Wilkinson D.J. Stochastic Modelling for Systems Biology
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<listOfProducts>
<SpeciesReference
species="P2"/>
</listOfProducts>
<kineticLaw>
<math
xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<Ci>
Cell
</Ci>
<Ci>
kl
</Ci>
<Ci>
P
</Ci>
<Ci>
P
</Ci>
</apply>
</math>
<listOfParameters>
<parameter
id=
11
kl
11
value="500000
11
/>
</listOfParameters>
</kineticLaw>
</reaction>
<reaction
id=
11
Dissociation"
reversible="false
11
>
<listOfReactants>
<SpeciesReference
species="P2
11
/>
</listOfReactants>
<listOfProducts>
<speciesReference
species=
11
P"
stoichiometry=
11
2
11
/>
</listOfProducts>
<kineticLaw>
<math
xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<Ci>
Cell
</ci>
<Ci>
k2
</Ci>
<Ci>
P2
</ci>
</apply>
</math>
<listOfParameters>
<parameter
id="k2"
value=
11
0.2
11
/>
</listOfParameters>
</kineticLaw>
</reaction>
</listDfReactions>
</model>
</sbml>
A.3.2 Discrete stochastic version
SBMLMODELS
The model below is the SBML for the discrete stochastic version
of
the dimerisation
kinetics model, discussed in Section 7 .2.
<?xml
version="l.0
11
encoding="UTF-8
11
?>
<sbml
xmlns="http:
I
/www.
sbml.org/sbml/level2"
level=
11
2
1
'
version="l">
<model
id="DimerKineticsStoch"
name="Dimerisation
Kinetics
(stochastic)">
<listOfUnitDefinitions>
<unitDefinition
id="substance·
11
>
<listOfUnits>
<unit
kind="item
11
multiplier="1
11
offset=
11
0
11
/>
</listOfUnits>
</unitDefinition>
</listOfUnitDefinitions>
<listOfCompartments>
<Compartment
id="Cell
11
size=
11
1e-15"/>
</listOfCompartments>
<listOfSpecies>
<species
id="P"
compartment=
1
'Cell
11
initia1Amount="301"
hasOnlySubstanceUnitS=
11
tru
<species
id=
11
P2
11
compartment=
11
Cell"
initialAmount="
0
11
hasOnlySubstanceUnits=
11
true
</listOfSpecies>
<listOfReactions>
248
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252
constant, 14 2
equilibrium distribution,
112
Euler
method, 144
Euler-Maruyama approximation, 134
event, 45
exclusive,
46
expectation, 58
continuous,
72
linear combination, 62
linear transformation,
60
product, 62
sum,
61
exponential distribution, 77
memory less property,
79
simulation, 94
first event method, 181
first reaction method, 182
Fokker-Planck equation, 188
gamma
distribution,
86
function,
86
Gaussian distribution,
82
simulation, 96
geometric distribution,
65
Gibbs sampler,
202
fixed sweep, 203
forward-backward, 205
random
scan, 205
Gibson-
Bruck
algorithm, 182
Gillespie algorithm, 149
graph
directed,
20
reaction,
21
theory,
20
hybrid
discrete/CLE, 193
discrete/ODE, 191
maximal timestep,
192
next reaction, 193
NRH, 193
simulation algorithms, 190
immigration-death process, 126
importance sampling,
92
incidence
matrix,
26
inference
network structure, 234
parameter,
220
INDEX
inhomogeneous Poisson process, 129
intersection, 46
intervention analysis, 176
invariants,
29
inverse distribution method, 93.
Ito
process, 133
kinetics
chemical, 139
mass-action, 139
molecular, 145
stochastic, 145
Kolmogorov equations, 123
lac operon
stochastic model, 176
law
of
large numbers, 73
strong, 75
weak, 75
likelihood,
197
linear congruential generator, 92
LLN,
73
lookup method,
97
Lotka-Volterra dynamics, 141
lower quartile,
71
Markov
chain,
109
order,
109
process, 109
simulation, 114
Markov chain Monte Carlo (MCMC),
202
Markov's inequality,
74
mass-action kinetics
deterministic,
139
stochastic, 147
master equation, 157
matrix,
24
sparse,
24
maximal timestep method, 192
MCMC,202
Gibbs sampler, 202
hybrid schemes, 216
independence sampler, 215
