Abstract

In this model, we simulate the insulin secretion behavior of pancreatic β cells, trying to realize the similar curve in a single β cell, as that of glucose-insulin secretion which has been shown in literature, according to the reported insulin secretion mechanisms.

In general, we divide the process from glucose sensation to insulin secretion into three sessions. The first session covers the metabolic process from glucose intake to production of ATP. The second session covers the behavior of ion channels after the change in [ATP]/[ADP] ratio. The last session depicts the insulin secretion activated by cellular [Ca²⁺] rise.

This single-cell model is key to the overall insulin secretion curve due to the synchronization of the cells in the same pancreas islet.

Introduction

In physiology, the secretion of insulin is tightly regulated. After food intake and rising of blood glucose concentration, insulin is quickly secreted to down tune the blood glucose. Lack of insulin as well as its overproduction causes harm to human bodies. Thus it is really a need to determine the physiological parameters during insulin secretion. Of the first priority is the [glucose]-insulin secretion curve.

Task Analysis

Our model is in fact a time-amount model addressing the total insulin secretion amount with time under given glucose concentration.

The secretion of insulin is considered as the result of a series of regulation, which includes acceleration of metabolism, opening of ATP-sensitive K⁺ channel, depolarization of membrane, influx of Ca²⁺, etc. While this is not the whole picture, there is another pathway leading to the secretion of insulin, as is shown in the graph above, but due to its complexity and lack of studies, we focus on the major and clearer part of the pathway.

There are two phases of insulin secretion. First of them comes from the drastic reaction to glucose of β cells in all islets, and the second comes from the difference of secretion paces of different islets.

The main events are shown in the following chart:

[Glc] rising → [ATP]/[ADP] change → K_ATP Ch closure

→ Ca²⁺ Ch opening → [Ca²⁺]_c rising → insulin secretion

As the insulin secretion-[Ca²⁺] is quite expectable, we focus mainly on the [Ca²⁺]-time curve.

Modeling

We make the following assumptions:

1. The reactions in metabolic process obey the M-M equations;
2. There is a time interval between [ATP[/[ADP] ratio reaches the threshold and closure of K+ ch;
3. The infux of Ca2+ is only subject to the chemical and electrical gradient, and cellular retrieval of Ca2+ is constant.

Stage I

Stage II

Results and Analysis

Our program gives the following [Ca2+]-t graph:

Fig. 2 simulated [Ca2+]-t curve (x-axis in unit of 0.01min)

Physiological curve as follows:

Fig. 3 physiological insulin secretion curve

Reference

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