The Berg-Purcell Limit Revisited Kazunari Kaizu, Wiet de Ronde, Joris Paijmans, Koichi Takahashi, Filipe Tostevin, Pieter Rein ten Wolde  Biophysical Journal  Volume 106, Issue 4, Pages 976-985 (February 2014) DOI: 10.1016/j.bpj.2013.12.030 Copyright © 2014 Biophysical Society Terms and Conditions

Figure 1 The power spectrum of the receptor state Pn(ω) for c = 0.4 μM. The simulation results (black circles) agree well with the theoretical prediction of Eq. 13 (solid red line). At high frequencies ω > 1/τm = D/σ2, the effect of diffusion is negligible and the receptor dynamics is that of a Markovian switching process with intrinsic rates kac and kd (dashed red line), while at low frequencies it is that of a Markovian switching process with effective rates konc and koff, respectively (solid gray line). The zero-frequency limit determines the precision of the concentration estimate. Parameters: n¯=0.5, D = 1 μm2 s−1, σ = 10 nm, L = 1 μm, and ka = 552 μM−1 s−1. To see this figure in color, go online. Biophysical Journal 2014 106, 976-985DOI: (10.1016/j.bpj.2013.12.030) Copyright © 2014 Biophysical Society Terms and Conditions

Figure 2 The zero-frequency limit of the power spectrum as a function of the average receptor occupancy n¯ for c = 0.4 μM; n¯ is varied by changing kd. It is seen that the agreement between the theoretical prediction of Eq. 13 and the simulation results is very good (red line). In contrast, the prediction of Bialek and Setayeshgar (9) (black line) differs markedly from our results. Parameters: see Fig. 1. To see this figure in color, go online. Biophysical Journal 2014 106, 976-985DOI: (10.1016/j.bpj.2013.12.030) Copyright © 2014 Biophysical Society Terms and Conditions

Figure 3 Cartoon of the coarse-grained model. (a) A typical time trace of the receptor state n(t) of the original system. (b) Time trace of the coarse-grained model. (Top-left cartoon; red) a successful and an unsuccessful binding trajectory; (blue) a trajectory in which a ligand molecule undergoes a number of rounds of receptor dissociation and rebinding before it escapes into the bulk. The key observation is that the time a molecule spends near the receptor is very short on the timescale at which molecules arrive from the bulk. This makes it possible to integrate out the receptor rebindings and the unsuccessful arrivals of molecules from the bulk, giving the two-state model of Eq. 19. Fig. S1 in the Supporting Material quantifies the timescale separation. To see this figure in color, go online. Biophysical Journal 2014 106, 976-985DOI: (10.1016/j.bpj.2013.12.030) Copyright © 2014 Biophysical Society Terms and Conditions