# Modeling the Effects of Calcium Overload on Mitochondrial Ultrastructual Remodeling
## 3 Results and Discussion
In addition, the cristae junctions were significantly wider, being about 17 nm when calcium phosphate granules were present in the matrix (Figure 3D). Based on this finding, we believe that this increase in the cristae junction width led to a redistribution of cytochrome c from the cristae lumen to the intermembrane space. A recent modeling study demonstrated that a small decrease in the cytochrome c concentration in the cristae lumen or an increase in the diffusion distance between complexes III and IV may result in a kinetic disadvantage and lower the maximum electron flux through the respiratory system [51]. Figure 2: Mitochondria with an abundant, interconnected cristae. (**A**) Representative portion of the tomogram from a mitochondrion in the absence of calcium. The sample was taken approximately five minutes after mitochondria were added to the respiration buffer. To remove all calcium from the system, 1 mM EGTA was added before the addition of the mitochondria. The image resolution is approximately 4 Å per pixel. The solid magenta lines highlight inner or outer membrane boundaries. Structures of interest, including the ATP synthase, crista, and crista junctions, are labeled. (**B**) The reconstructed model shows a complex cristae distribution, occupying nearly half of the total volume. The small, black, dot-like structures are ATP synthase molecules. (**C**) The 3D reconstructed model shows a densely packed, interconnected cristae network. Scale bar = 250 nm. This would lead to a decrease in the maximum oxygen consumption rates we observe in calcium-loaded mitochondria. We speculate that the cristae remodeling we saw in our vitrified, isolated mitochondria impaired mitochondrial function by limiting the ability of mitochondria to (1) establish and maintain a large proton electrochemical gradient and (2) impede metabolite diffusion and transport. Additionally, calcium uptake leads to a drop in the membrane potential and an increase in the matrix pH [8,14]. This limits the ability of mitochondria to generate a strong membrane potential and thus lower ATP synthesis rates [4]. In addition, the opening of the cristae junctions leads to a redistribution of cytochrome c from the cristae lumen to the inner membrane space. This further limits the ability of the proton pumps to maintain a local chemiosmotic gradient to support high rates of ATP production. Figure 3: Calcium-loaded mitochondria with granules alters cristae structure. (**A**) Representative portion of a tomogram from a mitochondrion with calcium phosphate granules exposed to a 50 uM bolus of calcium at an approximate resolution of 4 Å. The solid magenta lines highlight the inner or outer membrane boundaries. (**B**) 2D reconstructed model showing that calcium phosphate granules disrupted the cristae membrane surface area, consisting of most of the enzymes responsible for oxidative phosphorylation. (**C**) 3D reconstructed model showing a densely packed, interconnected cristae network. (**D**) Cristae junction widths in calcium-loaded mitochondria, which were significantly larger than the control widths. Approximately 10 cristae junctions from each type of mitochondrion were selected at random and measured. The bars are plotted as means of the data, with error bars representing the standard error of the mean. A * signifies a \(p\) value less than 0.01. Gray dots are individual data points. Scale bar = 250 nm. The mitochondrial morphology and the effects of calcium phosphate granules were simulated using the well-established CH model framework. The CH equation was first implemented in the situation of the absence of calcium. In Figure 4, four snapshots of the CH equation simulation are presented with a time step \(\Delta t=0.001\) for Equations (14) and (15) on a circle domain with a radius of four (relative to the unit circle). The parameter \(\gamma\) is one for the transition region length, which is indicated by the white, rim-like features in Figure 4. The red domain of Figure 4 is the fluid matrix, while the blue domain is the inner membrane.