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Antagonistic cooperativity between crystal growth modifiers

Abstract

Ubiquitous processes in nature and the industry exploit crystallization from multicomponent environments1,2,3,4,5; however, laboratory efforts have focused on the crystallization of pure solutes6,7 and the effects of single growth modifiers8,9. Here we examine the molecular mechanisms employed by pairs of inhibitors in blocking the crystallization of haematin, which is a model organic compound with relevance to the physiology of malaria parasites10,11. We use a combination of scanning probe microscopy and molecular modelling to demonstrate that inhibitor pairs, whose constituents adopt distinct mechanisms of haematin growth inhibition, kink blocking and step pinning12,13, exhibit both synergistic and antagonistic cooperativity depending on the inhibitor combination and applied concentrations. Synergism between two crystal growth modifiers is expected, but the antagonistic cooperativity of haematin inhibitors is not reflected in current crystal growth models. We demonstrate that kink blockers reduce the line tension of step edges, which facilitates both the nucleation of crystal layers and step propagation through the gates created by step pinners. The molecular viewpoint on cooperativity between crystallization modifiers provides guidance on the pairing of modifiers in the synthesis of crystalline materials. The proposed mechanisms indicate strategies to understand and control crystallization in both natural and engineered systems, which occurs in complex multicomponent media1,2,3,8,9. In a broader context, our results highlight the complexity of crystal–modifier interactions mediated by the structure and dynamics of the crystal interface.

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Fig. 1: Cooperativity between four pairs of inhibitors in suppressing bulk growth of β-haematin crystals.
Fig. 2: Cooperativity of inhibitor pairs in suppressing layer generation and spreading.
Fig. 3: Characterization of the effects of the kink blockers MQ and AQ on layer nucleation.
Fig. 4: Solid-on-solid kinetic Monte Carlo modelling of the action of kink blockers and step pinners on step propagation.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding authors on reasonable request.

Code availability

The custom computer code used in these simulations is available upon reasonable request to J.F.L. (jim@lutsko.com).

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Acknowledgements

We thank K. Olafson for help with haematin crystallization and AFM analysis, D. Sullivan for discussions on haemozoin formation and drug–haematin interactions, and D. Maes for insights on experiment statistics. This work was supported by the National Science Foundation (award number DMR-1710354), the National Institutes of Health (award number 1R21AI126215-01), NASA (award numbers NNX14AD68G and NNX14AE79G), the European Space Agency (ESA) and the Belgian Federal Science Policy Office (BELSPO) in the framework of the PRODEX Programme (contract number ESA17 AO-2004-070) and The Welch Foundation (grant E-1794).

Author information

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Authors

Contributions

J.D.R. conceived this work, P.G.V. and J.D.R. designed the experiments, W.M. performed all experiments, P.G.V. and W.M. analysed data, P.G.V. developed interpretive models, J.F.L. carried out the kMC simulations, and P.G.V., J.F.L. and J.D.R. wrote the paper. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Jeffrey D. Rimer or Peter G. Vekilov.

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The authors declare no competing interests.

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Peer review information Nature thanks Baron Peters and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Effects of step pinners and kink blockers on bulk haematin crystallization.

a, Scanning electron microscopy micrographs of crystals grown in the presence of inhibitors at the concentrations listed in each panel for 16 d at 23 °C. b, c, Variations of the average length-to-width, l/w, aspect ratio Asp of crystals grown in the presence of increasing concentrations of CQ/MQ and CQ/AQ (b) and QN/MQ and QM/QA (c) at the displayed ratios relative to the Asp reached after growth in pure CBSO solutions for 16 d at 23 °C. Lines are guides for the eye. Variations of the corresponding average crystal length l and width w are displayed in Fig. 1f–i. d, Isobolograms characterizing the cooperativity of the CQ/MQ, CQ/AQ, QN/MQ and QN/AQ inhibitor pairs in suppressing the length of β-haematin crystals. Open symbols indicate the concentrations of individual inhibitors that elicit a certain percentage of inhibition, referred to as ICs. Dashed lines correspond to additive cooperativity between the paired inhibitors for a certain percentage of inhibition and are horizontal if the inhibitor in the abscissa is inactive when applied alone. Solid symbols represent the concentrations of the paired inhibitors that evoke the same inhibition. Rightward shifts of the solid symbols from the respective dashed lines indicate antagonistic cooperativity. The corresponding combination index values are listed in Extended Data Table 1.

Extended Data Fig. 2 Isobolograms characterizing the cooperativity of the CQ/MQ, CQ/AQ, QN/MQ and QN/AQ inhibitor pairs.

a, b, Cooperativity in suppressing the step velocity v (a) and the rate of two-dimensional nucleation rate J2D of new layers (b). Open symbols indicate the concentrations of individual inhibitors that elicit a certain percentage of inhibition (ICs). Dashed lines correspond to additive cooperativity between the paired inhibitors for a certain percentage of inhibition and are horizontal if the inhibitor in the abscissa is inactive when applied alone. Solid symbols represent the concentrations of the paired inhibitors that evoke the same inhibition. Rightward shifts of the solid symbols from the respective dashed lines indicate antagonistic cooperativity. The corresponding combination index values are listed in Extended Data Table 1.

Extended Data Fig. 3 Lack of complexation between kink blockers and step pinners in the solution.

ad, Lack of CQ/MQ (a), CQ/AQ (b), QN/MQ (c) and QN/AQ (d) complexes. The ultraviolet-visible absorption spectra of the individual inhibitors and binary combinations indicated in the plots. The spectra of the binary solutions are nearly identical to the sum of the spectra of the individual inhibitors. el, Lack of ternary compounds that include haematin and the CQ/MQ (e, i), CQ/AQ (f, j), QN/MQ (g, k) and QN/AQ (h, l) pairs of inhibitors. eh, The ultraviolet-visible spectra of haematin at concentration cH = 0.38 mM in the presence of various combinations of QN, CQ, AQ and MQ (as indicated in the plots) at 1:1 molar ratios, where the inhibitor concentrations increase from top to bottom, as indicated by arrows. il, The relative decrease of the absorbance of a solution with initial cH = 0.38 mM at 594 nm as a function of the concentration of the respective inhibitor pair (1:1 ratio) compared with a model assuming the presence of complexes of haematin with each of the individual inhibitors in the mixture, evaluated using the haematin–inhibitor binding constants from Olafson et al.13.

Extended Data Fig. 4 The correlation between the step velocity v and the inhibitor concentration.

ad, Data are presented in linearized coordinates \({v^{\prime} }_{0}{({v^{\prime} }_{0}-v)}^{-1}\) and \({c}_{{\rm{B}}}^{-1}\) (cB, kink blocker concentration) according to Supplementary equation (7), for cB = [B] (a, c) and cB = [H2B] (b, d), respectively, for MQ (a, b) and AQ (c, d). Original data on the dependence of the step velocity on the concentration of the kink blockers MQ and AQ are from Olafson et al.13. The values of the Langmuir constant KLB determined from the slope of the straight lines are shown. The two leftmost data points for AQ, measured at CAQ > 7 μM, correspond to an unphysical increase in v at increasing concentration of AQ and were not considered in the regression analysis to determine KLB.

Extended Data Fig. 5 The step velocity v in the presence step pinners and kink blockers, relative to that in pure solutions v0.

Data calculated using Supplementary equation (22). The values of ξ and KLB are listed in Extended Data Table 4. γ0 = 25 mJ m−1 is evaluated from the Rc determinations in Fig. 3. KLP = 0.0027 μM−1 for CQ and 0.0013 μM−1 QN is evaluated from the v(cp) correlations for CQ and QN determined by Olafson et al.13 using Supplementary equations (14), (17) and (19). The surface area per adsorption site S0 = 1.12 nm2 from the structure of β-haematin crystals10. a, The correlation between the velocity of a step with radius of curvature R, vR, and the concentrations of a step pinner (CQ or QN), cp, and kink blocker (MQ or AQ), cb, for the four listed inhibitor combinations. b, The step velocity v in the presence step pinners and kink blockers, relative to that in pure solutions v0, at the listed constant ratios of kink blocker to step pinner, corresponding to experimental determinations in Fig. 2c, e, compared with v in the presence of the listed step pinners only.

Extended Data Fig. 6 The regions of antagonistic and synergistic cooperativity in the plane of the concentrations of step pinners cP and kink blockers cB.

Solid line represents the equation \({(\partial {v}_{{\rm{R}}}/\partial {c}_{{\rm{B}}})}_{{c}_{{\rm{H}}},{c}_{{\rm{P}}}}=0\), where \({(\partial {v}_{{\rm{R}}}/\partial {c}_{{\rm{B}}})}_{{c}_{{\rm{H}}},{c}_{{\rm{P}}}}\) follows Supplementary equation (28). This line corresponds to additive cooperativity and divides the (cPcB) plane into fields where \({(\partial {v}_{{\rm{R}}}/\partial {c}_{{\rm{B}}})}_{{c}_{{\rm{H}}},{c}_{{\rm{P}}}} < 0\) marks that step pinners and kink blockers cooperate synergistically, and \({(\partial {v}_{{\rm{R}}}/\partial {c}_{{\rm{B}}})}_{{c}_{{\rm{H}}},{c}_{{\rm{P}}}} > 0\) indicates antagonistic cooperativity between the two inhibitors.

Extended Data Table 1 The combination index for the four listed step pinner/kink blocker pairs
Extended Data Table 2 The analysis of variance test parameters
Extended Data Table 3 Concentrations of free haematin [H], free inhibitors [D] and kink blocker–haematin complexes [H2B]
Extended Data Table 4 The Langmuir constant for adsorption of MQ and AQ at kinks

Supplementary information

Supplementary Information

This file contains supplementary text 1-5.

Video 1

Video 1 (MPEG) displays the attachment of molecules to steps resulting in step growth in pure solutions.

Video 2

Video 2 (MPEG) illustrates blocking of kinks by kink blockers and the resulting delay in step growth.

Video 3

Video 3 (MPEG) illustrates how a regular array of step pinners adsorbed on the crystal surface force the steps to curve; the enforced curvature delays step growth.

Video 4

Video 4 (MPEG) shows how at supersaturation lower than in Video 3 the presence of step pinners adsorbed on the surface completely arrests step growth.

Video 5

Video 5 (MPEG) shows that at the same supersaturation and concentration of step pinners as in Video 4 the adsorption of kink blockers on the step edge stabilises the step edge fluctuations, which, in turn, allows the step to grow.

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Ma, W., Lutsko, J.F., Rimer, J.D. et al. Antagonistic cooperativity between crystal growth modifiers. Nature 577, 497–501 (2020). https://doi.org/10.1038/s41586-019-1918-4

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