffusion; D007700:Kinetics; D008024:Ligands; D008956:Models, Chemical; D011485:Protein Binding; D011956:Receptors, Cell Surface / Q000378:metabolism*
chemical_list: D008024:Ligands; D011956:Receptors, Cell Surface