Phosphorylation of Insulin Receptors

Model, simulate and analyze biochemical pathways involved in insulin signaling

Insulin signaling in fat cells plays an important role in controlling the glucose level in the body. Insulin binding to receptors causes them to phosphorylate, transducing the insulin signal into the cells, controlling glucose uptake.

Download the Bio Chem library from the System Modeler Modelica Library Store.

Import the library:

In[1]:=

Import["BioChem_2.0.0.sma","MO"]

Out[1]=

Load a model of insulin signaling:

In[2]:=

insulinModel="InsulinSignaling.InsulinModel";

View the model diagram:

In[3]:=

SystemModelinsulinModel,"Diagram",



Out[3]=

Simulate the model:

In[4]:=

sim1=SystemModelSimulate[model,{0,30}];

Plot the internalized insulin receptor rates:

In[5]:=

SystemModelPlot[sim1,"InternalizedIRRates",ImageSizeLarge]

Out[5]=

	Endocytosis Rate
	Internalized Ins…
	Recycling Rate
	Insulin Receptor…

Plot the phosphorylated and un-phosphorylated IRS concentrations:

In[6]:=

SystemModelPlot[sim1,"IRS1Concentrations",ImageSizeLarge]

Out[6]=

	Phosphorylated I…
	Unphosphorylated…

Simulate an insulin input to the model with the given sets of parameter values, starting with the steady state initial values:

In[7]:=

simSweep=SystemModelSimulateinsulinModel,{0,30},"ParameterValues""Xactivation.k2"Table

,{i,1,10};

Compare the insulin response of the phosphorylated IRS1 (IRS1p.c) for the different parameter sets:

In[8]:=

SystemModelPlotsimSweep,{"IRS1p.c"},



Out[8]=

	Sim-1: IRS1p.c
	Sim-2: IRS1p.c
	Sim-3: IRS1p.c
	Sim-4: IRS1p.c
	Sim-5: IRS1p.c
	Sim-6: IRS1p.c
	Sim-7: IRS1p.c
	Sim-8: IRS1p.c
	Sim-9: IRS1p.c
	Sim-10: IRS1p.c

Perform a local sensitivity analysis with respect to each parameter, to find out which parameters influence the phosphorylated IRS1 response the most.

Filter out the rate constant parameters to calculate sensitivities for them:

In[9]:=

param=SystemModel[insulinModel]["ParameterNames"];

In[10]:=

sensParNames=Flatten@DeleteCases[StringCases[Map[QuantityVariableIdentifier,param],__~~"."~~"k1"|"k2"],{}];

Run a sensitivity simulation:

In[11]:=

simSens=SystemModelSimulateSensitivity[insulinModel,{0,30},sensParNames];

Get a list of the sensitivity parameters in string form:

In[12]:=

parNames=simSens[{"ParameterNames","*."~~"k1"|"k2"}];

Plot with sensitivity bounds to see which parameters are most important for the phosphorylated insulin:

In[13]:=

significantQ[p_]:=If[Abs[0.5Times@@simSens[{{"IRS1p.c",p},p},30]]>0.3,True,False];sensitivityPlots=Quiet@TableSystemModelPlotsimSens,{{"IRS1p.c",p,0.5}},{0,30},

,{p,parNames}

Out[13]=





Note that there are four rate constants for which the rate constant has little to no effect, while the other four have a significant impact. In the cases where the green curve is higher than the orange, increasing the value of the corresponding rate constant increases the concentration.

Run a Monte Carlo simulation to find out how parameter uncertainties affect the result:

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Contributed by: Jan Brugård

Phosphorylation of Insulin Receptors

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