An algebraic approach to signaling cascades with N layers
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An algebraic approach to signaling cascades with N layers. / Feliu, Elisenda; Knudsen, Michael; Andersen, Lars Nørvang; Wiuf, Carsten.
I: Bulletin of Mathematical Biology, Bind 74, Nr. 1, 2012, s. 45-72.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
Y1 - 2012
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
VL - 74
SP - 45
EP - 72
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
IS - 1
ER -
ID: 40285294