Emergence of the mitochondrial reticulum from fission and fusion dynamics

Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging

Anomalous Diffusion Induced by Cristae Geometry in the Inner Mitochondrial Membrane

Diffusion of inner membrane proteins is a prerequisite for correct functionality of mitochondria. The complicated structure of tubular, vesicular or flat cristae and their small connections to the inner boundary membrane impose constraints on the mobility of proteins making their diffusion a very complicated process. Therefore we investigate the molecular transport along the main mitochondrial axis using highly accurate computational methods. Diffusion is modeled on a curvilinear surface reproducing the shape of mitochondrial inner membrane (IM). Monte Carlo simulations are carried out for topologies resembling both tubular and lamellar cristae, for a range of physiologically viable crista sizes and densities. Geometrical confinement induces up to several-fold reduction in apparent mobility. IM surface curvature per se generates transient anomalous diffusion (TAD), while finite and stable values of projected diffusion coefficients are recovered in a quasi-normal regime for short- and long-time limits. In both these cases, a simple area-scaling law is found sufficient to explain limiting diffusion coefficients for permeable cristae junctions, while asymmetric reduction of the junction permeability leads to strong but predictable variations in molecular motion rate. A geometry-based model is given as an illustration for the time-dependence of diffusivity when IM has tubular topology. Implications for experimental observations of diffusion along mitochondria using methods of optical microscopy are drawn out: a non-homogenous power law is proposed as a suitable approach to TAD. The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes

Molecular diffusion in mitochondrial membranes

Mitochondria are dynamic organelles indispensible for viability of eukaryotic cells. Diffusion of proteins in mitochondrial membranes is a prerequisite for the correct functionality of the organelles. However, its study is made complicated due to the nontrivial geometry, small size and positional instability of the organelle, restricting the usability of regular experimental methods and theoretical understanding of acquired data. Therefore, here the molecular transport along the main mitochondrial axis was investigated using highly accurate computational methods combining them with traditional experimental approaches. Using recently reported electron microscopic tomography data concerning the constitution of mitochondria [Fre02], a lattice model of the inner mitochondrial membrane (IM) reproducing its structure in great details was built up. With Monte Carlo (MC) simulations of particle dynamics on this model, it was found that the membrane geometry induces nonlinear effects in the motion of molecules along the mitochondrial axis, which in turn lead to a transient violation of the 2nd Fick?s equation. We show that mere curvature of the IM resulting from the presence of cristae is sufficient for the emergence of transient anomalous diffusion (TAD) in the membrane. The MC calculations have enabled an accurate estimation of regularities in the extent of deviations from the normal regime, therefore allowing us to propose non-homogenous power law as a suitable generalization of the current approach to the analysis of experimental data for the transient dynamics. The general cause of TAD resulting from the membrane curvature alone, without any involvement of specific inter-particle interactions prompted us to predict the similar dynamical effect also for other curved cellular membranes, be it diffusion in endoplasmic reticulum or in plasma membrane of cells possessing dense microvilli. The data indicate that the geometry-induced anomalous diffusion should be easily detectable with current experimental methods, but only in the restricted range of time scales corresponding to high temporal resolution. Until now, experimental measurements of molecular diffusion in biological membranes indiscriminately assumed either pure normal or pure anomalous diffusion schemes for the analysis of data acquired in very wide range of temporal resolutions, which often lead to ambiguities in the interpretation of diffusion parameters. The MC calculations have clearly illustrated the necessity for a more subtle treatment of experimental conditions: the assumption of pure Gaussian diffusion model is justified only if the applied temporal resolution is sufficiently low (as is often the case when using scanning techniques exemplified further); otherwise, the transient regime should be tested for by means of the non-homogenous power function. In the second part of the study the Fluorescence Recovery after Photobleaching (FRAP) with the laser scanning microscope is introduced as a method of choice for studying protein mobility within mitochondrial membranes. The conventional FRAP methodology [Axe76] was extended to enable its application for the determination of confined diffusion with conventional laser scanning microscopes which allowed us to communicate for the first time the direct measurement of protein diffusion in mitochondrial membranes of living cells. This is achieved through adaptation of FRAP data analysis to account for the spatial dimensions of the organelle and the spatiotemporal pattern of light pulses induced by the microscope. The experimental circumstances existing during the particular measurement session are computationally recreated and this way the best suited values of diffusion parameters are found. The method is validated experimentally for four FP-tagged mitochondrial membrane proteins: the IM OxPhos complexes F1F0 ATPase and cytochrome c oxidase and for Tom7 and hFis1 - components of the mitochondrial protein import and fission machineries respectively localized in the outer membrane. We find that for all proteins simple normal diffusion is not a sufficient description. In the inner membrane, diffusion coefficient of F1F0 ATPase expressed in HeLa cell line is found to be 0.2 ?m2/s, with more than 1/3 of the protein molecules being immobilized, while cytochrome c oxidase (in CEF primary cells) demonstrated a similar diffusivity pattern (0.4 ?m2/s, 30% immobile). In the outer membrane, the D (0.7 ?m2/s) and immobile fraction (7-8%) of GFP-Tom7 and GFP-hFis1 (both in HeLa cells) are identical, which designates a substantial difference in comparison to the IM protein mobility. Diffusion coefficients of mitochondrial membrane proteins studied here lay in the intermediate region between those measured in artificial bilayers and in plasma membranes. Protein crowding and intermolecular interactions will be among the major causes responsible for the detected slowdown of diffusion.Mitochondrien sind dynamische, für die Entwicklungsfähigkeit eukaryotischer Zellen unentbehrliche Organellen. Grundvoraussetzung für ihre einwandfreie Funktionalität ist die Diffusion von Proteinen in der mitochondrialen Membran, die aber bis jetzt rätselhaft ist. Hauptgründe hierfür sind die geringe Größe, nicht triviale Geometrie und Lageinstabilitäten der Organellen. Deshalb wurde mittels sehr sorgfältiger und genauer Rechenmethoden in Kombination mit herkömmlichen experimentellen Vorgehensweisen der Molekültransport längs der mitochondrialen Hauptachse untersucht. Mit Monte Carlo Simulationen der Teilchendynamik wurde gezeigt, dass die Geometrie der inneren Membran (IM) nicht lineare Effekte bei der Molekülbewegung längs der Mitochondrien induziert. Dies wiederum hat eine transiente Verletzung des 2-ten Fick'schen Gesetzes zur Folge. Die durch das Vorhandensein der Cristae bedingte Krümmung der IM bewirkt das transiente Auftauchen der anomalen Diffusion, während in quasi-normalen Regimen innerhalb kurz- und langzeitiger Grenzen für den projizierten Diffusionskoeffizienten endliche und feste Werte wiedergewonnen werden. Für diese Fälle hat ein einfaches Flächenskalierungsgesetz sich als ausreichend herausgestellt zur Erklärung der Diffusionskoeffizienten für durchlässige Cristae-Junctions. Innerhalb langzeitiger Grenzen bewirken die geometrischen Beschränkungen eine mehrfache Reduzierung der sichtbaren Mobilität. Methoden der optischen Mikroskopie betreffend wurden Folgerungen gezogen für die experimentelle Beobachtung der Diffusion längs der Mitochondrien: Die Daten zeigen, werden geometrische Effekte nicht angemessen berücksichtigt, führt dies zu signifikanten Fehlinterpretationen bei Messungen der Molekülmobilität in zellulären, krummlinigen Membranen. ''Fluorescence Recovery after Photobleaching'' (FRAP), ausgeführt mit einem Laser Scanning Mikroskop, wurde als Methode zur Erforschung der Proteindiffusion in der mitochondrialen Membran ausgewählt. Die herkömmliche FRAP-Methode [Axe76] wurde erweitert, um sie zur Bestimmung begrenzter Bewegungen nutzbar zu machen. Dies versetzte uns in die Lage, erstmalig die direkte Messung der Diffusion von Proteinen in der Mitochondrienmembran lebender Zellen bekannt zu machen. Erreicht wird dies, indem bei der FRAPDatenanalyse die räumlichen Dimensionen der Organelle und die raumzeitliche Reihenfolge der durch das Mikroskop verursachten Lichtimpulse berücksichtigt werden. Die vorgeschlagene Methode bildet rechnerisch die experimentellen Verhältnisse nach, die während der Messsitzungen existierten. Auf diese Weise lässt sich die beste Werteanpassung der Diffusionsparameter erzielen. Die Gültigkeit der Methode wird experimentell für vier FP-markierte mitochondriale Membranproteine bestätigt, und zwar für die IM OxPhos Komplexe F1F0 ATPase, und cytochrome c oxidase, und auch für Tom7 und hFis1 - die Komponenten der Import- und Teilungsmaschinerie der mitochondrialen Proteine, lokalisiert in der äußeren Membran. Für den Diffusionskoeffizienten der inneren Membran wurde für die F1F0 ATPase (in HeLa Zellenlinien) ein Wert von 0.2 μm2/s ermittelt, wobei mehr als 1/3 der Proteinmoleküle immobilisiert sind. Cytochrome c oxidase (in CEF Primärzellen) zeigte eine ähnliche Diffusität (0.4 μm2/s, 30% immobil). Bezüglich der äußeren Membran sind der Diffusionskoeffizient (0.7 μm2/s) und die immobile Fraktion (7-8%) von GFPTom7 und GFP-Fis1 (beide in HeLa Zellen) identisch, was im Vergleich mit der Proteinmobilität der IM eine beträchtliche Differenz erkennen lässt. Die statistisch signifikante Abnahme der immobilen Fraktion von GFP-Tom7 auf 2% nach einstündiger Hemmung der zellulären Proteinproduktion zeigt an, dass Tom7 auf ladungsabhängige Weise immobilisiert wird mit erhöhter Immobilisierung bei aktivem Transport von Proteinen durch die äußere Membran. Die ermittelten Diffusionskoeffizienten der Mitochondrienmembran sind viel kleiner als jene, die in künstlichen Doppelschichten gemessen wurden. Proteinüberbevölkerung und intermolekulare Wechselwirkungen sind zu den Hauptursachen zu zählen für die nachgewiesene Verlangsamung der Diffusion

Structural Heterogeneity of Mitochondria Induced by the Microtubule Cytoskeleton.

By events of fusion and fission mitochondria generate a partially interconnected, irregular network of poorly specified architecture. Here, its organization is examined theoretically by taking into account the physical association of mitochondria with microtubules. Parameters of the cytoskeleton mesh are derived from the mechanics of single fibers. The model of the mitochondrial reticulum is formulated in terms of a dynamic spatial graph. The graph dynamics is modulated by the density of microtubules and their crossings. The model reproduces the full spectrum of experimentally found mitochondrial configurations. In centrosome-organized cells, the chondriome is predicted to develop strong structural inhomogeneity between the cell center and the periphery. An integrated analysis of the cytoskeletal and the mitochondrial components reveals that the structure of the reticulum depends on the balance between anterograde and retrograde motility of mitochondria on microtubules, in addition to fission and fusion. We propose that it is the combination of the two processes that defines synergistically the mitochondrial structure, providing the cell with ample capabilities for its regulative adaptation

Diffusion in the inner membrane having tubular cristae.

<p>Relative diffusivities projected on the long mitochondrial axis for different tubular cristae configurations. <i>Red</i>: fully permeable junctions (p = (1,1)), <i>green</i>: fully impermeable junctions (p = (0,0)). (<i>A</i>) For indicated cristae lengths <i>L</i> (in units of mitochondrial radius <i>R_m</i> = 200 nm). Cristae junction radius <i>a</i> = 14 nm and density <i>σ</i> = 126 cristae per µm of mitochondrial length. (<i>B</i>) For indicated cristae junction radii, (in units of <i>a</i> = 14 nm), <i>L</i> = 0.8<i>R_m</i>, <i>σ</i> = 126, p = (1,1). (<i>C</i>) For indicated cristae densities, <i>a</i> = 14 nm, <i>L</i> = 0.8<i>R_m</i>, p = (1,1).</p

Probability distribution of escape times from tubular cristae.

<p>Cristae have radius <i>a</i> = 14 nm and lengths as indicated in the legend (in units of mitochondrial radius <i>R_m</i> = 200 nm). Power law <i>t</i>^−3/2 (<i>magenta</i>) is shown for comparison. Insert: Average time spent inside a crista versus cristae length (<i>circles</i>), linear fit (<i>line</i>).</p

Lattice architecture of lamellar cristae.

<p>Tracers are positioned at nodes of the triangular lattice. <i>Red</i>: Inner boundary membrane, <i>violet</i>: Crista junction, <i>blue</i>: Tubular crista subcompartment, <i>turquoise</i>: Crista main body.</p

Examplary cristae configurations.

<p>(<i>A</i>) tubular; (<i>B</i>)–(<i>D</i>) lamellar.</p

Relative projected diffusivities for tubular cristae of the same membrane area.

<p>Ratios of junction radius <i>a</i> to crista length <i>L</i> are as indicated. Cristae density <i>σ</i> = 126 cristae per µm of mitochondrial length, fully permeable junctions.</p

Limiting values of projected diffusivities: comparison of the MC results to the area scaling theory.

<p>Long-term (<i>open markers</i>) and short-term (<i>filled markers</i>) limiting values for tubular (<i>circles</i>) and lamellar (<i>squares</i>) cristae topologies obtained from fits to the Monte Carlo simulations (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004604#pone-0004604-g004" target="_blank">Figs. 4</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004604#pone-0004604-g005" target="_blank">5</a>) for different cristae sizes (<i>i.e.</i> cristae length in the case of tubular topology, lamellae diameter in the case of lamellar one), fully permeable junctions and <i>a</i> = 14 nm. Other paramemters are as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004604#pone-0004604-g004" target="_blank">Fig. 4<i>A</i></a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0004604#pone-0004604-g005" target="_blank">Fig. 5<i>A</i></a>. Statistical errors (40 configurations) are in the range from ±0.001 to ±0.004. The same variables computed according to the area scaling model (Eqs. 4, 5) are shown as <i>lines</i>.</p