Modeling of a cellular transmembrane signaling system through
interaction with G proteins in the ntcc calculus:
The interaction of G protein–coupled receptors (GPCRs) with
heterotrimeric G proteins, and
the Control of Intracellular Metabolic Processes: The Signal
transduction pathway of glycogen breakdown
Diana Hermith, B.S., M.S. (C)
Research Group AVISPA, FORCES project: FORmalisms from Concurrency for Emergent Systems
Technical Report, February 2010 (In progress)
Biological Problem Formulation
At the cellular level of abstraction, molecular mechanisms to communicate with the
environment involve many concurrent processes, objects, and relationships that dynamically
drive the cell's function over time. The cell membrane, the surface that acts as the boundary,
contains many receptors that are responsible for concurrently interacting with diverse signals
molecules and sensing external information over time. Each receptor recognizes specific
molecules that may bind to it. Binding activates signaling pathways that regulate molecular
mechanisms and the flow of information in the cell. A receptor is typically described in three
parts: the extracellular domain, the transmembrane domain and the intracellular domain.
There is a special class of receptors, which constitutes a common target of pharmaceutical
drugs, the G-protein-coupled receptors (GPCRs). These receptors interact with their
respective G proteins to induce an intracellular signaling.
The interaction of G protein–coupled receptors
heterotrimeric G proteins: First level of abstraction1.
1
(GPCRs)
with
E. Sontag, Molecular Systems Biology and Control, European J. of Control, Vol. 11, 1-40 pp, 2005.
1
To develop the model based on process calculi (ntcc) we are going to use a compositional
framework in which the first level of abstraction is divided into 3 sublevels according to the
domain of interaction, considering all the objects and processes as a coupled system.
This network of biochemical reactions that governs the signaling events to processing
information in the cellular membrane trough interactions between receptors and ligands, are
usually modeled using chemical equations of the form R1+..+Rn  k P1+..+Pm, where the n
reactants Ri’s (possibly in multiple copies) are transformed into m products Pj’s. Either n or m
can be equal to zero; the case m=0 represents a degradation reaction, while the case n=0
represents an external feeding of the products, performed by a biological reactive
environment. Each reaction has an associated rate k, representing essentially its basic
speed.
The Mathematical Model2.
We shall represent the cellular signaling events by a finite set of equations of the form:
r1 :  ai1Si  bi1Si
iI
iI
rm :  aim Si  bim Si
iI
iI
n  I will be used to denote the number of components involved in the cellular
transmembrane signalling and m to denote the number of reactions (equations) considered.
The chemical stoichiometric coefficients are represented by contants a1j ,..., anj and b1j ,..., bnj .
Thus, a1j S1 , a2j S 2 ,..., a3j S n are the reactants, while b1j S1 , b2j S2 ,..., b3j Sn are the products. We also
assume that each equation r j has associated a duration dur (rj ) defining the number of timeunits required for that reaction to produce the components on the right-hand side.
2
Davide Chiarugi, Moreno Falaschi, Carlos Olarte and Catuscia Palamidessi. Compositional modelling of signalling
pathways in Timed Concurrent Constraint Programming. In Proc. of ACM-BCB 2010. August 2010.
2
In general terms, the reaction proceeds as follows, in the equation r j , a1j molecules of
reactant S1 interacts with a 2j molecules of reactant S 2 , … and with a nj molecules of reactant
S n and are thus consumed, yielding b1j molecules of product S1 , … and bnj molecules of
product S n .
Models in ntcc3
Generalities of the ntcc model:
Each type of molecule will be represented as a variable whose value will be the number of
occurrences present in the biochemical system. Each chemical reaction will be described by
a recursive definition. When the reactants in the biochemical system are available, the
reaction occurs to form products or complexes required in cellular signaling.
We assume a well stirred mixture of N molecular species S1,S2,...,SN in a fixed volume V at a
constant temperature. These N species can chemically interact through M reactions
R1,R2,...,RM. We define in the model, the following variables:
xi : with domain 1,2,...,N representing the number of molecules or the current concentration of
the components S1,…,Sn, according to the mathematical model formulation.
eqi : with domain 1,2,...,M representing the equation to be applied in the current time unit.
Each model consist of three different components:
(i) The process to choose the rule to be applied in each time-unit:
This component chooses non-deterministically one of the reactions (equations) to be applied
in a current time unit by binding the variable eq , using the non-deterministic choice operator:
def
choose  when x11  a11 
+when x12  a12 
 x1n  a1n do tell(eq  1)
 xn2  an2 do tell(eq  2)
+
+when x1m  a1m 
 xnm  anm do tell(eq  m)
Roughly speaking, the process choose selects non-deterministically one of the equations
such that the current concentration of each component is higher than the reactant
necessaries for the equation to take place (e.g., xij  aij ). This process binds the variable eq
to the number of the equation chosen.
(ii) The process to modeling the chemical reactions:
A reaction r j is modeled by a process ( equationj ) binding the variables xij and xij to ai j and
bi j respectively. Those variables determine how the concentration of the component Si must
3
Ibid.
3
be affected due to the application of the reactions as follows, ai j units are consumed and bi j
units are produced.
def
equation j
= when eq  j do
next tell(x1j  a1j  xnj  anj ) ||
next
dur ( r j )
tell(x1j  b1j  xnj  bnj )
The process equationj checks if the selected equation is r j (i.e., eq  j ). Then, in the next
time-unit, the concentrations of the reactants in the left-hand side in the equation are reduced.
Recall that dur (rj ) stands for the duration of the reaction r j to take place. Then, dur (rj ) timeunits later, the concentration of the right-hand side components in the reaction (equation) are
incremented.
(iii) The process to change the state of the concentrations of each reactant / product
according to the equation applied.
This process computes the current concentration of the components according to the
concentration of them in the previous time-unit.
def
init = tell(x1  in1 in1 ) ||
|| tell(x1  inn inn )
def
m
m
j 1
j 1
m
m
j 1
j 1
state = next!(tell(x1  x1. prev   x1j  x1j ) ||
tell(xn  xn . prev   xnj  xnj ))
As a parameter of the simulation, the user must provide the range of the initial concentration
of each component ( ini , ini ). The process init asserts that the initial concentration of a
component Si should be a value between ini and ini .
The process state imposes the necessary constraints to update the concentration of the
components. The concentration of Si in the current time-unit (i.e., xi ) is calculated by taking
the value of xi in the previous time-unit (i.e., xi . prev ) and: 1) adding the variables xi1 ,..., xim ,
which are the components produced when a rule is applied, and 2) subtracting xi1 ,..., xim
which are the required reactants to apply a rule.
Thereby, the whole system will be represented like this:
4
def
system
= init
state
choose
equation1
…
equationn
5
Focus on the Intracellular Domain: Models the trimeric G Protein Cycle4.
In the inactive heterotrimeric state, GDP is bound to the G -subunit and -subunit. Upon
activation, GDP is released, GTP binds to G, and subsequently GGTP dissociates from G
and from the receptor. Both GGTP and G are then free to activate downstream effectors.
Biochemical Equations:
Reaction for molecular complex formation:
kass
G GDP
EQ1: G GDP   
Reactions EQ2 and EQ3 are enzimatic:
The transmembrane receptor (actived) promotes GDP/GTP exchange:
Rc*
G GTP   is represented like this:
EQ2: G GDP 
G GDP  Rc
EQ2.1: G GDP  Rc
kdiss
EQ2.2: G GDP  Rc 
G GTP    Rc
Reaction of hydrolysis:
GAP
 Ga GDP is represented like this:
EQ3: Ga GTP 
GaGTP  GAP
EQ3.1: Ga GTP  GAP
hydr
 GaGDP  GAP  Pi
EQ3.2: GaGTP GAP 
k
4
V. Katanaev and M. Chornomorets, Kinetic Diversity in G-Protein-Coupled Receptor Signaling, Biochem. J., Vol. 401,
2007.
6
Simulation parameters and encoding. Signaling modes with stoichiometric and kinetic parameters:
Variables
Variables definition
Variables encoding
G GDP
G protein GDP-bound alpha
subunit
a:gAlpha_GDP

G protein  subunit
b:beta_gamma
G GDP
trimeric G Protein Complex
t:tMC
G GTP
G protein GTP-bound alpha
subunit
w:gAlpha_GTP
Rc 
GPCR-transmembrane
receptor (Actived)
r:actived_receptor
G GDP  Rc
Complex of G protein and
GPCR
c:gpcr_complex
Biochemical state equations
ass
G GDP
EQ1: G GDP   
k

EQ2.1: G GDP  Rc
G GDP  Rc
kdiss
EQ2.2: G GDP  Rc 
G GTP    Rc
EQ3.1: Ga GTP  GAP
GaGTP  GAP
hydr
EQ3.2: GaGTP  GAP 
 GaGDP  GAP  Pi
k
7
GAP
GTP hydrolysis enzyme
g:gap
GaGTP GAP
Complex of GTP hydrolysis
h:gtp_hydrolysis
Pi
Inorganic phosphorus
p:inor_phosp
Concentration of variables5 (nM) : GPCR: [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500],
G proteins: [200-3000:[ ]InfLim=200; [ ]MedLim=1400; [ ]MaxLim=3000], GAP: [10-300: [ ]InfLim=10; [ ]MedLim=145, [ ]MaxLim=300],
G GDP  Rc : [200-500: [ ]InfLim=200; [ ]MedLim=350; [ ]MaxLim=500], G GTP GAP :[200-300: [ ]InfLim =200; [ ]MedLim =250; [ ]MaxLim=300],
a
Pi : [4000]
Time Simulation: 1’000.000 (time-units)
MODE 1
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical state equations
G GDP   Association k ass  1
Formation of the complex of G protein and
GPCR receptor
unkown rates = 1
GPCR-driven dissociation of the trimeric G
proteins
k diss  1
5
EQ1:
EQ2.1:
Equations encoding
kass
G GDP   
G GDP
G GDP  Rc
G GDP  Rc

eq1:1 = a:~1 b:~1 t:1;

eq2:1 = t:~1 r:~1 c:1;
eq3:1 = c:~1 r:1 t:1;
EQ2.2:
k
G GTP    Rc
G GDP  Rc 
diss
eq4:1 = c:~1 w:1 b:1 r:1;
It will be used the inferior, medium and maximun limit of the molar concentration of each variable according with the literature available for each mode of simulation.
8
Formation of the complex of GTP hydrolysis
unkown rates = 1
EQ3.1:
eq6:1 = h:~1 g:1 w:1;
GAP-driven GTPase
k hydr  2
GaGTP  GAP
Ga GTP  GAP
eq5:1 = w:~1 g:~1 h:1;
EQ3.2:
k
 GaGDP  GAP  Pi
GaGTP GAP 
hydr
eq7:2 = h:~1 a:1 g:1 p:1;
MODE 2
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical state equations
G GDP   Association k ass  3
Formation of the complex of G protein and
GPCR receptor
unkown rates = 1
GPCR-driven dissociation of the trimeric G
proteins
k diss  128
EQ1:
kass
G GDP   
G GDP
Equations encoding
eq1:3 = a:~1 b:~1 t:1;
eq2:1 = t:~1 r:~1 c:1;
EQ2.1:
G GDP  Rc
G GDP  Rc
eq3:1 = c:~1 r:1 t:1;
EQ2.2:
k
G GTP    Rc
G GDP  Rc 
diss
eq4:128 = c:~1 w:1 b:1 r:1;
eq5:1 = w:~1 g:~1 h:1;
Formation of the complex of GTP hydrolysis
unkown rates = 1
EQ3.1:
Ga GTP  GAP
GaGTP  GAP
eq6:1 = h:~1 g:1 w:1;
9
GAP-driven GTPase
k hydr  1200
EQ3.2:
k
 GaGDP  GAP  Pi
GaGTP GAP 
hydr
eq7:1200 = h:~1 a:1 g:1
p:1;
MODE 3
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical state equations
G GDP   Association k ass  5
Formation of the complex of G protein and
GPCR receptor
unkown rates = 1
GPCR-driven dissociation of the trimeric G
proteins
k diss  286
Formation of the complex of GTP hydrolysis
unkown rates = 1
EQ1:
EQ2.1:
Equations encoding
kass
G GDP   
G GDP
G GDP  Rc
G GDP  Rc

eq1:5 = a:~1 b:~1 t:1;
eq2:1 = t:~1 r:~1 c:1;

eq3:1 = c:~1 r:1 t:1;
k
G GTP    Rc
G GDP  Rc 
diss
EQ2.2:
EQ3.1:
Ga GTP  GAP
GaGTP  GAP
eq4:286 = c:~1 w:1 b:1 r:1;
eq5:1 = w:~1 g:~1 h:1;
eq6:1 = h:~1 g:1 w:1;
GAP-driven GTPase
k hydr  2400
EQ3.2:
k
 GaGDP  GAP  Pi
GaGTP GAP 
hydr
eq7:2400 = h:~1 a:1 g:1
p:1;
10
Focus on the Extracellular Domain: Models the reaction scheme of G Protein
signaling6.
One molecule of ligand can activate one G GDP -bound receptor, and phosphorylate the
G GDP to G GTP . The G GTP subunit can dissociate from the ligand-bound receptor. The
recombinatior of the  and  subunits of the G protein is considered to be fast, and so the
deactivation of the G protein is described by one reaction corresponding to the hydrolysis of
GTP to GDP, thus, the G signaling, and  subunits are neglected. The deactivated free
G GDP can associate with a free receptor and form a G GDP -bound receptor complex,
which can be activated again by one molecule of the ligand. Phosphate required for
phosphorylation reactions is present in a great excess.
Biochemical Equations:
The binding of the ligand ( L ) by the ( G GDP )-bound receptor ( R(G GDP) ), and receptorinduced exchange of GDP for GTP on the G subunit:
k1
EQ1: R[G GDP]  L
k1
R[G GTP]L
The dissociation of G GTP from the ligand-bound receptor ( RL ):
EQ2: R[G GTP]L
k2
k2
G GTP  RL
The hydrolysis of G GTP to G GDP catalyzed by GAP enzyme:
EQ3: G GTP  GAP
hydr
[G GTP]GAP 
 G GDP  GAP  Pi
k
Inactive G GDP binds G  (ommited) and the free receptor:
EQ4: G GDP  R
k5
k5
R[G GDP]
The dissociation of the ligand from the receptor is described in the form:
EQ5: RL
k4
k4
RL
6
D. Csercsik, K. Hangos and G. Nagy, A Simple Reaction Kinetic Model of Rapid (G Protein Dependent) and Slow (Arrestin Dependent) Transmission, Journal of Theoretical Biology, Vol. 255, 2008.
11
Simulation parameters and encoding. Signaling modes with stoichiometric and kinetic parameters:
Variables
Variables definition
Variables encoding
Biochemical state equations
R[G GDP]
Receptor G protein GDP-bound
alpha subunit complex
t:receptor_ gAlpha_GDP
EQ1: R[G GDP]  L
L
Ligand
l:ligand
EQ2: R[G GTP]L
R[G GTP]L
Receptor G protein GTP-bound
alpha subunit ligand tetrameric
complex
m:recep_
gAlpha_GTP_ligand
G GTP
G protein GTP-bound alpha
subunit
w:gAlpha_GTP
EQ4: G GDP  R
RL
Receptor Ligand complex
o:receptor_ligand
EQ5:
G GDP
G protein GDP-bound alpha
subunit
a:gAlpha_GDP
GAP
GTP hydrolysis enzyme
g:gap
R
GPCR-transmembrane
receptor
r:receptor
GaGTP GAP
Complex of GTP hydrolysis
h:gtp_hydrolysis
Pi
Inorganic phosphorus
p:inor_phosp
k1
R[G GTP]L
k1
k2
k2
G GTP  RL
EQ3:
G GTP  GAP
hydr
[G GTP]GAP 
 G GDP  GAP  Pi
k
RL
k5
k5
k4
k4
R[G GDP]
RL
12
Concentration of variables7 (nM) : GPCR: [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500],
G proteins: [200-3000:[ ]InfLim=200; [ ]MedLim=1400; [ ]MaxLim=3000], GAP: [10-300: [ ]InfLim=10; [ ]MedLim=145, [ ]MaxLim=300],
R G GDP  : [200-500: [ ]InfLim=200; [ ]MedLim=350; [ ]MaxLim=500], GaGTP GAP :[200-300: [ ]InfLim =200; [ ]MedLim =250; [ ]MaxLim=300],
Pi : [4000], L : [1-1000:[ ]InfLim=1; [ ]MedLim=500; [ ]MaxLim=1000], R[G GTP ]L : [200-1000: [ ]InfLim=200; [ ]MedLim=600; [ ]MaxLim=1000],
RL: [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500]
Time Simulation: 1’000.000 (time-units)
MODE 1
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Ligand, G protein-bounded receptor and


exchange reaction k1  41 , k1  41
G protein dissociation from receptor


k 2  31 , k 2  31
EQ2: R[G GTP]L
k1
k2
k2

k5  2 , k5  1
G GTP  GAP

k4  1 , k4  1
7
eq1:41 = t:~1 l:~1 m:1;
eq2:41 = m:~1 l:1 t:1;
eq3:31 = m:~1 w:1 o:1;
eq4:31 = w:~1 o:~1 m:1;
eq6:1 = h:~1 g:1 w:1;
eq7:2 = h:~1 a:1 g:1 p:1;
k5
EQ4: G GDP  R
Dissociation of receptor and ligand

G GTP  RL
EQ3:
khydr
[G GTP]GAP 
 G GDP  GAP  Pi
Association of receptor and G protein

R[G GTP]L
eq5:1 = w:~1 g:~1 h:1;
GAP-driven GTPase
unkown rates = 1
k hydr  2
k1
EQ1: R[G GDP]  L
Equations encoding
EQ5:
RL
k5
k4
k4
R[G GDP]
RL
eq8:2 = a:~1 r:~1 t:1;
eq9:1 = t:~1 r:1 a:1;
eq10:1 = o:~1 r:1 l:1;
eq11:1 = r:~1 l:~1 o:1;
It will be used the inferior, medium and maximun limit of the molar concentration of each variable according with the literature available for each mode of simulation.
13
MODE 2
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Ligand, G protein-bounded receptor and


exchange reaction k1  3 , k1  3
G protein dissociation from receptor


k2  2 , k2  1
EQ2: R[G GTP]L
GAP-driven GTPase
unkown rates = 1
k hydr  1
k1
EQ1: R[G GDP]  L
k1
k2
k2

k5  2 , k5  1

k4  1 , k4  1
G GTP  RL
eq2:3 = m:~1 l:1 t:1;
eq3:2 = m:~1 w:1 o:1;
eq4:1 = w:~1 o:~1 m:1;
eq5:1 = w:~1 g:~1 h:1;
G GTP  GAP
eq6:1 = h:~1 g:1 w:1;
eq7:1 = h:~1 a:1 g:1 p:1;
k5
EQ4: G GDP  R
Dissociation of receptor and ligand

eq1:3 = t:~1 l:~1 m:1;
R[G GTP]L
EQ3:
khydr
[G GTP]GAP 
 G GDP  GAP  Pi
Association of receptor and G protein

Equations encoding
EQ5:
RL
k5
k4
k4
R[G GDP]
RL
eq8:2 = a:~1 r:~1 t:1;
eq9:1 = t:~1 r:1 a:1;
eq10:1 = o:~1 r:1 l:1;
eq11:1 = r:~1 l:~1 o:1;
14
Focus on the Transmembrane Domain: Models the G Protein coupled receptor
(GPCR) signaling including G Protein activation and receptor desensitization8.
G-protein coupled receptor signaling includes G-protein activation and receptor
desensitization. R is the inactive form of the receptor, R is the active form of the receptor,
LR is the inactive ligand/receptor complex, LR is the active ligand/receptor complex, LRds is
the desensitized ligand/receptor complex, G is inactive G-protein, G  is activated G-protein,
L is free ligand, and Rds is the desensitized receptor.
According to [23] the list of parameters to take into account to the model description were
taken from experimental data for the neutrophil N-formyl peptide receptor. This receptor has
been well-studied because is linked to important physiological responses. We will use this
data to extrapolate in a arbitrary time framework , our kinetic parameters in time-units, in
order to represent the overall behavior of this domain of interaction.
Activation of the receptor and (Activation and deactivation of G protein):
EQ1: R
k fR
k fR / K act
R + G
ka
ki
G
Association of Ligand and inactive Receptor:
EQ2: R
kf
kr
LR
8
T. Riccobene, G. Omann and J. Linderman, Modeling Activation and Desensitization of G-Protein Coupled Receptors
Provides Insight into Ligand Efficacy, J. Theor. Biol., Vol. 200, 1999.
15
Association of Ligand and Active Receptor:

EQ3: R
k f
LR 
kr
Activation-deactivation of the ligand receptor complex and (Activation and deactivation of G
protein):
EQ4: LR
k fR
k fR / K act
LR + G
ka
ki
G
Desensitization of ligand receptor complex:
kds

 LRds
EQ5: LR 
Reaction for uncoupling of ligand from desensitized receptor:
EQ6: LRds
kr 2
kf 2
L  Rds
16
Simulation parameters and encoding. Signaling modes with stoichiometric and kinetic parameters:
Variables
Variables definition
Variables encoding
R
GPCR-transmembrane
receptor (Inactived)
ir:receptor_inact
R
GPCR-transmembrane
receptor (Actived)
ar:actived_receptor
G
G Protein (Inactived)
igp:g_protein_inact
G
G Protein (Actived)
agp:g_protein_act
LR
Ligand Receptor (inactived)
complex
o:receptor_ligand
L
Ligand
l:ligand
LR
Ligand Receptor (actived)
complex
oa:ligand_receptor_act
Rds
Desensitized receptor
dr:des_receptor
LRds
Desensitized ligand receptor
complex
do:des_receptor_ligand
Biochemical equations
EQ1:
R
k fR
k fR / K act
EQ2:
EQ3:
EQ4:
LR
R
R
k fR
k fR / K act
EQ5:
EQ6:
R
kf
kr
k f
kr
+
G
G
ka
ki
LR
LR 
LR + G
ka
ki
G
kds
LR  
 LRds
LRds
kr 2
kf 2
L  Rds
17
Concentration of variables9 (nM) : GPCR (Receptor): [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500],
G proteins: [200-3000:[ ]InfLim=200; [ ]MedLim=1400; [ ]MaxLim=3000], L : [1-1000:[ ]InfLim=1; [ ]MedLim=500; [ ]MaxLim=1000],
Receptor-Ligand: [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500]
Time Simulation: 1’000.000 (time-units)
MODE 1
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Equations encoding
Activation of the receptor and activationdeactivation of G protein
k fR  10 , k fR / K
 100 , k  1 ,
a
act
eq1:10 = ir:~1 ar:1 igp:1;
EQ1:
R
k fR
k fR / K act
R
+
G
ka
G
ki
eq3:1 = ar:~1 igp:~1 agp:1;
k i  100
eq4:100 = agp:~1 igp:1 ar:1;
Association of ligand and inactive receptor
kr  1 , k f  3
EQ2:
R
Association of ligand and active receptor
 k f  30 , k  1
r
EQ3:
R

kf
kr
k f
kr
eq5:1 = ir:~1 o:1;
LR
eq6:3 = o:~1 ir:1;
LR
eq7:30 = ar:~1 oa:1;

eq8:1 = oa:~1 ar:1;
Activation-deactivation of the ligand receptor
complex and activation-deactivation of G
protein
k fR  10 , k fR / K
 10 , k  1 ,
a
act
k i  100
9
eq2:100 = ar:~1 igp:~1 ir:1;
eq9:10 = o:~1 oa:1 igp:1;
EQ4:
LR
k fR
k fR / K act
LR + G
ka
ki
G
eq10:10 = oa:~1 igp:~1 o:1;
eq11:1 = oa:~1 igp:~1 agp:1;
eq12:100 = agp:~1 igp:1 oa:1;
It will be used the inferior, medium and maximun limit of the molar concentration of each variable according with the literature available for each mode of simulation.
18
Desensitization of ligand receptor complex
kds
LR  
 LRds
EQ5:
k ds  1
Reaction for uncoupling of ligand from
desensitized receptor
EQ6:
k r 2  1 , k f 2  25
LRds
eq13:1 = oa:~1 do:1;
eq14:1 = do:~1 l:1 dr:1;
L  Rds
kr 2
kf 2
eq15:25 = dr:~1 l:~1 do:1;
MODE 2
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Equations encoding
Activation of the receptor and activationdeactivation of G protein
k fR  10 , k fR / K
 100 , k  1 ,
a
act
eq1:10 = ir:~1 ar:1 igp:1;
EQ1:
R
k fR
k fR / K act
R
+ G
G
ka
ki
eq3:1 = ar:~1 igp:~1 agp:1;
ki  1
eq4:1 = agp:~1 igp:1 ar:1;
Association of ligand and inactive receptor
kr  1 , k f  3
EQ2:
Association of ligand and active receptor
 k f  30 , k  1
r
EQ3:
R
R
eq5:1 = ir:~1 o:1;
kf
LR
kr
eq6:3 = o:~1 ir:1;
k f
eq7:30 = ar:~1 oa:1;
LR 
kr
eq8:1 = oa:~1 ar:1;
Activation-deactivation of the ligand receptor
complex and activation-deactivation of G
protein
k fR  10 , k fR / K
 10 , k  1 ,
a
act
ki  1
eq2:100 = ar:~1 igp:~1 ir:1;
eq9:10 = o:~1 oa:1 igp:1;
EQ4:
LR
k fR
k fR / K act

LR +
G
ka
ki
G
eq10:10 = oa:~1 igp:~1 o:1;
eq11:1 = oa:~1 igp:~1 agp:1;
eq12:1 = agp:~1 igp:1 oa:1;
19
Desensitization of ligand receptor complex
kds
LR  
 LRds
EQ5:
k ds  1
Reaction for uncoupling of ligand from
desensitized receptor
EQ6:
k r 2  1 , k f 2  25
LRds
eq13:1 = oa:~1 do:1;
eq14:1 = do:~1 l:1 dr:1;
L  Rds
kr 2
kf 2
eq15:25 = dr:~1 l:~1 do:1;
MODE 3
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Equations encoding
Activation of the receptor and activationdeactivation of G protein
k fR  10 , k fR / K
 100 , k  1 ,
a
act
eq1:10 = ir:~1 ar:1 igp:1;
EQ1:
R
k fR
k fR / K act
R
+ G
G
ka
ki
eq3:1 = ar:~1 igp:~1 agp:1;
ki  1
eq4:100 = agp:~1 igp:1 ar:1;
Association of ligand and inactive receptor
kr  1 , k f  3
EQ2:
Association of ligand and active receptor
 k f  3000 , k  1
r
EQ3:
R
R
eq5:1 = ir:~1 o:1;
kf
LR
kr
eq6:3 = o:~1 ir:1;
k f
eq7:3000 = ar:~1 oa:1;
LR 
kr
eq8:1 = oa:~1 ar:1;
Activation-deactivation of the ligand receptor
complex and activation-deactivation of G
protein
k fR  10 , k fR / K
 10 , k  1 ,
a
act
ki  1
eq2:100 = ar:~1 igp:~1 ir:1;
eq9:10 = o:~1 oa:1 igp:1;
EQ4:
LR
k fR
k fR / K act

LR +
G
ka
ki
G
eq10:10 = oa:~1 igp:~1 o:1;
eq11:1 = oa:~1 igp:~1 agp:1;
eq12:1 = agp:~1 igp:1 oa:1;
20
Desensitization of ligand receptor complex
kds
LR  
 LRds
EQ5:
k ds  1
Reaction for uncoupling of ligand from
desensitized receptor
EQ6:
k r 2  1 , k f 2  25
LRds
eq13:1 = oa:~1 do:1;
eq14:1 = do:~1 l:1 dr:1;
L  Rds
kr 2
kf 2
eq15:25 = dr:~1 l:~1 do:1;
MODE 4
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Equations encoding
Activation of the receptor and activationdeactivation of G protein
k fR  10 , k fR / K
 100 , k  1 ,
a
act
eq1:10 = ir:~1 ar:1 igp:1;
EQ1:
R
k fR
k fR / K act
R
+
G
ka
G
ki
eq3:1 = ar:~1 igp:~1 agp:1;
ki  1
eq4:100 = agp:~1 igp:1 ar:1;
Association of ligand and inactive receptor
kr  1 , k f  3
EQ2:
R
Association of ligand and active receptor
k f  1, k  1
r
EQ3:
R

kf
kr
k f
kr
eq5:1 = ir:~1 o:1;
LR
eq6:3 = o:~1 ir:1;
LR
eq7:1 = ar:~1 oa:1;

eq8:1 = oa:~1 ar:1;
Activation-deactivation of the ligand receptor
complex and activation-deactivation of G
protein
k fR  10 , k fR / K
 10 , k  1 ,
a
act
ki  1
eq2:100 = ar:~1 igp:~1 ir:1;
eq9:10 = o:~1 oa:1 igp:1;
EQ4:
LR
k fR
k fR / K act
LR + G
ka
ki
G
eq10:10 = oa:~1 igp:~1 o:1;
eq11:1 = oa:~1 igp:~1 agp:1;
eq12:1 = agp:~1 igp:1 oa:1;
21
Desensitization of ligand receptor complex
k ds  1
EQ5:
Reaction for uncoupling of ligand from
desensitized receptor
k r 2  1 , k f 2  25
EQ6:
kds
LR  
 LRds
LRds
kr 2
kf 2
L  Rds
eq13:1 = oa:~1 do:1;
eq14:1 = do:~1 l:1 dr:1;
eq15:25 = dr:~1 l:~1 do:1;
22
Control of Intracellular Metabolic Processes: The Signal transduction
pathway of glycogen breakdown10: Second level of abstraction.
This signal transduction system is modular, consisting of three protein components –a
receptor, a transducer, and an effector. The receptor, as was explained before, is a
membrane-spanning protein that recognizes and binds a specific ligand, such as a hormone,
in this case, glucagon. The transducer is a G protein, so-called because of its high affinity for
guanine nucleotides.
Interaction of the hormone (ligand)-receptor complex with the
transducer stimulate an exchange reaction, in which GDP bound to the G protein is replaced
by GTP. This exchange activates the G protein, which then interacts with the effector, the
enzyme adenylate cyclase. In the response of liver cells to glucagon, that interaction
stimulates adenylate cyclase, which catalyzes the conversion of ATP to cyclic AMP, the
intracellular second messenger. cAMP activates a protein kinase. Some enzymes are
activated by phosphorylation, whereas others are inhibited; reactions in the metabolic
cascade leading to glycogenolysis are activated. Thus, binding of the ligand at the cell
surface stimulates synthesis of the second messenger inside the cell, which in turn effects a
desirable metabolic response.
10
Mathews, C. K., Van Holde, K. E. & Ahern, K. G. Biochemistry. Addison Wesley, 3rd edn, 2000.
23
Glycogen represents the most immediately available large-scale source of metabolic energy,
and hence it is important that animals be able to activate glycogen mobilization rapidly.
Moreover, glycogen breakdown is a hormone-controlled process, in which the biochemical
activity is explained in literature.
11
The synthesis and degradation of glycogen in the liver is under the control of a cascade of
protein phosphorylation and dephosphorylation reactions. Glycogenolysis, or the degradation
of glycogen is stimulated in liver cells by the action of the hormone glucagon.
The ligand, the hormone glucagon, binds to specific receptors in the plasma membrane of
liver cells, called -adrenergic receptors12 causing an allosteric change in the receptor. On
the intracellular domain, these receptors are heterotrimeric G-coupled proteins composed of
the alpha, beta and gamma subunits. Upon glucagon binding, the alpha subunit releases the
bound GDP in exchange for GTP.
11
R. Fletterick, and S. Sprang, Glycogen Phosphorylase Structures and Function, Acc. Chem. Res., Vol. 15, 1982.
M. Roden, G. Perseghin, K. Petersen, J-H. Hwang, G. Cline, K. Gerow, D.. Rothman, and G. Shulman, The Roles of
Insulin and Glucagon in the Regulation of Hepatic Glycogen Synthesis and Turnover in Humans, The American Society for
Clinical Investigation, Inc., Volume 97, Number 3, February 1996.
12
Frayn, K. N. (1996) Metabolic Regulation: A Human Perspective, p. 100. Portland Press, London.
24
The GTP-bound alpha subunit is released of its inhibitory beta/gamma subunits and binds to
adenylate cyclase, that is a transmembrane protein, a lyase enzyme that it is a part of the
cAMP-dependent pathway.
The binding of the GTP-bound alpha subunit to adenylate cyclase protein, triggers the
production of cyclic AMP (cAMP) from ATP. cAMP is a small molecule second messenger
which acts on the cAMP dependent protein kinase (cAPK), also known as protein kinase A
(PKA).
cAPK is an oligomeric protein consisting of different types subunits: two regulatory and two
catalytic. In the absence of cAMP, this tetrameric complex is inactive. When cAMP is
available, the binding of two molecules of cAMP to each of the regulatory subunits promotes
the dissociation of the tetrameric complex. The dissociated catalytic subunits, are now
enzymatically active and capable of phosphorylating serine or threonine residues of target
proteins.
Glucagon signal is needed for an increase in blood glucose level. Therefore, the activated
cAPK has a dual function. By phosphorylating glycogen synthase, cAPK inhibits the
synthesis of glycogen. cAPK also phosphorylates glycogen phosphorylase kinase, the
penultimate enzyme in the pathway of glycogen degradation.
Glycogen phosphorylase kinase then phosphorylates glycogen phosphorylase converting it
into the active form capable of degrading glycogen to glucose 1-phosphate.
The Signal Transduction Cascade of Glycogenolysis: Reaction pathway for
glycogen breakdown:
Activation of -adrenergic receptor by the ligand (glucagon) and exchange of GDP for GTP
on the G subunit:
EQ1: R  adrngc [G GDP]  Lglcgn
R  adrngc [G GTP]Lglcgn
The dissociation of G GTP from the ligand (glucagon)-bound to the -adrenergic receptor :
EQ2: R  adrngc [G GTP ]Lglcgn
G GTP  R  adrngc Lglcgn
The hydrolysis of G GTP to G GDP catalyzed by GAP enzyme:
EQ3: G GTP  GAP
hydr
[G GTP]GAP 
 G GDP  GAP  Pi
k
Inactive G GDP binds G  (ommited) and the free -adrenergic receptor:
EQ4: G GDP  R  adrngc
R  adrngc [G GDP]
The dissociation of the ligand (glucagon) from the -adrenergic receptor is described by:
R  adrngc  Lglcgn
EQ5: R  adrngc Lglcgn
25
The association of G GTP to adenylate cyclase (AC) enzyme:
EQ6: G GTP  AC
AC[G GTP ]
The production of cyclic AMP (cAMP) from ATP, catalyzed by the G GTP -bound to the
enzyme (adenylate cyclase):
EQ7: AC[G GTP ]  ATP
[ AC[G GTP]] ATP 
 cAMP  2 Pi  AC[G GTP]
cAMP activates the cAMP dependent protein kinase (cAPK):
2cAPK act
EQ8: 4cAMP  2cAPKinact
The activated cAPK has a dual function:
(1) cAPKact stimulates the glycogen degradation pathway:
Notation:
GPK : glycogen  phosphorylase  kinase
GP : glycogen  phosphorylase
cAPKact phosphorylates glycogen phosphorylase kinase (GPK):
[cAPK act GPK inact ]
EQ9: cAPK act  GPK inact
k3
(GPK  P) act  ADP  cAPK act
EQ9.1: [cAPK act GPKinact ]  ATP 
Glycogen phosphorylase kinase (activated) phosphorylates glycogen phosphorylase to
activate it:
[(GPK  P ) act GPinact ]
EQ10: (GPK  P) act  GPinact
k5
(GP  P) act  ADP  (GPK  P) act
EQ10.1: [(GPK  P) act GPinact ]  ATP 
The active form of glycogen phosphorylase degrades glycogen to glucose 1-phosphate:
(GP  P) act Glycogen
EQ11: (GP  P) act  Glycogen
 Glu cos e1 P  (GP  P) act
EQ11.1: (GP  P) act Glycogen  Pi 
26
(2) cAPKact inhibits the glycogen synthesis pathway: Glycogen synthesis involves five
reactions13. The first two, conversion of glucose 6-phosphate to glucose 1-phosphate and
synthesis of UDP-glucose from glucose 1-phosphate and UTP, are shared with several other
pathways. The next three reactions, the auto-catalyzed synthesis of a glucose oligomer on
glycogenin, the linear extension of the glucose oligomer catalyzed by glycogen synthase, and
the formation of branches catalyzed by glycogen branching enzyme, are unique to glycogen
synthesis. Repetition of the last two reactions generates large, extensively branched
glycogen polymers. The catalysis of several of these reactions by distinct isozymes in liver
and muscle allows them to be regulated independently in the two tissues. At this point we
want point out that (cAPKact) affects the metabolism of the glycogen synthesis by inhibiting the
enzyme glycogen synthase activity. For future work, will be interesting to make a ntcc model
for this pathway.
Notation:
GS : glycogen  synthase
cAPKact phosphorylates glycogen synthase (GS):
[cAPK act GS act (GPK  P) act ]
EQ12: (GPK  P) act  cAPK act  GS act
k7
(GS  P)inact  ADP  cAPK act  (GPK  P) act
EQ12.1: [cAPK act GSact (GPK  P) act ]  ATP 
13
http://www.reactome.org/cgi-bin/eventbrowser?DB=gk_current&ID=70302
27
Simulation parameters and encoding. Signaling modes with stoichiometric and kinetic parameters:
Variables
Variables definition
Variables encoding
R  adrngc [G GDP]
GPCR-transmembrane adrenergic receptor G subunit
rgp:recept_gprotein
Lglcgn
Ligand (glucagon)
l:ligand
R  adrngc [G GTP ]Lglcgn
GPCR-G protein-Ligand
Complex
rgtpl:recpt_gtp_ligand
G GTP
G protein
gtp:gAlpha_GTP
R  adrngc Lglcgn
Ligand Receptor complex
o:receptor_ligand
GAP
GTP hydrolysis enzyme
g:gap
Biochemical equations
EQ1:
R  adrngc [G GDP]  Lglcgn
R  adrngc [G GTP]Lglcgn
EQ2:
G GTP  R  adrngc Lglcgn
R  adrngc [G GTP ]Lglcgn
EQ3:
G GTP  GAP
hydr
[G GTP]GAP 
 G GDP  GAP  Pi
k
EQ4:
G GDP  R  adrngc
R  adrngc [G GDP]
EQ5:
R  adrngc  Lglcgn
R  adrngc Lglcgn
EQ6:
G GTP  AC
AC[G GTP ]
AC[G GTP]  ATP
[G GTP]GAP
Complex of GTP hydrolysis
h:gtp_hydrolysis
EQ7:
[ AC[G GTP]] ATP 

cAMP  2 Pi  AC[G GTP]
G GDP
EQ8:
G protein
gdp:gAlpha_GDP
4cAMP  2cAPKinact
2cAPK act
28
R  adrngc
GPCR-transmembrane adrenergic receptor
EQ9:
ir:receptor_inact
cAPK act  GPK inact
[cAPK act GPK inact ]
EQ9.1:
AC
Adenylate cyclase enzyme
ac:aden_cycl
k3
[cAPK act GPKinact ]  ATP 

(GPK  P)act  ADP  cAPK act
EQ10:
AC[G GTP]
Complex of AC enzyme and G
protein
acgp:aden_cycl_gtp
ATP
Adenosine triphosphate
atp:atp
(GPK  P) act  GPinact
[(GPK  P ) act GPinact ]
EQ10.1:
k5
[(GPK  P)act GPinact ]  ATP 

(GP  P)act  ADP  (GPK  P)act
[ AC[G GTP]] ATP
Complex of AC enzyme, G
protein and ATP
acgpatp:
aden_cycl_gtp_atp
cAMP
Cyclic AMP
camp:cyclic_amp
EQ11:
(GP  P) act  Glycogen
(GP  P) act Glycogen
EQ11.1:
(GP  P) act Glycogen  Pi 
 Glu cos e1 P  (GP  P) act
EQ12:
Pi
Inorganic phosphorus
p:inor_phosp
(GPK  P) act  cAPK act  GSact
[cAPK act GSact (GPK  P) act ]
EQ12.1:
cAPKinact
cAMP dependent protein
kinase (Inactived)
capki:cAPK_inact
cAPK act
cAMP dependent protein
kinase (Actived)
capka:cAPK_act
GPKinact
Glycogen phosphorylase
kinase (Inactived)
gpki:gpk_inact
k7
[cAPK act GSact (GPK  P)act ]  ATP 

(GS  P)inact  ADP  cAPK act  (GPK  P)act
29
[cAPKact GPKinact ]
Complex cAPKactGPKinact
agpk:cAPKa_GPKi
(GPK  P) act
Phosphorylate glycogen
phosphorylase kinase
gpkp:gpk_P_act
ADP
Adenosine diphosphate
adp:adp
GPinact
Glycogen phosphorylase
(Inactivated)
gpi:glyc_phosp_inact
[(GPK  P)act GPinact ]
Complex glycogen
phosphorylase kinaseglycogen phosphorylase
gpkpi:gpkp_gp
(GP  P)act
Glycogen phosphorylase
(Activated)
gpa: glyc_phosp_act
Glycogen
Glycogen
glyc:glyc
(GP  P)act Glycogen
Complex Glycogen
phosphorylase - glycogen
gpaglyc: :
glyc_phosp_act_glyc
Glu cos e1 P
Glucose 1-phosphate
gluc:gluc_1_phosp
GSact
Glycogen synthase (Activated)
gsa:glyc_synt_act
[cAPKact GSact (GPK  P)act ]
Complex protein kinase
glycogen synthase
pkgs:prot_kin_glyc_synt
(GS  P)inact
Glycogen synthase
(Inactivated)
gsi:glyc_synt_inact
30
Concentration of variables14 (nM) : GPCR (Receptor): [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500],
G proteins: [200-3000:[ ]InfLim=200; [ ]MedLim=1400; [ ]MaxLim=3000], L : [1-1000:[ ]InfLim=1; [ ]MedLim=500; [ ]MaxLim=1000],
Receptor-Ligand: [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500]
Time Simulation: 1’000.000 (time-units)
MODE 1
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Equations encoding
Activation of the receptor and activationdeactivation of G protein
k fR  10 , k fR / K
 100 , k  1 ,
a
act
EQ1:
R  adrngc [G GDP]  Lglcgn
R  adrngc [G GTP]Lglcgn
k i  100
Association of ligand and inactive receptor
kr  1 , k f  3
Association of ligand and active receptor
 k f  30 , k  1
r
Activation-deactivation of the ligand receptor
complex and activation-deactivation of G
protein
k fR  10 , k fR / K
 10 , k  1 ,
a
act
k i  100
14
It will be used the inferior, medium and maximun limit of the molar concentration of each variable according with the literature available for each mode of simulation.
31
Desensitization of ligand receptor complex
k ds  1
Reaction for uncoupling of ligand from
desensitized receptor
k r 2  1 , k f 2  25
Concentration of variables15 (nM) : GPCR (Receptor): [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500],
G proteins: [200-3000:[ ]InfLim=200; [ ]MedLim=1400; [ ]MaxLim=3000], L : [1-1000:[ ]InfLim=1; [ ]MedLim=500; [ ]MaxLim=1000],
Receptor-Ligand: [1-500:[ ]InfLim=1; [ ]MedLim=250; [ ]MaxLim=500]
Time Simulation: 1’000.000 (time-units)
MODE 1
Duration of the reaction (time-units)
Rate constants (sec-1)
Biochemical equations
Equations encoding
EQ1:
eq1:1 = rgp:~1 l:~1 rgtpl:1;
R  adrngc [G GDP]  Lglcgn
R  adrngc [G GTP]Lglcgn
eq3:1 = rgtpl:~1 gtp:1 o:1;
EQ2:
G GTP  R  adrngc Lglcgn
R  adrngc [G GTP ]Lglcgn
eq4:1 = gtp:~1 o:~1 rgtpl:1;
eq5:1 = gtp:~1 g:~1 h:1;
EQ3:
G GTP  GAP
eq2:1 = rgtpl:~1 l:1 rgp:1;
hydr
[G GTP]GAP 
 G GDP  GAP  Pi
k
eq6:1 = h:~1 g:1 gtp:1;
eq7:1 = h:~1 gdp:1 g:1 p:1;
15
It will be used the inferior, medium and maximun limit of the molar concentration of each variable according with the literature available for each mode of simulation.
32
EQ4:
eq8:1 = gdp:~1 ir:~1 rgp:1;
G GDP  R  adrngc
R  adrngc [G GDP]
EQ5:
eq10:1 = o:~1 ir:1 l:1;
R  adrngc  Lglcgn
R  adrngc Lglcgn
EQ6:
eq11:1 = l:~1 ir:~1 o:1;
eq12:1 = gtp:~1 ac:~1 acgp:1;
G GTP  AC
AC[G GTP ]
EQ7:
AC[G GTP]  ATP
[ AC[G GTP]] ATP 

cAMP  2 Pi  AC[G GTP]
EQ8:
4cAMP  2cAPKinact
2cAPK act
eq13:1 = acgp:~1 ac:1 gtp:1;
eq14:1 = acgp:~1 atp:~1
acgpatp:1;
eq15:1 = acgpatp:~1 atp:1
acgp:1;
eq16:1 = acgpatp:~1 camp:1 p:2
acgp:1;
eq17:1 = camp:~4 capki:~2
capka:2;
eq18:1 = capka:~2 capki:2
camp:4;
eq19:1 = capka:~1 gpki:~1
agpk:1;
EQ9:
cAPK act  GPK inact
eq9:1 = rgp:~1 ir:1 gdp:1;
[cAPK act GPK inact ]
eq20:1 = agpk:~1 gpki:1 capka:1;
EQ9.1:
k3
[cAPK act GPKinact ]  ATP 

(GPK  P)act  ADP  cAPK act
EQ10:
(GPK  P) act  GPinact
[(GPK  P ) act GPinact ]
EQ10.1:
k5
[(GPK  P)act GPinact ]  ATP 

(GP  P)act  ADP  (GPK  P)act
eq21:1 = agpk:~1 atp:~1 gpkp:1
adp:1 capka:1;
eq22:1 = gpkp:~1 gpi:~1 gpkpi:1;
eq23:1 = gpkpi:~1 gpi:1 gpkp:1;
eq24:1 = gpkpi:~1 atp:~1 gpa:1
adp:1 gpkp:1;
33
EQ11:
(GP  P) act  Glycogen
(GP  P) act Glycogen
eq25:1 = gpa:~1 glyc:~1
gpaglyc:1;
eq26:1 = gpaglyc:~1 glyc:1
gpa:1;
EQ11.1:
(GP  P) act Glycogen  Pi 
 Glu cos e1 P  (GP  P) act
eq27:1 = gpaglyc:~1 p:~1 gluc:1
gpa:1;
EQ12:
eq28:1 = gpkp:~1 capka:~1
gsa:~1 pkgs:1;
eq29:1 = pkgs:~1 gsa:1 capka:1
gpkp:1;
(GPK  P) act  cAPK act  GSact
[cAPK act GSact (GPK  P) act ]
EQ12.1:
k7
[cAPK act GSact (GPK  P)act ]  ATP 

(GS  P)inact  ADP  cAPK act  (GPK  P)act
eq30:1 = pkgs:~1 atp:~1 gsi:1
adp:1 capka:1 gpkp:1;
34
A Compositional Modeling: Reasoning about a biological model, the case of a
transmembrane signaling system.
35
37
The interaction of G protein–coupled receptors (GPCRs) with heterotrimeric G proteins: First level of
abstraction
Extracellular Domain: Models the reaction
scheme of G Protein signaling
EQ1:
EQ2:
k1
R[G GDP]  L
R[G GTP]L
G GTP  GAP
EQ4:
k1
k2
k2
Transmembrane Domain: Models the G
Protein coupled receptor (GPCR) signaling
including G Protein activation and receptor
desensitization
EQ1:
R[G GTP]L
R
G GDP  R
EQ5:
RL
k5
k4
k4
k fR
R + G
k fR / K act
ka
ki
G
EQ1:
kass
G GDP   
G GDP
EQ2.1:
G GTP  RL
EQ2:
EQ3:
khydr
[G GTP]GAP 
 G GDP  GAP  Pi
k5
Intracellular Domain: Models the trimeric G
Protein Cycle
EQ3:
R
R
kf
kr
k f
kr
G GDP  Rc
LR
LR 
G GDP  Rc


EQ2.2:
kdiss

G GTP    Rc
EQ4:
R[G GDP]
RL
LR
k fR

k fR / K act
EQ5:
EQ6:
LR + G
ka
ki
kds
LR  
 LRds
LRds
kr 2
kf 2
G

G GDP  Rc
EQ3.1:
Ga GTP  GAP
GaGTP  GAP
EQ3.2:
 GaGDP  GAP  Pi
GaGTP GAP 
khydr
L  Rds
38
Simulation Results:
Focus on the Intracellular Domain: Models the trimeric G Protein Cycle16.
16
V. Katanaev and M. Chornomorets, Kinetic Diversity in G-Protein-Coupled Receptor Signaling, Biochem. J., Vol. 401, 2007.
39
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1: Lower
limit of the rate
constant
Mode 2: The
mean value of
the rate
constant
Mode 3: The
maximum value
of the rate
constant
40
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1: Lower
limit of the rate
constant
Mode 2: The
mean value of
the rate
constant
Mode 3: The
maximum value
of the rate
constant
41
Focus on the Transmembrane Domain: Models the G Protein coupled receptor (GPCR) signaling including G
Protein activation and receptor desensitization17.
17
T. Riccobene, G. Omann and J. Linderman, Modeling Activation and Desensitization of G-Protein Coupled Receptors Provides Insight into Ligand Efficacy, J. Theor.
Biol., Vol. 200, 1999.
42
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1:
Varied values
for the rate
constant
Mode 2:
Varied values
for the rate
constant
Mode 3:
Varied values
for the rate
constant
Mode 4:
Varied values
for the rate
constant
43
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1:
Varied values
for the rate
constant
Mode 2:
Varied values
for the rate
constant
Mode 3:
Varied values
for the rate
constant
Mode 4:
Varied values
for the rate
constant
44
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1:
Varied values
for the rate
constant
Mode 2:
Varied values
for the rate
constant
Mode 3:
Varied values
for the rate
constant
Mode 4:
Varied values
for the rate
constant
45
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1:
Varied values
for the rate
constant
Mode 2:
Varied values
for the rate
constant
Mode 3:
Varied values
for the rate
constant
Mode 4:
Varied values
for the rate
constant
46
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1:
Varied values
for the rate
constant
Mode 2:
Varied values
for the rate
constant
Mode 3:
Varied values
for the rate
constant
Mode 4:
Varied values
for the rate
constant
47
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1:
Varied values
for the rate
constant
Mode 2:
Varied values
for the rate
constant
Mode 3:
Varied values
for the rate
constant
Mode 4:
Varied values
for the rate
constant
48
Focus on the Extracellular Domain: Models the reaction scheme of G Protein signaling18.
18
D. Csercsik, K. Hangos and G. Nagy, A Simple Reaction Kinetic Model of Rapid (G Protein Dependent) and Slow (-Arrestin Dependent) Transmission, Journal of
Theoretical Biology, Vol. 255, 2008.
49
Lower limit of concentration
The mean value of concentration
The maximum value of concentration
Mode 1:
Varied
values
for the
rate
constant
Mode 2:
Varied
values
for the
rate
constant
50
Preguntas:
1.
2.
3.
4.
Representación de cada uno de los modelos en ntcc.
Ajustar código para correr a más unidades de tiempo.
Extensión probabilística, que se tiene?
Verificación de propiedades empleando LTL.
http://www.nature.com/news/2011/110112/full/news.2011.13.html?WT.ec_id=NEWS-20110118
Multiscale Modeling in Biology: Whether on one scale or many, then, modeling can serve two
purposes. When the details of the biology of a system are known, a mathematical model can be used in
place of the biological system, providing a way to carry out virtual experiments. In this case the model
does not add to our understanding of the system; it simply replicates the system. Where the fine detail
is not known, modeling serves as a tool for testing hypotheses and generating predictions. In this case,
the modeling enhances understanding of the system but does not replace it. Increased understanding
can arise only from simplifying the model. Therefore we need a suite of models, each designed to
address a specific biological question. (American Scientist, Volume 95, Multiscale Modeling in
Biology, ref: Schnell, S. and Grima, R. and Maini, P. K. (2007) Multiscale modeling in biology.
American Scientist, 95 (1). pp. 134-142.)
http://www.rpi.edu/dept/bcbp/molbiochem/MBWeb/mb1/part2/signals.htm
http://sandwalk.blogspot.com/2007/05/regulating-glycogen-metabolism.html
pag 431
pag474
http://www.ncbi.nlm.nih.gov/bookshelf/br.fcgi?book=stryer&part=A2937#A2944
http://www.cryst.bbk.ac.uk/PPS2/projects/shulte/phosphorylation/glyco_pic.html
The modular nature of this hormonal control system allows diversity metabolic responses to be based on the same operating
principles. File 001
http://www.biologia.edu.ar/celulamit/gp.htm
http://web.mit.edu/catalog/inter.gradu.csb.html interesante para la discusion del modelamiento
composicional
51
Interesante si se puede, validar esta curva con los datos de sumulacion
Para la reflexion sobre velocida dde reaccionhttp://mit.ocw.universia.net/7.51/f01/pdf/fa01-lec02.pdf
Mirar tareas del curso de sistemas complejos para ver que esquema de validacion puedo emplear sobre
la base de mis resultados.
Buscar en los archivos de la tesis a ver si encuentro el script para calcular el tiempo de simulacion por
unidad de tiempo y ver a 100000 ua detiempo, como me hacerco al tiempo real.
Biomolecular interactions and cellular processes assembled into
authoritative human signaling pathways
http://pid.nci.nih.gov/search/pathway_landing.shtml?what=graphic&jpg=on&pathway_id=100073&so
urce=2&output-format=graphic&ppage=1&genes_a=
http://pid.nci.nih.gov/
http://www.montefiore.ulg.ac.be/~fey/Pubs/student_thesis.pdf
52