The story behind this work is long and winding, has a fair share of twists and turns, serendipitous conversations and connections, goes back about twenty years in our hands, and nearly a hundred in the broader field. It all really began for us in the mid-2000s when as a postdoc in Germany I stumbled upon the “like-charge attraction problem”. I had decided I wanted to replicate a really captivating experiment by colleagues at Princeton who had stretched out DNA molecules in long, thin nanochannels¹. I began by spending many a happy hour in a dark room peering down a microscope at DNA molecules squeezed into slit-like boxes that were supposed to flatten a molecular coil of DNA into a pancake-like shape. I started noticing a striking phenomenon whereby, rather than form a pancake, DNA molecules would align along the thin edge of the box, stretching out from end to end, rather like an unravelled ball of wool being pulled taut². Since we were not applying any external forces the only way this could happen was if there were some form of attraction between the molecule and the sidewalls of the slit. A leading biophysicist, Joachim Raedler, had in fact done a very similar sort of experiment on grooved lipid bilayers and DNA, and they had seen the same effect except for one little detail. The bilayers in Joachim’s experiment were positively charged, and DNA is manifestly negatively charged; so the behaviour in their experiment was entirely expected on Coulombic grounds: opposite charges attract and the grooves caused the DNA to align and stretch out along them³. In our experiment the glass walls of the box were negatively charged, and if the textbooks were right, only repulsions were to be expected between DNA and the edges of the box: there was no way we should have been seeing evidence for an attractive force of the kind of range and strength that the observations indicated.

That was how I became aware of the like-charge attraction problem between colloidal particles in solution - a conundrum it turned out that Langmuir had tried to address in the early part of the 20^th century, Rosalind Franklin had pointed out in the 1950s, and that had found no resolution to date^4-6. Sifting through the literature revealed that the 1990s had been a fraught time in the field, when a spate of measurements and theoretical work had been done on the problem only for the effort to prove largely inconclusive. To make matters much worse, because several families of measurements had been conducted under conditions where the particles attracted very weakly (and in my view were therefore amenable to misinterpretation), whole swathes of published data had been debunked as having arisen from experimental artifacts, now implying that there had been no real effect at all. The community, it appeared, had (understandably) had quite enough of the problem. But in our hands this spontaneous unravelling of DNA was a huge effect - whatever it was that was driving it - and the observations were manifestly not the result of a glitch in data processing. It was clear that some aspect of the overall phenomenon was real and important, and that rather than being dissuaded by the problem’s tangled history I would soldier on.

Wondering if this anomalous interaction had something to do with geometry-related effects in a nanoscale system I went on to do other experiments that did not resolve the like-charge attraction problem, but thankfully for me, segwayed far away from it into much safer territory for a fairly junior academic. These efforts led to the invention of the electrostatic fluidic trap which spawned an entirely new measurement technique - molecular electrometry: the backbone of a new area of investigation and the mainstay of the lab to this day^7-10. Here we performed measurements that relied on the textbook theories being right, and in fact we were quite successfully using these theories in regimes where they worked very well to measure the charge and related properties of biomolecules in solution¹¹. Things were going fairly well here. But the awareness that there was something deeply amiss, lurking in the shadows of the parameter space that we were deliberately steering clear of, was a gnawing feeling that would not subside.

Electrometry – a relentlessly sensitive and accurate technique - would simply not let us ignore the fact that in experiment, the repulsive interaction between two like-charged objects did not grow exponentially with decreasing separation as the textbooks promised. Experiments now yet again threw up the same anomaly: the onset of a mitigating effect - along the lines of an attraction of as yet unknown origin, forcing an acceptance of the fact that there was going to be no way around this problem other than facing it squarely, working things out and hoping to succeed.

I constructed a highly simplified “toy-model” calculation that suggested that if one accounted for the entropy of molecular water at a surface that changed its charge ever so slightly as another particle approached, then the overall free energy of interaction behaved in a manner that explained the electrometry observations rather well; these results remain unsubmitted for publication to this day. Excited by the prospect that a “non-monotonic free energy of the solvent” at a charged surface was the key ingredient to explaining this body of effects, and convinced that the molecular nature of the solvent was what was missing in standing theories (which, it is worth pointing out here, treat the solvent as a smooth continuum rather than a grainy, discrete, molecular medium), I now went looking for molecular simulations experts who could help put these nascent if slightly hazy notions on firmer footing.

Three weeks before my lab moved from Zurich to Oxford I had what in hindsight was a life-changing conversation with Juerg Hutter, a truly wonderful Physical Chemist colleague and expert in molecular simulations in my department at the University of Zurich. On hearing I was looking for a “non-monotonic charging free energy” for a surface in water, Juerg said to me, “there’s one person who might be able to help you with this. He’s written an x-1000 page book on solvation and works up the hill (at ETH Zurich)”. Just days later I was in Phil Hunenberger’s office, who listened to my story very carefully. Phil agreed: yes, they did see the type of free energy I was looking for in molecular simulations…! But it turned out that if this really was what was behind our experiments then the effect would also be ‘charge asymmetric’. This meant that simulations of the solvation free energy in water did show the behaviour I required, but only for one sign of charge (negative) and not for the other! Unusual and unexpected as that first sounded, it later turned out that asymmetric solvation of ions was a related effect that was rather well known in that area of physical chemistry¹². Regardless, a revelation of this severity, at this juncture, ought to have hit like a ton of bricks and seen me off crushed, despondent. All but for the memory of a rather strange and intriguing paper that my biochemist husband had sent me many moons ago, which now came careening into mental view. A study by Jay Groves’ lab had used lipid-bilayer- coated colloidal particles to show that negatively coated particles attracted and positives repelled: like-charge attraction could indeed be asymmetric with respect to the sign of the charge¹³! The message of that study and this new lynchpin bit of information from simulations slotted resoundingly in place together; to my mind, bolstering the new concept rather than dismantling it.  

The lab moved to Oxford in the summer of 2018, and we began publishing small bits of theoretical work showing how this new view could explain a range of previous observations^14-16. Of course we lost no time getting started on our own experiments on colloidal particles - an effort spearheaded at the time by a highly motivated and talented undergraduate Annabel Lawrence who managed to reproduce the Groves experiment showing silica particles formed ordered clusters in water; we were all pretty chuffed when Annabel got a departmental prize for the achievement. So, experiments were showing negative particles attracted and positives repelled, the theory seemed to be capturing the results, I thought this was all great and probably as good as it was ever going to get. But Phil, very rightly, had at the very outset raised the bar pretty high: for the proposed mechanism to be deemed plausible we would need to show that the effect would flip in other solvents – i.e., that positive particles would attract and negatives would repel when suspended in something other than water, because that is what the molecular-simulation behaviour the model relied on would imply. Indeed, even a number-theorist friend had asked, “what happens if you change the solvent…?” Much as the suggestion made sense, with my experimentalist hat on I knew that even if such experiments were broadly feasible, it was not at all obvious that they would be unequivocal in their verdicts, or that the phenomenon would even be observable under experimentally accessible conditions, even though the minimal theory I had conjured up indicated this ought to be true. Loads of experiments still needed to be done and there was no knowing how things would play out…

It was roughly at this point that the project was fortunate enough to be joined by two graduate students who took the enterprise to a whole new level, and are joint first authors on the paper. One is an extremely diligent and fastidious experimentalist, the other an essentially self-taught molecular simulations aficionado. The two banded together on the experiments and simulations, and, reinforced by noteworthy contributions from a couple more generations of talented undergraduates, made the study as it appears today! We now know that there’s a lot more behind intermolecular and interparticle interactions in solution than previously thought: mainly that the solvent has a huge impact on the interaction, even when the objects are at very large distances from each other; and depending on the conditions, can even dictate the nature of the interaction - whether attractive or repulsive. We also know that there is much more to come, far more to be learnt…

 References

1. Tegenfeldt, J. O. et al. The dynamics of genomic-length DNA molecules in 100-nm channels. Proceedings of the National Academy of Sciences of the United States of America 101, 10979-10983 (2004).

2. Krishnan, M., Monch, I. & Schwille, P. Spontaneous stretching of DNA in a two-dimensional nanoslit. Nano Letters 7, 1270-1275 (2007).

3. Hochrein, M. B., Leierseder, J. A., Golubovic, L. & Rädler, J. O. DNA localization and stretching on periodically microstructured lipid membranes. Physical Review Letters 96, 038103 (2006).

4. Langmuir, I. The role of attractive and repulsive forces in the formation of tactoids, thixotropic gels, protein crystals and coacervates. Journal of Chemical Physics 6, 873-896 (1938).

5. Klug, A., Franklin, R. E. & Humphreys-Owen, S. P. F. The crystal structure of Tipula iridiscent virus as determined by Bragg reflection of visible light. Biochimica et Biophysica Acta 32, 203-219 (1959).

6. Grier, D. G. A surprisingly attractive couple. Nature 393, 621-623 (1998).

7. Krishnan, M., Mojarad, N., Kukura, P. & Sandoghdar, V. Geometry-induced electrostatic trapping of nanometric objects in a fluid. Nature 467, 692-695 (2010).

8. Mojarad, N. & Krishnan, M. Measuring the size and charge of single nanoscale objects in solution using an electrostatic fluidic trap. Nature Nanotechnology 7, 448-452 (2012).

9. Myers, C. J., Celebrano, M. & Krishnan, M. Information storage and retrieval in a single levitating colloidal particle. Nature Nanotechnology 10, 886-891 (2015).

10. Ruggeri, F., Zosel, F., Mutter, N., Różycka, M., Wojtas, M., Ożyhar, A., Schuler, B. & Krishnan, M. Single-molecule electrometry. Nature Nanotechnology 12, 488-495 (2017).

11. Bespalova, M., Behjatian, A., Karedla, N., Walker-Gibbons, R. & Krishnan, M. Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule-Solvent Interface. Macromolecules 55, 6200-6210 (2022).

12. Reif, M. M. & Hunenberger, P. H. Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity-Basity Scale Revisited. Journal of Physical Chemistry B 120, 8485-8517 (2016).

13. Gomez, E. W., Clack, N. G., Wu, H. J. & Groves, J. T. Like-charge interactions between colloidal particles are asymmetric with respect to sign. Soft Matter 5, 1931-1936 (2009).

14. Kubincova, A., Hunenberger, P. H. & Krishnan, M. Interfacial solvation can explain attraction between like-charged objects in aqueous solution. Journal of Chemical Physics 152, 104713 (2020).

15. Walker-Gibbons, R., Kubincova, A., Hunenberger, P. H. & Krishnan, M. The Role of Surface Chemistry in the Orientational Behavior of Water at an Interface. Journal of Physical Chemistry B 126, 4697-4710 (2022).

16. Behjatian, A., Walker-Gibbons, R., Schekochihin, A. A. & Krishnan, M. Nonmonotonic Pair Potentials in the Interaction of Like-Charged Objects in Solution. Langmuir 38, 786-800 (2022).