Extended Data Figure 10: Collection of simulated data for l-cystine along with a single simulation of d-cystine.

a, A suite of calculations of the crystal growth of l-cystine at a supersaturation of 0.6 kcal mol⁻¹ viewed down the [001] direction, showing characteristic pin-wheel surface topology and hexagonal step bunching. Simulations are based on four characteristic free energies of crystallization: (i) in the strong binding direction where l-cystine molecules are bound by two hydrogen bonds and S….S contacts; (ii) and (iii) in the weak, slow growth directions, labelled A+ and A− in refs 25 and 26, with one hydrogen bond; and (iv) in the c direction with two hydrogen bonds. Interaction types (ii) and (iii) are maintained at half the strength of (iv), with a minimal difference between (ii) and (iii). These interactions can be combined into 491 growth sites that are computed in the simulation. The grid explores the effect of changing the relative magnitude of interaction (i) (number on the x axis), relative to the sum of the other interactions (number on the y axis); all values given in kcal mol⁻¹. When all of these interactions are too weak, isotropic sticky growth is observed; when they are too high, the growth is too geometrical. The optimum balance is highlighted (black outline), for which the sum of the free energies of crystallization is 7.0 kcal mol⁻¹, compared to the value of 4.3 kcal mol⁻¹ derived from the solubility of l-cystine at pH 7 directly³¹. Similar to the results of ref. 25, the step bunching is closer than observed experimentally because lattice strain at the screw core weakens interactions and prevents the core region, which is advancing by attachment to the slow step alone, from forming a closed hexagonal step bunch as quickly as predicted. b, A set of simulations demonstrating the effect of small differences in the energy of slow growth directions A+ and A−; energies given in kcal mol⁻¹. If there were no difference in energy, then the pin-wheel structure would have a step bunch height of only half a unit cell, owing to the symmetry that is produced every 180° turn around the screw core. A difference of 0.1 kcal mol⁻¹ is sufficient to eradicate this symmetry and make the step bunches one unit cell high. c, Reversal of the handedness of the screw core is not immediately apparent because the pin-wheel structure and handedness remain the same whatever the handedness of the screw core as this is driven by the symmetry of the crystal structure at the molecular level. However, differences can be observed in the surface topology close to the screw core, depending on whether the handedness of the crystal structure is the same or the reverse of the handedness of the screw core. d, l-cystine and d-cystine present identical surface structures with opposite handedness, as expected.