  Gene expression via transcription-translation is the most fundamental
reaction to sustain biological systems, and complex reactions such as this one
occur in a small compartment of living cells. There is increasing evidence that
t physical effects, such as molecular crowding or excluded volume effects of
transcriptional-translational machinery, affect the yield of reaction products.
On the other hand, transcriptional feedback that controls gene expression
during mRNA synthesis is also a vital mechanism that regulates protein
synthesis in cells. However, the excluded volume effect of spatial constraints
on feedback regulation is not well understood. Here, we study the confinement
effect on transcriptional autoregulatory feedbacks of gene expression reactions
using a theoretical model. The excluded volume effects between molecules and
the membrane interface suppress the gene expression in a small cell-sized
compartment. We find that negative feedback regulation at the transcription
step mitigates this size-induced gene repression and alters the scaling
relation of gene expression level on compartment volume, approaching the
regular scaling relation without the steric effect. This recovery of regular
size-scaling of gene expression does not appear in positive feedback
regulation, suggesting that negative autoregulatory feedback is crucial for
maintaining reaction products constant regardless of compartment size in
heterogeneous cell populations.
