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Anomalous diffusion induced by cristae geometry in the inner mitochondrial membrane.

Sukhorukov VM, Bereiter-Hahn J - PLoS ONE (2009)

Bottom Line: Geometrical confinement induces up to several-fold reduction in apparent mobility.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.The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.

View Article: PubMed Central - PubMed

Affiliation: Kinematic Cell Research, Institute for Cell Biology and Neurosciences, Johann Wolfgang Goethe University, Frankfurt am Main, Germany. sukhorukov@kizefo.de

ABSTRACT
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.

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Time dependence of the projected diffusivities.Comparison of MC results for tubular cristae geometry (dots) to the theoretical model, Eq. 8, (red lines) for two examplary membrane configurations. Cristae density σ = 126 cristae per micrometer, fully permeable junctions. Definition of the transition time for alternative models of transient anomalous diffusion is illustrated with black lines.
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pone-0004604-g008: Time dependence of the projected diffusivities.Comparison of MC results for tubular cristae geometry (dots) to the theoretical model, Eq. 8, (red lines) for two examplary membrane configurations. Cristae density σ = 126 cristae per micrometer, fully permeable junctions. Definition of the transition time for alternative models of transient anomalous diffusion is illustrated with black lines.

Mentions: Eq. 8 can be compared to the Monte Carlo results obtained in membranes with cristae having finite lengths as is shown in Fig. 8 for exemplary configurations. Generally, for L/a≫1 Eq. 8 offers a good approximation to the simulation data everywhere except the transition region t∼T (the discrepancy is probably due to the hexagonal cross-section of cristae in the MC lattice model). However, because Eqs. 7 and 8 assume infinitely long tubes, for cristae with L/a∼1 the exponent α in Eq. 9 differs from 1 decreasing the applicability of Eq. 8 (the deviation is in the range of several percent). In real membranes with tilted or curved cristae, the effective radius should be taken bigger than the tube's radius, resulting in a longer range of the short-time diffusivity regime. Even though Eq. 8 was introduced as a model for the tubular geometry only, the MC results (Fig. 5) indicate that the functional shape of Eq. 9 (with different values of parameters) can be valid for both tubular and lamellar cristae geometry.


Anomalous diffusion induced by cristae geometry in the inner mitochondrial membrane.

Sukhorukov VM, Bereiter-Hahn J - PLoS ONE (2009)

Time dependence of the projected diffusivities.Comparison of MC results for tubular cristae geometry (dots) to the theoretical model, Eq. 8, (red lines) for two examplary membrane configurations. Cristae density σ = 126 cristae per micrometer, fully permeable junctions. Definition of the transition time for alternative models of transient anomalous diffusion is illustrated with black lines.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2643486&req=5

pone-0004604-g008: Time dependence of the projected diffusivities.Comparison of MC results for tubular cristae geometry (dots) to the theoretical model, Eq. 8, (red lines) for two examplary membrane configurations. Cristae density σ = 126 cristae per micrometer, fully permeable junctions. Definition of the transition time for alternative models of transient anomalous diffusion is illustrated with black lines.
Mentions: Eq. 8 can be compared to the Monte Carlo results obtained in membranes with cristae having finite lengths as is shown in Fig. 8 for exemplary configurations. Generally, for L/a≫1 Eq. 8 offers a good approximation to the simulation data everywhere except the transition region t∼T (the discrepancy is probably due to the hexagonal cross-section of cristae in the MC lattice model). However, because Eqs. 7 and 8 assume infinitely long tubes, for cristae with L/a∼1 the exponent α in Eq. 9 differs from 1 decreasing the applicability of Eq. 8 (the deviation is in the range of several percent). In real membranes with tilted or curved cristae, the effective radius should be taken bigger than the tube's radius, resulting in a longer range of the short-time diffusivity regime. Even though Eq. 8 was introduced as a model for the tubular geometry only, the MC results (Fig. 5) indicate that the functional shape of Eq. 9 (with different values of parameters) can be valid for both tubular and lamellar cristae geometry.

Bottom Line: Geometrical confinement induces up to several-fold reduction in apparent mobility.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.The data demonstrate that if not taken into account appropriately, geometrical effects lead to significant misinterpretation of molecular mobility measurements in cellular curvilinear membranes.

View Article: PubMed Central - PubMed

Affiliation: Kinematic Cell Research, Institute for Cell Biology and Neurosciences, Johann Wolfgang Goethe University, Frankfurt am Main, Germany. sukhorukov@kizefo.de

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus