An algebraic approach to signaling cascades with N layers

TY - JOUR

T1 - An algebraic approach to signaling cascades with N layers

AU - Feliu, Elisenda

AU - Knudsen, Michael

AU - Andersen, Lars Nørvang

AU - Wiuf, Carsten

PY - 2012/1

Y1 - 2012/1

N2 - Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes. We demonstrate that many steady-state concentrations are related through rational functions that can be found recursively. For example, stimulus-response curves arise as inverse functions to explicit rational functions. We show that the stimulus-response curves of the modified substrates are shifted to the left as we move down the cascade. Further, our approach allows us to study enzyme competition, sequestration, and how the steady state changes in response to changes in the total amount of substrates. Our approach is essentially algebraic and follows recent trends in the study of posttranslational modification systems.

AB - Posttranslational modification of proteins is key in transmission of signals in cells. Many signaling pathways contain several layers of modification cycles that mediate and change the signal through the pathway. Here, we study a simple signaling cascade consisting of n layers of modification cycles such that the modified protein of one layer acts as modifier in the next layer. Assuming mass-action kinetics and taking the formation of intermediate complexes into account, we show that the steady states are solutions to a polynomial in one variable and in fact that there is exactly one steady state for any given total amounts of substrates and enzymes. We demonstrate that many steady-state concentrations are related through rational functions that can be found recursively. For example, stimulus-response curves arise as inverse functions to explicit rational functions. We show that the stimulus-response curves of the modified substrates are shifted to the left as we move down the cascade. Further, our approach allows us to study enzyme competition, sequestration, and how the steady state changes in response to changes in the total amount of substrates. Our approach is essentially algebraic and follows recent trends in the study of posttranslational modification systems.

KW - Kinetics

KW - Models, Biological

KW - Protein Processing, Post-Translational

KW - Proteins

KW - Signal Transduction

U2 - 10.1007/s11538-011-9658-0

DO - 10.1007/s11538-011-9658-0

M3 - Journal article

C2 - 21523510

SN - 0092-8240

VL - 74

SP - 45

EP - 72

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

IS - 1

ER -