Physical approaches to receptor sensing and ligand discrimination

Multiplexing and its upper bound in biological sensory receptors

“…3, r s ≤ n nt s − 1 is a loose bound because the actual probability distribution of S can be a subspace of (n nt s − 1)-simplex due to certain symmetries or the statistical quality of the trajectory, explained below: First, the trajectory probability P θ [S] could contain symmetries. In the exam-ple of n t = 2 and n s = 2, we find that the symmetry P θ [01] = P θ [10] further removes one degree of freedom (see SI.3) and thus the trajectory probability simplex, and thus the probability space is reduced to the 2-dim dashed triangle "ABC". For n t = 3 and n s = 2, the 7-simplex is reduced to a 4-dim manifold due to 3 symmetries (see SI.…”

“…To date, the studies of ligand-receptor chemical sensing have been extended to more complex models. An incomplete set of examples include cooperative sensing by multiple ligand-receptor sensors [8,9], multiple ligand sensing by single sensor [10,11], ligand-receptor networks [12][13][14], etc. Additionally, Markovian signal detection [15], effect of receptor diffusion [16], etc have also been considered in the study of ligand-receptor accuracy.…”

“…Thus, given a fixed environmental condition θ * , the probability density or the trajectories can be denoted by P θ * [00], P θ * [01], P θ * [10], and P θ * [11]. At steady state for binary-state sensors, it is straightforward to show that P θ [01] = P θ [10] for any stationary θ. (See SI.3) In summary, the probability space is reduced from the 3-simplex into a 2-dim triangle ABC, i.e., d(n t = 2, n s = 2) = n nt s − 2 = 2.…”

“…At a given condition θ, the sensor, sketched as a ligand receptor in (b) evolves with a stochastic trajectory s(t). From the statistics of 2-point trajectories S = [00], [01],[10], or[11] one can obtain the 2-point trajectory probabilities P θ [S], shown in (c) for two choices of θ's. Shown in (d), when ns = 2 and nt = 2, the trajectory probability lives in a 3-simplex.…”

Digital immunoassay for biomarker concentration quantification using solid-state nanopores

“…In order to reach the required level of sensitivity while preserving specificity, digital immunoassay schemes are being developed that are able to overcome the limits imposed by both analog optical readout and relatively weak antibody pairings 42,44 . Some of these schemes are based on the use of paramagnetic micron-sized beads decorated with hundreds of thousands of capture antibodies 45 , effectively turning each bead into a capture antibody with a significantly higher on-rate than that of individual antibodies, but while the same off-rate is maintained 46,47 . In one method, this is followed by partitioning of beads into individually optically addressable microwells for digital readout of the fraction of beads with bound targets, overcoming analog error modes by transitioning to a digital scheme while still using optical detection 42,48 .…”