Vývoj nových metod a nástrojů pro metadynamické simulace Phantom metadynamika, Pohyblivé kopce a Metadynamický prohlížeč Petr Hošek Ústav biochemie a mikrobiologie, Vysoká škola chemicko-technologická v Praze, Technická 3, Praha 6, 166 28, Česká republika, e-mail: hosekp@vscht.cz 9.6.2014 ENBIK, Kouty na Vysočině

Sbalování proteinu Problém s překonáváním energetických bariér >tr|Q56G89|Q56G89_HUMAN Serum albumin OS=Homo sapiens PE=2 SV=1 MKWVTFISLLFLFSSAYSRGVFRRDAHKSEVAHRFKDLGEENFKALVLIAFAQYLQQCPFEDHVKLVNEVTEFAKTCVADESAENCDKSLHTLFGDKLCTVATLRETYGEMADCCAKQEPERNECFLQHKDDNPNLPRLVRPEVDVMCTAFHDNEETFLKKYLYEIARRHPYFYAPELLFFAKRYKAAFTECCQAADKAACLLPKLDELRDEGKASSAKQGLKCASLQKFGERAFKAWAV…. Náhodné skládání – moc moc dlouho (Levinthalův paradox) Skládání v buňce – ~10 ms (pro 100AMK protein) Skládání v počítači – 7,5 let na PC (10ms, 100amk, implicitní solvent) Problém s překonáváním energetických bariér

Metadynamika Metoda s vylepšeným vzorkováním Přidává umělý potenciál Snadnější překonávání energetických bariér Přidává umělý potenciál => zmapování plochy volné energie (v prostoru kolektivních souřadnic) But, sometimes conformation changes are too slow for simulations :-) That‘s why enhanced sampling methods have been developed, especially Metadynamics. Metadynamics simulation visits other local minima in shorter time, because it disfavor already visited states by applying the potential. You can see here, that after several steps, system moved into this local minimum, because this one is full of bias potential. And later on, this minumum have been visited too. After the end of the simulation, we got this energy profile, or ,as we call it, energy landscape.

Metadynamika K čemu potřebujeme plochu volné energie? Pravděpodobnosti stavů Reakční koordináta Termodynamika + Kinetika reakce But why we need energy landscapes? Because they can tell us a lot of about the simulated systems, mainly termodynamic and kinetic attributes. We can estimate, how many molecules will rest in this local minimum, or this one, because we know the energy difference between them. We can estimate, how fast the molecules will move from the this minumum to the second minumum, because we know energy of the saddle point between them. This can be valuable for real applications, such as ….

Metody FEP FEP metadynamika Odhad rozdílu volné energie mezi navzájem obtížně dostupnými stavy. Využití Hessova zákona If you want to get energy difference between states, where you cannot find any easy path connecting them, you need to cheat. By use of free energyperturbations methods. Here, you can see two examples of such systems, where free energy perturbations can be used. Popsat tyto dva systémy When I started dealing with FEP, I wonder, if it can be combined with my favourite method – with metadynamics. I found, that it already have been done in QM4D simulation package, but not in plumed, which is more common among metadynamics users. Lawrenz M, Baron R, McCammon JA - J Chem Theory Comput (2009) FEP metadynamika Metadynamika, kde FEP parametr λ je jako kolektivní souřadnice

Solvatační energie Firstly, we applied our method to solvation energy calculations. Solvation energy of molecule (which is here) can be obtained as a sum of these three steps. Phantomization of the molecule in vacuum, transfer to water or other solvent and dephantomization. Now we will focus on one of these phantomization processes.

Solvatační energie Testováno na 3-methylindolu = vedlejší řetězec tryptofanu Phantomization of 3-methylindole in water. By phantom metadynamics, you can get nice continuous energy profile, not the couple of points, what is the case of FEP with Bennett acceptance ratio. And results, there are nearly the same. These slight deviations are caused by the smoothing. But if we get energy difference between normal and phantomized states by substracting these two values, the result would not be precise. 3-methylindol ve vodě – srovnání s klasickou FEP. Tvar průbehu coulombické a vdW lambdy na main_lambda parametru

Solvatační energie Vedlejší řetězce aminokyselin (Ala, Asn, Cys, Gln, His, Ile, Leu, Met, Phe, Ser, Thr, Trp, Tyr, Val) Testing the method on only one molecule is not enough, so we conducted tests on several small molecules. We chose sidechains od amino acids as a good set of diverse molecules. And you can see, that obtained solvation energies are very close to experimental values. Solvation energies increase with hydrofility of molecule, so here are non-polar molecules as methane, ethane, … and at the other end, there are sidechains of glutamine and asparagine together with two forms of histidine sidechain.

Katenany Phantom: obě molekuly X jedna molekula X malá část molekuly Cyclobis(paraquat-p-phenylen) Successful tests on small molecules was only the start. More complicated experiment was a creation of catenanes. Two entwined cyclic molecules. We used 1,5-dinaphtho[38]crown-10 and cyclobis(paraquat-p-phenylene), because these aromatic rings should facilitate formation of catenane by Pi-interactions. We try several simulation settings – phantomize both molecules, or only one of them or just small part, as this loop. And as a second CV, we used coordination number of this naphtalene, hoping, that after formation of catenane, the naphtalene would be surrounded by the second molecule from both sided, which is only possible in catenane. 1,5-dinaphto[38]crown-10 Phantom: obě molekuly X jedna molekula X malá část molekuly Koordinační číslo jako druhá CV

Katenany Dvě propletené molekuly And here example of succesful result. You can see, that molecules are truly interlocked. At this graph, three important minima are visible, around 0 - with molecules totally separated, around 100 with the naphtalene half-surrounded and third, around 200 nicely formed catenane. Dvě propletené molekuly

1 paralelní simulace = 1 gaussian Pohyblivé kopce Paralelizovatelná metadynamická metoda - ukládání potenciálu do již navštívených míst 1 paralelní simulace = 1 gaussian Vzájemné „odpuzování“ mezi paralelami Přidání umělého potenciálu na začátku And there is my addition to the metadynamic methods, called Moving hills. It‘s features are: „první“ „druhý“ potentials – what is different from common metadynamics „třetí“ – , by which it explores the energy landscape

Pohyblivé kopce Srovnání s Metadynamikou Výhody: Nevýhody: Výborná paralelizovatelnost Rychlejší konvergence Omezené množství potenciálu Nevýhody: Výrazné fluktuace Rozdíly mezi paralelami Výpočetně náročnější So, Moving hills featured (have) great parallelizability (ability to run on superclusters), faster covergence than metadynamics, mainly at the beginning of simulation. Limited amount of potential can be advantage in particular subset of simulations. And disadvantages (which i will not hide from you) Fluctuations and oscilations – I managed to lower them significantly by method settings and by averaging In the case of the discrepancy and the overhead, I have been unable to suppress one of them without the increasing the other one. But with appropriate setting, the overall error can be lowered.

Pohyblivé kopce Srovnání s Metadynamikou And finally, the comparison of results between moving hills and metadynamics. In this two graphs, differences are negligible. Some artifacts, you can see here or here ale induced by vizualization method, not by the moving hills. Further testing of this method, now on proteins, are currently under way. Alanin-dipeptid ve vakuu a vodě Rozdíly jsou zanedbatelné

Metadynamický prohlížeč Vizualizace Metadynamiky Suma 100000 2D gaussianů Příliš náročné pro webovou aplikaci? Odpověď je NE Za použití HTML5, WebGL and typovaných polí Dost výkonné i pro zobrazení jako videa But with use of advanced technologies (HTML5 canvas, computations on grafic card and faster typed arrays), I was able to create viewer powerful enough to display metadynamics in progress. And you only need modern internet browser. And now, I will show you the viewer in action

Poděkování Díky za pozornost Můj školitel – Vojtěch Spiwok I would like to thank my supervisor, Vojtěch Spiwok, for guidance and my group for psychical support. Unfortunately, I haven‘t any photo of them to show you. Thank you for your attention. If you have any questions or suggestions to my project, feel free to speak.