Product dependence and bifunctionality compromise the ultrasensitivity of signal transduction cascades

Abstract

Covalent modification cycles are ubiquitous. Theoretical studies have suggested that they serve to increase sensitivity. However, this suggestion has not been corroborated experimentally in vivo. Here, we demonstrate that the assumptions of the theoretical studies, i.e., irreversibility and absence of product inhibition, were not trivial: when the conversion reactions are close to equilibrium or saturated by their product, ''zero-order'' ultrasensitivity disappears. For high sensitivities to arise, not only substrate saturation (zero-order) but also high equilibrium constants and low product saturation are required. Many covalent modification cycles are catalyzed by one bifunctional 'ambiguous' enzyme rather than by two independent proteins. This makes high substrate concentration and low product concentration for both reactions of the cycle inconsistent; such modification cycles cannot have high responses. Defining signal strength as ratios of modified (e.g., phosphorylated) over unmodified protein, signal-to-signal response sensitivity equals 1: signal strength should remain constant along a cascade of ambiguous modification cycles. We also show that the total concentration of a signalling effector protein cannot affect the signal emanating from a modification cycle catalyzed by an ambiguous enzyme if the ratio of the two forms of the effector protein is not altered. This finding may explain the experimental result that the pivotal signal transduction protein PII plus its paralogue GlnK do not control steady-state N-signal transduction in Escherichia coli. It also rationalizes the absence of strong phenotypes for many signal-transduction proteins. Emphasis on extent of modification of these proteins is perhaps more urgent than transcriptome analysis.

Multisite protein phosphorylation makes a good threshold but can be a poor switch

“…Once again, these assumptions have commonly been made in previous work. Reversibility and product inhibition can make a theoretical difference (16)(17)(18), but their physiological relevance in P&D is unclear. We continue to follow tradition by using Eq.…”

Nitrogen Assimilation in Escherichia coli: Putting Molecular Data into a Systems Perspective

“…Although a monocyclic cascade per se is no guarantee of high sensitivity and typically even results in subsensitivity (106,634), it may nevertheless exhibit enormous sensitivities; Hill coefficients as high as 800 can be achieved, although this value was not considered of any real physiological significance (629,631). Third, in a multicyclic cascade, additional sensitivity can be achieved, because the response coefficient of the entire cascade equals the product of the local coefficients of the individual cycles (623)(624)(625).…”

“…Ortega et al (106) showed that considering that, in many cases, the modification and the demodification enzymes are identical, one should take product inhibition and the consequent increase in elasticities into account, largely removing the ultrasensitivity of such cascades. The sensitivity of the response to signal can be expressed in terms that are equivalent to Hill coefficients or in MCA terms as response coefficients.…”

Skeletal development is regulated by fibroblast growth factor receptor 1 signalling dynamics

“…phosphorylation or ubiquitinylation) is usually linked to a process in which the modification is reversed or inhibited (reviewed by Ferrell, 1999;Salazar and Hofer, 2003;Germain, 2001;Germain and Stefnova, 1999). Thus, the difference between the two types of signalling characteristics is explained by the presence of limiting inhibitory pathways in threshold signalling; in morphogen type systems these inhibitory pathways are absent or compromised (Ortega et al, 2002), and there is therefore a direct relationship between receptor occupancy and signal output. The results reported here therefore show that the development of the axial skeleton and digit I of the hind limb involve Fgfr1-mediated signalling pathways that have different regulatory properties from those involved in the sternum and cranial sutures.…”