Acknowledgments Authors are deeply in debt with David K. Smith, University of York, UK, for the longstanding, fruitful collaboration, the challenges in heparin binder design and optimization, the inspiring discussions and, above all, the invaluable personal friendship. Funding This research was funded by the Italian Association for Cancer Research (AIRC), grant IG17413 to SP. The assistant position (RTDa) of SA is fully supported by the University of Trieste, in agreement with the actuation of the strategic planning financed by the Italian Ministry for University and Research (MIUR, triennial program 2016–2018) and the Regione Friuli Venezia Giulia (REFVG, strategic planning 2016-18), assigned to SP. This award is deeply acknowledged. Conflicts of Interest The authors declare no conflict of interest. Appendix A Table A1 EC50 and CE50 values for protamine and for ethylenediamine-based covalent PAMAM dendrimers (G0-G6) as heparin binders. Values were obtained by fitting the data in Figure 2a. The last column shows the relevant dosage, i.e., the mass of binder required to bind 100 international units (IU) of heparin (i.e., the clinical standard. Adapted from [33] with the permission of The Royal Society of Chemistry. Heparin Binder Charge EC50 (µM) CE50 Dose (mg Binder/100 Heparin IU) Protamine +24 2.34 ± 0.23 0.52 ± 0.05 0.32 ± 0.03 G0 +4 too weak too weak too weak G1 +8 10.10 ± 0.32 0.75 ± 0.02 0.44 ± 0.01 G2 +16 2.55 ± 0.32 0.38 ± 0.04 0.25 ± 0.03 G3 +32 1.33 ± 0.21 0.45 ± 0.02 0.32 ± 0.04 G4 +64 0.64 ± 0.04 0.38 ± 0.02 0.27 ± 0.02 G5 +256 0.22 ± 0.04 0.53 ± 0.09 0.39 ± 0.06 Table A2 Effective free energy of binding (∆Gbind,eff), number of effective protamine /dendrimer positive charges (Neff), and effective-charge-normalized free energy of binding (∆Gbind,eff/Neff) for protamine and the different generation EDA-core PAMAM dendrimers (G1-G6) in complex with heparin as derived from atomistic MD simulations. Adapted from [33] with the permission of The Royal Society of Chemistry. Heparin Binder Neff ∆Gbind,eff (kcal/mol) ∆Gbind,eff/Neff (kcal/mol) Protamine 12 ± 1 −3.96 ± 0.41 −0.33 ± 0.04 G1 6 ± 1 −1.14 ± 0.22 −0.19 ± 0.05 G2 13 ± 1 −16.9 ± 0.5 −1.30 ± 0.11 G3 15 ± 1 −15.9 ± 0.3 −1.06 ± 0.07 G4 16 ± 3 −14.6 ± 0.8 −0.91 ± 0.18 G5 45 ± 5 −18.0 ± 1.3 −0.40 ± 0.05 Figure A1 (a) TEM images of worm-like micelles of L-G1 bound to heparin, scale bar = 100 nm. On drying, the worm-like micelle-heparin complex hierarchically assembles into larger aggregates. Worm like micelles can most clearly be visualized curved into ‘U shapes’ in the lower aggregates—multiple cylindrical micelles appear to be packed together in these regions. (b) TEM images of spherical micelles of L-G2 bound to heparin, scale bar = 50 nm. Some free micelles can be seen within the image, but most have further aggregated hierarchically on binding to heparin and drying to yield a nanostructure which in this case is ca. 50 nm in diameter. Adapted from [26] with the permission of The Royal Society of Chemistry. Figure A2 Electron spray mass spectra for the degradation of L-G1 (a) and L-G2 (b) self-assembled dendrimers dissolved in ammonium bicarbonate at pH = 7.4 TEM images of worm-like micelles of L-G1 bound to heparin, scale bar = 100 nm. On drying, the worm-like micelle-heparin complex hierarchically assembles into larger aggregates. Worm like micelles can most clearly be visualized curved into ‘U shapes’ in the lower aggregates—multiple cylindrical micelles appear to be packed together in these regions. (b) TEM images of spherical micelles of L-G2 bound to heparin, scale bar = 50 nm. Some free micelles can be seen within the image, but most have further aggregated hierarchically on binding to heparin and drying to yield a nanostructure which in this case is ca. 50 nm in diameter. Adapted from [26] with the permission of The Royal Society of Chemistry.