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fuss1

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Bistable switching and excitable behaviour in the activation of Src at mitosis.

  • Hendrik Fuss
  • Werner Dubitzky
  • Stephen Downes
  • Mary Jo Kurth
Bioinformatics 2006; 22 (14):
Abstract
MOTIVATION: The protein tyrosine kinase Src is involved in a multitude of biochemical pathways and cellular functions. A complex network of interactions with other kinases and phosphatases obscures its precise mode of operation.
RESULTS: We have constructed a semi-quantitative computational dynamic systems model of the activation of Src at mitosis based on protein interactions described in the literature. Through numerical simulation and bifurcation analysis we show that Src regulation involves a bistable switch, a pattern increasingly recognised as essential to biochemical signalling. The switch is operated by the tyrosine kinase CSK, which itself is involved in a negative feedback loop with Src. Negative feedback generates an excitable system, which produces transient activation of Src. One of the system parameters, which is linked to the cyclin dependent kinase cdc2, controls excitability via a second bistable switch. This topology allows for differentiated responses to a multitude of signals. The model offers explanations for the existence of the positive and negative feedback loops involving protein tyrosine phosphatase alpha (PTPalpha) and translocation of CSK and predicts a specific relationship between Src phosphorylation and activity.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
default 3.0 1.0
Id Name Initial quantity Compartment Fixed
CSK_cytoplasm 1.0 default
Cbp 1.0 default
Cbp_P 0.0 default
Cbp_P_CSK 0.0 default
PTP 1.0 default
PTP_pY789 0.0 default
srca 0.0 default
srcc 0.0 default
srci 1.0 default
srco 0.0 default

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
CSK_translocation CSK_cytoplasm + Cbp_P = Cbp_P_CSK

(Cbp_P * kCSKon * CSK_cytoplasm - kCSKoff * Cbp_P_CSK) * default
Cbp_phosphorylation Cbp > Cbp_P

kCbp * src_activity * Cbp * default
PTP_phosphorylation PTP = PTP_pY789

default * ((kPTP * src_activity + p3) * PTP - p2 * PTP_pY789)
v1 srci = srco

(k2 * ptp_activity * srci - k1 * Cbp_P_CSK * srco) * default
v2 srco = srca

(k3 * src_activity * srco - p1 * srca) * default
v3 srca = srcc

(k1 * Cbp_P_CSK * srca - k2 * ptp_activity * srcc) * default
v4 srcc > srci

default * k4 * p1 * srcc

Global parameters

Id Value
Kser 1.0
PTP_background 0.0
acsk0 0.0
k1 1.0
k2 0.8
k3 1.0
k4 10.0
kCSKoff 0.01
kCSKon 0.1
kCbp 1.0
kPTP 1.0
p1 0.05
p2 0.15
p3 0.035
ptp_activity 0.0
rho_srca 1.0
rho_srcc 1.0
rho_srco 0.0
src_activity 0.0
src_background 0.0001

Local parameters

Id Value Reaction

Assignment rules

Definition
ptp_activity = PTP_background + Kser * PTP_pY789
src_activity = rho_srco * srco + rho_srca * srca + src_background + rho_srcc * srcc

Rate rules

Definition

Algebraic rules

Definition
Definition
Trigger Assignments