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neves1

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Model

neves1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000182) Biomodels notes:The plot corresponds to Fig S1 in the supplement of the paper. Results obtained using MathSBML. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Manuscript information

Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks.

  • Susana R Neves
  • Panayiotis Tsokas
  • Anamika Sarkar
  • Elizabeth A Grace
  • Padmini Rangamani
  • Stephen M Taubenfeld
  • Cristina M Alberini
  • James C Schaff
  • Robert D Blitzer
  • Ion I Moraru
  • Ravi Iyengar
Cell 2008; 133 (4): 666-680
Abstract
The role of cell size and shape in controlling local intracellular signaling reactions, and how this spatial information originates and is propagated, is not well understood. We have used partial differential equations to model the flow of spatial information from the beta-adrenergic receptor to MAPK1,2 through the cAMP/PKA/B-Raf/MAPK1,2 network in neurons using real geometries. The numerical simulations indicated that cell shape controls the dynamics of local biochemical activity of signal-modulated negative regulators, such as phosphodiesterases and protein phosphatases within regulatory loops to determine the size of microdomains of activated signaling components. The model prediction that negative regulators control the flow of spatial information to downstream components was verified experimentally in rat hippocampal slices. These results suggest a mechanism by which cellular geometry, the presence of regulatory loops with negative regulators, and key reaction rates all together control spatial information transfer and microdomain characteristics within cells.

Unit definitions 14

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
— 1000000000000.0 item metre^(-2.0) second^(-1.0)
— 1.0 item
— 9.999999999999999e-19 metre^(3.0)
— 1e-12 metre^(2.0)
— 1.0 item
— 1e-12 metre^(2.0)
— 1000000000000.0 item^(-1.0) mole litre^(-1.0) metre^(-3.0)
— 1.0 dimensionless ampere metre^(-2.0)
— 1.0 second^(-1.0)
— 1000000.0 dimensionless metre^(6.0) mole^(-2.0) second^(-1.0)
— 0.001 dimensionless metre^(-3.0) mole second^(-1.0)
— 0.001 dimensionless metre^(-3.0) mole
— 1000.0 dimensionless metre^(3.0) mole^(-1.0) second^(-1.0)
— 1000000000000.0 item metre^(-2.0)

Compartments 3

Id Name Spatial dimensions Size
cyto cyto 3.0 1.0
cyto_mem cyto_mem 2.0 0.2 um2
extra extra 3.0 0.111111111111111

Species 37

Id Name Initial quantity Compartment Fixed
AC_PKA_cyto_mem — 0.0 molecules/um2 cyto_mem (cyto_mem) ✘
AC_active_cyto_mem — 0.0 molecules/um2 cyto_mem (cyto_mem) ✘
AC_cyto_mem — 300.0 molecules/um2 cyto_mem (cyto_mem) ✘
AMP_cyto — 3010000.0 molecules/<compartment size units> cyto (cyto) ✘
ATP_cyto — 3010000.0 molecules/<compartment size units> cyto (cyto) ✘
BAR_G_cyto_mem — 0.0 molecules/um2 cyto_mem (cyto_mem) ✘
BAR_cyto_mem — 94.0 molecules/um2 cyto_mem (cyto_mem) ✘
B_Raf_active_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
B_Raf_cyto — 120.4 molecules/<compartment size units> cyto (cyto) ✘
GRK_bg_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
GRK_cyto — 0.602 molecules/<compartment size units> cyto (cyto) ✘
G_GDP_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
G_a_s_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
G_protein_cyto — 2167.2 molecules/<compartment size units> cyto (cyto) ✘
MAPK_active_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
MAPK_cyto — 216.72 molecules/<compartment size units> cyto (cyto) ✘
MEK_active_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
MEK_cyto — 108.36 molecules/<compartment size units> cyto (cyto) ✘
PDE4_P_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
PDE4_cyto — 240.8 molecules/<compartment size units> cyto (cyto) ✘
PDE_high_km_cyto — 301.0 molecules/<compartment size units> cyto (cyto) ✘
PKA_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
PP2A_cyto — 60.2 molecules/<compartment size units> cyto (cyto) ✘
PP_PDE_cyto — 120.4 molecules/<compartment size units> cyto (cyto) ✘
PTP_PKA_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
PTP_PP_cyto — 60.2 molecules/<compartment size units> cyto (cyto) ✘
PTP_cyto — 120.4 molecules/<compartment size units> cyto (cyto) ✘
R2C2_cyto — 120.4 molecules/<compartment size units> cyto (cyto) ✘
bg_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
c2_R2C2_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
c3_R2C2_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
cAMP_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
c_R2C2_cyto — 0.0 molecules/<compartment size units> cyto (cyto) ✘
iso_BAR_G_cyto_mem — 0.0 molecules/um2 cyto_mem (cyto_mem) ✘
iso_BAR_cyto_mem — 0.0 molecules/um2 cyto_mem (cyto_mem) ✘
iso_BAR_p_cyto_mem — 0.0 molecules/um2 cyto_mem (cyto_mem) ✘
iso_extra — 6020.0 molecules/<compartment size units> extra (extra) ✘

Initial assignments 0

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
Reactions 32
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
A1 A1 c2_R2C2_cyto + cAMP_cyto = c3_R2C2_cyto

(Kf * 0.00166112956810631 * c2_R2C2_cyto * 0.00166112956810631 * cAMP_cyto + -(Kr * 0.00166112956810631 * c3_R2C2_cyto)) * cyto * 1 * (1 / KMOLE)
A2 A2 c3_R2C2_cyto + cAMP_cyto = PKA_cyto

(Kf * 0.00166112956810631 * c3_R2C2_cyto * 0.00166112956810631 * cAMP_cyto + -(Kr * 0.00166112956810631 * PKA_cyto)) * cyto * 1 * (1 / KMOLE)
AC_activation AC_activation G_a_s_cyto + AC_cyto_mem = AC_active_cyto_mem

(Kf_AC_activation * 0.00166112956810631 * G_a_s_cyto * AC_cyto_mem + -(Kr_AC_activation * AC_active_cyto_mem)) * cyto_mem
AC_active AC_active ATP_cyto = cAMP_cyto

Vmax_AC_active_AC_active * 0.00166112956810631 * ATP_cyto * (1 / (Km_AC_active + 0.00166112956810631 * ATP_cyto)) * cyto_mem
AC_basal AC_basal ATP_cyto = cAMP_cyto

Vmax_AC_basal_AC_basal * 0.00166112956810631 * ATP_cyto * (1 / (Km_AC_basal + 0.00166112956810631 * ATP_cyto)) * cyto_mem
B1 B1 R2C2_cyto + cAMP_cyto = c_R2C2_cyto

(Kf * 0.00166112956810631 * R2C2_cyto * 0.00166112956810631 * cAMP_cyto + -(Kr * 0.00166112956810631 * c_R2C2_cyto)) * cyto * 1 * (1 / KMOLE)
B2 B2 c_R2C2_cyto + cAMP_cyto = c2_R2C2_cyto

(Kf * 0.00166112956810631 * c_R2C2_cyto * 0.00166112956810631 * cAMP_cyto + -(Kr * 0.00166112956810631 * c2_R2C2_cyto)) * cyto * 1 * (1 / KMOLE)
GRK GRK iso_BAR_cyto_mem = iso_BAR_p_cyto_mem

Vmax_grk_GRK * iso_BAR_cyto_mem * (1 / (Km_grk + iso_BAR_cyto_mem)) * cyto_mem
GRK_bg GRK_bg iso_BAR_cyto_mem = iso_BAR_p_cyto_mem

Vmax_GRK_bg_GRK_bg * iso_BAR_cyto_mem * (1 / (Km_GRK_bg + iso_BAR_cyto_mem)) * cyto_mem
GTPase GTPase G_a_s_cyto = G_GDP_cyto

(Kf_GTPase * 0.00166112956810631 * G_a_s_cyto + -(Kr_GTPase * 0.00166112956810631 * G_GDP_cyto)) * cyto * 1 * (1 / KMOLE)
G_binds_BAR G_binds_BAR BAR_cyto_mem + G_protein_cyto = BAR_G_cyto_mem

(Kf_G_binds_BAR * BAR_cyto_mem * 0.00166112956810631 * G_protein_cyto + -(Kr_G_binds_BAR * BAR_G_cyto_mem)) * cyto_mem
G_binds_iso_BAR G_binds_iso_BAR iso_BAR_cyto_mem + G_protein_cyto = iso_BAR_G_cyto_mem

(Kf_G_binds_iso_BAR * iso_BAR_cyto_mem * 0.00166112956810631 * G_protein_cyto + -(Kr_G_binds_iso_BAR * iso_BAR_G_cyto_mem)) * cyto_mem
MEK_activates_MAPK MEK_activates_MAPK MAPK_cyto = MAPK_active_cyto

Vmax_MEK_activates_MAPK * 0.00166112956810631 * MAPK_cyto * (1 / (Km + 0.00166112956810631 * MAPK_cyto)) * cyto * 1 * (1 / KMOLE)
PDE4 PDE4 cAMP_cyto = AMP_cyto

Vmax_PDE4_PDE4 * 0.00166112956810631 * cAMP_cyto * (1 / (Km_PDE4 + 0.00166112956810631 * cAMP_cyto)) * cyto * 1 * (1 / KMOLE)
PKA_P_PDE PKA_P_PDE PDE4_cyto = PDE4_P_cyto

Vmax_PKA_P_PDE * 0.00166112956810631 * PDE4_cyto * (1 / (Km + 0.00166112956810631 * PDE4_cyto)) * cyto * 1 * (1 / KMOLE)
PKA_P_PTP PKA_P_PTP PTP_cyto = PTP_PKA_cyto

Vmax_PKA_P_PTP * 0.00166112956810631 * PTP_cyto * (1 / (Km + 0.00166112956810631 * PTP_cyto)) * cyto * 1 * (1 / KMOLE)
PKA_activates_Raf PKA_activates_Raf B_Raf_cyto = B_Raf_active_cyto

Vmax_PKA_activates_Raf * 0.00166112956810631 * B_Raf_cyto * (1 / (Km + 0.00166112956810631 * B_Raf_cyto)) * cyto * 1 * (1 / KMOLE)
PPase_MAPK PPase_MAPK MAPK_active_cyto = MAPK_cyto

Vmax_PPase_MAPK * 0.00166112956810631 * MAPK_active_cyto * (1 / (Km + 0.00166112956810631 * MAPK_active_cyto)) * cyto * 1 * (1 / KMOLE)
PPase_Raf PPase_Raf B_Raf_active_cyto = B_Raf_cyto

Vmax_PPase_Raf * 0.00166112956810631 * B_Raf_active_cyto * (1 / (Km + 0.00166112956810631 * B_Raf_active_cyto)) * cyto * 1 * (1 / KMOLE)
PPase_mek PPase_mek MEK_active_cyto = MEK_cyto

Vmax_PPase_mek * 0.00166112956810631 * MEK_active_cyto * (1 / (Km + 0.00166112956810631 * MEK_active_cyto)) * cyto * 1 * (1 / KMOLE)
PTP PTP MAPK_active_cyto = MAPK_cyto

Vmax_PTP * 0.00166112956810631 * MAPK_active_cyto * (1 / (Km + 0.00166112956810631 * MAPK_active_cyto)) * cyto * 1 * (1 / KMOLE)
PTP_PKA PTP_PKA MAPK_active_cyto = MAPK_cyto

Vmax_PTP_PKA * 0.00166112956810631 * MAPK_active_cyto * (1 / (Km + 0.00166112956810631 * MAPK_active_cyto)) * cyto * 1 * (1 / KMOLE)
Raf_activates_MEK Raf_activates_MEK MEK_cyto = MEK_active_cyto

Vmax_Raf_activates_MEK * 0.00166112956810631 * MEK_cyto * (1 / (Km + 0.00166112956810631 * MEK_cyto)) * cyto * 1 * (1 / KMOLE)
activate_Gs activate_Gs iso_BAR_G_cyto_mem = iso_BAR_cyto_mem + bg_cyto + G_a_s_cyto

(Kf_activate_Gs * iso_BAR_G_cyto_mem - Kr_activate_Gs * iso_BAR_cyto_mem * 0.00166112956810631 * bg_cyto * 0.00166112956810631 * G_a_s_cyto) * cyto_mem
bg_binds_GRK bg_binds_GRK GRK_cyto + bg_cyto = GRK_bg_cyto

(Kf_bg_binds_GRK * 0.00166112956810631 * GRK_cyto * 0.00166112956810631 * bg_cyto + -(Kr_bg_binds_GRK * 0.00166112956810631 * GRK_bg_cyto)) * cyto * 1 * (1 / KMOLE)
highKM_PDE highKM_PDE cAMP_cyto = AMP_cyto

Vmax_highKM_PDE * 0.00166112956810631 * cAMP_cyto * (1 / (Km + 0.00166112956810631 * cAMP_cyto)) * cyto * 1 * (1 / KMOLE)
iso_binds_BAR iso_binds_BAR BAR_cyto_mem + iso_extra = iso_BAR_cyto_mem

(Kf * BAR_cyto_mem * 0.00166112956810631 * iso_extra + -(Kr * iso_BAR_cyto_mem)) * cyto_mem
iso_binds_BAR_g iso_binds_BAR_g iso_extra + BAR_G_cyto_mem = iso_BAR_G_cyto_mem

(Kf * 0.00166112956810631 * iso_extra * BAR_G_cyto_mem + -(Kr * iso_BAR_G_cyto_mem)) * cyto_mem
pde4_p pde4_p cAMP_cyto = AMP_cyto

Vmax_pde4_p_pde4_p * 0.00166112956810631 * cAMP_cyto * (1 / (Km_pde4_p + 0.00166112956810631 * cAMP_cyto)) * cyto * 1 * (1 / KMOLE)
pp2a_4 pp2a_4 PDE4_P_cyto = PDE4_cyto

Vmax_pp2a_4_pp2a_4 * 0.00166112956810631 * PDE4_P_cyto * (1 / (Km_pp2a_4 + 0.00166112956810631 * PDE4_P_cyto)) * cyto * 1 * (1 / KMOLE)
pp_ptp pp_ptp PTP_PKA_cyto = PTP_cyto

Vmax_pp_ptp * 0.00166112956810631 * PTP_PKA_cyto * (1 / (Km + 0.00166112956810631 * PTP_PKA_cyto)) * cyto * 1 * (1 / KMOLE)
trimer trimer bg_cyto + G_GDP_cyto = G_protein_cyto

(Kf_trimer * 0.00166112956810631 * bg_cyto * 0.00166112956810631 * G_GDP_cyto + -(Kr_trimer * 0.00166112956810631 * G_protein_cyto)) * cyto * 1 * (1 / KMOLE)

Parameters 55   28

Global parameters

Id Value
KMOLE 0.00166112956810631 uM_um3_molecules_1
Vmax_AC_active_AC_active <assignment rule> molecules_um_2_s_1
Vmax_AC_basal_AC_basal <assignment rule> molecules_um_2_s_1
Vmax_GRK_bg_GRK_bg <assignment rule> molecules_um_2_s_1
Vmax_MEK_activates_MAPK <assignment rule> uM_s_1
Vmax_PDE4_PDE4 <assignment rule> uM_s_1
Vmax_PKA_P_PDE <assignment rule> uM_s_1
Vmax_PKA_P_PTP <assignment rule> uM_s_1
Vmax_PKA_activates_Raf <assignment rule> uM_s_1
Vmax_PPase_MAPK <assignment rule> uM_s_1
Vmax_PPase_Raf <assignment rule> uM_s_1
Vmax_PPase_mek <assignment rule> uM_s_1
Vmax_PTP <assignment rule> uM_s_1
Vmax_PTP_PKA <assignment rule> uM_s_1
Vmax_Raf_activates_MEK <assignment rule> uM_s_1
Vmax_grk_GRK <assignment rule> molecules_um_2_s_1
Vmax_highKM_PDE <assignment rule> uM_s_1
Vmax_pde4_p_pde4_p <assignment rule> uM_s_1
Vmax_pp2a_4_pp2a_4 <assignment rule> uM_s_1
Vmax_pp_ptp <assignment rule> uM_s_1
kcat_PKA_P_PTP 0.2 s_1
kcat_PKA_activates_Raf 10.0 s_1
kcat_PPase_MAPK 0.636 s_1
kcat_PPase_Raf 5.0 s_1
kcat_PPase_mek 5.0 s_1
kcat_PTP 1.06 s_1
kcat_PTP_PKA 0.1 s_1
kcat_pp_ptp_pp_ptp 5.0 s_1

Local parameters

Id Value Reaction
I 0.0 pA_um_2 activate_Gs (activate_Gs)
Kf_activate_Gs 0.025 s_1 activate_Gs (activate_Gs)
Kr_activate_Gs 0.0 activate_Gs (activate_Gs)
Km_pde4_p 1.3 uM pde4_p (pde4_p)
Km 15.7 uM PPase_Raf (PPase_Raf)
I 0.0 pA_um_2 iso_binds_BAR (iso_binds_BAR)
Kf 1.0 uM_1_s_1 iso_binds_BAR (iso_binds_BAR)
Kr 0.2 s_1 iso_binds_BAR (iso_binds_BAR)
Km_PDE4 1.3 uM PDE4 (PDE4)
Kf_bg_binds_GRK 1.0 uM_1_s_1 bg_binds_GRK (bg_binds_GRK)
Kr_bg_binds_GRK 0.25 s_1 bg_binds_GRK (bg_binds_GRK)
Km 0.046296 uM MEK_activates_MAPK (MEK_activates_MAPK)
Km 0.5 uM PKA_activates_Raf (PKA_activates_Raf)
I 0.0 pA_um_2 AC_active (AC_active)
Km_AC_active 32.0 uM AC_active (AC_active)
Kf_GTPase 0.06667 s_1 GTPase (GTPase)
Kr_GTPase 0.0 s_1 GTPase (GTPase)
Kf_trimer 6.0 uM_1_s_1 trimer (trimer)
Kr_trimer 0.0 s_1 trimer (trimer)
I 0.0 pA_um_2 G_binds_iso_BAR (G_binds_iso_BAR)
Kf_G_binds_iso_BAR 10.0 uM_1_s_1 G_binds_iso_BAR (G_binds_iso_BAR)
Kr_G_binds_iso_BAR 0.1 s_1 G_binds_iso_BAR (G_binds_iso_BAR)
Kf 8.35 uM_1_s_1 A2 (A2)
Kr 0.0167 s_1 A2 (A2)
Km 15.0 uM highKM_PDE (highKM_PDE)
Km 0.1 uM PKA_P_PTP (PKA_P_PTP)
I 0.0 pA_um_2 AC_activation (AC_activation)
Kf_AC_activation 500.0 uM_1_s_1 AC_activation (AC_activation)
Kr_AC_activation 1.0 s_1 AC_activation (AC_activation)
I 0.0 pA_um_2 AC_basal (AC_basal)
Km_AC_basal 1030.0 uM AC_basal (AC_basal)
Kf 0.0059 uM_1_s_1 B1 (B1)
Kr 0.00028 s_1 B1 (B1)
I 0.0 pA_um_2 GRK (GRK)
Km_grk 15.0 molecules_um_2 GRK (GRK)
Km 0.5 uM PKA_P_PDE (PKA_P_PDE)
Km 0.15909 uM Raf_activates_MEK (Raf_activates_MEK)
Km 9.0 uM PTP_PKA (PTP_PKA)
Kf 0.0059 uM_1_s_1 B2 (B2)
Kr 0.00028 s_1 B2 (B2)
Km 0.46 uM PTP (PTP)
I 0.0 pA_um_2 iso_binds_BAR_g (iso_binds_BAR_g)
Kf 1.0 uM_1_s_1 iso_binds_BAR_g (iso_binds_BAR_g)
Kr 0.062 s_1 iso_binds_BAR_g (iso_binds_BAR_g)
Km 0.77 uM PPase_MAPK (PPase_MAPK)
Km_pp2a_4 8.0 uM pp2a_4 (pp2a_4)
Km 6.0 uM pp_ptp (pp_ptp)
I 0.0 pA_um_2 GRK_bg (GRK_bg)
Km_GRK_bg 4.0 molecules_um_2 GRK_bg (GRK_bg)
I 0.0 pA_um_2 G_binds_BAR (G_binds_BAR)
Kf_G_binds_BAR 0.3 uM_1_s_1 G_binds_BAR (G_binds_BAR)
Kr_G_binds_BAR 0.1 s_1 G_binds_BAR (G_binds_BAR)
Km 15.7 uM PPase_mek (PPase_mek)
Kf 8.35 uM_1_s_1 A1 (A1)
Kr 0.0167 s_1 A1 (A1)

Rules 0   0   19

Assignment rules

Definition
Vmax_pde4_p_pde4_p = 20.0 * 0.00166112956810631 * PDE4_P_cyto
Vmax_PPase_mek = kcat_PPase_mek * 0.00166112956810631 * PP2A_cyto
Vmax_GRK_bg_GRK_bg = 1.34 * 0.00166112956810631 * GRK_bg_cyto
Vmax_pp_ptp = kcat_pp_ptp_pp_ptp * 0.00166112956810631 * PTP_PP_cyto
Vmax_pp2a_4_pp2a_4 = 5.0 * 0.00166112956810631 * PP_PDE_cyto
Vmax_PPase_MAPK = kcat_PPase_MAPK * 0.00166112956810631 * PP2A_cyto
Vmax_PTP = kcat_PTP * 0.00166112956810631 * PTP_cyto
Vmax_PTP_PKA = kcat_PTP_PKA * 0.00166112956810631 * PTP_PKA_cyto
Vmax_Raf_activates_MEK = 0.105 * 0.00166112956810631 * B_Raf_active_cyto
Vmax_PKA_P_PDE = 10.0 * 0.00166112956810631 * PKA_cyto
Vmax_grk_GRK = 0.104 * 0.00166112956810631 * GRK_cyto
Vmax_AC_basal_AC_basal = 0.2 * AC_cyto_mem
Vmax_PKA_P_PTP = kcat_PKA_P_PTP * 0.00166112956810631 * PKA_cyto
Vmax_highKM_PDE = 8.0 * 0.00166112956810631 * PDE_high_km_cyto
Vmax_AC_active_AC_active = 8.5 * AC_active_cyto_mem
Vmax_PKA_activates_Raf = kcat_PKA_activates_Raf * 0.00166112956810631 * PKA_cyto
Vmax_MEK_activates_MAPK = 0.15 * 0.00166112956810631 * MEK_active_cyto
Vmax_PDE4_PDE4 = 8.0 * 0.00166112956810631 * PDE4_cyto
Vmax_PPase_Raf = kcat_PPase_Raf * 0.00166112956810631 * PP2A_cyto

Rate rules

Definition

Algebraic rules

Definition

Events 0

Trigger Assignments