Trade-Offs and Constraints in Allosteric Sensing

Abstract

Sensing extracellular changes initiates signal transduction and is the first stage of cellular decision-making. Yet relatively little is known about why one form of sensing biochemistry has been selected over another. To gain insight into this question, we studied the sensing characteristics of one of the biochemically simplest of sensors: the allosteric transcription factor. Such proteins, common in microbes, directly transduce the detection of a sensed molecule to changes in gene regulation. Using the Monod-Wyman-Changeux model, we determined six sensing characteristics – the dynamic range, the Hill number, the intrinsic noise, the information transfer capacity, the static gain, and the mean response time – as a function of the biochemical parameters of individual sensors and of the number of sensors. We found that specifying one characteristic strongly constrains others. For example, a high dynamic range implies a high Hill number and a high capacity, and vice versa. Perhaps surprisingly, these constraints are so strong that most of the space of characteristics is inaccessible given biophysically plausible ranges of parameter values. Within our approximations, we can calculate the probability distribution of the numbers of input molecules that maximizes information transfer and show that a population of one hundred allosteric transcription factors can in principle distinguish between more than four bands of input concentrations. Our results imply that allosteric sensors are unlikely to have been selected for high performance in one sensing characteristic but for a compromise in the performance of many.

Allosteric proteins as logarithmic sensors

“…1A), and at the same time, they must have a broad response range because many natural signals vary over several orders of magnitude (Fig. 1B) (1). To achieve these conflicting goals, it has been proposed that many sensory systems have evolved to tune their sensitivity over a wide range (Fig.…”

Napoleon Is in Equilibrium

“…The general idea is now just five decades old and goes under the name of allostery, and refers to the fact that many biological macromolecules can switch back and forth between two conformations: an active and an inactive state (55–58). The relative probability of these two states is controlled, in turn, by the binding of some ligand to the allosteric molecule (59, 60). In this section of the article, we explore how these ideas can be converted into statistical mechanical language and then applied to the problem of cellular decision making, although the scope of the allostery concept is much broader than the limited application considered here in the context of transcriptional regulation (59, 60).…”

“…That model, sometimes referred to by the initials of its founders Monod, Wyman, and Changeux (hence, the MWC model), has now been applied to a host of different problems (57, 59–66). At roughly the same time, a second class of models was introduced that differs in subtle ways from the MWC model, which need not concern us here because we are trying to make a broader point about molecules that have several conformational states with different activity (67).…”

“…As seen in Figure 14 b , the idea that all three data sets can be viewed from the point of view of the MWC framework is very appealing. Interestingly, altering the DNA binding strength causes the side effect of changes to the leakiness of the circuit as well as its dynamic range (59, 60). …”

Analysis of substrate competition in regulatory network motifs: Stimulus–response curves, thresholds and ultrasensitivity

“…4): (i) it narrows the dynamic range of the response as measured by the maximal phosphorylation level of the substrate and (ii) it increases the threshold beyond which the maximal phosphorylation level is reached. In general, the dynamic range can be defined as the difference between the responses in the absence and with saturating amounts of an input signal (Martins and Swain, 2011). Since ½YP vanishes as K T goes to zero the dynamic range (in our case) is simply given by the maximal phosphorylation level of Y.…”