Beta Cell Model, Grespan-Mari, 2017

This repository contains the code implementing Grespan-Mari's model of the beta cell described in the paper...

Grespan E, Giorgino T, Arslanian S, Natali A, Ferrannini E, Mari A. Defective Amplifying Pathway of β-Cell Secretory Response to Glucose in Type 2 Diabetes: Integrated Modeling of In Vitro and In Vivo Evidence. Diabetes. 2018 Mar 1;67(3):496–506.

The model is coded in Matlab and Simulink (both are required). The Matlab script betacell_model_sim.m reproduces the main figures of the article. The script produces the html file betacell_model_sim.html (preview) with the Matlab Publish function.

This readme file shortly describes the Matlab functions and the Simulink model files and summarizes the data used in the simulations.

The script has been tested with Matlab 2010b.

Matlab functions

Matlab file	Description
fCa.m	Implements fk of the article
fCaGlu.m	Implements fr of the article
glu2ca.m	Implements Cs(G) of the article
casim.m	Calculates C(t) when it is not experimentally available
secsim.m	Calculates S(t), Q(t) and r(t) in the article
betasim.m	Core wrapper for the main Simulink model betavars.mdl
loadpar.m	Loads the model parameter for a specific experiment
setAxes.m	Auxiliary function to format figure axes
saveas_ifsvg.m	Auxiliary function to save plots is svg format

Simulink models

Simulink file	Description	Figure
betavars.mdl	Main glucose-calcium-insulin secretion model	1
capeakmod.mdl	Simulator of the dynamic component of the calcium model	2

Remarks:

• The functions fCa.m and fCaGlu.m complement the Simulink model betavars.mdl, representing f_k and f_r.

• The Simulink model betavars.mdl provides insulin secretion, the IRP and refilling (S(t), Q(t) and r(t) in the article).

• The full calcium model is implemented in casim.m, where the static component C_s(G) (function glu2ca.m) is used.

Dataset and parameters

The data (glucose concentration, calcium concentration and insulin secretion) are stored in mat files named as shown in the tables below. The data file also stores the model parameters (as a vector p) appropriate for the data.

In vitro tests

Data file	Description	Reference
Henquin_2002.mat	Glucose and calcium decoupling	1
Henquin_2006.mat	Hyperglycemic clamp	2
Jonkers_2001.mat	Stepped hyperglycemic clamp	3

References:

1. J-C Henquin et al., Diabetes, 2002.
2. J-C Henquin et al., Diabetes, 2006.
3. J.C. Jonkers et al., Diabetes, 2001.

In vivo tests

Data file	Description	Reference
Toschi_2002.mat	Stepped hyperglycemic clamp	1
Mari_1998.mat	IVGTT	2
Muscelli_2006.mat	OGTT-like test	3,4
Seghieri_2016.mat	Glucose ramp	5
Mychaliszin_2014.mat	Hyperglycemic clamp	6

Remark: The data file name has the suffix _NGT for the subjects with normal glucose tolerance and _T2D for type 2 diabetic subjects.

References:

1. Toschi et al., 2002
2. Mari A., Diabetologia, 1998
3. Muscelli E. et al, Am. J. Physiol. Endocrinol. Metab., 2006
4. Muscelli E. et al, Diabetes, 2008
5. Seghieri et al., Am. J. Physiol. Endocrinol. Metab., 2016
6. Mychaliszin et al., Diabetes, 2014