Sonic Hedgehog (Shh) is a critical signaling molecule involved in multiple developmental processes, including limb patterning, neural tube organization, and craniofacial morphogenesis. Mice homozygous for mutations in the Shh gene provide vital models for understanding the gene’s role in morphogenesis and congenital abnormalities.

Phenotypes Observed in Shh Mutant Mice

• Midline Facial Defects and Holoprosencephaly:
  Homozygous Shh mutant mice exhibit severe reduction or loss of the midline facial structures, often resulting in a single eye located centrally—a condition known as cyclopia. This abnormal development is a hallmark of holoprosencephaly (HPE), where the cerebral hemispheres fail to divide properly.

• Limb Development Defects:
  Shh is expressed in the Zone of Polarizing Activity (ZPA) of the limb bud and is vital for specifying anterior-posterior digit identity. Mutations can cause digit malformations, including loss or duplication of digits, reflecting disrupted limb patterning.

• No Normal Limb Without Shh:
  Both neural and limb structures fail to develop normally without Shh signaling, underscoring its essential morphogen role.

• Molecular Mechanism:
  Shh functions by binding to the Patched receptor, alleviating repression of Smoothened, and activating downstream Gli transcription factors. Loss of Shh halts these signaling cascades, leading to extensive developmental malformations.

• Shh and Tumors:
  Dysregulation of the Shh pathway is linked to cancer formation in some contexts; however, the scenario described involving Patched and Smoothened leading to tumorigenesis involves pathway overactivation, not the mutations causing complete loss of Shh.

Why Other Options Are Incorrect

• Limbs do not form normally in Shh homozygous mutants (option 1 is incorrect).

• Eyes do not form normally; instead, cyclopia occurs, indicating severe midline defects (option 3 is incorrect).

• Tumor formation is related to pathway overactivation, not loss-of-function Shh mutations as asked here (option 4 is incorrect).

Summary

Mice homozygous for mutant alleles of sonic hedgehog exhibit severe midline developmental defects resulting in cyclopia and holoprosencephaly, highlighting the gene’s crucial role in facial morphogenesis and limb patterning. The midline facial reduction and central eye formation phenotype is diagnostic of Shh loss of function.

Final Answer:
(2) Midline of the face would be reduced and a single eye would form in the center of the forehead.