To complicate matters further, fission and fusion proteins may also be co-regulated at the transcriptional level [ 52 ], and may interact with each other to modulate their activity [ 53 ]. Understanding the interdependence between the geometrical features of mitochondrial networks will require a combination of quantitative experimentation and computational modeling. From the computational side, models of mitochondrial network organization can be generated based on any given set of assumptions.
Models need to be based on experimentally perturbable parameters with output properties that can be experimentally measured. Several studies have begun carefully documenting the types of fission and fusion events and the biophysical requirements for them to occur [ 50 , 51 ]. These studies are a crucial first step and provide the first extensive quantitative data for incorporation into any computational models of mitochondrial dynamics. Their main limitation is that they focus on specific sub-regions of the mitochondrial network and thus do not encompass the entire network and the way the distribution of fission and fusion impact its organization on the scale of the entire cell.
To do so, new methods will be needed that can automatically track all fission and fusion events within a network to provide data on the frequency of remodeling events and their location within the network. Simultaneous measurements of the other network morphology features size, position, topology will then permit an analysis of how fission and fusion affect each other and how they are affected by the geometry of the network itself. Several computational models of mitochondrial networks have been generated.
These models currently only take into account the fission and fusion dynamics themselves, not the physical size, shape and distribution of the mitochondria within the cell.
Recently, a new model has been built that for the first time incorporates the fact that mitochondria move in space, can form networks, and undergo continuous biogenesis that is not necessarily coupled to mitochondrial turnover [ 56 ].
This model makes testable predictions about where in parameter space real mitochondrial networks should fall to maintain mitochondrial function most successfully. On the other hand, models can be built to determine the underlying requirements for generating the organization of mitochondrial networks without considerations of their functional impact.
An example is a recent graph-based model that was built based on a set of simple rules of network connectivity [ 23 ]. This model predicts several topological properties that mitochondrial networks should display, and thus can now be tested with directed experiments measuring network topology.
A key limitation of this model is that it is purely topological and does not take any spatial information into account. The next generation of computational models will depend on more extensive quantitative experimental measurements of the interdependent geometric features of mitochondrial network morphology and, eventually, simultaneous mitochondrial functional state. Bereiter-Hahn J: Behavior of mitochondria in the living cell.
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Cite Icon Cite. Email alerts Article activity alert. Accepted manuscripts alert. Table of contents alert. Latest published articles alert. View Metrics. Cited by Crossref. Social media. The Node preLights FocalPlane. Grants Journal Meetings Workshops. A proton gradient establishes itself along the mitochondrial cable and protons diffuse thereby transmitting chemical potential. This is the main idea of mitochondrial power cabling; a replacement of diffusion of ATP or oxygen through the cytoplasm by proton movement along mitochondrial filaments, which may result in an increased speed of energy transmission.
The causal relationship between higher ATP levels and mitochondrial fusion is still 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 that this rate increased during OXPHOS stimulation as the result of increased OPA1 cleavage by Yme1l 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 S2.
Calcium is known to stimulate certain enzymes of the TCA cycle — , which in turn influences the rate of ATP production. ER calcium channels are thought to take up calcium efficiently , The calcium concentration in these mitochondria rises significantly during ER depletion or calcium entry into the cell.
Fusion therefore increases the amount of mitochondrial volume affected by a calcium signal, which subsequently increases total energy production. Fusion may increase controllability of TCA cycle activity and total energy production.
The bottom figure indicates the position of the mitochondria on the sigmoid relating calcium concentration to enzymatic activity. When even more mitochondria fuse, total enzyme stimulation will drop again because the mitochondria moved too far down the sigmoid.
This plot is a schematic illustration of principle, details are given in section S1. The idea that fusion increases the number of mitochondria that experiences a given calcium signal in the cell has been suggested before in Ref.
This hypothesis is based on several assumptions that are debated in the literature. While several studies show that higher calcium concentrations lead to increases in NADH production and oxygen consumption 68 , , , mathematical modelling 56 and uniporter studies suggest that calcium perturbations may have little effect on respiration. Other studies have observed that calcium only has an effect on NAD P H concentrations in glucose-stimulated conditions , or that only a single TCA enzyme is controlled by calcium The mechanisms of calcium uptake that are mainly used, the dependence of these mechanisms on calcium concentrations, and the number of sites close to sources of calcium are also debated , for details, see section S1.
Mitochondria have been observed to experience calcium transients, meaning that they extrude calcium quite rapidly after having absorbed it 53 and the simple model we discuss in section S1. Finally, calcium signalling linked to mitochondrial ultrastructure is by no means the only, or simplest, way in which the cell regulates its energy status.
By changing their morphological state, mitochondria can make themselves less susceptible to perturbations for example, fluctuations in electrochemical membrane potential. The fused neighbours of a mitochondrial element can act as a buffer for biochemical or physical fluctuations. If failure of individual mitochondria has severe consequences for the cell, this increased robustness through fusion will be beneficial when mitochondria are subject to perturbations. There are some experimental indications that fused mitochondria are better protected against stress This hypothesis could account for why hyperfusion occurs during stress 10 , and may also be an explanation as to why fusion protects the cell against apoptosis 10 , 13 — 16 or at least delays apoptosis , because prior to cytochrome c release which induces apoptosis remodelling of the cristae structure has been seen as a cause of changes in membrane potential If a larger network protects against fluctuations in membrane potential, it may be able to prevent cristae remodelling, thereby potentially delaying or preventing apoptosis.
In stressful conditions, it may thus be disadvantageous for the cell to have its mitochondria fragmented because all of them are vulnerable to membrane potential fluctuations. If the cell fuses its mitochondria, they become more robust to the fluctuations, which may prevent the failure of many individual mitochondria, and subsequent cell death.
A biophysical calculation considering the change in membrane potential upon changes in permeability of the inner mitochondrial membrane see section S1. Fusing mitochondria thus protects them from perturbations, as illustrated in Fig.
This model assumes spherical mitochondrial geometry. Small fragmented mitochondria are often seen to have a spherical shape and the fusion of two small spherical mitochondria may produce a mitochondrion that itself has an approximate spherical shape. The model discussed here may therefore be applied to fusion events involving small mitochondrial fragments. We provide an alternative model that is independent of volume and surface area scaling and involves picturing mitochondria as individual agents coupled with spin-like interactions This model, in which a mitochondrion prefers to be in a similar state as its neighbours, shows that groups of mitochondria are less likely to undergo a catastrophic loss of function than individuals see section S1.
Even though fluctuations in larger mitochondria fused mitochondria may be of smaller relative magnitude, they will occur more frequently because of the larger surface area which increases the probability that, for example, a pore opens or an ETC component fails. Stress does not always lead to a fused mitochondrial state, but can also lead to mitochondrial fragmentation , It can be that the level of stress is important, and that too much stress leads to fragmentation and subsequent apoptosis.
The function of mitochondrial networks is currently unclear, suggesting that new research strategies may be of use. We have shown that ideas from physics and mathematics provide a framework to suggest and critically evaluate hypothesised functions. Which hypothesis is most likely to be true?
Three hypotheses that we find attractive are i increased robustness; ii blind surveillance; and iii increased ATP production through non-linear dependence of ATP flux on the properties of fusing mitochondria.
Hypothesis i suggests a reason why mitochondrial morphology is dependent on cellular stress, which seems to be the main regulator of mitochondrial morphology. Hypothesis ii also links fusion with oxidative stress, because in stress conditions improved quality control is beneficial.
Hypothesis iii provides intuitive mechanisms by which fusion may improve the energetic status of the cell, compatible with a large amount of evidence that mitochondrial structure is correlated with bioenergetic capabilities of the cell. We stress again the observation that with increased fusion, ATP concentration, rather than merely the rate of production and consumption of ATP, changes. This implies an acceleration of cellular processes and suggests that fusion serves as a cellular accelerator pedal.
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Abstract Mitochondria can change their shape from discrete isolated organelles to a large continuous reticulum. Keywords: hypotheses, mathematical biology, mitochondrial dynamics, mitochondrial networks, non-linearities, ultrastructure.
Introduction Mitochondria are highly dynamic organelles of central importance for ATP production in most eukaryotic cells. Open in a separate window. Figure 1. Hypothesised reasons for mitochondrial meso- and hyperfusion In this section, we list existing hypotheses regarding the function of mitochondrial meso- and hyperfusion. Table 1 An overview of hypotheses discussed in this paper including criticism. If no autophagy is present, one needs to create additional assumptions to obtain the same results Faster or more effective complementation 38 — 43 Matrix protein complementation through small fusion events is efficient 43 , cells with low fusion levels show no major dysfunctions 44 , and ongoing fission and fusion events can, according to one estimate, lead to better mixing after 2 hours than stress induced hyperfusion 41 Increases in ATP production caused by: i Changes in inner membrane shape discussed in section S2.
Fluctuations in larger mitochondria will occur more frequently because of the larger surface area Enables energy transmission power cabling along mitochondria discussed in section S2.
Some mitochondria with harmful mtDNA mutations may not be able to fuse, and are likely to be degraded regardless of increased fusion rates. If mtDNA mutations are not harmful, increased fusion is not required per se to create new mutations No function discussed in section S2. Additionally, the main argument to support this hypothesis many proteins involved in mitochondrial dynamics are involved in other processes is also an argument for the importance of mitochondrial dynamics.
Table 2 Suggestions for future modelling and experiments for further analyses of the hypotheses. Hypothesis for forming mitochondrial networks Further modelling Experimental tests Increased selection bias in quality control The ordinary differential equation model we describe in section S1. More powerful models could be constructed by including these stochastic influences and relaxing some of the simplifying assumptions of our model One of the assumptions of our model is that only small mitochondrial fragments are degraded.
The existence of a threshold size above which a mitochondrial filament is not degraded by mitophagy can be measured. Alternatively, construct two populations of cells, one wild-type and one with increased fusion rates.
The autophagy rate parameter should be the same in both populations. A model that does not explicitly position nodes in space has been developed 58 , but it does not consider diffusion on the network. The model in Ref. Calculate the diffusion coefficient of proteins and the root mean squared distance travelled by these proteins while slowly changing fission or fusion rate Increased ATP production caused by non-linear response of ATP synthesis rate to membrane potential Numerous biophysical models of the respiratory chain in mitochondria have been developed e.
Whether this asymmetry is simply a reversion to a pre-existing asymmetry in potential before the preceding fusion event fusion events are usually followed quite soon by fission events 24 should be determined. Alternatively, take snapshots of cells and quantify the amount of mitochondrial mass that is fused by e.
Do this for many cells in order to search for a correlation between the amount of fused mitochondria and cellular [ATP]. Such correlations have been found before 8 — 11 but not without perturbing the cell.
We propose to take advantage of natural fluctuations in connectedness. Alternatively, observe passive fluctuations in network size of mitochondria in single cells, while reading out [ATP]. This result, however, is only true for specific conditions. To make physiologically relevant predictions, these models can be integrated into biophysical models of the TCA cycle and respiratory chain. Ordinary differential equation-based biophysical models linking calcium and mitochondrial physiology can also be probed to explore this relationship 56 Prepare two populations of cells, one wild-type and one with more fused mitochondria.
However, one must be careful to use models that define the flux of ions into the mitochondrion to be proportional to surface area. The model presented in Ref. Alternatively, increase the permeability of the mitochondrial inner membrane in cells with fused mitochondria, and cells with fragmented mitochondria.
Selective fusion creates the possibility of quality control without needing selective mitophagy Summary Mitochondrial quality control is the process that maintains a healthy mitochondrial population by identifying and degrading dysfunctional mitochondria 24 , 72 , degrading damaged mitochondrial components 73 and transporting damaged components out of the mitochondrion 74 , Coarse-grained quantitative model Mathematical models of mitochondrial quality control have been constructed previously 85 — 87 and show that fission, selective fusion and selective autophagy together increase mitochondrial functionality.
Small changes in fusion state can cause large changes in complementation rate Summary Large-scale fusion facilitates sharing of mitochondrial machinery, as this machinery moves through the mitochondrial network. Experimental support Functional complementation through fusion has been observed in numerous experimental studies 40 , 89 , 90 , indicating that fused mitochondria do exchange contents. Coarse-grained quantitative model We can study the diffusion of species along mitochondrial networks by simulations in which the network is represented by a 2D or 3D lattice.
Figure 2. Experimental support Several studies suggest that hyperfusion increases ATP levels and mitochondrial respiratory capacity 8 — Coarse-grained quantitative model We focus mathematically on hypothesis iv which we have not seen discussed elsewhere.
Figure 3. Figure 4. Experimental support The idea that fusion increases the number of mitochondria that experiences a given calcium signal in the cell has been suggested before in Ref. Fusion provokes state changes protective against perturbations Summary By changing their morphological state, mitochondria can make themselves less susceptible to perturbations for example, fluctuations in electrochemical membrane potential.
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