Tellurium Introduction:

Motivation ... a minimal example!

Just a few lines of code allow a model to be loaded, simulated and plotted!



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import tellurium as te; te.setDefaultPlottingEngine('matplotlib')
%matplotlib inline

antimony_model = '''J0: -> y; -x;J1: -> x; y;x = 1.0;y = 0.2;'''
r = te.loada(antimony_model)
r.simulate(0,100,1000)
r.plot()

Everything in a single tool - tellurium:

As you could see, tellurium allows you to create and manipulate a model in a pythonic way. The tellurium package consists of formerly two distinct packages: antimony which is a modeling-language and roadrunner a sbml-simulator. The main advantage of tellurium is how both work together in python: as soon as you load a model a roadrunner simulator will be instanciated simultaniously. This way your model and the solver are a python object - the same object! This allows you to have real power over your model and the solver and control everything within your python script.

For further reading:

Full documentation http://tellurium.readthedocs.io/en/latest/index.html

Short documentation http://tellurium.analogmachine.org/documentation/antimony-documentation

Antimony (bio-)models library http://antimony.sourceforge.net/antimony-biomodels.html

Tutorial Part I - Create a Model :

Let us start from scratch and define a new model (if you execute the next cell then tellurium tries to load your model and performs a basic syntax check at the same time!):



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import tellurium as te

model = ''''''

model_backup = '''
model example
    # UNITS:
    #

    #unit alienliters = 0.123 liters
    #unit fL = 1.e-15 liters

    # COMPARTMENTS:
    #

    compartment cell = 100;
    compartment mitochondria = 10;
    mitochondria in cell;

    #mitochondria has fL;
    #cell has fL;

    # INITIAL VALUES
    #

    TOM1 = 10;
    A_c = 100;
    A_m = 1;
    I = 1;

    TOM1 in cell;
    A_c in cell;
    A_m in mitochondria;
    I in cell;

    # REACTIONS
    #


    T0: A_c + TOM1 -> 2 A_m + TOM1; kineticLaw;
    kineticLaw := k1 * TOM1 * (A_c - A_m)/I

    k1 = 0.01

    # EVENTS:

    #E1: at (A_c < 50): k1 = 0;
    #E2: at (time>300): TOM1 = 20, A_c = 120;
end

'''

r = te.loada(model)

def aa(line, cell):
    global model
    #print line,cell
    model = model + str(cell) + "\n"
    te.loada(str(model))
get_ipython().register_magic_function(aa, "cell")

Antimony is a language that is analog to SBML Systems Biology Markup Language but human-readable. Therefore the concepts that are present in SBML can be found in antimony too. The definition of a compartment is such a SB concept!

Step 1: Define a compartment!



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%%aa # %%aa: A-ppend to A-ntimony model, only for educational purpose!

Ok... But that's just boring. Let's define something truly special and add a second compartment which is located in your previous one:



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%%aa

Awesome! But be aware... circular definitions are not allowed. Something like this won't work:

comp_a in comp_b; comp_b in comp_c; comp_c in comp_a;

SBML has a system of unit definition. But the numbers we assigned to the compartments are without any specified unit at the moment. It is good practice to always use units and it is possible to define custom units!



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%%aa

To specify units you can write the value and the unit combined in the same line:



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%%aa

Or simply change the units:



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%%aa

Step 2: Define some species.



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%%aa

Smart! You already initialized your species. But you forgot to specify the location of your species! Add these lines:



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%%aa

Step 3: Define reactions.



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%%aa

Syntax in antimony is subtile:

There are 3 (+1) important bits in a reaction:

0) The name of your reaction:

name: A + E -> B + 2C + E; kineticLaw;

i) The direction '->' (sets the sign in an ODE in front the kineticLaw: plus or minus):

ii) The stoichiometry:

iii) The kinetic law:

The kinetic law is always in units of amount/time! This way it is consistent with stochastic simulations (you can directly run the 'gillespie'-algorithm in tellurium's solver: roadrunner) and furthermore any considerations regarding compartment sizes (even time depending compartment changes or transport reactions) are automatically done by the solver to get the correct concentrations for your species.

About Assignments and ODE's:

This " = " is a simple assignment, basically an initialization:

parameter = 5
species = 1
species2 = species + parameter

This " := " is a time-dependend assignment, the variable at the left will adapt, if the right hand side changes:

species0 := 3 * time
species1 := species0

This " '= " will create an ODE:

species'= k * species

Step 4: Events.

You can define events, which may change values depending on boolean expressions...



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%%aa

Or set a time dependend event. You may notice that time is special and the already predefined model time:



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%%aa

Ok, now you may want to test your model and simulate it. You should definitly do this before we continue. Make sure that your model is correctly defined at the top of this jupyter notebook (you may execute the cell again!). Then you can run it:



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Import/Export Models:

First, we need the tellurium package:



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Load a model... You can choose from:

i) load a test model from tellurium itself.



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ii) download 'curated BioModels translated to Antimony' from here http://antimony.sourceforge.net/antimony-biomodels.html:



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iii) load your own model:



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You can also convert models between modeling-languages:



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Then save the SBML model in a file:



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An read it again...



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You can also draw your model:



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def draw(model):
    diagram = te.visualization.SBMLDiagram(model.getSBML())
    diagram.draw()

Parameter estimation

Important concept: Reset a model!

.reset() # reset species to initial values

.resetAll() # reset species + paramters

.resetToOrigin() # similar to load the model



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Stochastic vs. deterministic



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