Rapid two-dimensional characterisation of proteins in solution

Microfluidic platforms provide an excellent basis for working with heterogeneous samples and separating biomolecular components at high throughput, with high recovery rates and by using only very small sample volumes. To date, several micron scale platforms with preparative capabilities have been demonstrated. Here we describe and demonstrate a microfluidic device that brings preparative and analytical operations together onto a single chip and thereby allows the acquisition of multidimensional information. We achieve this objective by using a free-flow electrophoretic separation approach that directs fractions of sample into an on-chip analysis unit, where the fractions are characterised through a microfluidic diffusional sizing process. This combined approach therefore allows simultaneously quantifying the sizes and the charges of components in heterogenous mixtures. We illustrate the power of the platform by describing the size distribution of a mixture comprising components which are close in size and cannot be identified as individual components using state-of-the-art solution sizing techniques on their own. Furthermore, we show that the platform can be used for two-dimensional fingerprinting of heterogeneous protein mixtures within tens of seconds, opening up a possibility to obtain multiparameter data on biomolecular systems on a minute timescale.

Q cm + Q s + 2 · Q d + 2 · Q el,in = Q out + 2 · Q el,out (S.1) 2 · Q d + Q lm + Q a + Q hm = Q out (S.2) 2 · Q d + Q a = Q sizing (S.3) R cm · Q cm = R s · Q s (S.4) R bridge · (Q el,in − Q el,out ) N = R el,out · Q el,out + R cm · Q cm (S.5) R lm · Q lm = R hm · Q h, (S.6) R lm · Q lm = R a · Q a + R sizing · Q sizing (S.7) where Q i and R i correspond to the flow rate in channel i and to the hydraulic resistance of that channel, respectively, as indicated in Supplementary   Figure S1.  Bridge Q bridge 18 6.9 704 7 * Two parallel channels of that length. The flow rate is given as the combined flow rate from the two channels.

S2 The effect of the electrolyte infusion rate on the device performance
We observed that when the electrolyte infusion rate into the system is low, the solution gets withdrawn into the main chamber without reaching its outlet ( Supplementary Figure 1b).

S3 Flow splitting at the device outlet
In order to avoid partial short-circuiting of the device at its outlet, we used a Y-shaped flow splitter that would prevent the oppositely charged electrolyte streams coming into contact with each other at the device outlet but only further downstream ( Figure Table 1). It would therefore take around t = π · ( D 2 ) 2 Q (S.9) t 1 = 43 min and t 2 = 170 min for the fluid to reach the flow splitter from the two sides. Even when accounting for Taylor dispersion in the tubing, this time scale is significantly longer than the imaging period (∼ 7 minutes) and as such the voltage efficiency of the device can be assumed to remain unaffected throughout its operation.

S4 Estimating the effective voltage drops across the separation chamber
To estimate the effective voltage drop across the separation chamber, simultaneously with applying the voltages, we also recorded the currents flowing in the system. This allowed us to estimate the resistance of the micron scale device to be R device = 644 kΩ. To obtain an estimate for the electrical resistance of the electrodes, we filled the device with a highly conductive solution (3M KCl) to short-circuit it. By doing so, we obtained an estimate of R electrodes = 521 kΩ for the resistance of the electrodes. These data indicate that at each of the applied voltage, around 14% of it drops across the separation chamber.

S5 Resolution of the device
The resolution of the setup depends on the extent of beam broadening that the analyte molecules undergo when moving down the separation area. With the collection area for analysis being around 15% of the total width of the separation chamber away from its cen-