Nkx6.1 decline accompanies mitochondrial DNA reduction but subtle nucleoid size decrease in pancreatic islet β-cells of diabetic Goto Kakizaki rats

Hypertrophic pancreatic islets (PI) of Goto Kakizaki (GK) diabetic rats contain a lower number of β-cells vs. non-diabetic Wistar rat PI. Remaining β-cells contain reduced mitochondrial (mt) DNA per nucleus (copy number), probably due to declining mtDNA replication machinery, decreased mt biogenesis or enhanced mitophagy. We confirmed mtDNA copy number decrease down to <30% in PI of one-year-old GK rats. Studying relations to mt nucleoids sizes, we employed 3D superresolution fluorescent photoactivable localization microscopy (FPALM) with lentivirally transduced Eos conjugate of mt single-stranded-DNA-binding protein (mtSSB) or transcription factor TFAM; or by 3D immunocytochemistry. mtSSB (binding transcription or replication nucleoids) contoured “nucleoids” which were smaller by 25% (less diameters >150 nm) in GK β-cells. Eos-TFAM-visualized nucleoids, composed of 72% localized TFAM, were smaller by 10% (immunochemically by 3%). A theoretical ~70% decrease in cell nucleoid number (spatial density) was not observed, rejecting model of single mtDNA per nucleoid. The β-cell maintenance factor Nkx6.1 mRNA and protein were declining with age (>12-fold, 10 months) and decreasing with fasting hyperglycemia in GK rats, probably predetermining the impaired mtDNA replication (copy number decrease), while spatial expansion of mtDNA kept nucleoids with only smaller sizes than those containing much higher mtDNA in non-diabetic β-cells.

Synergy of these pathologic progressions leads to a partial impairment of the glucose-stimulated insulin secretion and to an early progressive development of the peripheral insulin resistance in GK rats [1][2][3][4]13 . Since the elevated oxidative phosphorylation in mitochondria is the key component of the β-cell glucose sensor, findings of the reduced amount of mitochondrial DNA (mtDNA) 14,15 are compatible with the impaired mitochondrial function in GK rats 15 . Using 3D high-resolution 4Pi microscopy, we have found that the mitochondrial network was much more frequently fragmented in β-cells of GK rats, even though mitochondrial volume was preserved 16 . This also indicates a certain kind of stress of yet unknown origin. Also, the disrupted microRNA regulation was found in GK rat β-cells 17 .
Since mtDNA exists in the cell in numerous copies contained in the protein complexes, termed nucleoids [18][19][20][21][22][23][24][25][26][27] , we aimed to study how the profound reduction in mtDNA is reflected on the level of nucleoids. mtDNA is compacted in nucleoids by the mitochondrial (mt) transcription factor A (TFAM) in extreme densities. Such densities can be found only in prokaryotic DNA packing 28,29 . Therefore, changes in TFAM have to be investigated. In addition, numerous proteins of the DNA replication and transcription machinery are recruited to nucleoids. Among them the mt single-stranded-DNA-binding protein (mtSSB) is bound on single-stranded mtDNA of the non-coding D-loop region or in replicating and transcribing nucleoids 18,19,30,31 . These particular mtDNA loci are unwinded by Twinkle helicase 32,33 . In spite of extensive studies of mtDNA and nucleoids, contradictions between a uniform size [18][19][20] and range of nucleoid sizes exist [23][24][25] ; as well as contradictions concerning the number of mtDNA molecules per nucleoid 18,19 . Experiments showing the non-existence of mtDNA mixing between nucleotides have indicated one single copy of mtDNA 18,20,34 . However, other findings support an average of six multiple mtDNA copies per nucleoid 19 . No particular evidence for a nucleoid division has been observed. However, our preliminary data indicated the possible existence of nucleoid division 24 . Dividing nucleoids must have at least two mtDNA by definition (i.e. doubled number of mtDNA molecules per dividing nucleoid).
We can theoretically predict how the profound reduction in mtDNA in primary β-cells may be reflected on the level of nucleoids. Assuming the single mtDNA molecule per nucleoid, the only obvious variant would exist, lying in the exactly proportional reduction in number of nucleoids. In the model of multiple mtDNA copies per nucleoid, also redistribution variants exist. Under the assumption of the same (higher) number of nucleoids within the mitochondrion in two cells despite the mtDNA copy number decrease in one of them, one may imagine that the reduction of mtDNA copies per nucleoid might exist in such a cell. A "proportional" variant, reducing the nucleoid number is thus possible for multiple mtDNA copies per nucleoid, as well as the "heterogenous" variant of reduced mtDNA molecules only within certain nucleoids. Concerning the nucleoid size, it relies on the definition of a nucleoid 19 . If one considers a nucleoid as the TFAM-contained space, the size can be exactly measured by TFAM-based superresolution microscopy, specifically using 3D imaging 20,21,23,24 . TFAM stabilizes mitochondrial genome 29 and plays a role of transcriptional function as well 18,19 . TFAM also regulates mt genome copy number 28 . It has also been observed that TFAM overexpression preserves the copy number and respiration as well as ATP synthesis 35,36 . Hence, TFAM-visualized size of nucleoids may change even with constant mtDNA content within nucleoids, or vice versa.
We may also consider as well the "mtSSB space" of "active" replicating or transcribing nucleoids encompassing single-stranded DNA-containing regions that should be smaller than the TFAM-confined space 24 . mtSSB ensures replication, repair and maintenance 18,19,31 of mtDNA, while it binds to the exposed single-stranded mtDNA segments and also promotes mtDNA polymerase 30 and helicase reactions 32 . Another protein, Twinkle, acting as a mtDNA helicase, unwinds mtDNA in concert with the mtDNA polymerase and mtSSB 32,33 . In the resulting forks, transcription and replication is ensured by specific mitochondrial mtRNA-or mtDNA-polymerases, respectively 18 . Unfortunately, three-strand D-loops exist in each mtDNA molecule, i.e. D-loops representing non-coding mtDNA regions and serving as main replication/transcription origins. Hence, a substantial portion of mtSSB molecules is bound in the D-loop locations and represents a high "background" for the active transcribing or replicating nucleoids 24 .
Finally, a nucleoid core is composed of mtDNA 19,24 . Theoretically, under the assumption of the same packing mtDNA density, the observed 75% mtDNA reduction would result in only a 37% decrease of the sphere diameter for the 75% reduced spherical volume. Nevertheless, if the number of mtDNA molecules within a single nucleoid is to be reduced (e.g. from four molecules in the single nucleoid down to a single one), but is simultaneously unpacked, this may also result in a false negative (higher) volume. Thus, spatial immunocytochemistry against DNA will not resolve the problem, unless density of localized points is quantified 24 .
To elucidate the nature of mtDNA pathology changes in Goto Kakizaki PI β-cells, we employed novel 3D superresolution microscopy methods 24 BiplaneFPALM and direct stochastic optical reconstruction microscopy (dSTORM) and found correlations corresponding to the reduced mtDNA amount in PI β-cells of diabetic GK rats. A theoretical ~70% decrease in nucleoid spatial density was not observed upon a 70% reduced mtDNA copy number, rejecting model of single mtDNA per nucleoid. In parallel, we found a profound decline in β-cell-specifying transcription factor Nkx6.1 with age (~12-fold after 10 months) and with increasing fasting hyperglycemia in GK rats. The observed correlation suggests that Nkx6.1 may stimulate mtDNA replication and that the diminished Nkx6.1-mediated maintenance results in decreased mtDNA replication and hence decreased mtDNA copy number in Goto Kakizaki PI β-cells.

Results
Diabetic Goto Kakizaki rat pancreatic islets contain much less mitochondrial DNA relatively to Wistar rat controls. Previously, we reported a 75% decrease of mtDNA (copy number) in primary β-cell cells sorted from the Accutase-digested pancreatic islets (PIs) of diabetic Goto Kakizaki (GK) rats (48 week old), relatively to samples from age-matched non-diabetic Wistar rats 15 . For routine checking of PI samples, we intended to verify, whether such mtDNA decline can be reflected when the entire islets are analyzed.  (c) amounts for ascribed nuclear and mtDNA (ND5) transcripts for 30-55 week old rats; (d) protein amounts for selected factors as indicated derived from at least three western blots (typical results illustrated below; here Wistar and GK rat PI samples were always run and are displayed together, while the alternative development for β-actin is displayed below; typical full-length blots and Ponceau Red-stained membranes are included in a Supplementary Information file). (e) Volumes of mitochondrial network or sum of volumes of all their fragments as derived from 3D 4Pi microscopy images, where each bar represents a single cell (8 cells for each; an average for Wistar rats in μm 3 was 18 ± 12, median 12, and for GK rats 15 ± 8, median 15); (f) Volume per length of mitochondrial network of the same data (for Wistar rats an average in μm 2 was 0.036 ± 0.012, median 0.036, and for GK rats 0.031 ± 0.012, median 0.031). ***P < 0.001; **P < 0.05.
shows the relative copy number decline in PI samples from 12 and 30 to 55 week old GK vs. Wistar rats down to 40% and 25-30%, respectively. Also ratios of 7S mtDNA to the nuclear amplicon declined similarly (Fig. 1b).
In parallel, mRNA of transcription factor TFAM and typical mtDNA-encoded transcripts, such as ND5, decreased even more profoundly vs. mtDNA down to 25% and 30%, respectively, in 12 week old GK rats (Fig. 1c). A proportional decrease was indicated for mitochondrial polymerase γ (polγ) and ATPase (Fig. 1c), while transcription factor reflecting mitochondrial biogenesis PGC1α declined less (just to half values) in 12 week old GK vs. Wistar rats (Fig. 1c). In contrast, NRF1 changed insignificantly. We have also confirmed the similar TFAM, mtSSB and PGC1α decrease in protein levels in the oldest GK rats (Fig. 1d).
In order to relate changes of mtDNA to a "mitochondrial mass", we employed an analysis of mitochondrial volume as conveniently estimated from our database of 3D high resolution 4Pi images of GK and Wistar rat β-cells 16 . Volume of continuous network in β-cell cells of Wistar rats was insignificantly different as the sum of volumes for fragments of disintegrated mitochondrial network in β-cell cells of GK rats (Fig. 1e). Even the volume per a unit length of mitochondrial network/fragment was the same (Fig. 1f). In conclusion, mtDNA was reduced in GK rat β-cells despite the similar mass or volume of mitochondrion.
Single-stranded-DNA binding protein accumulated in smaller nucleoid compartments in Goto Kakizaki rat β-cells. Employing lentiviral transduction of mtSSB-Eos and 3D superresolution BiplaneFPALM microscopy, we have visualized nucleoids of mtDNA in primary pancreatic β-cells of PI isolated from non-diabetic Wistar control rats and age-matched diabetic GK rats. Among eight PI isolations, raw data indicated each Eos molecule localized within the experiment (Fig. 2a,b). Their grouping into apparent nucleoids 24 within the equally-sized space regions did not show any significant decline in number (spatial density) of visualized nucleoids (Table 1), despite the profound reduction in mtDNA copy number (Fig. 1a). The nucleoid density within the cell rather increased in β-cells of GK rat PI, with exception of a 10% decrease indicated by dSTORM-assisted 3D TFAM immunocytochemistry (Table 1, vide infra).
Therefore, we have performed a thorough data tessellation (grouping) using the Delaunay 3D triangulation, i.e. fitting polyhedrons within a group of localized points forming a candidate nucleoid (Fig. 2c). A step A max (tetrahedron base size) has been properly selected 24 . The resulting nucleoid size distribution plots indicated more frequently smaller mtSSB-Eos-visualized nucleoids in β-cells from PIs of diabetic GK rats, when compared to those of non-diabetic Wistar rats (Fig. 3a,b; A max = 60 nm). This was valid for both spherical (Fig. 3a,b) as well as ellipsoidal modelling of nucleoids (Fig. 3c,d). Only a few ellipsoids were oriented with their longest axis closer towards the xy-plane (pink data in Fig. 3c,d).
Using the spherical modelling of nucleoid 3D images, i.e. when a sphere represents a nucleoid of an equal volume V as obtained for the adequate smoothed polyhedron, we obtained an average nucleoid diameter d diminished by 27% in PI β-cells from GK rats (n = 650) when compared to Wistar rats (n = 460) ( Table 2). When modelling rotational ellipsoids 24 , we obtained a similar shortening of both long and short axes ( Table 2). An alternative is the Delaunay spherical modelling, when diameters d D of spheres are set equal to volumes of Delaunay polyhedrons V D . Such calculations yielded d D of 100 ± 57 nm and 76 ± 49 nm for Wistar and GK rat β-cells, respectively. Nevertheless, the resulting 24% diameter d decrease represents a 58% decrease in spherical nucleoid volume in GK rat β-cells. Such decrease well matches the mtSSB protein level decline (Fig. 1d). If the corresponding nucleoid volume was filled with mtDNA mass, this should be considered to decrease also by 58%. Expressing averages plus standard deviations or medians (Table 2), however, does not describe the entire statistics. Hence, we analyzed histograms of the data within 10 nm intervals. Figure 4a,b shows detailed histograms of Delaunay spherical models for diameters d D . Histograms for PI β-cells of both Wistar and GK rats contain two maxima at 45 nm and ~135 nm ( Fig. 4a,b). Despite the same most frequent values given by these maxima, a fraction of small nucleoids was at least twice as higher for nucleoid models of diabetic GK rat PI β-cells than for Wistar rat PI β-cells (Fig. 4a,b). In contrast, a fraction of 140 to 160 nm nucleoids was diminished more than twice (Fig. 4b). Thus, diabetic GK rat PI β-cells contain less nucleoids with diameter >150 nm and more nucleoids around 50 nm. One may speculate that these largest nucleoids are actually twins representing dividing nucleoids 24 . One may also consider these mtSSB-containing regions as the nucleoid cores 19 . Since mtSSB is considered to reflect mtDNA replication (or transcription), we may conclude that the portion of replicating mtDNA is much less abundant in diabetic Goto Kakizaki rat PI β-cells.
However, the density of localized Eos-mtSSB molecules within a single nucleoid fit into a wide range independently of nucleoid size. This range was slightly wider and on average 1.25-fold higher for GK PI rat PI β-cells (Fig. 3a,b; Table 2). Thus within an ensemble, "pointilistic" nucleoid images were composed of both dense and more diffuse points for PALM imaging, whereas the lower and narrow-range point density was characteristic for dSTORM imaging of larger nucleoids (vide infra). In conclusion, the resolved mtEos-mtSSB-contoured "nucleoids" were by 25% smaller but appear to be 1.25 times denser in β-cells of PI isolated from GK vs. Wistar rats. Since the density of blinking molecules might increase partially due to a repeatable occurrence of a molecule slightly shifted meanwhile during the data acquisition, one should consider density calculations with a caution.
Slight decrease in TFAM-visualized nucleoid volume but a drop in localized point density in diabetic PI β-cells. Much less differences were found for nucleoid size distribution, when visualized by Eos-TFAM, lentivirally-transfected into primary β-cells of PIs isolated from non-diabetic Wistar control rats and diabetic GK rats (Fig. 5a-d; Table 2). TFAM-contained space within the nucleoids was bigger than the mtSSB-contained space, as already recognized for HepG2 cells 24 . Medians for d D were equal, while averages of d D were only by 10% smaller in PI β-cells of GK rats vs. those for Wistar rats (Table 2). Detailed histograms of Delaunay spherical models for diameters d D again indicated two maxima at 45 nm and ~135 nm (Fig. 4c,d). Here, the maximum fraction of small ~45 nm nucleoids had nearly equal proportions in both Wistar rat PI β-cells (Fig. 4c,d). A fraction of ~140 to 160 nm nucleoids was even slightly more frequent in diabetic Goto Kakizaki rat PI β-cells. This may represent an expansion of TFAM-acquired space. Wistar rat PI β-cells, however, had more nucleoids (clusters) of sizes exceeding 200 nm. In contrast, the average density of localized TFAM molecules within a single nucleoid diminished by 19% (by 28% for medians) in PI β-cells of GK rats, which may reflect up to ~30% loss of total TFAM. Note that mRNA or protein semiquantification of TFAM yielded even larger decrease (Fig. 1c,d).
Overexpression of Eos-conjugated proteins employed in the above experiments also tests the vitality of isolated PIs, indicating functional protein expression machinery. To make a snapshot of native TFAM protein present, we have alternatively employed anti-TFAM antibodies in 3D dSTORM-assisted immunocytochemistry with Alexa Fluor 647 conjugated secondary antibodies (Fig. 6a-d; Table 2). The resulting histograms for diameters d D of Delaunay spherical models, however, exhibited again a single most frequent diameter d D around 45 nm in both Wistar and Goto Kakizaki PI rat β-cells (Fig. 4e,f). The only differences in histograms were apparent as less population of nucleoids >100 nm in Goto Kakizaki rat PI β-cells. However, within ensembles of nucleoids for GK samples, dSTORM yielded by 10% lower number of nucleoids per cell volume (Table 1), despite only a subtle decline in sizes -diameters d D or any parameters of ellipsoid models (Fig. 6a-d; Table 2).
The lack of biogenic transcription factors may reduce/impair mtDNA replication machinery in GK rat PI β-cells. Previously, we reported on δ-cell hyperplasia developed after six weeks of age in PI of diabetic GK rats. This finding with the well established decrease of β-cells in PI of GK rats with age (and their peripheral insulin resistance developed already prior to the six weeks of age) suggest that the impaired or deregulated biogenesis of islet cells and resulting disharmony in their paracrine relationships contribute to the diabetic phenotype. To further elucidate it, we assayed for a β-cell-specifying transcription factor 12,13 Nkx6.1. In PI of adult GK rats, and of less extent in 6-weeks old, we found a profound decrease of Nkx6.1 transcript. Thus, RT PCR assessment (relatively to β-actin) in isolated PI at weeks 35, 37, or 39-41 has shown a ~12-fold decrease of Nkx6.1 mRNA (Fig. 7a) in GK rats as compared to Wistar controls. Similar decrease was found for Nkx6.1 protein (Fig. 7b). Young, six week old GK rats exhibited still high Nkx6.1 mRNA levels but 60-75% of those in Wistar rats (Fig. 7c,d). In both, non-diabetic and diabetic rats, Nkx6.1 decreased with age but more profoundly in diabetic GK rats, for which turned out to be a good marker of hyperglycemia (Fig. 7c). For both rat strains reciprocal correlation was found between Nkx6.1 mRNA levels and body weight (Fig. 7d).
We have also confirmed a decrease in protein levels of Nkx6.1 with age, while a more intensive decline was found for old GK rats (Fig. 7b).

Discussion
Organization of mtDNA within the nucleoids is still a matter of debate 18,19 , as well as detailed changes during the typically physiological situations, including mtDNA transcription and mtDNA replication. It is not known, whether, when and how nucleoids divide, despite the first snapshots of such possible events have been reported 24 . Variations of TFAM-contoured nucleoid size have been reported under numerous pathological conditions as well as decline of mtDNA copy number 37,38 . However, when conventional confocal microscopy was used, one could not distinguish single nucleoids from nucleoid clusters. We do not know, whether cells with lower mtDNA copy number should contain less nucleoids or nucleoids with a smaller size or a combination of both.
In this work we have elucidated some of these aspects in the case of a highly reduced (by 75%) mtDNA copy number, as found in PI β-cells of one year old Goto Kakizaki rats 15 . The apparent mitochondrial volume, however, remained the same. Either nucleoid diameter reduction by ~37% or nucleoid number by 75% or combination of both was expected. Surprisingly, the prediction of lower nucleoid number turned out to be invalid. We have even obtained an increased nucleoid spatial density with some employed markers; alternatively a 10% decrease was observed by 3D TFAM immunocytochemistry (Table 1). In contrast, the prediction of 37% reduction of nucleoid size at 75% mass losses turned out to be reflected only when employing mtSSB protein for visualizing nucleoid cores which might be active in mtDNA replication and/or transcription. In principle, such visualization indicates the extent of mtDNA cores containing single-stranded DNA regions, which are much smaller than the TFAM-containing regions 24 . Using spherical modelling, volumes of these regions decreased on average by ~25%, corresponding to a ~58% mass (mtSSB bound to ss mtDNA) reduction (cf. Figure 1a,b). This reduction was also matched by western blots, indicating more than 50% mtSSB decline. Diabetic GK rat PI β-cells contained less nucleoids with diameter >150 nm but more small nucleoids (around 50 nm). Thus the detailed diameter histograms indicated shift from 140 nm to 160 nm regions down to a <100 nm region for GK rat PI β-cells when compared to Wistar controls. However in these smaller regions, more dense Eos-mtSSB molecules were bound. A partial contribution of a drift of blinking molecules (though existing in both types of samples) might artificially increase such density. We may conclude that the regions with any "active" mtDNA (transcribing or replicating, i.e. requiring Eos-mtSSB) within the nucleoids are diminished in diabetic GK PI β-cells.
In the case of TFAM-Eos, GK PI β-cells contained less nucleoids in the range over 200 nm that might represent rather clusters of several nucleoids or even dividing nucleoids 24 . Moreover, GK rat PI β-cells had reduced density of localized points (blinking Eos molecules) within model nucleoids with only slightly diminished nucleoid diameters. This might indicate expansion of mtDNA with similar or lower stoichiometric TFAM amount.  The model of single mtDNA molecule within a single nucleoid is rejected by our results. In any of multiple imaging ways, the nucleoid number (exactly spatial density, see Table 1) rather increased despite the diminished mtDNA copy number. Our preliminary data counting D-loops visualized by a poly-fluorophore DNA probe against the 7S DNA indicate the existence of several nucleoid fractions, nucleoids having 2, 3, 4, 5 and even in ~1% fraction 6 D-loops within a single nucleoid (Capková N, unpublished data), beside the prevailing fraction with single D loop. When considering the single mtDNA per nucleoid, those nucleoids with multiple D-loops should represent nucleoids under mtDNA replication. However, the maintained nucleoid number at drastic copy number reduction cannot be explained.
We have also pointed out to the link between the decreased mtDNA in diabetic β-cells and even more declining β-cell identifying and maintenance transcription factor Nkx6.1 (down to ~8%). Although Nkx6.1 transcript decreased with age in both non-diabetic Wistar and diabetic Goto Kakizaki rats, the decrease was much stronger in PI of diabetic rats (the oldest tested exhibited Nkx6.1 protein down to ~4%). Since Nkx6.1 is controlling a gene regulatory network required for establishing and maintaining β-cell mass within PIs 10,11 , its negative effect on factors and proteins required for mitochondrial biogenesis is expected. More drastic Nkx6.1 decline above     Fig. 5a,b). (e,f) TFAM dSTORM (data of Fig. 6a,b).
that occurring naturally with aging must impair β-cell function. Although mitochondrial biogenesis factors such as PGC1α decreased in less extent, synergy of these housekeeping and biogenetic impairments must affect the resulting mtDNA replication and content. This corresponds also to lowered transcript of mitochondrial polγ. Previously, also a diabetic phenotype has been found in aged mice with ablated β 2 -adrenergic receptor accompanied by the reduced expression of peroxisome proliferator-activated receptor (PPARγ), pancreatic duodenal home homeobox-1 (PDX-1) transcription factor, and glucose transporter (GLUT2) 39 . Finally, we would like to point out that the mitochondrion exists in the cell (the single network of mitochondrial reticulum in intact cells) and that the term mitochondria represents, in fact, the existing fragments of the network when fission prevails over fusion 40 , such as found in diabetic Goto Kakizaki rats 16 . The isolated mitochondria are then produced from the artificially cut network. Hence the term mitochondrial mass must refer to the mass of all fragments of the network or to the whole continuous network and can be approximated by the mitochondrial volume as we derived from our 3D 4Pi high resolution microscopic images. We prefer this approximation of "mitochondrial amount" to measurements of aconitase activity or marker proteins which have some limitations 41 .
In conclusion, we hypothesize that the diminished Nkx6.1-mediated maintenance results in decreased mtDNA replication and hence decreased mtDNA copy number in diabetic Goto Kakizaki PI β-cells. However, mtDNA is more spread within the single nucleoid, consequently maintaining their size at least in a fraction of a nucleoid ensemble.

Methods
Vector Constructs for nucleoid visualization. The pLenti6.3/V5-DEST vector (Life Technologies, currently Thermo Fisher Scientific, Waltham, MA) has been adopted for conjugation of any ORF with the dimerizing Eos. A single Eos sequence was amplified from pcDNA3-Flag1-td-EosFP vector (MoBiTec Rastatt, Germany) and subcloned behind the attR2 site into the pLenti6.3/V5-DEST using XhoI restriction site giving rise to pLenti6.3-C-EOS-V5-DEST enabling c-terminal fusion with dimeric Eos sequence after LR-recombination reaction, since ptd-EostFP encodes dimeric Eos protein 42 due to the T/R substitution of wt Eos. Expression thus causes dimerization of the fusion protein with its other dimeric counterpart. The resulting vector enables C-terminal fusion of protein of interest with respective fluorescent protein. Accordingly, the entry clones (ORFs in pENTR221 vector, Life Technologies/Thermo Fisher) of TFAM (ID IOH42148), and mtSSB (ID IOH63190), were subcloned into our pLenti6.3-C-EOS-V5-DEST vectors using LR-recombination reaction. Lentiviral particle production. The pLenti6.3-C-EOS-V5-DEST-based constructs have been multiplied, purified and used for lentiviral particle production according to the manufacturer instructions. Thus the lentiviral stock (containing the packaged pLenti expression construct) was produced by co-transfecting the optimized packaging plasmid mix (packaging plasmids pLP1, pLP2, and pLP/VSVG, which supplies the helper functions as well as structural and replication proteins required to produce the lentiviruses) and our expression construct into the 293LTV cell line, a derivative of the 293F Cell Line. The 293 LTV cell line is stably and constitutively expressing the SV40 large T antigen facilitating an optimal lentivirus production. Lipofectamine 2000 (Thermo Fisher) was used as the transfection reagent. The lentiviral stock was filtered and concentrated by PEG-it Virus Precipitation Solution or using its separation by ultracentrifugation. mtDNA copy number estimation. The mtDNA from PIs or primary β-cells was isolated by phenolchloroform extraction. SYBR Green qPCR amplification used primers annealing on the UCP2 nuclear gene (intron 2 and exon 3) and the ND5 mitochondrial gene (bp 11092 to 11191 according to Genebank sequences from The National Center for Biotechnology Information, USA). Alternatively, 7S mtDNA sequence bp 15412 to bp 16309 bp was used to include mtDNA with possible deletions. The ratio between ND5 amplicon (7S mtDNA) and half of nuclear amplicon amounts was taken as the mtDNA copy number per cell.
For GK PI only the cells stained for β-cell-selective markers (see below) were imaged. Eos fluorophore of conjugate marker proteins was activated with the 405 nm laser line and Eos red fluorescence was read out as excited with the 561 nm laser line at ~5 kW/cm 2 . Two raw images (512 × 256 pixels, 16 bit) were taken at rate 33 frames per second. To ensure an even distribution of detected molecules over the entire axial range, the objective position was stepped at 500 nm intervals over a range of about 3 μm for the selected cell. The axial scanning procedure was therefore repeated several times with only a fraction of the molecules activated during each cycle. This ensures nearly constant particle yields over the complete axial range. Measurement took place over the course of several minutes and resulted from ten up to ~1500 of localized fluorophores per nucleoid. The average photon count from a single signal detected and localized was 400. The average number of events per frame was 6.2.
3D immunocytochemistry by dSTORM. Cells were fixed by 4% paraformaldehyde for 10 min and washed twice in phosphate buffered saline (PBS). Further steps were done in "washing PBS" containing 0.05% Triton ×100, 0.05% Tween 20, and 0.1 M glycine. The fixed cells were blocked by 5% donkey serum (Jackson ImmunoResearch, West Grove, PA) for one hour and then the selected primary antibodies were applied, rabbit anti-insulin and mouse anti-TFAM antibodies (Abcam/Thermo Fisher); alternatively, after the bromo-deoxyuridine (BrdU) pretreatment prior to fixation, mouse anti-BrdU antibodies (Progen Biotechnik, Heidelberg, Germany) were applied. Coverslips were then washed three times in "washing PBS" and incubated with donkey anti-rabbit and anti-mouse IgG secondary antibody conjugated with Alexa Fluor 488 and 647, respectively (Life Technologies/Thermo Fisher). Finally, samples were washed three times in PBS and mounted in the "dSTORM buffer" (10% glucose, 50 mM β-mercaptoethanol, 169 units of glucose oxidase, 1.4 units of catalase all in 10 mM NaCl, 50 mM Tris-HCl (pH 8.0). Only Alexa Fluor 488 positive cells were imaged. Imaging was performed using the BiplaneFPALM instrument at 641 nm, 3.5 kW/cm 2 . The average photon count from a single signal detected and localized was ~1400 for anti-TFAM; ~2300 for anti-BrdU. The typical number of events per frame was around 1.
Single nucleoid determination from 3D data. 3D image reconstruction was done as described elsewhere 24 . Paraview software (www.paraview.org) was used including Python programming language modules for tetrahedron parameter functions, thus ensuring filtering or drawing of bounding ellipsoid. Routinely in each image, only nucleoids constructed from more than 10 localized Eos or Alexa Fluor 647 molecules were considered. Sets of localized particles were segmented into individual nucleoids by Delaunay triangulation algorithm 45 . The resulting convex hulls were filled with the corresponding tetrahedrons (pyramids) with the base of size A max (in nm). Tetrahedrons with all edges shorter than the threshold value A max represented rough nucleoid models, where an individual nucleoid is given by polyhedrons given by a set of connected tetrahedrons (Fig. 2c). For spherical modelling the resulting polyhedrons were approximated by spheres of the equal volume as either i) the resulting polyhedron for each nucleoid (volume V D yielding the corresponding diameter d D ); or ii) smoothed polyhedron with tetrahedrons added to get convex shapes (volume V yielding the corresponding diameter d). Ellipsoid modelling was also performed as further refinement based upon the Principal component analysis. Rotational ellipsoids were illustrated with a volume equal to V D (detailed description see 24 ), yielding the diameter of the longest and the short ellipsoid axis d max and d min . We have also taken account of ellipsoid orientation, given by unit space vectors oriented as the the longest ellipsoid axis. Their axial projections are denoted as a x , a y , a z . Defining θ as the angle between the longest ellipsoid axis and z axis, we have sorted out the nucleoids oriented with the longest axis tilted more towards the xy plane as those with θ < 45° Since, it is valid that θ = arctg [(a x 2 + a y 2 ) 1/2 /a z ], the ratio |A r /a z | has to be higher 24 than 1 for θ < 45°.
3D 4Pi microscopy and image analysis. 3D images were obtained and analyzed essentially as described elsewhere 16 . Briefly, custom measurements at the Jackson laboratory, Bar Harbor, MN with a Leica TCS 4PI microscope have been performed with GK and control Wistar PI samples lentivirally transduced with mtRoGFP. Images were visualized in 3D projections created with Amira 5.3 (FEI, originally Visage Imaging, Berlin, Germany) in an iso-surface mode. The intensity threshold IT for surface rendering was set to 30-35 to obtain similar tubule diameters as measured from the original data 16 . Volumes of the continuous or fragmented mitochondrial network were derived with the aid of the Autoskeleton function.
Data availability statement. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.