Long Signaling Cascades Tend to Attenuate Retroactivity

HR OSSAREH; ALEJANDRA C VENTURA; DOMITILLA DEL VECCHIO; SOFIA D MERAJVER

Conferencia; 11th International Conference on Systems Biology; 2010

It has been shown that signaling pathways consisting of phosphorylation/dephosphorylation (PD) cycles allow signals to propagate not only from upstream (wherethe stimulus is) to downstream (where the targets are) but also from downstream toupstream. This is due to the effects of retroactivity (RA), which, similar to impedance inelectrical systems, affects the behavior of an upstream component upon interconnectionwith a downstream client [1]. Here, we take a control systems approach to quantify theextent to which a downstream perturbation can propagate upstream in a PD cascadeand analytically determine the downstream-to-upstream gain at each stage of thecascade as a function of the cascade parameters. This gain can be made smallerthan 1 (attenuate RA) at a stage by a combination of the following: sufficiently fastcatalytic rate for the kinase compared to the phosphatase; sufficiently large Michaelis-Menten constants; sufficiently low amounts of total stage protein. RA attenuation ata stage is associated with a less ultrasensitive response and/or increased upstreamto downstream amplification. Numerical studies performed on biologically relevantparameters indicated that cascades are more likely to attenuate RA than to amplify it.Specifically, we found probability of amplification to be 0−0.2 depending on the dataset. For a cascade of length 3, which is the most common length found in practice (e.g.MAPK), while the probability of some stage amplifying RA can be as high as 0.5, theprobability of the entire cascade being a RA amplifier is no more than 0.2. Also, as thenumber of stages in the cascade increases, the probability of the cascade providingoverall attenuation from the last stage to the first stage increases and finally reaches1 for a cascade of length at least 6. These findings open questions regarding whetheramplifying a downstream perturbation has any useful physiological function or whetherit is just a (possibly undesirable) consequence of signal transduction. On the one hand,amplifying a downstream perturbation toward upstream can lead to disruptive effectsin the presence of crosstalk among pathways, possibly leading to aberrant signaling asfound in pathological conditions such as cancer. On the other hand, this capability mayoffer a powerful mean to deliver drugs that target specific signaling components.[1] D. Del Vecchio, et al. Modular cell biology: Retroactivity and insulation. Nature/EMBOMSB, 4:161, 2008