Signal processing in the Futile Cycle

The covalent modification cycle (also called the futile cycle, or the push-pull cycle) is the standard building block for signal processing in biochemical signaling networks. An unmodified molecule X is changed by the presence of a modifier-signal S (usually a kinase) into a modified form X ^* , which is the "unmodified" back into X by another molecule (potentially, also a signal), usually a phosphotase. The instantaneous abundance of the modified molecule X ^* is the output of the signaling system. Briefly, the dynamics of X ^* is given by

$\frac{dX^*}{dt}=F[X, S] - G[X^*,P],$

with a molecular conservation law

X + X ^* = X_t,

where X_t is the total (modified and modified) abundance of the signaling molecule. Different F and G is what differs between various signaling systems, but the overall motif stays the same.

The name futile cycle comes from the molecule X being constantly modifed and de-modified (with the energy loss) even when a signal is constant. This allows a faster and a more reliable response to a change in the signal, but at a cost of a constantly proceeding energy dissipation.

Usually the X + S interactions happen on (or are catalyzed by) yet another protein, a scaffold C. The function of the scaffold is not well understood.

Signaling properties of the futile cycle domain are very well understood in a linear regime and for slowly varying signals -- see below.

A good model of a MAPK pathway (yeast pheromone sensing pathway, which is often viewed as a quintessential example of a futile cycle, can be found at http://yeastpheromonemodel.org/wiki/Main_Page .

Relevant Papers

1. P Detwiler, S Ramanathan, A Sengupta, and B Shraiman. Engineering Aspects of Enzymatic Signal Transduction: Photoreceptors in the Retina. Biophys J 79:2801–2817 (2000). PDF.

   Abstract

   Identifying the basic module of enzymatic amplification as an irreversible cycle of messenger activation/deactivation by a “push-pull” pair of opposing enzymes, we analyze it in terms of gain, bandwidth, noise, and power consumption. The enzymatic signal transduction cascade is viewed as an information channel, the design of which is governed by the statistical properties of the input and the noise and dynamic range constraints of the output. With the example of vertebrate phototransduction cascade we demonstrate that all of the relevant engineering parameters are controlled by enzyme concentrations and, from functional considerations, derive bounds on the required protein numbers. Conversely, the ability of enzymatic networks to change their response characteristics by varying only the abundance of different enzymes illustrates how functional diversity may be built from nearly conserved molecular components.

   Comments

   A great pedagogical paper on linear signal processing in push-pull enzymatic amplifiers. The paper analyzes noise/signal propagation in linear pathways of such circuits in the context of phototransduction, but MAPK signaling should be very similar. Some nonlinear effects and their mechanisms (such as mean adaptation) are also considered. A much more rigorous and fuller paper than most papers on the subject.

2. H Qian,Thermodynamic and kinetic analysis of sensitivity amplification in biological signal transduction. Biophys Chem 105: 585–593 (2003). PDF.

   Abstract

   Based on a thermodynamic analysis of the kinetic model for the protein phosphorylation–dephosphorylation cycle, we study the ATP (or GTP) energy utilization of this ubiquitous biological signal transduction process. It is shown that the free energy from hydrolysis inside cells, DG (phosphorylation potential), controls the amplification and sensitivity of the switch-like cellular module; the response coefficient of the sensitivity amplification approaches the optimal 1 and the Hill coefficient increases with increasing DG. We discover that zero-order ultrasensitivity is mathematically equivalent to allosteric cooperativity. Furthermore, we show that the high amplification in ultrasensitivity is mechanistically related to the proofreading kinetics for protein biosynthesis. Both utilize multiple kinetic cycles in time to gain temporal cooperativity, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein.

   Comments

   A careful analysis of conditions for ultrasensitivity of the cycle; all signal processing is done in the steady state, no speed of approach to the steady state is analyzed. Briefly, in terms of terminology above F,G are saturated w.r.t. to their substrates X,X ^* , respectively. But they are proportional to their respective enzymes S,P. Thus when, say, S crosses a threshold and wins over P, all X is immediately modified, resulting in a sharp step-like transition. Clearly, the speed of reaching the equilibrium, however, is strongly dependent on how much Sexceeds the threshold.

3. C Gomez-Uribe, G Verghese2, L Mirny. Operating Regimes of Signaling Cycles: Statics, Dynamics, and Noise Filtering. PLoS Comp Biol 3:e246 (2007). PDF.

   Abstract

   A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input–output characteristic in a certain steady-state regime. Here, we systematically study the cycle’s steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input–output characteristics. These results are obtained using the total quasi–steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle’s dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act—in all four regimes—as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

   Comments

   Four regimes (kinase/phosphotase saturated/unsaturated) for the futile cycle with first-order kinetics studied. Frequency response to small periodic signals characterized for all four cases, and interesting linear amplification regime found. Most of the paper is computational; theory is based on the total quasi-steady-state approximation. This is basically an MM approximation for small enzyme concentration, MM (but in substrate) for small substrate concentration, and is invalid for two concentrations similar to each other.