*2.2. Mitochondrial Dysfunction and Pathophysiological Hormone Secretion*

The separate modeling of aerobic and anaerobic pathways producing ATP in alpha and beta cells allows studying the effect of mitochondrial dysfunction on glucagon and insulin secretion. In cells with dysfunctional mitochondria, the net rate of aerobic ATP production is reduced, causing an insufficient lowering of KATP-channel conductance. As a result, the calcium influx through VDCC during hyperglycemia is inadequately increased in the beta cell and decreased in the alpha cell [29–31]. Dysregulation of ATP concentration due to the mitochondrial dysfunction severely impacts hormone granule exocytosis [34,35]. The qualitative effects of the impaired mitochondrial bioenergetics are schematically presented in Figure 2. In the alpha cell, the glucagon secretion typically peaks at low glucose concentrations. However, due to impaired mitochondrial function, the peak is shifted towards higher glucose concentrations. Conversely, in beta cells, the insulin secretion rates monotonically increase with increasing glucose concentrations and the anomalous mitochondrial functioning causes

the reduction of insulin secretion across the whole glucose concentration interval. The mechanisms behind the dysregulated hormone secretion in both cell types are modeled as described in more detail in the continuation.

The intracellular ATP concentration is in the steady-state approximation governed by the ATP production and ATP hydrolysis rates. The reduced net flux of ATP from mitochondria is modeled by multiplying the mitochondrial ATP flux *J*ATP,aerobic, as described by Grubelnik et al. [27], by an additional coefficient of mitochondrial dysfunction, *k*md:

$$f\_{\rm ATP} = f\_{\rm ATP, anaerobic} + (1 - k\_{\rm md}) f\_{\rm ATP, aerobic} \tag{1}$$

where *k*md is defined as the degree of mitochondrial dysfunction. *k*md lies in the range between 0 and 1, where 0 represents a normal mitochondrial function, and 1 signifies a complete mitochondrial breakdown. According to the model by Grubelnik et al. [27], the rate of ATP hydrolysis, *J*ATPase, obeys the Michaelis–Menten kinetic, which is modeled by:

$$J\_{\rm ATP} = J\_{\rm max, ATP} \frac{[\rm ATP]}{K\_{\rm m, ATP} + [\rm ATP]} (1 - k\_{\rm ATP, r} k\_{\rm md}) \tag{2}$$

where [ATP] is the ATP concentration, *J*max,ATPase is the maximal reaction rate (132 µM/s for the alpha cell, and 178 µM/s for the beta cell), *K*m,ATPase is the Michaelis-Menten constant (*K*m,ATPase = 2000 µM), and *k*ATPase,r is a scaling constant for the mitochondrial-dysfunction-dependent decrease in ATP hydrolysis. The *k*ATPase,r takes on a value of 0.6. Considering Equations (1) and (2), the ATP concentration is in the steady state given by:

$$\text{[ATP]} = \frac{K\_{\text{m,ATPase}}f\_{\text{ATP}}}{f\_{\text{max,ATPase}}(1 - k\_{\text{ATPase,r}}k\_{\text{md}}) - f\_{\text{ATP}}},\tag{3}$$

The model Equations (1)–(3) enable us to quantify the impact of mitochondrial dysfunction on glucagon and insulin secretion in pancreatic alpha and beta cells, respectively, as we describe in more detail in the next section.
