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Short description:

Chen-Wang-Sherman’s model of Insulin Secretion by Kinetic Modeling of Granule Exocytosis

Format:	PharmML (0.6.1)
Related Publication:	Identifying the targets of the amplifying pathway for insulin secretion in pancreatic beta-cells by kinetic modeling of granule exocytosis. Chen YD, Wang S, Sherman A Biophysical journal, 9/2008, Volume 95, Issue 5, pages: 2226-2241 Affiliation: Laboratory of Biological Modeling, National Institute of Diabetes, Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-5621, USA. Abstract: A kinetic model for insulin secretion in pancreatic beta-cells is adapted from a model for fast exocytosis in chromaffin cells. The fusion of primed granules with the plasma membrane is assumed to occur only in the "microdomain" near voltage-sensitive L-type Ca(2+)-channels, where [Ca(2+)] can reach micromolar levels. In contrast, resupply and priming of granules are assumed to depend on the cytosolic [Ca(2+)]. Adding a two-compartment model to handle the temporal distribution of Ca(2+) between the microdomain and the cytosol, we obtain a unified model that can generate both the fast granule fusion and the slow insulin secretion found experimentally in response to a step of membrane potential. The model can simulate the potentiation induced in islets by preincubation with glucose and the reduction in second-phase insulin secretion induced by blocking R-type Ca(2+)-channels (Ca(V)2.3). The model indicates that increased second-phase insulin secretion induced by the amplifying signal is controlled by the "resupply" step of the exocytosis cascade. In contrast, enhancement of priming is a good candidate for amplification of first-phase secretion by glucose, cyclic adenosine 3':5'-cyclic monophosphate, and protein kinase C. Finally, insulin secretion is enhanced when the amplifying signal oscillates in phase with the triggering Ca(2+)-signal.
Contributors:	Roberto Bizzotto

Context of model development:	Mechanistic Understanding;
Discrepancy between implemented model and original publication:	This model implementation is a refactoring of the original XPP implementation provided as supplementary material (found in http://mrb.niddk.nih.gov/sherman/gallery/beta/Vesicle/henquin-pools.ode). Differences between this implementation and the XPP code related to the power of the DDMoRe languages are explained in the MDL file, at its top.;
Long technical model description:	chen.txt;
Model compliance with original publication:	No;
Model implementation requiring submitter’s additional knowledge:	No;
Modelling context description:	Chen et al. assumed that a single beta-cell would secrete insulin with the same biphasic kinetics as an islet, although insulin measuring assays were not sensitive enough to confirm this experimentally. The biphasic secretion pattern is also seen in vivo, and it has been suggested that diabetes is correlated with the loss of the first phase. Thus, understanding how a stimulated beta-cell secretes insulin at the molecular level was not only of academic interest but also potentially useful for understanding the disease process and guiding target selection for diabetes drug development.;
Modelling task in scope:	simulation;
Nature of research:	In vitro;
Therapeutic/disease area:	Endocrinology;

Validation Status:	Annotations are correct.
Certification Comment:	This model is not certified.

Mandatory file
- chen.xml

Additional Files

Model owner: Roberto Bizzotto
Submitted: Dec 11, 2015 7:49:33 PM
Last Modified: May 18, 2016 3:18:44 PM

Revisions

Version: 15
- Submitted on: May 18, 2016 3:18:44 PM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.
Version: 11
- Submitted on: May 18, 2016 3:04:49 PM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.
Version: 9
- Submitted on: May 18, 2016 2:54:05 PM
- Submitted by: Roberto Bizzotto
- With comment: Updated model annotations.
Version: 6
- Submitted on: Dec 11, 2015 7:49:33 PM
- Submitted by: Roberto Bizzotto
- With comment: Edited model metadata online.

Independent variable T

Structural Model sm

Variable definitions

tcycle = (ton + toff)

GlucFact = {\begin{matrix} 0 & if & (GLU = 0) \\ 1.2 & if & (GLU = 3) \\ 3 & if & (GLU \geq 10) \end{matrix}

modulus = (T - (tcycle \times floor (\frac{T}{tcycle})))

heav1 = \frac{(abs (modulus) + modulus)}{((2 \times abs (modulus)) + 1.0E-4)}

heav2 = \frac{((abs ((modulus - toff)) + modulus) - toff)}{((2 \times abs ((modulus - toff))) + 1.0E-4)}

V = (Vrest + ((Vburst - Vrest) \times (heav1 - heav2)))

minf = \frac{1}{(1 + exp (\frac{(Vm - V)}{sm}))}

IL = ((gL \times minf) \times (V - Vca))

IR = (0.25 \times IL)

JL = \frac{(alpha \times IL)}{vmd}

JR = \frac{(alpha \times IR)}{vcell}

Jserca = \frac{(Jsercamax \times {Ci}^{2})}{({Kserca}^{2} + {Ci}^{2})}

Jpmca = \frac{(Jpmcamax \times Ci)}{(Kpmca + Ci)}

Jncx = (Jncx0 \times (Ci - 0.25))

L = (((Jserca + Jpmca) + Jncx) + Jleak)

r2 = \frac{(r20 \times Ci)}{(Ci + Kp2)}

r3 = \frac{((GlucFact \times r30) \times Ci)}{(Ci + Kp)}

\frac{dCmd}{dT} = (ts \times ((- fmd \times JL) - ((fmd \times B) \times (Cmd - Ci))))

\frac{dCi}{dT} = (ts \times (((- fi \times JR) + (((fv \times fi) \times B) \times (Cmd - Ci))) - (fi \times L)))

\frac{dN1}{dT} = (ts \times (((- (((3 \times k1) \times Cmd) + rm1) \times N1) + (km1 \times N2)) + (r1 \times N5)))

\frac{dN2}{dT} = (ts \times (((((3 \times k1) \times Cmd) \times N1) - ((((2 \times k1) \times Cmd) + km1) \times N2)) + ((2 \times km1) \times N3)))

\frac{dN3}{dT} = (ts \times (((((2 \times k1) \times Cmd) \times N2) - (((2 \times km1) + (k1 \times Cmd)) \times N3)) + ((3 \times km1) \times N4)))

\frac{dN4}{dT} = (ts \times (((k1 \times Cmd) \times N3) - (((3 \times km1) + u1) \times N4)))

\frac{dN5}{dT} = (ts \times (((rm1 \times N1) - ((r1 + rm2) \times N5)) + (r2 \times N6)))

\frac{dN6}{dT} = (ts \times ((r3 + (rm2 \times N5)) - ((rm3 + r2) \times N6)))

\frac{dNF}{dT} = (ts \times ((u1 \times N4) - (u2 \times NF)))

\frac{dNR}{dT} = (ts \times ((u2 \times NF) - (u3 \times NR)))

\frac{dSE}{dT} = (ts \times (u3 \times NR))

ISR = ((9 \times ts) \times (u3 \times NR))

Initial conditions

Cmd = 0.0674

Ci = 0.06274

N1 = 14.71376

N2 = 0.612519

N3 = 0.0084499

N4 = 5.098857E-6

N5 = 24.539936

N6 = 218.017777

NF = 0.003399

NR = 0.50988575

SE = 0

Covariate Model

Continuous covariate toff

Continuous covariate ton

Continuous covariate GLU

Parameter Model

Parameters

B

;

gL

;

k1

;

km1

;

r1

;

rm1

;

r20

;

rm2

;

r30

;

rm3

;

u1

;

u2

;

u3

;

Kp

;

Kp2

;

Vrest = - 70

Vburst = - 20

fmd = 0.01

fi = 0.01

fv = 0.00365

alpha = 5.18E-15

vmd = 4.2E-15

vcell = 1.15E-12

Vm = - 20

Vca = 25

sm = 5

Jsercamax = 41

Kserca = 0.27

Jpmcamax = 21

Kpmca = 0.5

Jleak = - 0.94

Jncx0 = 18.67

tau = 2

ts = 60

Observation Model

Observation Y1
Continuous / Residual Data

Parameters

$Y1 = ISR$

Observation Y2
Continuous / Residual Data

Parameters

$Y2 = Cmd$

Observation Y3
Continuous / Residual Data

Parameters

$Y3 = Ci$

Simulation Steps

Simulation step s1

Variable assignments

$B = 200.0$

$gL = 250.0$

$k1 = 20.0$

$km1 = 100.0$

$r1 = 0.6$

$rm1 = 1.0$

$r20 = 0.006$

$rm2 = 0.001$

$r30a = 1.205$

$rm3 = 1.0E-4$

$u1 = 2000.0$

$u2 = 3.0$

$u3 = 0.02$

$Kp = 2.3$

$Kp2 = 2.3$

DDMODEL00000108: Chen’s exocytosis model

Revisions

Structural Model sm

Covariate Model

Parameter Model

Observation Model

Observation Y1
Continuous / Residual Data

Observation Y2
Continuous / Residual Data

Observation Y3
Continuous / Residual Data

Simulation Steps

Simulation step s1

Variable assignments

Step Dependencies

DDMODEL00000108: Chen’s exocytosis model

Revisions

Structural Model sm

Covariate Model

Parameter Model

Observation Model

Observation Y1Continuous / Residual Data

Observation Y2Continuous / Residual Data

Observation Y3Continuous / Residual Data

Simulation Steps

Simulation step s1

Variable assignments

Step Dependencies

Observation Y1
Continuous / Residual Data

Observation Y2
Continuous / Residual Data

Observation Y3
Continuous / Residual Data