Have any experiments been carried out involving sprouting and growing plants in a zero gravity environment? If so, what was the outcome? How did the plants sprout out of the soil without gravity? Did they grow outward or toward light sources?
There have been several experiments in growing plants in microgravity (strictly speaking, we do not achieve "zero-g" since astronauts remain in orbit about the Earth).
Changes in plant growth due to the influence of a gravity field is sometimes called gravimorphogenesis. More specifically, gravitropism is a differential growth response of plant organs to gravity. For example, roots grow downwards (positive gravitropism) and shoots grow upwards (negative gravitropism) on Earth.
Studies (e.g. 1) suggest that in micro-g, there is no preferred direction; roots may grow "up" and shoots "down".
It is thought that this growth response is due to the relative distribution of auxin in the plant. On Earth, auxin will preferentially move down into the root-tips due to the location of amyloplasts in the root-cap cells. In micro-g, amyloplasts do not settle at the "bottom" of the plant, therefore there is a more generalized distribution of auxin, and therefore there will be no preferred growth direction.
In addition, changes in plant gene expression as a response to micro-g environments are also being investigated (2) and suggest that auxin transport inhibitors may block the activation of the auxin responsive promoters in Nicotiana spp. (tabacco).
(1) Mechanisms in the Early Phases of plant Gravitropism CRC Crit Rev Plant Sci. 2000 ;19 (6):551-73 11806421 Cit:65
(2) Transcription Profiling of the Early Gravitropic Response in Arabidopsis Using High-Density Oligonucleotide Probe Microarrays, Plant Physiol. 2002 October; 130(2): 720–728. doi: 10.1104/pp.009688
I find over 100 articles returned by a PubMed query for "Arabidopsis microgravity." Arabidopsis was taken aboard at least one if not more Space Shuttle missions to answer this and other similar questions. A couple recent papers from this search are:
Spaceflight transcriptomes: unique responses to a novel environment. Paul AL, Zupanska AK, Ostrow DT, Zhang Y, Sun Y, Li JL, Shanker S, Farmerie WG, Amalfitano CE, Ferl RJ. Astrobiology. 2012 Jan;12(1):40-56. PMID: 22221117
An endogenous growth pattern of roots is revealed in seedlings grown in microgravity. Millar KD, Johnson CM, Edelmann RE, Kiss JZ. Astrobiology. 2011 Oct;11(8):787-97. doi: 10.1089/ast.2011.0699. PMID: 21970704
Parabolic flight induces changes in gene expression patterns in Arabidopsis thaliana. Paul AL, Manak MS, Mayfield JD, Reyes MF, Gurley WB, Ferl RJ. Astrobiology. 2011 Oct;11(8):743-58. doi: 10.1089/ast.2011.0659. PMID: 21970703
Gene expression changes in Arabidopsis seedlings during short- to long-term exposure to 3-D clinorotation. Soh H, Auh C, Soh WY, Han K, Kim D, Lee S, Rhee Y. Planta. 2011 Aug;234(2):255-70. PMID: 21416242
A novel phototropic response to red light is revealed in microgravity. Millar KD, Kumar P, Correll MJ, Mullen JL, Hangarter RP, Edelmann RE, Kiss JZ. New Phytol. 2010 May;186(3):648-56. PMID: 20298479