Are simulations more messy than experiments? (I need help…)

The intuitive answer would be no, right? I mean in a computer, nothing can go wrong, the results won’t depend on some silly batch of reagent containing an unknown but critical impurity. I won’t depend if it was sunny that day, or on whether the experimenter was listening to some really exciting music.

Well, I am no theorist but that was certainly how I felt until recently. Readers of this blog will know of the stripy nanoparticles controversy. Simulations are beginning to play an interesting role…

Consider first the structure. Singh et al predict the existence of stripes if the ligands are free to diffuse at the nanoparticle surface because of gains in conformational entropy. To the contrary, Gkeka et al predict that if ligands diffuse at the nanoparticle surface, minimization of electrostatic repulsion will lead to an homogeneous configuration. Who is right? Comments very much welcome here! [Suggestion for future theoretical studies: consider ligand exchange rather than diffusion as a mechanism for ligand self organization; probably more difficult, but more realistic…].

Consider next the question of insertion into, and penetration through, membranes. Three group of authors have published theoretical articles trying to explain why stripy nanoparticles penetrate membranes (we have challenged both the existence of stripy nanoparticles and their special cell-penetrating properties). All three papers conclude that those particles -which have a substantial hydrophobic coverage – have a gain in energy when inserted into the membrane. The values, rankings, and interpretations however wildly differ. Thus, Li et al predicts a lower energy gain for stripy nanoparticles than for random ones. Gkeka et al predicts the opposite and Van Lehn predicts that the morphology does not make any difference at all! Van Lehn however interpret high gain upon fusion as indicating particles which are likely to translocate through membranes: they write that “bilayer fusion is the critical intermediate step in membrane penetration”. To the contrary, both of the other papers focus on the energy profile along the translocation path (as also this paper about C60) and interpret a low energy gain as a low energy barrier therefore favouring translocation (the ideal being a flat energy profile effectively corresponding to free diffusion).

Of course, messiness is a good thing, but I could do with some help, comments (as usual) welcome…

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6 comments

  1. Theory is, I think, often like this. This is why careful measurement that has a clear ability to distinguish between theoretical outcomes is critical. I would distinguish careful measurement from experiment designed to “support” a hypothesis, which to me is closer to metaphysics than physics…

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  2. Why do some nanoscale objects seamlessly translocate through lipid membranes and the others do not? If we knew the answer to this question, we would be able to assess cytotoxicity of various man-made and natural nano-objects and also harvest their specific behaviour for antibacterial, drug delivery and other applications.

    At the heart of the matter is the way in which nanoparticles (or nano-objects in general) interact with the membranes. Not surprisingly the experimentalists in the field turn to their simulation/theory colleagues to provide an explanation and a clear picture of what is going on at the molecular level. And all the answers should be exact… Right?

    Well, far from it. Nanoparticle behaviour in vivo is complex, because the very system is complex. A typical cell membrane is a multilayer entity featuring a complex composition of lipids, proteins and other components. The environment in the vicinity of the membrane is also a complex solution, containing ions, proteins and other species. A nanoparticle approaching a cell membrane will be most likely covered with some proteins adhered to its surface. Naturally, in order to understand what is going on, both experimentalists and theoreticians resort to simplified systems, which allow to assess and decouple the influence of various factors. In this simplified systems, the cell membrane is usually represented by a lipid bilayer of a simplified composition (either one or two types of lipids) while surrounding solution is free from any species other than water and ions (and, obviously, nanoparticles).

    In the ideal world, a theoretician (here, a molecular modeller) would construct an atomistically accurate model of this simplified system, including the nanoparticle, and explore its behaviour. Since accurate force fields now exist for a variety of components, including water, the molecular simulation observations should have direct correlation and relevance to the experiments carried out on the same system. This however is not possible and here is the reason why. Consider an example from our recent work on coarse-grained models of these systems, which would typically include more than 8000 lipid molecules and ca. 240000 water particles[1]. In atomistic representation, this system would contain about 1∙106 water molecules alone, not counting lipids. The time scale required to construct a full potential of mean force (PMF) across membranes spans several microseconds. This combination of the system size and time scales is simply not assessable on a routine basis even with the modern multicore supercomputers. A systematic exploration of how this PMF depends on the particle morphology and other conditions is most likely out of question.

    Hence, in the molecular modelling approach one must focus on a system, simplified even further. And this is where problems begin. Construction of a simplified model is systematic process of selecting which factors are believed to be important for the behaviour of the model and which are not. However, this is invariably a very subjective process. For example, self-assembly of lipid molecules into a bilayer, driven by the hydrophobic interactions between their tails, can be captured in the model that does not include water molecules explicitly, and the hydrophilic/hydrophobic interactions are captured through effective potentials between “like” and “un-like” species. This model is very computationally efficient and useful in understanding various aspects of self-assembly processes (such as the phase transitions in the bilayer etc). However, it may not be applicable to other phenomena, such as for example processes that crucially depend on the arrangement and structure of the water molecules. In other words, the choice of the model depends on the process under investigation and always involves certain assumptions.

    Here, it is also important to distinguish two broad classes of simplified models. In the first class, which I call here “toy models”, the idea is to qualitatively reflect the underlying physical behaviour. The implicit solvent model of the lipid self-assembly is an example of this model. Toy models are computationally very efficient and allow one to quickly enumerate different possible types or modes of behaviour possible in the system (we can broadly call a result of this enumeration a phase diagram).

    A different class of simplified models is coarse-grained (CG) models. These models result from a direct mapping of an atomistic representation of a molecule onto a simplified representation, where several atoms are grouped together into one interaction site. The principle difference of the coarse grained models from the toy models is that their development aims to accurately reproduce the behaviour of the underlying atomistic system. The properties of the CG pseudo-atoms are calibrated with this objective. For example, a well known MARTINI forcefield is validated by reproducing structural and dynamical properties of the lipid bilayers and free energy profiles of various molecules across them[2,3]. There still however limitations of CG models, one has to be aware of.

    All of the current studies on the field with a focus on striped nanoparticles use simplified (either toy of CG), and not atomistic models[1,4-6]. And ALL these models are different from each other and employ different assumptions. Not surprisingly the results are different and may offer a completely different explanation of the same phenomena. I believe in application to striped nanoparticles, there are several challenges (if we do not want to call them controversies) that can be resolved only by (selective) using of accurate fully atomistic models. Below I describe these challenges:

    1) Formation of striped patterns.

    Formation of patterns and domains of different shapes on flat gold surfaces has been observed, experimentally, for various binary mixtures. The study of Singh et al (PRL 99, 226106 (2007)[7]) uses a toy model (they start with fully atomistic potentials, but then modify them so that “nonbonded interactions between unlike atoms or groups of atoms are modeled via the Buckingham potential without the attractive component”) and nicely demonstrates that striped domains can form on the surface of a nanoparticle and that the domain size becomes larger as the size of the nanoparticle decreases. This provides the overall phase diagram for the system behaviour.

    What still remains unclear is what the simulations would predict for the specific system(s) of Stellacci and co-workers, including the actual propensity to form striped domains and size and shape of the stripes. Therefore, it seems there is a need to complement the study of Singh et al with a fully atomistic simulation, replicating as accurately as possible the experimental procedure Stellacci and co-workers.

    2) Do the membrane interact with the striped domains?

    A number of recent studies, including our own, using MARTINI CG approach[1], assumes a specific domain pattern on the surface of the nanoparticle. This pattern is static (fixed) and does not change depending on the location or the environment of the nanoparticle. This is clearly an oversimplification, leading to the conditional nature of the observations (“IF the nanoparticle features this pattern throughout the translocation process, THEN this is it’s behaviour).

    It is recognized now that the flexibility of the chains on the surface of the nanoparticle is important. Although the underlying pattern at the very surface of the nanoparticle may be stripes (or other type of domains), the flexibility of the chains within the surface layer, allows them to re-arrange. The resulting surface chemistry may a) be very different from the underlying surface pattern (and this has been recently demonstrated in our CG study), b) change in response to the environment.

    The importance of this surface flexibility has been recently recognized in a series of works by Alexander-Katz and co-workers[5,8], who in their most recent study include explicit chains of ligands attached to a model nanoparticle. First of all, they confirmed that the actual underlying pattern may not be important as the ligands tend to re-arrange themselves (but then the question arises whether we need to aim for striped domains altogether). Furthermore, they proposed an interesting mechanism of reaction of this flexible layer to its environment, where within the lipid bilayer the chains re-arrange themselves so that their polar/charged heads “snorkel” to the surface. In this model, however, bilayer is modelled implicitly, with the nanoparticle behaving in the “field” of the bilayer. This approach may be too oversimplified to correctly capture the process of lipid molecule reorganization around the nanoparticle, which, as has been shown in several studies, is also substantial and important[1,9]. In a recent study by Lin and co-workers, the authors considered nanoparticles decorated with explicit ligand chains (using MARTINI approach), and the preliminary inspection of the snapshots of such nanoparticles interacting with DPPC bilayer do not allow to detect any signs of “snorkelling” behaviour[10].

    Hence, again, this is clearly an issue that should be revisited using fully atomistic simulations. A model nanoparticle with explicit ligands on its surface should be placed in different environments (water+ions, lipid core) and the arrangement/response of the ligands investigated.

    These are only some of the challenges. There are also broader issues for the simulation (and experimental) community. Is it possible to accurately recover PMFs from the Umbrella sampling, given that the bilayer has certain degree of freedom to move away from the nanoparticles, wrap around it and so on, confusing the definition of the reaction coordinate[11]? What should be called “seamless, direct translocation of a nano-object through the bilayer”? Does this process involve formation of holes and defects and substantial warping of the bilayer (“membrane disruption” as recently suggested by Lin et al[10])? Is the process associated with a flat free energy profile or a deep potential minimum within the bilayer (the latter would seem to lead to strong accumulation of particles within the bilayer as has been shown for hydrophobic silver nanoparticles by Bothun[12])? Is it a single particle process or does the nanoparticle need help from another nanoparticle to lower the free energy barrier of entrance?

    The story of striped nanoparticles brought up several interesting challenges for both the experimentalist and simulation communities and it would be naïve to think that there will be easy answers. The consistent picture is yet to be developed.

    (1) Gkeka, P.; Sarkisov, L.; Angelikopoulos, P. Journal of Physical Chemistry Letters 2013, 4, 1907-1912.
    (2) Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. Journal of Physical Chemistry B 2007, 111, 7812-7824.
    (3) Monticelli, L.; Kandasamy, S. K.; Periole, X.; Larson, R. G.; Tieleman, D. P.; Marrink, S. J. Journal of Chemical Theory and Computation 2008, 4, 819-834.
    (4) Li, Y.; Li, X.; Li, Z.; Gao, H. Nanoscale 2012, 4, 3768-3775.
    (5) Van Lehn, R. C.; Alexander-Katz, A. Soft Matter 2011, 7, 11392-11404.
    (6) Lin, X.; Li, Y.; Gu, N. Journal of Computational and Theoretical Nanoscience 2010, 7, 269-276.
    (7) Singh, C.; Ghorai, P. K.; Horsch, M. A.; Jackson, A. M.; Larson, R. G.; Stellacci, F.; Glotzer, S. C. Physical Review Letters 2007, 99, 4.
    (8) Van Lehn, R. C.; Atukorale, P. U.; Carney, R. P.; Yang, Y.-S.; Stellacci, F.; Irvine, D. J.; Alexander-Katz, A. Nano Letters 2013.
    (9) Ramalho, J. P. P.; Gkeka, P.; Sarkisov, L. Langmuir 2011, 27, 3723-3730.
    (10) Lin, J.; Zhang, H.; Chen, Z.; Zheng, Y. ACS Nano 2010, 4, 5421-5429.
    (11) Ban, Y. M.; Tasseff, R. A.; Kopelevich, D. I. Molecular Simulation 2011, 37, 525-536.
    (12) Bothun, G. Journal of Nanobiotechnology 2008, 6, 13.

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    1. Lev, I am very grateful for this most interesting and detailed comment!

      Experimentally, I am not aware of a convincing demonstration of nanoparticles seamlessly going through cell membranes (and even less so through model membranes).

      On the ligand self-organization question, as I allude in my post, I also think that the Singh model assumption of free diffusion of the ligands at the surface is incorrect. It is likely that – if patterns exist – they form through ligand exchange rather than diffusion.[1,2]

      1. Supramolecular Domains in Mixed Peptide Self-Assembled Monolayers on Gold Nanoparticles; Duchesne, L., Wells, G., Fernig, D.G., Harris, S.A. and Lévy, R. (2008). ChemBioChem, 9, 13, 2127 – 2134
      2. Lateral diffusion of thiol ligands on the surface of au nanoparticles: an electron paramagnetic resonance study. Anal Chem. 2008 Jan 1;80(1):95-106. Ionita P, Volkov A, Jeschke G, Chechik V.

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  3. I attended a talk by the first author of the Nano Letters paper mentioned above, Reid C. Van Lehn. https://twitter.com/raphavisses/status/407587704990220288

    I used the question session to note that their paper suggests high energy gain when particles are in the membranes which would lead to trapping rather than going through.

    He agreed and suggested that “uptake” in their liposomes experiments (figs 2-3) could be hopping from membrane to membrane rather than through fluid transport.

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  4. Experimental measurements trump theory musing. I’m all for theory trying things and publishing them and all. But a theory paper is not really strong “proof” of a structure. Not like diffraction experiments or an SEM or the like. Nothing against theory and it should be encouraged and grow and get better, but still…it’s generally speculative. And often more about creating rationales for explaining what we did observe experimentally. Hopefully, the day will come when we can just calculate everything in material science. But it’s in the future…

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