# π Zamponi 2018

Mitochondrial network complexity emerges from fission/fusion dynamics

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Mitochondrial networks exhibit a variety of complex behaviors, including coordinated cell-wide oscillations of energy states as well as a phase transition (depolarization) in response to oxidative stress.

## Introduction

A typical mitochondrion comprises a network of tube-like structures, with fragments of all sizes (ranging from less than 1βΞΌm to 15βΞΌm or more). A quantitative description of such complexity is still lacking.

In this work, we present a quantitative description of mitochondrial network structure using tools of network and percolation theory. To do that, we developed a pipeline to extract structural parameters from confocal images.

## Results

**Fig1** Network structure from mitochondrial images.

- (a) Confocal image of a MEF in which mitochondria are shown in green and the actin cytoskeleton in magenta. Image processing:
- (b) Grayscale images were converted to binary images by choosing the indicated threshold.
- (c) Detected lines in binary images were reduced to a single pixel width (skeleton). The mean degree β©kβͺ of each skeleton was computed by analysing the nearest neighbors of each pixel occupied.
- (d) Cluster mass distributions p(s) were computed by counting the number of pixels that made up each segment within clusters. Red curves represent power laws with exponents β1 (dashed) and β2 (continuous). Scale bars represent 10βΞΌm.

The long-tail behaviour displayed by p(s) was in accordance with recent work suggesting that mitochondrial networks operate near a percolation phase transition. Long-tail distributions in Fig. 1(d) indicated that mitochondrial networks exhibited scale free properties, such as the coexistence of numerous small fragments with few massive clusters.

**Fig2** Typical examples of mitochondrial network images obtained under different conditions.
Confocal images of MEFs transfected with mYFP under control conditions (ctl), paraquat treatment (pqt) or mitofusin 1 over-expression (mfn). Pixel intensity is depicted using a pseudocolor (calibration bar). Insets highlight the effect asserted by each treatment on mitochondrial structure. Scale bars represent 10βΞΌm.

### Quantification of mitochondrial network properties

The application of different intensity thresholds (th) resulted in different skeletons and hence different network architectures. We reasoned that a way to avoid this arbitrariness would be to compare the behavior of network parameters as a function of the threshold.

### Fission/fusion balance is linked to mitochondrial network complexity

We investigated the scaling properties of mitochondrial networks by performing a finite size scaling analysis.

Given the functional relevance of the spatial distribution of mitochondria36β39, we decided to quantify the **fractal dimension** Df of the networks.

Alterations in the fission/fusion balance tended to reduce network complexity, as shown by normalized Kolmogorov complexity.

Shannonβs entropy of cluster masses (Hj)

### Are mitochondrial networks poised at criticality

This view propose that a steady-state mitochondrial network requires a proper balance of the two opposing tendencies, one towards fusing segments and one favoring fragmentation.

## Discussion

- Mitochondria organize as complex networks that display temporal and spatial coordination, pressumably by operating close to the edge of dynamic instability.
- A straightforward approach to quantify structural properties of mitochondrial networks.
- Promoting fission or fusion lowered the fractal dimension of the networks, reducing the space-filling capacity of mitochondria, lowering the Kolmogorov complexity.
- Balanced fission/fusion dynamics lead to a network capable of a phase transition : three different regimes, subcritical (pqt), critical (ctl) and supercritical (mfn),
- Under normal physiological conditions, mitochondrial networks are poissed near a percolation transition point

## Materials and Methods

- Mouse embryonic fibroblast (MEF) expressing a mitochondria-targeted yellow fluorescent protein (mYFP)
- Microscopy -> binarize -> skeletons of mitochondrial network -> cluster mass (s) and degree (k)
- Perturbed the structure of mitochondrial networks either by increasing mitochondrial fission using paraquat (pqt)12β15, or by promoting mitochondrial fusion by mitofusin 1 (mfn) over-expression.

Zamponi N, Zamponi E, Cannas SA, Billoni OV, Helguera PR, Chialvo DR. Mitochondrial network complexity emerges from fission/fusion dynamics. Sci Rep. 2018 Jan 10;8(1):363.PMC5762699 ↩︎