## Materials and Methods  
### Materials  
The nanoporous alumina membranes (NPAMs) used as supports in this study were synthesized by the electrochemical two-step anodization method using high purity aluminum discs (Al 99.999%, Goodfellow (UK); 0.5 mm thickness). Two different aqueous electrolyte solutions and anodization voltages were used in order to have membraneswith different pore size and interpore distance: 0.3 M solution of sulfuric acid and applied voltage of 25 V for the Sf-NPAM sample, and 0.3 M solution of oxalic acid and 40 V in the case of the Ox-NPAM sample; detailed information on this process is given in the literature [1; 3; 35]. In Supplementary Information, scanning electron microscope (SEM) pictures of both membrane surfaces are presented as Figure S1. Modification of Sf-NPAM and Ox-NPAM surfaces, both external and internal (porewall), with a thin TiO\({}_{2}\) layer coated by the atomic layer deposition (ALD) technique was performed in a Savannah 100 thermal ALD reactor from Cambridge Nanotech (Waltham, MA, USA), using high purity argon as carrier gas. Two precursors, titanium tetraiso-propoxide (metal precursor) at 75 \({}^{\circ}\)C and water (for substrate functionalization and as oxidant agent) at 60 \({}^{\circ}\)C, were used for deposition of the conformal coating, as explained in a previous work [20]. These nanoporous alumina-based membranes will hereafter be called Sf-NPAM/TiO\({}_{2}\) and Ox-NPAM/TiO\({}_{2}\), respectively. Almost total TiO\({}_{2}\) coverage of both alumina supports was already determined in a previous paper [36] by the XPS technique, and the atomic concentration percentage (A.C. %) of the different elements found on the surfaces of each membrane is shown in Supplementary Information (Table S1); only superficial slight differences associated with manufacture/environmental contamination (sulfur detection for Sf-NPAM/TiO\({}_{2}\) or excess carbon in the case of the Ox-NPAM/TiO\({}_{2}\) sample) were determined. The thickness of the TiO\({}_{2}\) layer was also determined (from depth-profile XPS analysis [36]), obtaining a value of \(\sim\)6 nm, which agrees quite well with published results [21]. Figure 1 shows SEM surface micrographs of both NPAM/TiO\({}_{2}\) samples. The following values for average pore-radii (r\({}_{\text{p}}\)), interpore distance (D\({}_{\text{int}}\)) and porosity (\(\Theta\) = (2\(\pi\)/\(\surd\))(r\({}_{\text{p}}\)/D\({}_{\text{int}}\))\({}^{2}\)) [1]), were determined by surface analysis of SEM micrographs [36]: <r\({}_{\text{p}}\)> = 10 nm, <D\({}_{\text{int}}\)> = 65 nm, and <O> = 9% for the Sf-NPAM/TiO\({}_{2}\) sample, and <r\({}_{\text{p}}\)> = 13 nm, <D\({}_{\text{int}}\)> = 105 nm, and <O> = 6% for the Ox-NPAM/TiO\({}_{2}\) sample, with both membranes having a thickness of \(\sim\)65 \(\upmu\)m. Taking into account geometrical parameter values, rather similar theoretical hydraulic permeability was determined for both TiO\({}_{2}\)-covered membranes [9]: L\({}_{\text{H}}\)\({}^{\text{Sf-NPAM/TiO2}}\) = 1.92 \(\times\) 10\({}^{-12}\) m/s.Pa and L\({}_{\text{H}}\)\({}^{\text{Ox-NPAM/TiO2}}\) = 2.17\(\times\)10\({}^{-12}\) m/s.Pa. It should be mentioned that both NPAMs and NPAM/TiO\({}_{2}\) samples were obtained in the Unidad de Membranas Nanoporosas, Universidad de Oviedo (Spain) and kindly submitted by Prof. [PERSON] and Dr. [PERSON]. Membranes were statically fouled with the protein bovine serum albumin (BSA), which had the following characteristic parameters: 66.5 kDa molecular weight and Stokes radius of 3.48 nm. Membrane fouling was performed by mounting each sample in the dead-end electrochemical cell shown in Supplementary Information (Figure S2), filling one half-cell with a BSA aqueous solution of 5 g/L and the other half-cell with distilled water for 24 h, after which the cell was emptied and the membrane surface softly cleaned with distilled water. These samples will hereafter be called Sf-NPAM/TiO\({}_{2}\)(f) and Ox-NPAM/TiO\({}_{2}\)(f).