Optimal Length and Signal Amplification in Weakly Activated Signal Transduction Cascades

Abstract

Weakly activated signaling cascades can be modeled as linear systems. The input-tooutput transfer function and the internal gain of a linear system, provide natural measures for the propagation of the input signal down the cascade and for the characterization of the final outcome. The most efficient design of a cascade for generating sharp signals, is obtained by choosing all the off rates equal, and a "universal" finite optimal length.

Signal amplification in biological and electrical engineering systems

“…Not only the factor of amplification was of interest, but also how fast the signal arrives at its destination and how long the signal lasts [26][27][28][29]. For linear kinese-phosphatese cascades, Heinrich et al…”

“…Here a simplified model of protein cascades is considered in which each kinase has only one phosphorylation site, as it can be found in several previous studies; for example, it has been applied for studying time courses of signal transfers through cascades [26,28,29], selective decoding [37] and smoothening of cellular signals [30]. The scheme of the protein cascade used in our analyses is shown in Figure …”

“…This also seems to be of some physiological importance since for the steady-state responses of protein kinase networks it has been shown that the most efficient cascade design for generating sharp signals has equal on rates, and to achieve the highest amplification and the shortest duration response, the cascade should have equal off rates [28]. In all…”

“…The amplitude of the frequency-dependent gain ) ( u,1 ω A decreases rapidly at frequencies higher than c ω , so that high amplification is limited to the frequencies within the bandwidth: , as usually considered in the modelling of protein kinase cascades [11,28,29], we obtain the following equations for the biological amplifier:…”

A Passivity-Based Approach to Stability of Spatially Distributed Systems With a Cyclic Interconnection Structure

“…A linear model also arises when considering weakly activated pathways, the behavior of the pathway when there is only a low level of kinase phosphorylation. In this case, one assumes that the inactive forms dominate: 1 − x i ≈ 1; this is the analysis in [58] and [59]. An intermediate case would be that in which activations are weak but the coefficients c i are small enough that the negative terms in the above equations cannot be replaced by linear functions; in that case, we are lead to equations as follows, for the closed-loop system:ẋ…”