Final answer:
The engineered protein with both an ER signal sequence and a nuclear localization signal would likely be recognized by an SRP and enter the ER, as this process occurs early in protein synthesis and localization.
Step-by-step explanation:
Investigators have engineered a gene that encodes a protein with an ER signal sequence followed by a nuclear localization signal. The most likely fate of that protein is that it will be recognized by a Signal Recognition Particle (SRP) and enter the Endoplasmic Reticulum (ER). The presence of the ER signal sequence at the N-terminus of the growing polypeptide chain directs it to enter the ER, where it begins to co-translationally translocate into the ER lumen.
This sequence acts as a 'train ticket' to its destined compartment and is usually clipped off once the protein reaches its destination. Although the protein also has a nuclear localization signal, this ER targeting happens early in the synthesis and translocation process, essentially prioritizing the ER signal. Modifications and proper folding may occur within the ER before any subsequent signaling influences the protein's ultimate localization.