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How does auxin promote stem growth?

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fern life cycle — plant development The life cycle of the fern. (1) Clusters (sori) of sporangia (spore cases) grow on the undersurface of mature fern leaves. (2) Released from its spore case, the haploid spore is carried to the ground, where it germinates into a tiny, usually heart-shaped, gametophyte (gamete-producing structure), anchored to the ground by rhizoids (rootlike projections). (3) Under moist conditions, mature sperm are released from the antheridia and swim to the egg-producing archegonia that have formed on the gametophyte's lower surface. (4) When fertilization occurs, a zygote forms and develops into an embryo within the archegonium. (5) The embryo eventually grows larger than the gametophyte and becomes a sporophyte.

Auxins, most notably indoleacetic acid (IAA), promote stem growth primarily by stimulating cell elongation.312

Synthesized in young, growing organs like shoot tips, these hormones are transported downward to growing regions. Once they reach their target cells, auxins act on the chemical bonds of the carbohydrates that comprise plant cell walls. This action allows the cell walls to be irreversibly deformed or loosened, a process accompanied by the entry of water and the synthesis of new cell-wall material, which results in the physical lengthening of the stem.312

Beyond general elongation, auxins facilitate directional growth responses:
* Phototropism: Auxin accumulates on the shaded side of a stem, causing those cells to elongate more than those on the illuminated side, which forces the stem to curve toward the light.312
* Geotropism: Auxin accumulates along the lower side of a stem, stimulating greater elongation there and causing the stem to bend upward against the force of gravity.312