Final answer:
The Mediator complex serves as the 'integrator of positive and negative signals' in eukaryotic gene regulation, bridging transcription factors with the transcription machinery and modulating transcription initiation.
Step-by-step explanation:
The factor that has been called an "integrator of positive and negative signals" in the regulation of gene expression in eukaryotic cells is known as the Mediator. This complex plays a central role in the transcription process by acting as a bridge between specific transcription factors, which can be activators or repressors, and the general transcription machinery including RNA polymerase II. It integrates the signals from various transcription factors and regulatory pathways, then modulates the initiation and regulation of transcription. The Mediator is essential for the response to diverse signaling cues and can positively or negatively regulate transcription based on the context and combination of signals it receives.