TOKYO—Global private equity firm Carlyle said on Wednesday it led a $312 million funding round for Japanese biotech company Spiber Inc, joining other global investors in betting on a growing number of late-stage Japanese startup firms. Carlyle’s 10 billion yen ($91 million) stake in Spiber represents the group’s first non-buyout, minority investment in an unlisted startup in Japan, where startup funding is soaring. The round, which also includes investments from fund managers Fidelity and Baillie Gifford, will be made through a combination of the allotment of new shares and a capital infusion at a valuation of about 135 billion yen ($1.22 billion). Spiber makes plant-based protein polymers through microbial fermentation, which can be spun into animal—and plastic-free fibres for clothing, auto parts and other uses. The 14-year-old company plans to use the proceeds to build a mass production facility in Iowa and to prepare itself for an initial public offering …