- Anomalous diffusion induced by cristae geometry in the inner mitochondrial membrane (2009)
- 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 (2009)
- 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.
- Emergence of the mitochondrial reticulum from fission and fusion dynamics (2012)
- 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.