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Normalize both fluorescent reporter intensities by their respective means, correcting unequal brightness and background, and denote them $c,y$. Extrinsic gene-expression noise changes shared cellular conditions and moves both signals together: the scatter is a long narrow cloud around $y=c$. Intrinsic gene-expression noise comes from distinct random expression events in the two genes and broadens the cloud across that diagonal. Comparable contributions therefore give a noticeably wider, still positively correlated cloud. The two right-hand panels in the preceding original illustration show these two cases.

For matched fluorescent reporters with conditionally independent intrinsic fluctuations and corrected measurement noise,The first quantity measures differential variation; the second measures common variation. A clone's successive observations can remain correlated in time, so they need not be independent samples. Shared activation transients should also be separated from the fluctuations of interest.^[ref]

Normalize each reporter by its mean intensity, after correcting background and unequal brightness, so equal expression lies on $y=x$. Write $x=1+e+i_C$, $y=1+e+i_Y$, where the common fluctuation $e$ is extrinsic gene-expression noise and the independent reporter-specific fluctuations $i_C,i_Y$ are intrinsic gene-expression noise. The extrinsic gene-expression noise includes shared variation in cell size, expression machinery and growth state; intrinsic gene-expression noise includes independent molecular production and removal events at each reporter.

If intrinsic gene-expression noise is much smaller, points form a narrow elongated cloud along $y=x$: a cell that is bright in cyan is usually bright in yellow. If the two contributions have comparable magnitude, the cloud is still positively correlated but has substantial width perpendicular to $y=x$, because the two reporters can differ within the same cell. With variance ${\sigma }_e^2$ in $e$ and equal variance ${\sigma }_i^2$ in each independent intrinsic term,Equal intrinsic and extrinsic variances therefore give correlation coefficient $1/2$, rather than an uncorrelated circular cloud. For mean-normalized reporters, ${\eta }_{\mathrm{int}}^2=⟨(x-y{)}^2⟩/2$ and ${\eta }_{\mathrm{ext}}^2=⟨xy⟩-1$. Measurement noise must be separately estimated before assigning perpendicular scatter to expression itself. These are the geometric diagnostics of the original dual-reporter experiment.^[ref]

The lower panels of c show these two cases. Repeated observations of one cell can move both along and across the diagonal; a static population cloud alone does not determine the time scales of the fluctuations.

Intrinsic gene-expression noise is variability from the random reaction events of the expression process itself, conditional on the cell's shared state: transcript production and removal, translation events and protein loss. It remains possible in nominally identical cells in the same environment and is particularly visible when molecule numbers are small.

Extrinsic gene-expression noise comes from fluctuations in shared cellular conditions, such as cell size, growth state, expression machinery abundance or environmental signals. It can correlate otherwise distinct expression processes. In a matched two-reporter measurement, reporter differences reveal an intrinsic component while correlated cell-to-cell changes reveal a shared component, after reporter-specific measurement noise is accounted for.^[ref]

Intrinsic fluctuations can be beneficial when a population gains a diversity of temporary physiological states, or when a noisy threshold crossing helps a cell explore or select a state. They can be detrimental when an essential product transiently falls too low, when tightly coordinated components become imbalanced, or when a regulatory threshold is crossed at an inappropriate time. These are context-dependent effects: noise is not automatically adaptive, and increasing a Fano factor is not synonymous with improving a cellular function.