The origin of eukaryotic cell size and complexity is often thought to have required an energy excess supplied by mitochondria. Recent observations show energy demands to scale continuously with cell volume, suggesting that eukaryotes do not have higher energetic capacity. However, respiratory membrane area scales superlinearly with the cell surface area. Furthermore, the consequences of the contrasting genomic architectures between prokaryotes and eukaryotes have not been precisely quantified. Here, we investigated (1) the factors that affect the volumes at which prokaryotes become surface area-constrained, (2) the amount of energy divested to DNA due to contrasting genomic architectures and (3) the costs and benefits of respiring symbionts. Our analyses suggest that prokaryotes are not surface area-constrained at volumes of 10⁰‒10³ µm³, the genomic architecture of extant eukaryotes is only slightly advantageous at genomes sizes of 10⁶‒10⁷ base pairs and a larger host cell may have derived a greater advantage (lower cost) from harbouring ATP-producing symbionts. This suggests that eukaryotes first evolved without the need for mitochondria since these ranges hypothetically encompass the last eukaryotic common ancestor and its relatives. Our analyses also show that larger and faster-dividing prokaryotes would have a shortage of respiratory membrane area and divest more energy into DNA. Thus, we argue that although mitochondria may not have been required by the first eukaryotes, eukaryote diversification was ultimately dependent on mitochondria.

真核细胞大小和复杂性的起源通常被认为需要线粒体提供的能量过剩。最近的观察表明能量需求随着细胞体积的增加而不断增加，这表明真核生物没有更高的能量容量。然而，呼吸膜面积与细胞表面积成超线性关系。此外，原核生物和真核生物之间基因组结构对比的后果尚未被精确量化。在这里，我们调查了 (1) 影响原核生物体积的因素，在该体积下原核生物变得受表面积限制，(2) 由于对比基因组结构而分配给 DNA 的能量量，以及 (3) 呼吸共生体的成本和收益。我们的分析表明，原核生物在体积为 10 时不受表面积限制⁰ ∼10 ³  µm ³，现存真核生物的基因组结构在基因组大小为 10 ⁶ ∼10 ⁷ 碱基对时仅略微具有优势，而更大的宿主细胞可能从容纳产生 ATP 的共生体中获得更大的优势（成本更低）。这表明真核生物最初是在不需要线粒体的情况下进化的，因为这些范围假设涵盖了真核生物的最后一个共同祖先及其亲属。我们的分析还表明，更大和更快分裂的原核生物会缺乏呼吸膜面积，并将更多能量转移到 DNA 中。因此，我们认为，虽然第一批真核生物可能不需要线粒体，但真核生物的多样化最终取决于线粒体。