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Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This burden can be partially decreased by using discrete models, however even then the practical application is limited to relatively small material volumes. This paper formulates a homogenization scheme for discrete diffusion models. Asymptotic expansion homogenization is applied to distinguish between (i) the continuous macroscale description approximated by the standard finite element method and (ii) the fully resolved discrete mesoscale description in a local representative volume element (RVE) of material. Both transient and steady‐state variants with nonlinear constitutive relations are discussed. In all the cases, the resulting discrete RVE problem becomes a simple linear steady‐state problem that can be easily pre‐computed. The scale separation provides a significant reduction of computational time allowing the solution of practical problems with a negligible error introduced mainly by the finite element discretization at the macroscale. [ABSTRACT FROM AUTHOR]

Biogenesis of F1Fo ATP synthase, the key enzyme of mitochondrial energy provision, depends on transmembrane protein 70 (TMEM70), localized in the inner mitochondrial membrane of higher eukaryotes. TMEM70 absence causes severe ATP-synthase deficiency and leads to a neonatal mitochondrial encephalocardiomyopathy in humans. However, the exact biochemical function of TMEM70 remains unknown. Using TMEM70 conditional knockout in mice, we show that absence of TMEM70 impairs the early stage of enzyme biogenesis by preventing incorporation of hydrophobic subunit c into rotor structure of the enzyme. This results in the formation of an incomplete, pathologic enzyme complex consisting of F1 domain and peripheral stalk but lacking Fo proton channel composed of subunits c and a. We demonstrated direct interaction between TMEM70 and subunit c and showed that overexpression of subunit c in TMEM70-/- cells partially rescued TMEM70 defect. Accordingly, TMEM70 knockdown prevented subunit c accumulation otherwise observed in F1-deficient cells. Altogether, we identified TMEM70 as specific ancillary factor for subunit c. The biologic role of TMEM70 is to increase the low efficacy of spontaneous assembly of subunit c oligomer, the key and rate-limiting step of ATP-synthase biogenesis, and thus to reach an adequately high physiologic level of ATP synthase in mammalian tissues. [ABSTRACT FROM AUTHOR]