We first consider a single-MOF sensor, either IRMOF-1 or HKUST-1, immersed in a three-component mixture: CH 4 /N 2 /CO 2 , CH 4 /N 2 /C 2 H 6 , or CH 4 /C 2 H 6 /CO 2 at 1 bar and 298 K. Fig. visualizes, under these six scenarios, the adsorption function m = a(x) as well as the unresponsive v 2 (red arrow) and sensitive v 1 (green arrow) directions-given by the right singular vectors of the Jacobian matrix J(x op )-at a reference gas composition x op (black dot). The rows correspond to the three different gas mixtures; the columns correspond to the two different single-MOF sensors. Each panel displays the 2D gas composition space pertaining to the row. The colored lines are contours of the adsorption function a(x) and are labeled by the total adsorbed mass of gas m in the respective single-MOF sensor. Each map a : x → m is clearly non-injective, as an unresponsive locus of points elicits the same sensor response m. Within each panel, (i) the non-linearity of the contours and the different areas between successive contours reflect the non-linearity of a(x) and (ii) the slant of the contours reflects the different affinity for the MOF among the three different components of the gas. The sensitive direction v 1 is orthogonal to the contour {x : a(x) = m op }. Among all fixed-magnitude changes in gas composition, the change in the sensitive direction will elicit the largest response (see eqn. 5). The unresponsive direction is tangential to the contour {x : a(x) = m op }. The unresponsive subspace is one-dimensional owing to the single constraint imposed by the response of the sensor on the two degrees of freedom in the gas composition. For a small change in gas composition in the unresponsive direction, the sensor response remains approximately the same and, hence, the composition change is not detected by the sensor.