## 3 Results and Discussion
### Fluorescence Calibration
#### 3.3.3 Surface Density Analysis  
The theoretical density of the immobilised Con A was calculated based on published dimensional data of a Con A monomeric unit in an aqueous solution [43]. The corresponding hydrodynamic diameter would be approximately 4 nm, and if packed side by side would yield a total number of 6.25 \(\times\) 10\({}^{12}\) molecules per cm\({}^{2}\), (or 7.22 \(\times\) 10\({}^{12}\) per cm\({}^{2}\) if stacked hexagonally). This is comparable to the calculated value published in the literature [47], and would also be the theoretical maximum number of fluorescence dextran molecules if we consider one active binding site per Con A molecule. This assumption is based on an ideally flat quartz surface, and any additional surface roughness would increase the effective area and consequently the number of immobilised Con A molecules per cm\({}^{2}\). Hence, an increased surface roughness could potentially improve the sensitivity of a gravimetric sensor when used to detect glucose using Con A. The number of Alexa 488 dextran and FITC dextran that binds to the immobilised surface is calculated from the fluorescence intensity measurements and the results are presented in Table 2. It was found that the maximum amount of Alexa 488 dextran after immobilisation was about one third of the maximum theoretical density.  
The ratio between surface density of Alexa 488 dextran and FITC dextran bound to an immobilised Con A surface is calculated to be approximately 12, which is comparable to the ratio between their hydrodynamic diameters (D\({}_{\rm F}\)/D\({}_{\rm A}\))\({}^{2}\approx\) 19. This suggests that larger labelling molecules may cover multiple binding sites as explained in Section 3.3.2.  
\begin{table}
\begin{tabular}{l c c c c} \hline  & \multicolumn{3}{c}{**Alexa (\(M_{W}\) = 3 kDa)**} & \multicolumn{2}{c}{**FITC (\(M_{W}\) = 70 kDa)**} \\ \hline  & \(I\) (a.u.) & \(\sigma\) (cm\({}^{-2}\)) & \(I\) (a.u.) & \(\sigma\) (cm\({}^{-2}\)) \\ Incubation in MOPS buffer & 73 & 2.1 \(\times\) 10\({}^{12}\) & 69 & 1.8 \(\times\) 10\({}^{11}\) \\ Incubation, \(c_{glu}\) = 40 mM & 35 & 6.1 \(\times\) 10\({}^{11}\) & 33 & 4.8 \(\times\) 10\({}^{10}\) \\ Difference (\(c_{glu}\) = 0–40 mM) & 38 & 1.5 \(\times\) 10\({}^{12}\) & 36 & 1.3 \(\times\) 10\({}^{11}\) \\ Number of moles (mol cm  
The difference in the number of fluorescent labelled dextran before and after incubation in \(c_{glu}\) = 40 mM was found to be 1.5 \(\times\) 10\({}^{12}\) per cm\({}^{2}\) for the Alexa 488 dextran and 1.3 \(\times\) 10\({}^{11}\) per cm\({}^{2}\) for the FITC dextran. This would correspond to a theoretical mass change of 7.5 \(\times\) 10\({}^{-9}\) g per cm\({}^{2}\) and 1.5 \(\times\) 10\({}^{-8}\) g per cm\({}^{2}\) respectively (Table 2). Despite the Alexa 488 dextran yielding a larger change in absolute number and fluorescence intensity, the FITC dextran yields an almost 2 fold increase in mass change. This suggests that the FITC dextran will be more effective in triggering a mass change in a gravimetric glucose sensor compared to the Alexa 488 dextran in the presence of glucose.  
The polished SiO\({}_{2}\) substrates would not offer any large increase in the effective surface area, and the stacking of the Con A molecules would be a function of active binding sites to the underlying silane layer, which could have regions of defect. The estimated density assumed Con A to be in its monomeric form, and any other configurations (dimer, trimer or tetramer) or a combination thereof would most likely result in a lower stacking density due to a less ordered monolayer structure. Some of the binding sites on the Con A molecules may also have been inactive or oriented away from the surface, and as such did not bind to the dextran molecules masking away the presence of the underlying Con A. The approximately 3-fold reduction in density following incubation with 40 mM glucose demonstrates that the affinity assay is working and that glucose will displace most, but not all of the dextran molecules.