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RESEARCH ARTICLE
Mitochondrial fragmentation and network
architecture in degenerative diseases
Syed I. Shah, Johanna G. Paine, Carlos Perez, Ghanim UllahID*
Department of Physics, University of South Florida, Tampa, FL, United States of America
Abstract
Fragmentation of mitochondrial network has been implicated in many neurodegenerative,
renal, and metabolic diseases. However, a quantitative measure of the microscopic parame-
ters resulting in the impaired balance between fission and fusion of mitochondria and conse-
quently the fragmented networks in a wide range of pathological conditions does not exist.
Here we present a comprehensive analysis of mitochondrial networks in cells with Alzhei-
mer’s disease (AD), Huntington’s disease (HD), amyotrophic lateral sclerosis (ALS), Parkin-
son’s disease (PD), optic neuropathy (OPA), diabetes/cancer, acute kidney injury, Ca 2+
overload, and Down Syndrome (DS) pathologies that indicates significant network fragmen-
tation in all these conditions. Furthermore, we found key differences in the way the micro-
scopic rates of fission and fusion are affected in different conditions. The observed
fragmentation in cells with AD, HD, DS, kidney injury, Ca 2+
overload, and diabetes/cancer
pathologies results from the imbalance between the fission and fusion through lateral inter-
actions, whereas that in OPA, PD, and ALS results from impaired balance between fission
and fusion arising from longitudinal interactions of mitochondria. Such microscopic differ-
ence leads to major disparities in the fine structure and topology of the network that could
have significant implications for the way fragmentation affects various cell functions in differ-
ent diseases.
Introduction
Mitochondrion is a ubiquitous organelle and powerhouse of the cell that exists in living cells as
a large tubular assembly, extending throughout the cytoplasm and in close apposition with
other key organelles such as nucleus, the endoplasmic reticulum, the Golgi network, and the
cytoskeleton [1–5]. Its highly flexible and dynamic network architecture ranging from a few
hundred nanometers to tens of micrometers with the ability to rapidly change from fully con-
nected to fragmented structures makes it suitable for diverse cytosolic conditions and cell
functions [6–8]. Cells continuously adjust the rate of mitochondrial fission and fusion in
response to changing energy and metabolic demands to facilitate the shapes and distribution
of mitochondria throughout the cell [9–11]. Similarly, stressors such as reactive oxygen species
(ROS) and Ca 2+
dysregulation interfere with various aspects of mitochondrial dynamics [12–
14]. This is probably why many neuronal, metabolic, and renal diseases have been linked to
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OPEN ACCESS
Citation: Shah SI, Paine JG, Perez C, Ullah G
(2019) Mitochondrial fragmentation and network
architecture in degenerative diseases. PLoS ONE
14(9): e0223014. https://doi.org/10.1371/journal.
pone.0223014
Editor: Hemachandra Reddy, Texas Technical
University Health Sciences Center, UNITED
STATES
Received: April 18, 2019
Accepted: September 11, 2019
Published: September 26, 2019
Copyright: © 2019 Shah et al. This is an open access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: All relevant data are
within the manuscript and its Supporting
Information files.
Funding: This works was supported by National
Institute of Health through grant R01 AG053988
(to GU). URL of funder website: https://www.nih.
gov. The funders had no role in study design, data
collection and analysis, decision to publish, or
preparation of the manuscript.
Competing interests: The authors have declared
that no competing interests exist.
primary or secondary changes in mitochondrial dynamics [9, 15–37]. Neuronal cells, due to
their complex morphology and extreme energy dependent activities such as synaptic transmis-
sion, vesicle recycling, axonal transport, and ion channels and pumps activity, are particularly
sensitive to changes in the topology of mitochondrial network [38–41].
The mitochondrial network organization makes a bidirectional relationship with the cell’s
bioenergetics and metabolic variables [11, 42]. For example, the morphological state of mito-
chondria has been linked to their energy production capacity [43–46], as well as cell health and
death [10, 46–49] on one hand, alterations in mitochondrial energy production caused by
genetic defects in respiratory chain complexes lead to fragmentation of mitochondrial network
[50, 51] on the other hand. Similarly, while ROS induces fragmentation of mitochondrial net-
work [12–14], overproduction of ROS in hyperglycemic conditions requires dynamic changes
in mitochondrial morphology and fragmentation of the network [52]. Furthermore, high cyto-
solic Ca 2+
induces mitochondrial fragmentation [14], whereas fragmentation blocks the propa-
gation of toxic intracellular Ca 2+
signals [53, 54] and can limit the local Ca 2+
uptake capacity of
mitochondria due to their smaller sizes. Thus dynamic changes in mitochondrial morphology
and fragmentation of its network can be part of the cycle that drives the progression of degen-
erative diseases [11–13, 18, 22, 52, 55–70].
Despite a clear association with many cell functions in physiological conditions, quantita-
tive measures of the microscopic fission and fusion rates leading to a given topology of the
mitochondrial network remain elusive. While fluorescence imagining has been instrumental
in providing biologically useful insights into the structure and function of mitochondria,
detailed description of the kinetics and the dynamical evolution of the complex mitochondrial
networks in health and disease are still out of reach of these techniques. Although it is difficult
to study such dynamics experimentally, computational techniques provide a viable alternative.
Various computational studies on the identification and analysis of network parameters from
experimental mitochondrial micrographs have been performed using either custom built
applications [71–76] or commercially available tools [77], depending upon the particular ques-
tion being asked. However, a comprehensive study quantifying the imbalance between fission
and fusion responsible for the network fragmentation observed in many diseases does not
exist.
In this paper, we adopt and extend the method developed in Refs. [75, 76] using a pipeline
of computational tools that process and extract a range of network parameters from mitochon-
drial micrographs recorded through fluorescence microscopy, and simulate mitochondrial
networks to determine microscopic rates of fission and fusion leading to the observed network
properties. We first demonstrate our approach by application to images of mitochondrial
networks in striatal cells from YAC128 Huntington’s disease (HD) transgenic mice (bearing a
111 polyglutamine repeat Q111/0 and Q111/1) and their control counterparts reported in
Ref. [78]. This is followed by the application of our technique to images of mitochondria in
cells with Alzheimer’s disease (AD) [79], amyotrophic lateral sclerosis (ALS) [80], Parkinson’s
disease (PD) [81], optic neuropathy (OPA) [66], diabetes/cancer [65], acute kidney injury [64],
Ca 2+
overload [14], and Down syndrome (DS) [36, 82] pathologies from the literature. The
images analyzed in this study were selected based on the following criteria. (1) The paper from
which the images were selected reported images of mitochondrial networks both in normal
and diseased cells from the same cell/animal model. (2) The images were of high enough qual-
ity so that they can be processed properly, making sure that the network extracted indeed
represented the actual mitochondrial network without introducing artifacts during the pro-
cessing. The cell/animal models used in these studies are listed in S1 Table in the Supplemen-
tary Information Text and detailed in the Results section below. Although we found
fragmented mitochondrial networks and imbalanced fission and fusion in all these pathologies
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in comparison to their respective control conditions, significant differences between the
microscopic properties underlying such fragmentation exist in different diseases.
Methods
Image analysis
Mitochondria in a cell can form networks of different topologies ranging from a fully disinte-
grated network with one mitochondrion per cluster to a well-connected network comprising
of clusters with several mitochondria per cluster to a fully connected network where all clusters
are connected to form a single giant cluster. These topologies can be uniquely distinguished by
various network parameters such as the mean degree <k> (the average number of nearest
neighbors), giant cluster Ng (the largest cluster in the network), giant cluster normalized with
respect to the total number of nodes (mitochondria) or edges (connections) Ng/N, and distri-
butions of various features such as the number of mitochondria in various linear branches,
cyclic loops, and clusters comprising both branches and loops.
To extract all this information from experimental images of mitochondrial networks, we
adopt and extend the procedure first reported in Ref. [75] using a pipeline of Matlab (The
MathWorks, Natick, MA) tools. Often, we are required to preprocess the images for removing
any legends or masking/removing areas that contain artifacts (Fig 1A). The colors representing
processes other than mitochondria are removed and the resulting image is converted to gray-
scale image (Fig 1B). Next, we take a series of steps to extract the underlying mitochondrial
network and the key information about the network.
Fig 1. Steps involved in the processing of the images and retrieval of various network features. (a) Original image, (b) the grayscale image containing mitochondrial
network only, (c) binary image, and (d) skeletonized image. Panel (e) shows a graph (partially shown) representation of the skeletonized image where red, green, and
blue colors represent nodes with degree 1, 2 and 3 respectively. Size distribution of cyclic loops (f) and linear branch lengths (g), and cumulative probability distribution
of cluster sizes (h) in mitochondrial network in striatal cells from wildtype (NL, red) and YAC128 HD (blue) transgenic mice. The image used for the mitochondrial
network extraction in panel (a) was adopted from Ref. [78] with permission.
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Step 1: We use Matlab function im2bw to generate a binary image (Fig 1C) from the prepro- cessed gray scale image (Fig 1B) of the micrograph by applying appropriate threshold intensity
using Matlab function graythresh. Step 2: The resulting binary image is reduced to a trace of one-pixel thick lines called skele-
ton using Matlab function bwmorph, which represents mitochondrial network (Fig 1D). Step 3: To extract various features of the mitochondrial network from skeletonized image,
we first label different clusters using Matlab routine bwlabel. The labeled clusters are then con- verted to a graph (Fig 1R, only partial graph is shown for clarity) where the nodes are color-
coded according to their degree. The graph is then used to extract network parameters such as
<k>, Ng, and Ng/N. We also extracted size distribution of loops or cycles with no open ends
(Fig 1F), size distribution of branches with at least one open end (Fig 1G), and cumulative
probability distribution of individual cluster sizes (Fig 1H) in terms of number of edges, where
a single cluster could have both loops and branches and is disconnected from other clusters.
All the above properties are extracted for mitochondrial networks in the cells with different
pathologies and the corresponding control cells for comparison. For example, we compare the
size distributions of loops, branches, and clusters in striatal cells from YAC128 Huntington’s
disease (HD) transgenic mice (blue) and their control counterparts (NL, red) reported in
Ref. [78] in Fig 1F–1H. A clear leftward shift in these distributions can be seen in HD, indicat-
ing a fragmented mitochondrial network as compared to NL cells. The overall number of
loops and branches also decreases in HD.
Modeling and simulating mitochondrial network
To simulate mitochondrial network, we used the model described in Sukhorukov et al. [76], where the network results from two fusion and two fission reactions (Fig 2). In the model, a
dimer tip representing a single mitochondrion can fuse with other dimer tips, forming a net-
work node. At most three tips can merge. The two possible fusion and corresponding fission
reactions are termed as tip-to-tip and tip-to-side reactions. The biological equivalent of the
tip-to-tip reaction would be the fusion of two mitochondria moving along the same microtu-
bule track in the opposite directions and interacting longitudinally [83]. Similarly, tip-to-side
reaction mimics the merging of two mitochondria moving laterally [83]. These two types of
Fig 2. Experimentally observed mitochondrial network and the scheme to model it. (a) Color coded mitochondrial network retrieved from experimental image of a
striatal cell from a wildtype mice and (b) its zoomed in version. (c) Model scheme representing the tip-to-tip fusion of two X1 nodes into X2 and tip-to-side fusion of
one X1 node with one X2 node to make one X3 node, and their corresponding fission processes. The image used for the mitochondrial network extraction in panel (a)
was adopted from Ref. [78] with permission.
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interactions are explained further in section “Mitochondrial interactions” of Supplementary
Information text and sketched in S1 Fig. This way, the network can have nodes with degree 1
(isolated tip), degree 2 (two merged nodes), and degree 3 (three merged nodes). To each fusion
process, there is an associated fission process. Thus, the four possible processes can be repre-
sented by the following two reaction equations.
X1 þX1 ! a1
b1
X2;
X1 þX2 ! a2
b2
X3:
Where X1 (Fig 2A, red), X2 (Fig 2A, green), and X3 (Fig 2A, blue) represent nodes with
degree 1, 2, and 3 respectively. Nodes with degree 4 are not included because of their extremely
low probability [75, 76]. Network edges connecting the nodes define minimal (indivisible)
constituents of the organelle. Therefore, all parameters are calculated in terms of number of
edges in the network.
Next, we implement the model as an agent-based model using Gillespie algorithm [75, 76,
84]. We initialize the simulation with the number of edges (N) estimated from experimental
micrographs of the cell that we intend to model and all nodes initially in X1 form with their
number equal to the mitochondrial components representing the cell. The number of edges in
the images processed in this paper ranges from as few as 72 to as many as 19519. The network
is allowed to evolve through a sequence of fusion and fission processes according to their pro-
pensities at a given time step. In all cases, we run the algorithm for 5N time steps to reach the
steady state and extract various network features (<k>, Ng, branch lengths etc.) at the end of
the run using various Graph and Network algorithms in Matlab. Depending on the fusion (a1
& a2) and fission (b1 & b2) rates used, networks of varying properties ranging from mostly
consisting of isolated mitochondria or branched clusters to a fully connected one giant cluster
can be generated [76].
To search for a network with specific properties, we follow the procedure in [75, 76] and
vary the ratio of fusion and fission processes, i.e. C1 = a1/b1 and C2 = a2/b2 by fixing b1 and
b2 at 0.01 and 3b1/2 respectively, and allowing a1 and a2 to vary. For every set of (C1, C2) val-
ues, we repeat the simulations 100 times with different sequences of random numbers and
report different parameters/features of the network averaged over all 100 runs. Results from a
sample run with N = 3000 are shown in Fig 3A1–3A3, where we plot <k> (Fig 3A1) and Ng/N
(Fig 3A2) as functions of C2 at fixed C1 = 0.0007. Ng/N versus <k> from the same simulation
is shown in Fig 3A3. Increasing C1 shifts the curve to the right. We scan a wide range of C1
and C2 values and plot <k> and Ng/N obtained from experimental images on this two param-
eter phase space diagram. As an example, the red crosses in the inset in Fig 3A3 represent Ng/
N versus <k> retrieved from experimental images of mitochondria in striatal cells from NL
and HD transgenic mice [78]. The values from the image are mapped with the corresponding
C1 and C2 values on the phase space diagram and reported as the values for that cell.
Larger values of C1 and C2 mean more frequent tip-to-tip and tip-to-side fusion respec-
tively, and vice versa. A very small value of C2 (or C1) results in a network mainly consisting
of linear chains and isolated nodes (Fig 3B1) with small <k> and Ng/N (Fig 3A1 & 3A2).
Medium value of C2 leads to a network having clusters with both branches and loops (Fig
3B2), whereas large C2 value results in a network having one giant cluster (Fig 3B3) with large
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<k> and Ng/N values. To demonstrate further that how low, intermediate, and large values of
C2 (or C1) affect the fine structure of the network, we show distributions of the loop, branch,
and cluster sizes from three simulations in Fig 3C1–3C3. We pick C2 values obtained for mito-
chondrial networks (details about C1 and C2 values for different conditions are given below)
in striatal cells with HD pathology (C2 = 0.22e-4, C1 = 4.9e-4), their corresponding NL cells
(C2 = 0.44e-4, C1 = 4.9e-4) [78], and NL cells from ALS experiments (C2 = 1.0e-4, C1 = 4.8e-
4) reported in Ref. [80] as representatives of the three cases. We also performed simulations
using C1 and C2 values representing mitochondrial networks in cells with DS pathology
(C2 = 0.32e-4 value) and their corresponding NL cells (C2 = 0.88e-4 value) [36, 82] and
observed a clear rightward shift in all three distributions at 0.88e-4 as compared to those at
C2 = 0.32e-4 (not shown). In addition to shifting to the right, the range of all three distribu-
tions widens as we increase the value of C2, indicating that both the sizes and diversity of the
network components increase.
Results
As pointed out above, we processed images of mitochondrial networks in cells with various
neurological pathologies including AD [79], ALS [80], PD [81], HD [78], OPA [66], Ca 2+
over-
load in astrocytes [14], and DS [36, 82] as well as other conditions such as kidney disease [64]
Fig 3. Model results at different C1 and C2 values. Mean degree (a1), Ng/N (a2), and Ng/N versus <k> (a3) as functions of C2 at a fixed value of C1. Inset in
(a3) shows a zoomed in version of the main plot in (a3) with superimposed Ng/N versus <k> from experimental images of mitochondria in striatal cells (red
cross) from wildtype (NL) and YAC128 HD transgenic mice [78]. Mitochondrial network changes from fragmented (b1) to physiologically viable, well-
connected (b2) to a fully connected network making one giant cluster (b3) as we increase C2 (or C1). Distribution of loop sizes (c1), branch lengths (c2), and
cluster sizes (c3) retrieved from simulated networks at two different C2 values corresponding to mitochondrial network in striatal cells from HD transgenic
mice (representative of low C2) (black bars) and striatal cells from wildtype mice in the same experiments (representative of intermediate C2) (red bars). The
insets in (c1) and (c2) and the blue bars in (c3) correspond to C2 value for the normal cells in ALS experiments (representative of high C2). The inset in (c3)
shows the tail of the blue distribution indicating the formation of a giant cluster at high C2. At smaller cluster sizes, the black, red, and blue bars in panel (c1) are
comparable and are skipped for clarity.
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and diabetes/cancer [65] from published literature. Details of the cell models analyzed are
given in the following paragraphs and tabulated in S1 Table. Key network parameters such as
<k>, Ng, Ng/N retrieved from the diseased cells and their normal counterparts are listed in
Table 1. A universal signature of all pathological conditions we analyzed in this study is that
mitochondrial networks in the diseased cells are fragmented as compared to normal cells. In
terms of network parameters, this translates into smaller <k>, average cluster size, Ng, and
Ng/N for mitochondrial networks in cells with pathological conditions as compared to control
cells.
Our observations are in agreement with previous studies investigating these diseases indi-
vidually. For example, it has been shown that mitochondrial dysfunction in fibroblasts from
human fetuses with trisomy of Hsa21 (DS-HFF) [82], human fibroblasts from subjects with
DS [36], and mouse embryonic fibroblasts derived from a DS mouse model [36] are correlated
with the significant fragmentation of the underlying mitochondrial network when compared
to healthy cells, in line with our results showing that <k> and Ng/N for the network in NL
cells are higher than those in DS affected cells. Another study investigating mitochondrial
dynamics in AD showed that neuroblastoma cells overexpressing APPswe mutant and amyloid
β display more fragmented mitochondrial networks as compared to control cells [79]. Along similar lines, cells with HD pathology were shown to be accompanied by mitochondrial frag-
mentation and cristae alterations in several cellular models of the disease. These alterations
were attributed to increased basal activity of the Ca 2+
-dependent phosphatase calcineurin that
dephosphorylates the pro-fission dynamin related protein 1 (Drp1) and mediates its transloca-
tion to mitochondria [85]. This study also showed that the upregulation of calcineurin activity
results from the higher Ca 2+
concentration in the cytoplasm in HD due to enhanced release
from intracellular stores such as the endoplasmic reticulum. Parkinson’s disease is another
complex multifactorial etiology, involving many genetic and environmental factors over the
Table 1. Network parameters obtained from images of cells with different pathologies. Column 1 lists the disease for which micrographs of normal (NL) and diseased
cells were analyzed (column 2). Column 3–8 lists the total number of edges, mean degree, total number of clusters (excluding isolated nodes), average cluster size (in terms
of number of edges), giant cluster size (in terms of number of edges), and the ratio of the giant cluster and network size.
Condition Normal vs diseased Number of edges Mean degree
<k>
Number of clusters Avg. cluster size Ng Ng/N
HD NL 2664 1.67 556 4.79 50 0.0188
HD 2150 1.63 512 4.20 40 0.0186
AD NL 642 1.64 144 4.46 27 0.042
AD 1061 1.62 258 4.11 40 0.038
DS NL 1916 1.52 623 3.08 34 0.017
DS 1365 1.47 502 2.72 14 0.010
PD NL 19519 1.72 3416 5.71 107 0.006
PD 8715 1.70 1691 5.15 45 0.005
ALS NL 103 1.75 19 5.42 38 0.369
ALS 72 1.69 13 5.54 16 0.222
Kidney injury NL 5038 1.66 1061 4.75 58 0.012
Kidney injury 5386 1.64 1207 4.64 59 0.011
Diabetes/Cancer NL 3546 1.67 715 4.96 82 0.023
Diabetes/Cancer 3504 1.65 769 4.55 35 0.010
OPA NL 5263 1.69 1045 5.04 49 0.0093
OP 7772 1.67 1656 4.69 43 0.0055
Ca 2+
NL 3195 1.59 903 3.54 126 0.039
Ca 2+
overload 2576 1.57 764 3.37 82 0.032
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course of time. An in-depth analysis of the human primary skin fibroblasts obtained from spo-
radic late-onset PD patients with those from healthy age-matched control subjects showed that
the diseased fibroblasts exhibit significantly compromised mitochondrial structure and func-
tion [81]–in line with the network parameters estimated in our study.
We also analyzed images of mitochondrial networks in mouse hippocampus-derived neu-
roblastoma cells, transduced with wildtype, R15L, and S59L mutations of Coiled-coil-helix-
coiled-coil-helix domain-containing protein 10 (CHCHD10) that were reported in Ref. [80].
Both <k> and Ng (and Ng/N) decrease in the presence of CHCHD10 mutations as compared
to wildtype CHCHD10. CHCHD10 mutations are associated with a spectrum of familial and
sporadic frontotemporal dementia-ALS diseases [86, 87], Charcot–Marie–Tooth disease type 2
[88], mitochondrial myopathy and spinal muscular atrophy Jokela type [89]. Recently, Woo
et al. [80] showed that CHCHD10 results in cytoplasmic accumulation of TAR DNA-binding protein 43 (TDP-43) that increases mitochondrial fission proteins Drp1 and Fis1, reduces
mitochondrial fusion protein Mfn1, and promotes mitochondrial fragmentation [90, 91].
TDP-43 pathology is associated with the vast majority of ALS and frontotemporal lobar degen-
erations [92] and plays a major role in other neurodegenerative diseases [93, 94] and cellular
toxicity in general [95, 96]. Overexpression of TDP-43 also promotes juxtanuclear aggregation
of mitochondria [90, 91]. The larger average cluster size we observe in cells with CHCHD10
mutations as compared to NL cells could reflect this behavior (Table 1, column 6).
Mitochondrial damage is also believed to be a key contributor to renal diseases like acute
kidney injury. By processing images of mitochondrial networks reported in Brooks et al. [64], we observe smaller <k> and Ng/N in rat proximal tubular cells and primary renal proximal
tubular cells treated with azide to induced ATP depletion and model in vivo ischemia. These values confirm the conclusions in Ref. [64], where a larger number of cells exhibited frag-
mented mitochondrial networks in cells treated with azide and cisplatin to induce nephrotoxi-
city as compared to control cells. The same study also reported that both ischemic acute
kidney injury and tubular apoptosis were observed to be ameliorated by Mdivi-1, a pharmaco-
logical inhibitor of Drp1.
A dimeric mitochondrial outer membrane protein, MitoNEET, is implicated in the etiology
of many pathologies including obesity, insulin resistance, diabetes, and cancer. Its downregula-
tion reduces cell proliferation and tumor growth in breast cancer adipocytes and in pancreatic
cells [97–100]. Our analysis of fluorescence images of MitoNEET knockout mouse embryonic
fibroblasts indicates that <k>, average cluster size, and Ng/N all decrease when compared with
control mouse embryonic fibroblasts. These results are in agreement with the observations sug-
gesting that the downregulation of MitoNEET in mouse embryonic fibroblasts and pancreatic β cells results in reduced connectivity of mitochondrial network and vice versa [99, 101].
Mitochondriopathies are also associated with many multisystemic diseases including infan-
tile-onset developmental delay, muscle weakness, ataxia, and optic nerve atrophy caused by a
homozygous mutation in the yeast mitochondrial escape 1-like 1 gene (YME1L1) [102].
YME1L1 plays a key role in mitochondrial morphology by mediating optic atrophy type 1
(OPA1) protein that is involved in mitochondrial fusion and remodeling, and is also believed
to be associated with hereditary Spastic Paraplegia 7 disease, Autosomal Recessive disorder,
obesity, and defective thermogenesis [73, 103–106]. We found that <k>, mean cluster size,
and Ng/N all decrease in cells expressing YME1L1 missense mutation R149W and YME1L1.
These results are in agreement with the observations of fragmented mitochondrial network in
HeLa cells and fibroblasts from mouse and patients with proliferation defect expressing
R149W or YME1L1 knockout cells [66] and SHSY5Y cells where YME1L1 is degraded in
response to distinct cellular stresses that depolarize mitochondria and deplete cellular ATP
[103].
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Interestingly, a common feature among the pathological conditions discussed in this paper
and several other degenerative diseases where mitochondrial fragmentation is observed, is that
intracellular Ca 2+
concentration in the cells affected by these pathologies is upregulated [107–
120]. Therefore, we analyzed images of mitochondrial networks in cells with higher intracellu-
lar Ca 2+
concentration. These images were reported in Ref. [14], where rat cortical astrocytes
were treated with Ca 2+
ionophore 4Br-A23187 that increases intracellular Ca 2+
concentration
in dose-dependent manner. We found that <k>, average cluster size, Ng, and Ng/N for mito-
chondrial network in astrocytes exposed to 4Br-A23187 are significantly lower than those
observed in control cells.
Next, we perform extensive stochastic simulations (see “Modeling and simulating mito-
chondrial network” section) to search for the tip-to-tip and tip-to-side fusion and fission rates
characterizing mitochondrial networks in cells with different pathologies and their respective
control conditions. Final results from these simulations are summarized in Table 2. As is evi-
dent from columns 7 and 8, in all cases the values of C1 or/and C2 for mitochondrial network
in diseased cells are smaller than those in control cells. This confirms the lower tip-to-tip or
tip-to-side fusion to fission ratios in the diseased cells.
In most cases, we identified C1 and C2 where the model gives the exact <k> and Ng/N val-
ues observed in the experiment. In some cases, the Ng/N value from simulation is slightly dif-
ferent than that retrieved from experimental images. However, it is possible to get C1 and C2
values that would result in the exact Ng/N values. This will require running the algorithm with
smaller C1 and C2 increments, which will significantly increase computational time. On aver-
age, simulating the network with one set of C1 and C2 values and 100 repetitions to minimize
the stochastic variability, takes 5 to 10 hours (depending on N). Thus, halving the increments
of one or both of C1 and C2 would double or quadruple the computational time respectively.
Table 2. Comparison of microscopic parameters of mitochondrial network obtained from simulations and experiments. Column 1 lists the condition for which
images of normal (NL) and diseased cells were analyzed (column 2). Columns 3 & 4 and 5 & 6 compare <k> and Ng/N respectively from experiment and theory. Columns
7 & 8 are the C1 (tip-to-tip fusion/fission) and C2 (tip-to-side fusion/fission) values obtained by fitting the model to the data and used in simulations.
Condition Normal vs diseased Mean degree <k>
Exp Theory
Ng/N
Exp Theory
C1 C2
HD NL 1.67 1.67 0.0188 0.022 4.9e-4 4.40e-5
HD 1.63 1.63 0.0186 0.0101 4.9e-4 2.20e-5
AD NL 1.64 1.64 0.042 0.108 7.0e-4 2.30e-4
AD 1.62 1.62 0.038 0.067 7.0e-4 1.90e-4
DS NL 1.52 1.52 0.017 0.017 5.0e-4 0.88e-4
DS 1.47 1.47 0.010 0.010 5.0e-4 0.32e-4
PD NL 1.72 1.72 0.006 0.008 1.2e-3 7.00e-6
PD 1.70 1.70 0.005 0.007 9.8e-4 7.00e-6
ALS NL 1.75 1.75 0.369 0.359 4.8e-4 1.00e-4
ALS 1.69 1.69 0.222 0.225 1.0e-4 1.00e-4
Kidney injury NL 1.66 1.66 0.012 0.016 9.1e-4 4.00e-5
Kidney injury 1.64 1.64 0.011 0.011 9.0e-4 0.25e-4
Diabetes/Cancer NL 1.67 1.67 0.023 0.020 9.8e-4 4.50e-5
Diabetes/Cancer 1.65 1.65 0.010 0.013 9.8e-4 2.50e-5
OPA NL 1.69 1.69 0.0093 0.0081 9.0e-4 1.00e-5
OPA 1.67 1.67 0.0055 0.0075 7.6e-4 1.00e-5
Ca 2+
NL 1.59 1.59 0.039 0.038 7.0e-4 1.46e-4
Ca 2+
overload 1.57 1.58 0.032 0.032 7.0e-4 1.13e-4
https://doi.org/10.1371/journal.pone.0223014.t002
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A close look at the values of C1 and C2 reveals two main trends (Table 3). In case of HD,
AD, DS, Ca 2+
overload, kidney disease, and diabetes/cancer the fusion to fission ratio for the
tip-to-tip reaction remains constant, while the fusion to fission ratio for the tip-to-side reaction
decreases when compared to the control conditions. As shown by an example from HD (Fig
4A1–4A4), this results in smaller number of X3 species with a gain in X1 and X2 species in the
diseased state (Fig 4A4 and Table 3). However, since the probability of cyclic loops depends on
both X2 and X3, the large decrease in X3 and moderate increase in X2 lead to smaller cyclic
loops and consequently smaller clusters in the diseased state (Fig 4A1 & 4A3). Larger number
of X2 species with no change in X1 would translate into longer and/or larger number of linear
branches. However, the simultaneous increase in the number of X1 species would result in
shorter branches (Fig 4A2) and higher number of isolated mitochondria. A relatively smaller
decrease in C2 leads to a smaller decrease in X3, and a smaller increase in X1 and X2, which
would lead to smaller but larger number of linear chains. The larger number of linear chains
could overcompensate for the small decrease in X3, resulting in a larger number of cyclic
loops. Such behavior is demonstrated by an example using network statistics for diabetes
(S2 Fig).
An opposite effect can be seen in case of OPA, PD, and ALS where C1 decreases and C2
remains constant when compared to normal cells. The lower fusion to fission ratio for the tip-
to-tip reaction leads to larger and smaller number of X1 and X2 mitochondrial species respec-
tively (Table 3). A larger decrease in C1 would lead to a larger increase in X1 and a larger
decrease in X2, and consequently shorter, fewer linear chains (and larger number of isolated
mitochondria) and vice versa. For example, the relatively smaller decrease in C1 in case of
OPA leads to shorter linear branches (leftward shift in Fig 4B2) but the number of branches
increases (taller bars) as compared to control conditions. Although the fusion to fission ratio
for the tip-to-side reaction does not change, the larger number of linear chains available to
make cyclic loops leads to a larger number of smaller loops (Fig 4B1). If the decrease in C1 is
larger, one would see a significant decrease in the number of loops and branches (and signifi-
cant increase in the number of isolated mitochondria) in addition to the leftward shift in the
diseased case. Such behavior is demonstrated by an example using network statistics for PD
(S3 Fig).
To see if the conclusions made above for a given disease holds when images of mitochon-
drial networks recorded from different cell/animal models or different experimental setup are
used, we analyzed two more examples each for AD [121], PD [122], and ALS [91]. As clear
from S2 Table, the results are largely consistent with our conclusions discussed above. The
Table 3. Comparison of the fusion to fission ratio for the tip-to-tip and tip-to-side reactions in the normal and diseased states predicted by the model. The sub-
scripts n and d indicate normal and diseased states respectively. The C1 and C2 values estimated for different conditions are used to estimate the fractions of X1, X2, and
X3 species in steady state and compare them with the diseased states.
Condition C1n/C1d C2n/C2d X1n X2n X3n X1n/X1d X2n/X2d X3n/X3d
HD 1.00 2.00 0.359 0.562 0.079 0.985 0.948 1.852
AD 1.00 1.21 0.432 0.429 0.140 0.992 0.969 1.143
DS 1.00 2.75 0.454 0.502 0.044 0.980 0.939 17.058
CA 1.00 1.29 0.441 0.459 0.100 0.990 0.969 1.238
Kidney 1.01 1.60 0.344 0.605 0.052 0.991 0.971 1.704
Diabetes/
Cancer
1.00 1.80 0.334 0.614 0.052 0.990 0.971 1.739
OPA 1.18 1.00 0.292 0.691 0.018 0.938 1.030 0.955
PD 1.22 1.00 0.260 0.728 0.012 0.922 1.032 0.954
ALS 4.80 1.00 0.341 0.468 0.191 0.875 1.129 0.976
https://doi.org/10.1371/journal.pone.0223014.t003
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mean degree is higher for mitochondrial networks in NL cells as compared to their diseased
counterparts. The microscopic rates (C2/C1) given by the simulations are also consistent with
the above conclusions. With the exception of one example for AD and PD each, the normal-
ized giant cluster (Ng/N) for all cases from our simulations also follows a consistent trend. For
the two examples where Ng/N is slightly larger for NL cells than the diseased cells, we noticed
that the overall mitochondrial network (network size in terms of the total number of edges in
the cell) in the imaged area of the NL cells were significantly larger than those in the diseased
cells. We suspect that this contributed to this discrepancy. Nevertheless, the mean degree in
the same two examples is still consistent with our conclusions in the preceding paragraphs.
Despite the fact that the overall cumulative probability of the cluster sizes shifts to the left in
all cases (see for example Fig 4A3 & 4B3), the different microscopic mechanisms for fragmen-
tation lead to mitochondrial networks with significantly different fine structures. This is dem-
onstrated by the fraction of X1, X2, and X3 species at steady state (Table 3, columns 4–9)
obtained from simulations using C1 and C2 values for mitochondrial networks in cells with
different pathologies and their respective control conditions. In the first group of conditions
described above, the fraction of X3 species decreases significantly while X1 and X2 both
increase moderately in the diseased state. This would lead to smaller and fewer cyclic loops. In
the second group of diseases, X1 increases significantly while X2 decreases moderately. Since
the propensity of X1+X2 ! X3 reaction is given by a1 × X1 × X2, the relatively larger increase in X1 with the moderate decrease in X2 leads to a larger fraction of X3 species in the diseased
Fig 4. Two different types of microscopic changes in the fusion to fission processes leading to mitochondrial network fragmentation demonstrated
with examples from HD (striatal cells from mouse embryos bearing a 111 polyglutamine repeat Q111/0 and Q111/1) versus control [78] for the first
type (top row) and OPA (mouse embryonic fibroblasts with the pathogenic mutation R149W in human YME1L1) versus control [66] for the
second type (bottom row) of microscopic changes. Distributions of (a1) loop sizes, (a2) branch lengths, and (a3) cluster sizes (cumulative
probability) for NL (red) and diseased cells (blue) from experimental images. (a4) Fraction of X1 (NL: green, diseased: red), X2 (NL: magenta,
diseased: blue) and X3 (NL: black, diseased: cyan) species from the model as functions of the number of iterations using C1 and C2 values for HD
experiments. The model results show average of 100 runs. (b1-b4) shows the same mitochondrial network features as (a1-a4) for mouse embryonic
fibroblasts with OPA pathology and their normal counterparts. Note that the curves for X3 species in cells with OPA pathology and NL overlap
(b4).
https://doi.org/10.1371/journal.pone.0223014.g004
Mitochondrial fragmentation in degenerative diseases
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state. A larger increase in X3 and a smaller decrease in X2 would lead to a larger number of
cyclic loops (although still smaller in sizes) and vice versa.
The large variability in the fine structure of the mitochondrial network resulting from the
different microscopic origins of fragmentation is highlighted further in Fig 5. We simulate
mitochondrial networks in different diseases and their respective control conditions using
their corresponding C1 and C2 values in the model, and extract the size distributions for
branch lengths, cyclic loops, and clusters. The means of these distributions are shown in Fig 5,
where the relative decrease vary significantly from one disease to another. A similar variability
can also be seen in the variances of these three distributions while comparing different diseases
to their respective control conditions (not shown).
Discussion
A tight balance between fission and fusion of mitochondria is crucial for the normal cell func-
tion [20, 29, 123]. This is probably why many degenerative diseases have been linked to the pri-
mary or secondary changes in mitochondrial dynamics leading to fragmented mitochondrial
networks [9, 15–36]. Our analysis of images of mitochondrial networks from several previ-
ously reported experimental studies indicates that in general mitochondria in normal cells
form a well-connected network that can be described by larger mean degree, giant cluster,
branch lengths, clusters, and loops as compared to fragmented network characterized by
smaller values of all these parameters in cells with nine different types of pathologies. We ex-
ploit these differences and model mitochondrial network to gain a quantitative understanding
Fig 5. The differences in the microscopic changes leading to mitochondrial network fragmentation lead to significantly differences in
the way the fine structure and topology of the network is affected in different diseases. The mean of size distribution of (a) cyclic loops, (b)
branch lengths, and (c) clusters for normal (red) and diseased (blue) cells given by the model using the estimated C1 and C2 values from the
experimental micrographs of mitochondrial networks with the condition modeled. Each data point is averaged over 100 runs with error bars
showing the standard error of the mean. Simulation results for ALS are plotted separately in the insets for clarity.
https://doi.org/10.1371/journal.pone.0223014.g005
Mitochondrial fragmentation in degenerative diseases
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of the changes in the fission and fusion processes due to lateral and longitudinal interactions
in all these pathologies.
It is worth mentioning that the class (transient versus complete) of fusion depends on the
way two mitochondria interact with each other (see for example [83] for further details). Tran-
sient fusion where two mitochondria come into close apposition, remain fused for less than 4s
to 5 min with a mean duration of 45s, and re-separate, preserving their original topologies,
results from oblique or lateral interaction of two mitochondria associated with separate tracks.
Complete fusion on the other hand results from longitudinal merging of organelles moving
along a single track.
We show that the nine conditions can be divided into two main groups. The fragmentation in
cells with AD, HD, DS, Ca 2+
overload, diabetes/cancer, and acute kidney injury pathologies mainly
results from the decreased fusion in favor of fission due to lateral interaction between mitochon-
dria. In case of OPA, PD, and ALS on the other hand, the balance between fusion and fission due
to lateral interaction remains intact. However, the increased fission at the expense of fusion due to
longitudinal interaction leads to fragmented mitochondrial network in these diseases.
The differences in the microscopic properties of mitochondrial fission and fusion could
have key implications for the way fragmentation affects cell function depending on the mor-
phology and the region of the cell where fragmentation occurs. For example, impaired balance
between fission and fusion due to longitudinal interaction would lead to shorter linear chains
of mitochondria that could significantly affect signaling along neuronal processes and synap-
ses. Increased rate of fission at the expense of fusion due to lateral interaction on the other
hand would likely have a more significant effect on the functions in regions such as cell body
where a healthy mitochondrial network is key for the function of organelles such as nucleus
and Golgi network.
We remark that our conclusions are based on limited data available. Consolidating these
conclusions will need further future experiments and analysis of the mitochondrial networks
in the different diseases using the approach discussed in this paper. Nevertheless, we believe
that our framework provides a solid foundation for developing computational tools that could
use these indicators for inferring the extent and types of signaling disruptions in different
pathologies. While beyond the scope of this study, we believe that validating our predictions
about the disruption of lateral and/or longitudinal fission/fusion in different diseases, experi-
mental techniques similar to that used in Ref. [83] could be useful. In this technique, the
exchange of matrix contents between individual mitochondria is visualized in real time as the
two mitochondria fuse or detach by using mitochondrial matrix-targeted green-photoacti-
vated, red-fluorescent Kindling fluorescent protein in combination with green or yellow
fluorescence protein or the cyan-photoactivated mtPAGEP (mitochondria-targeted photoacti-
vatable green-fluorescence protein) in combination with red fluorescence protein [83].
Supporting information
S1 Text. Description of different types of mitochondrial interactions, cell models, and dis-
eases investigated in this study.
(DOCX)
S1 Fig. Longitudinal and lateral mitochondrial interactions (fusion/fission). (a) End-to-
end fusion of two mitochondria moving towards each other along a common microtubule
(not shown), (b) Side-to-side and end-to-side fusion of two mitochondria moving on two dif-
ferent microtubule tracks (not shown). Arrows indicate the direction of motion.
(TIFF)
Mitochondrial fragmentation in degenerative diseases
PLOS ONE | https://doi.org/10.1371/journal.pone.0223014 September 26, 2019 13 / 21
S2 Fig. A smaller decrease in C2 leads to a smaller decrease in X3, and a smaller increase in
X1 and X2, which would lead to a smaller but larger number of linear chains and larger
number of cyclic loops. Here we compare mitochondrial network fragmentation in HD (stria-
tal cells from mouse embryos bearing a 111 polyglutamine repeat Q111/0 and Q111/1) versus
control [78] with C2n/C2d = 2.0 (top row) and diabetes (MitoNEET knockout mouse embry-
onic fibroblasts) versus control [65] with C2n/C2d = 1.8 (bottom row). Distributions of (a1)
loop sizes, (a2) branch lengths, and (a3) cluster sizes (cumulative probability) for NL (red) and
diseased cells (blue) from experimental images. (a4) Fraction of X1 (NL: green, diseased: red),
X2 (NL: magenta, diseased: blue) and X3 (NL: black, diseased: cyan) species from the model as
functions of the number of iterations using C1 and C2 values for HD experiments. The model
results show average of 100 runs. (b1-b4) shows the same mitochondrial network features as
(a1-a4) for MitoNEET knockout mouse embryonic fibroblasts with diabetes pathology and
their normal counterparts.
(TIFF)
S3 Fig. A larger decrease in C1 leads to a significant decrease in the number of loops and
branches. Here we compare mitochondrial network fragmentation in OPA (mouse embryonic
fibroblasts with the pathogenic mutation R149W in human YME1L1) versus control [66] with
C1n/C1d = 1.18 (top row) and PD (human primary skin fibroblasts obtained from sporadic
late-onset PD patients) versus those from healthy age-matched control subjects [81] with C1n/
C1d = 1.22 (bottom row). Distributions of (a1) loop sizes, (a2) branch lengths, and (a3) cluster
sizes (cumulative probability) for NL (red) and diseased cells (blue) from experimental images.
(a4) Fraction of X1 (NL: green, diseased: red), X2 (NL: magenta, diseased: blue) and X3 (NL:
black, diseased: cyan) species from the model as functions of the number of iterations using
C1 and C2 values for OPA experiments. The model results show average of 100 runs. (b1-b4)
shows the same mitochondrial network features as (a1-a4) for human primary skin fibroblasts
with PD pathology and their normal counterparts. Note that the curves for X3 species in dis-
eased and normal cells overlap (a4, b4).
(TIFF)
S1 Table. Experimental micrographs processed in this study. Column 1 provides the disease,
column 3 reports the cell/animal model, column 4 lists the condition for the experiment (nor-
mal versus diseased), and column 5 provides references where the images were originally pub-
lished.
Abbreviations: WT-Wild type, KO-Knockout, NL-Normal, MEF-Mouse embryonic fibro-
blasts, HSF-Human skin fibroblasts, MEMN Mouse embryonic motor neurons, TM-YAC128
Transgenic mice Yeast Artificial Chromosome 128, HSF Human Skin Fibroblasts, RPTCs rat
proximal tubular cells, RCA rat cortical astrocytes, CHCHD10—Coiled-coil-helix-coiled-coil-
helix domain-containing protein 10, YME1L1—Yeast mitochondrial escape 1-like 1 gene.
(DOCX)
S2 Table. Comparison of microscopic parameters of mitochondrial network obtained
from simulations and experiments for additional cell/animal models or experimental con-
ditions on AD, PD, and ALS diseases. Column 1 lists the condition for which images of nor-
mal (NL) and diseased cells were analyzed (column 2). Columns 3 & 4 and 5 & 6 compare
<k> and Ng/N respectively from experiment and theory. Columns 7 & 8 are the C1 (tip-to-tip
fusion/fission) and C2 (tip-to-side fusion/fission) values obtained by fitting the model to the
data and used in simulations.
(DOCX)
Mitochondrial fragmentation in degenerative diseases
PLOS ONE | https://doi.org/10.1371/journal.pone.0223014 September 26, 2019 14 / 21
Author Contributions
Conceptualization: Ghanim Ullah.
Data curation: Syed I. Shah, Johanna G. Paine, Carlos Perez, Ghanim Ullah.
Formal analysis: Syed I. Shah, Johanna G. Paine, Carlos Perez, Ghanim Ullah.
Funding acquisition: Ghanim Ullah.
Investigation: Syed I. Shah, Johanna G. Paine, Ghanim Ullah.
Methodology: Syed I. Shah, Johanna G. Paine, Ghanim Ullah.
Project administration: Ghanim Ullah.
Resources: Ghanim Ullah.
Software: Syed I. Shah, Johanna G. Paine, Carlos Perez, Ghanim Ullah.
Supervision: Ghanim Ullah.
Validation: Syed I. Shah, Johanna G. Paine, Carlos Perez, Ghanim Ullah.
Visualization: Syed I. Shah, Johanna G. Paine, Ghanim Ullah.
Writing – original draft: Syed I. Shah, Johanna G. Paine.
Writing – review & editing: Syed I. Shah, Ghanim Ullah.
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