Modeling Phosphorylation Dephosphorylation Cycles of Signal Transduction

Supporting Text S1

Modeling phosphorylation – dephosphorylation cycles of signal transduction

There are three distinct kinds of equation types used to capture the flow of information based on the nature of the kinases activation.

1] Single phosphorylation/dephosphorylation mediated covalent modification of kinases: The cartoon below shows the single phosphorylation-dephosphorylation mediated kinase activation.

Where, the K1 is a kinase that is active as an enzyme upon single phosphorylation, to an active form KI-P. The signal/kinase represents the incoming signal/active kinase that carries out the phosphorylation process. P1 represents a phosphatase which is assumed to carry out the dephosphorylation process [1-3].

Considering that no significant transcriptional induction or degradation of K1 takes place during the time of signal propagation the mass balance equation for K1 at any given time during the signal flow is given as

K1T = K 1 + K 1- P - (1) Where, K1T is the total concentration of K1, and the right hand side of equation (1) represents

the distribution of K1T is two possible forms.

During the simulations, the distribution of K1T in its two possible forms, calculated as

d[K1-P] V1.K1 =- (2) dt Km1 + K1 d[K1] V2.K1-P = - (3) dt Km2 + K1-P

[K 1T ]= [ K 1( t )] + [K1-P ( t )] - (4)

Where V1 captures the information from the signal/kinase and V2 captures the dephosphorylation carried out by the phosphatase P1. In the model syk, lyn, PI3-K and Raf-1 dephosphorylation process were single step dephosphorylation processes.

2] Single phosphorylation mediated Hill activation:

In the conditions where the direct physical interaction between the kinase and its substrate is not illustrated distinctly, for example Raf-1 phosphorylation by syk, PI3-K phosphorylation by lyn and MKK3/6 phosphorylation by PI3-K, the contribution of possible unknown intermediate kinases is addressed through the Hill equations [4] as below:

d[K1-P] V1.K1.(Kinase)n1 V2.K1-P = -- (5) dt Km1n1 + (Kinase) n1 Km2 + K1-P

Where, K1 is the substrate, K1-P is the phosphorylated substrate, Km1 is the Km for the hill activation and Kinase in the activator kinases of the substrate “K1”. For example, if K1 = Raf-1, and syk_P = Kinase of the equation (5), the hill coefficient n1 is assumed to capture the contribution of any unknown intermediate between Signal/kinase and K1.

3] Double phosphorylation mediated kinase activation: Activation of ERK-1/2, p38MAPK, MEK-1/2 and MKK-3/6 occurs through double phosphorylation

[1-3, 5]. MEK-1/2 activation by Raf-1 is a essential part of the three tier ERK-1/2 cascade.

MKK3/6 activation was considered to be dependent on the active PI3-K but in this case PI3-K is not a kinase of MKK-3/6 but is a hyperbolic modifier of it.

Schematics of double phosphorylation mediated kinase activation are given below:

Where, K-PP is the double phosphorylated form of the kinase K1 which is active.

The mass conservation equation in such conditions is modified to,

K1T = K 1 + K 1- P + K 1 - PP - (6)

And the distribution of K1T in its three distinct forms, the unphosphorylated (K1), the single phosphorylated (K1-P) and the fully active double phosphorylated form (KI-PP) .

For example, with K1 = MEK-1/2; kinase = Raf-1_P; distribution of K1T (MEK-1/2(t)) in its three possible forms during the signal propagation at given time is captured through the equations given below: d[MEK-1/2_P] k1.MEK-1/2.Raf-1_P V3.MEK-1/2_PP = + dt Km1*MEK-1/2_P Km3.MEK-1/2_P Km1 + MEK-1/2+ Km3 + MEK-1/2_PP + Km2 Km4 k2.MEK-1/2_P.Raf-1_P V4.MEK-1/2_P - - - (7) Km2*MEK-1/2 Km4.MEK-1/2_PP Km2 + MEK-1/2_P + Km4 + MEK-1/2_P + Km1 Km3

d[MEK-1/2_PP] k2.MEK-1/2_P.Raf-1_P V3.MEK-1/2_PP = -- (8) dt Km2*MEK-1/2 Km3.MEK-1/2_P Km2 + MEK-1/2_P + Km3 + MEK-1/2_PP + Km1 Km4

[MEK-1/2(t )]= [MEK-1/2T ] + [MEK-1/2- P ( t ) + [MEK-1/2- PP( t )] - (9)

The suffix of the kinetic parameters represents the reaction number showed in schematics of double phosphorylation above. The phosphorylation-dephosphorylation process is competitive

[2, 5, 6] where MEK-1/2 and MEK-1/2_P compete for their common kinase Raf-1_P. Similarly,

MEK-1/2_PP and MEK-1/2_P competes for their common phosphatase P1 [2, 5].

Kinetic parameters and concentrations of the model variables: Table below shows the kinetic constant used in the reciprocal model. Modeling literature on signal transduction pathways is abundant, from where the kinetic constants of phosphorylation and dephosphorylation were taken. During model construction, if the biochemical values of the systems parameter are not characterized well it is more important to capture the experimental behaviour of a system of interest and make meaningful predictions rather that attempting to find out the values of all the systems parameters and concentration [7]. Additionally, due to technical limitations determination of parameters of the kinase substrate reactions are still largely missing. The parameter values were considered from various modeling literatures [1-3, 5, 6, 8, 9, 12, 13]. The literature also suggests that phosphorylation-dephosphorylation of the kinases lie in the same order of magnitude [3, 6] which is reflected in our choice of parameter values.

Table-1: Kinetic parameters and concentrations of the model variables: Reaction Parameter Reaction parameter

1] syk à syk_P V1 = 1; 13] lyn à lyn_P V13 = 1;

K1 = 40; K13 = 40;

Ka1 = 15; Ka13 = 15;

n1 = 2; n13 = 2;

KI1 = 40 KI13 = 40

2] syk_P à syk V2 = 11; 14] lyn_P à lyn V14 = 2;

K2 = 40 K14 = 40

3] Raf à Raf-P k3= 0.1; 15] PI3K à PI3K-P K15= 0.1;

K3 = 15; K15 = 15;

n3 = 2 N15 = 2

4] Raf-P à Raf V4 = 0.5; 16] PI3K-P à PI3K V16 = 0.5;

K4 = 40 K16 = 40

5] MEK-1/2 à MEK-1/2-P k5 = 0.05; 17] MKK-3/6 à MKK-3/6-P K17 = 0.05;

K5 = 150 K17 = 150

6] MEK-1/2-P à MEK-1/2-PP k6 = 0.05; 18] MKK-3/6-P à MKK- K18 =0.05;

K6 = 150 3/6-PP K18 = 150

7] MEK-1/2-PP à MEK-1/2-P V7 = 0.5; 19] MKK-3/6-PP à MKK- V19 = 0.5;

K7 = 40 3/6-P K19 = 40

8] MEK-1/2-P à MEK-1/2 V8 = 0.5; 20] MKK-3/6-P à MKK-3/6 V20 = 0.5;

K8 = 40 K20 = 40

9] ERK-1/2 à ERK-1/2-P k9 = 0.05; 21] p38 à p38-P K21 = 0.05;

K9 = 150 K21= 150

10] ERK-1/2-P à ERK-1/2-PP k10 = 0.05; 22] p38-P à p38-PP K22 = 0.05;

K10 = 150 K22 = 150 11] ERK-1/2-PP à ERK-1/2-P V11 = 0.5; 23] p38-PP à p38-P V23 = 0.5;

K11 = 40 K24 = 40

12] ERK-1/2-P à ERK-1/2 V12 = 0.5; 24] p38-P à p38 V24 = 0.5;

K12 = 40 K24 = 40

Initial concentration of the kinases. Concentration of kinases used for model simulation is listed with their respective literature sources. The model here was made dimensionless. The biological equivalent of the concentrations is in the units of nM/ml which could be found from the literatures listed here.

Table -2: Initial concentration of the kinases.

Kinase Concentration Reference

( dimensionless) (model values in the same order of

magnitude as in the references below )

ERK, p38MAPK 500 2, 3, 5, 6, 8, 9

MEK-1/2, MKK-3/6 500 2, 3, 5, 6, 8

Raf-1 100 2, 3, 9

PI3K 100 10

Syk 700 11

Lyn 50 11

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