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Valentina Tozzini -

Riccardo Farchioni

Vito Dario Camiola

Khatuna Kakhiani

Tommaso Cavallucci

Giuseppe Maccari (CNI-iit)

Paolo Mereghetti (CNI-iit)

Riccardo Nifosí

Multi-Scale models: development and implementation
Applications to biomolecular systems
Applications to graphene systems


Multi-Scale models: development and implementation


A multi-scale representation is often needed to address in silico complex systems. In fact, reducing the resolution at which the system is represented allows sparing computational cost and reaching larger sizes and time scales in the simulation, up to bridging those typical of the experiment (i.e. nano-micro). On the other hand, one has to face the problem of maintaining sufficient accuracy in the representation of the structure, dynamics and thermodynamics, because it is not often possible to completely abandon the high-resolution (and computationally expensive) representations. One possibility is then to combine different levels of resolutions to obtain a complete and accurate description of the system. In doing that, one has to solve a number of different problems, mainly related to the achievement of the coherency among levels, choosing the relevant variables in coarser representation and parameterizing their force fields (FF), whose level of empiricity increases as the resolution decreases.
We address these problems both for biomolecular systems (exemplified in Fig 1 by the Green Fluorescent Protein) and for graphenic systems. For the former, we use the whole range of resolution levels. While for the atomistic levels (QM and MM) we use standard approaches, for the low-resolution level we developed specific models. We optimized CG models for biopolymers representing proteins and nucleic acids at the level of a single interacting center per amino acid or nucleotide. Due to their simplicity these “minimalist” models allow largely extending the size and time scale in molecular dynamics simulations. The accuracy and predictive power in such simple models can be preserved by an optimized parameterization. Our optimization strategy is to include information coming from experiment, in particular by using at best the huge amount of structural information from the PDB repository of experimental structures, and other macroscopic or thermodynamic information. To this aim, we developed SecStAnT, a freely distributed software tool for statistical analysis (distributions and correlations among internal variables). The structural information can be used as input for CG FF building and combined in a coherent parameterization with other source of information (of thermodynamic, energetic or kinetic origin) by means of a Genetic Algorithm (GA). This procedure was tested on RNA, DNA and polypeptides, and also employed in the parameterization of a model for proteins diffusion in a meso-scale model for the cytoplasm. This model, mimicking the cytoplasm of the bacterium Escherichia coli, is able to reproduce with high accuracy the diffusive behavior of the different species.



Fig 1: Summary of the multi-scale approaches for proteins (shown with the GFP, upper part) and graphene (lower part). From left to right, the QM level is shown, in which the electrons are treated explicitly (electrons densities are reported as iso-surfaces in green for the GFP chromophore and in orange of the rippled graphene sheet); the atomistic level, addressed with classical dynamics and empirical force fields; the coarse grained level (one bead per amino acid/nucleotide in biomolecules) is absent in the graphene case; the meso-scale includes entire proteins or macro-molecules in a single interacting center; the equivalent in for graphenic systems correspond to treat fullerenes or tubes a single rigid objects; the continuum level is implicit in the biomolecular systems from CG up, because they are embedded in implicit representation of the solvent treated as a 3D continuum; conversely, in graphene the system itself can be treated as a 2D continuum with mechanic and chemical properties mapped onto it.



     The minimalist model for proteins was combined with a quasi-atomistic representation in a hybrid representation capable of addressing long time scales in proteins, preserving accuracy in specific regions, namely the active site. This approach was tested on rhodopsins. Additionally, in this case the multi-scale models for the single optical states of the proteins were combined in a multi-stable model so that the whole photo-cycle was addressed.
We are also developing a multi-scale approach for graphene systems (Fig 1, lower part). As in the previous case, for the QM level we apply standard DFT based methods to study systems including ~100 to ~1500 atoms. In the latter case we use massively parallelized High Performance Computing Systems (BGQ-Fermi at CINECA). For the MM level we use both already available empirical FFs for hydrocarbons and ad hoc newly parameterized FFs to include specific effects such as the dependence of hydrogen adhesion on the local curvature of the sheet (see below). The parameterization is based on the DFT calculations. An intermediate semi-empirical approach based on the tight binding representation is used to evaluate transport properties in specific graphene based systems. We derive analytical expression for the elements of the Green’s function matrix as a function of the carriers density, in order to study the density of states and interpret the transmittivity calculated by the scattering matrix formalism.
Finally, we address the system at the macroscopic level by mapping mechanical, structural and chemical information onto a 2D surface representing the graphene sheet.


Multiscale Modeling of Proteins

V. Tozzini,

Accounts Chem Res 43, 220 (2010)


Vibrational spectroscopy of fluorescent proteins: a tool to investigate the structure of the chromophore and its environment

V Tozzini and S Luin in Springer Series on Fluorescence, 113, (2011)


Minimalist models for proteins: a comparative analysis

Valentina Tozzini,

Quart Rev Biophys, 43, 333-371 (2010)


Minimalist Models for Biopolymers: Open Problems, Latest Advances and Perspectives

Fabio Trovato, Valentina Tozzini,

AIP Conf. Proc. 1456 187-200 (2012)


SecStAnT: Secondary Structure Analysis Tool for data selection, statistics and models building

G Maccari, GLB Spampinato, V Tozzini

Bioinformatics, 30, 668–674 (2014)


Minimalist model for the dynamics of helical polypeptides: a statistics-based parameterization

GLB Spampinato, G Maccari, and V Tozzini

J Chem Theor Comput, 10, 3885–3895 (2014)


Genetic Algorithm Optimization of Force Field Parameters. Application to a Coarse-Grained Model of RNA

F Leonarski, F Trovato, V Tozzini, J Trylska,

Proceeding EvoBIO’11 – Lecture Notes in Computer Science, Springer, 6623 147-152 (2011)


RNA dynamics with one-bead coarse-grained model

Leonarski, F Trovato, V Tozzini, and J Trylska,

Abstract of the Papers of the American Chemical Society 241, 285-COMP (2011)


Evolutionary Algorithm in the Optimization of a Coarse-Grained Force Field

Filip Leonarski, Fabio Trovato, Valentina Tozzini, Andrzej Les, Joanna Trylska,

J Chem Theor Comput, 9, 4874−4889 (2013)


A minimalist model of proteins diffusion and interactions: the GFP within the cytoplasm

F Trovato, R Nifosì, A Di Fenza, V Tozzini,

Macromol, 46 8311–8322 (2013)


Diffusion within the cytoplasm: a meso-scale model of interacting macromolecules

F Trovato, V Tozzini,

Biophys J 107 2579–2591(2014)


A multi-scale – multi-stable model for the rhodopsins photocycle

F Tavanti, V Tozzini,

Molecules, 19 14961-14978 (2014)



Applications to biomolecular systems


The multi-scale approach are used in the study of a number of different biomolecular systems of bio-medical interest. We simulated the GFP diffusional and aggregation behavior using its CG model within a mesoscale cytoplasm model. These results can be directly compared with diffusional data in the cytoplasm: it is shown that this model is capable of predicting the changes in internal dynamics, interactions and diffusion of proteins within the cell environment. This study could aid the quantitative interpretation of a number of fluorescence microscopy experiments performed with advanced techniques such as FRET.
The action mechanism of proteins involved in the HIV replications was studied by means of CG models. In particular the binding of HIV-1 protease to the Gag viral poly-protein is currently being investigated. Other systems under examination are the self-aggregating β-2 microglobulin (involved in the dialyzed patients arthritis) and the unstructured α-syn nuclein (involved in the Parkinson disease). In all cases the goal of the study is to understand the molecular mechanisms underlying the pathological process in order to interfere with it.
An aptamer complex is involved in the cellular internalization of the aptamer GS24, a sequence of 50 nucleotides, which binds to the extracellular domain of the transferrin receptor. Since the aptamer structure is unknown, multi-scale simulations are used to perform folding and to test the stability of the various possible secondary structures. The predicted 3D structure of GS24 will be used for building a model for the GS24-transferrin receptor complex.


Fig 2: Sample bio-molecular systems simulated with CG or multi-scale techniques.




GCN5-dependent acetylation of HIV-1 integrase enhances viral integration

M. Terreni, P. Valentini, V. Liverani, M.I. Gutierrez, C. Di Primio, A. Di Fenza, V. Tozzini, A. Allouch, A. Albanese, M. Giacca, and M. Cereseto,

Retrovirology 7, 18 (2010)


A Coarse Grained Model for the dynamics of binding of the HIV-1 protease to Gag

M Galimberti, V Tozzini,

in preparation


Multi-scale dynamics of β-2 microglobulin: the fibrillogenic intermediate

A Bochicchio, O Carrillo, G Brancolini, S Corni, V Tozzini,

in preparation


From sequence to function: a study on DNA aptamer interaction with transferrin receptor

D Porciani, G Signore, L Marchetti, R Nifosì, P Mereghetti, F Beltram, (2013) submitted



Applications to graphene systems


The multi-scale approach is applied to the graphene systems. Nanoribbons of graphene sculpted in a fully hydrogenated matrix (called graphane) display semiconductor properties depending on their width. In addition, Car-Parrinello simulations show that controlled graphene hydrogenation could be obtained by corrugating graphene, which induces atomic hydrogen spontaneous chemisorption on the convex regions and desorption by curvature inversion. These mechanisms are under consideration for two practical applications: one is the possibility of using graphene based systems for a hydrogen storage device based on graphene, in which loading and release of H is controlled by the curvature manipulation. The second is the possibility of building nano-electronic devices with tailored properties by controlling the topology of the hydrogenated-dehydrogenated areas by means of the curvature. These possibilities are currently being explored combining DFT calculations and simulations based on empirical force fields, needed to address the multiple nm scale, with information coming from experiment.


Fig 3: Modeling graphene based systems. (a) Electronic properties of graphene-graphane hybrid systems. Gap value dependence on width in the graphene nanoribbon in graphane. (b) Corrugated graphene sheet by lateral compression, variation of binding energy vs curvature (red=convex, bla=flat, blue=concave); hydrogen loaded on convex sites.



     The tight binding approach is applied to the study of the transport properties of low dimensional graphene-like system arranged in the ladder polymer and in the polyacene lattice topology with embedded edge impurities or functionalized by side-attached atoms. A relevant aspect in the transport in these systems is the presence of Fano resonances in the form of dips followed by sharp rises in the transmission lineshapes, caused by interference effects between the impurities energy levels and the continuum of band states of ordered chains (Fig. 4(a) for a ladder polymer with side embedded impurity). In polyacene chains, the results are very different if the impurity is located on a site which interacts (two Fano resonances, Fig. 4(b)) or not (just one Fano resonance) with the adjacent chain. Moreover, if a short range order exists in the distribution of site energies of the impurities, a competition is observed between the strong localization induced by the presence of the attached atoms and the delocalization of the states due to the local order and it is possible to individuate specific parameters of the system to quench its transmittivity [lacking red left peak in Fig. 4(c)].


Fig 4: (a): transmittivity and density of states of a ladder polymer with an embedded impurity; (b) transmttivity of a polyacene chain with and edge impurity; (c) transmittivity of a one dimensional chain with side-attached impurities with a short range order ihe random site energies



Electronic structure and Peierls instability in graphene nanoribbons sculpted in graphane

V. Tozzini and V. Pellegrini,

Phys Rev B 81, 113404 (2010)


The influence of graphene curvature on hydrogen adsorption: towards hydrogen storage devices

S Goler, C Coletti, V Tozzini, V Piazza, T Mashoff, F Beltram, V Pellegrini, S Heun,

J. Phys. Chem. C 117 (22), 11506–11513 (2013)


Multi-scale simulations of hydrogenated graphene systems

R Farchioni, V Tozzini,

in preparation


Prospects for Hydrogen Storage in Graphene

V Tozzini, V Pellegrini,

Phys Chem Chem Phys, 15 80-89 (2013)


Reversible Hydrogen Storage by Controlled Buckling of Graphene Layers

V Tozzini, V Pellegrini,

J Phys Chem C, 115 25523-25528 (2011)


Electronic transmission through a ladder with a single side attached impurity

R Farchioni, G Grosso and G Pastori Parravicini,

Eur. Phys. J. B 84, 227-233 (2011)


Quenching of the transmittivity of a one-dimensional binary random dimer model through side-attached atoms

R Farchioni, G Grosso and G Pastori Parravicini,

Phys. Rev. B 85, 165115-165121 (2012)


Electronic trasmission through a polyacene ladder with a substitutional edge impurity

M Bravi, R Farchioni, G Grosso, and G Pastori Parravicini,

Phys. Rev. B 87, 035105- 035114 (2013)


Graphene, related two-dimensional crystals, and hybrid systems for energy conversion and storage

F Bonaccorso, L Colombo, G Yu, M Stoller, V Tozzini, A C Ferrari, R S Ruoff, V Pellegrini ,

Science 347, 1246501 (2015)


Hydrogen storage in rippled graphene: perspectives from multi-scale simulations

V D Camiola, R Farchioni, T Cavallucci, A Rossi, V Pellegrini, V Tozzini,

Front. Mater. 2, 00003 (2015)


Hydrogen transport within graphene multilayers by means of flexural phonons

V D Camiola, R Farchioni, V Pellegrini, V Tozzini,

2D Mater. 2, 014009 (2015)


Nano-Scale Corrugations in Graphene: A Density Functional Theory Study of Structure, Electronic Properties and Hydrogenation

A Rossi , S Piccinin, V Pellegrini, S de Gironcoli, and V Tozzini,

J. Phys. Chem. C, 119 (14), 7900–7910 (2015)


Graphene-based technologies for energy applications, challenges and perspectives

E Quesnel, F Roux, F Emieux, P Faucherand, E Kymakis, G Volonakis, F Giustino, B Martìn-Garcìa, I Moreels, S Alkan Gûrsel, A Bayrakçeken Yurtcan, V Di Noto, A Talyzin, I Baburin, D Tranca, G Seifert, L Crema, G Speranza, V Tozzini, P Bondavalli, G Pognon, C Botas, D Carriazo, G Singh, T Rojo, G Kim, W Yu, C P Grey and V Pellegrini,

2D Mater, 2, 030204 (2015)

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