Summary. Mitochondrial fusion may increase ATP production, through one or more of several possible mechanisms. We suggest the following mechanisms of particular interest: higher ATP production is caused by (i) fusion-induced changes in inner membrane shape; (ii) fusion-induced decreases in proton leak; (iii) fusion-induced decreases in mitochondrial degradation; (iv) a nonlinear response of ATP synthesis rate to membrane potential. (i)-(iii) are discussed in more detail in the appendix. We note that it is not entirely clear whether mitochondrial fusion is the cause of an observed increase in ATP production, or whether hyperfusion and high ATP production rates have a common cause, e.g. a recent study suggested that an increase in ATP production may precede mitochondrial fusion [236].
Experimental support. Several studies suggest that hyperfusion increases ATP levels and mitochondrial respiratory capacity [148, 149, 151, 157]. In nutrient-rich environments mito- chondria tend to be fragmented, whereas under starvation they are observed to form elongated networks [148, 158], which can be interpreted as an attempt to enhance energy production in challenging environments. Hyperfusion is also observed at the G1/S transition, before energet- ically costly DNA replication [151]. It is worth noting that in hyperfused states, concentrations of cellular ATP – not just the rate of ATP production – were measured to be higher [149]. These increased concentrations suggest a physiological role for fusion beyond that of meeting extra ATP demand. This role could be to act as a cellular ‘accelerator pedal’, because an increase in ATP/ADP ratio in the cell has the consequence that many reactions will go faster [237, 238]. Further support for specific hypotheses is described in Sections A.2.2.1 - A.2.2.3. Coarse-grained quantitative model. We focus mathematically on hypothesis (iv) which we have not seen discussed elsewhere. We first consider how the membrane potentials of two equally sized individual mitochondria ∆ψ1, ∆ψ2 are related to the overall membrane potential of their fused product, ∆ψ1+2. A simple model is that the fused product inherits the arithmetic average of the two individuals, i.e. ∆ψ1+2 = 12(∆ψ1 + ∆ψ2)‡. We will show that this simple averaging of potentials can lead to increases of total ATP synthesis rates due to a sigmoidal dependence of ATP synthesis rate (rAT P) on ∆ψ [239, 240] (Figure 2.4). We note that care must be taken in interpreting measured sigmoidal relations between ∆ψ and ATP synthesis rate [239]. The saturating behaviour observed at high ∆ψ may be an experimental artefact caused by the saturating relation between the ratio of ion concentrations at either side of the
‡Calculations based on considering charged capacitors show that it is possible that ∆ψ1+2> 1
2(∆ψ1+ ∆ψ2) (Section A.1.3), though this capacitor model does not necessarily capture the behaviour of mitochondria fusing in chains. A simple averaging is the most natural null model to consider.
inner mitochondrial membrane and ∆ψ itself, as predicted by the Nernst equation. In the analysis below we assume the saturating relation depicted in Figure 2.4 exists and investigate the consequences of this relation.
Fusion causes net decrease in rATP
Fusion causes net increase in rATP ATP synthesis rate
A
B
D
C
Figure 2.4: The effect of fusion on rate of ATP synthesis depends on the magnitude of the potentials of the pre-fusing mitochondria. In this figure, ri denotes the ATP synthesis rate (rAT P) per unit of mitochondrial size for mitochondrion i and ri+j denotes the rate per unit size for the fused product of mitochondria i and j (a definition of mitochondrial size is provided in the next chapter). For simplicity we assume all pre-fusion mitochon- dria to have unit size; our results still hold when this assumption is relaxed. Because of the nonlinear dependence of rAT P on ∆ψ, if two mitochondria in the exponential regime fuse (i.e. mitochondria A and B), then averaging their potentials upon fusion causes the net ATP synthesis rate to decrease. This is because 2rA+B < rA + rB (the fused mitochondrion is twice as large as the pre-fused mitochondria and the net post-fusion synthesis rate is therefore 2rA+B). In the plateau region, rAT P does not depend on ∆ψ so there will most likely be no ∆ψ-induced change in rAT P if two mitochondria in this regime fuse (e.g. mitochondria C and D). Fusion of mitochondria in the saturating region (e.g. mitochondria B and C), induces net rAT P increases because 2rB+C > rB+ rC.
To explain this, consider Figure 2.4. As illustrated, fusion of mitochondria (B) and (C), while averaging their potentials, results in a net increase in ATP production rate. This is because the segment of the sigmoid connecting these two mitochondria is saturating§. Fusion of mito- chondria (A) and (B), however, decreases net ATP production rates due to the strictly convex curve connecting them. Because fusion only occurs at sufficiently high membrane potential [59, 174, 175], we may expect events involving A-type mitochondria to be less common. Fusion then more often increases than decreases rAT P, leading to an overall increase in cellular ATP production rates.
§A function f (x) whose slope decreases with increasing x satisfies f (1
2(x1+ x2)) > 1
2(f (x1) + f (x2)) where x1, x2are any two points on the function. Similarly a decreasing slope with increasing x leads to f (12(x1+x2)) <
In the above, we assumed equally sized pre-fusion mitochondria and considered an averaging of potentials. This is equivalent to assuming a size-weighted averaging of potentials when fusion occurs between differently-sized mitochondria; the same argument as outlined above still hold. In the next chapter, we find some evidence for size-weighted averaging upon mitochondrial fusion/fission dynamics.
Limitations/Critique. The causal relationship between higher ATP levels and mitochondrial fusion is incompletely understood, and it may be possible that fusion is the effect of high [ATP] instead of the cause. A recent study showed that the rate of inner membrane fusion was closely correlated with oxygen consumption, and increased during OXPHOS stimulation as the result of increased Opa1 cleavage by Yme1l [236]. Also, in the model discussed above we have considered the role of ∆ψ in ATP synthesis rate, whereas actually the proton motive force (defined as ∆p = |∆ψ| + 2.3RT
F ∆pH) drives ATP production [239, 240]. The region of the ATP synthesis sigmoid at which mitochondria lie is not yet experimentally clear. Further critique of specific hypotheses is described in Sections A.2.2.1 - A.2.2.3.